Recent advances in Re-based double perovskites: Synthesis, structural characterization, physical properties, advanced applications, and theoretical studies Open Access

Perovskite oxides have been widely investigated during the past 70 years owing to their interesting multifunctional properties and versatile technical applications.^1–3 They possess a wide range of electrical properties such as insulating, semiconducting, metallic, and half-metallic behaviors, on the one hand, and ferromagnetic, ferrimagnetic, and antiferromagnetic behaviors, on the other hand.^4–6 In addition, they may demonstrate ferroelectric,⁷ magnetic–dielectric,⁸ and multiferroic behaviors.⁹ Thus, perovskite oxides have promising applications in electronic/spintronic devices,¹⁰ fuel cells,¹¹ solar cells,¹² and so on.^13,14 The above promising properties can be attributed to the high chemical and structural flexibilities of the perovskite structure. In an ideal cubic perovskite compound with the formula ABO₃, A-sited cations with a 12-fold coordination occupy the corners of a cubic unit cell and B-sited transition metal cations sit at the center of the octahedron. Normally, the BO₆ octahedra are required to distort and/or tilt in various possible directions to accommodate the size mismatches generated by the substituted cations at A and/or B sites. Therefore, almost all elements covered in the periodic table can be presented at the A or B site in the perovskite structure, opening up vast possibilities for the formation of perovskite compounds.^15,16 In recent years, with the research and development of quantum electronic/spintronic devices without dissipation, intensive research studies are focused on double perovskite (DP) oxides with the general formula A₂B′B″O₆ (A being divalent or trivalent metals, B′ and B″ being 3d, 4d, or 5d transition metal cations) because of their intriguing magnetic properties [e.g., ferromagnetic insulator (FMI) at high temperatures and spin polarized transport above room temperature]. DP oxides exhibit rich physical properties owing to a wide variety of combinations of the metal ions at B′ and B″ sites, which offers much tunable B′–O–B″ magnetic interactions via superexchange.¹⁰ The first study of DP oxides was reported in the early 1950s, and it was widely carried out at the end of 1950s.^17,18 In the mid 1970s, a wide variety of DP oxides were reported. In 1998, Kobayashi et al.⁵ reported a low-field room temperature magnetoresistance (MR) in an ordered Sr₂FeMoO₆ DP compound; this finding stimulated the research studies on searching for new ferromagnetic compounds with a DP crystallographic structure.^19–22 Among the various DP oxides, rhenium (Re)-based DP oxides (e.g., A₂BReO₆, Sr₂(Fe_1−xCr_x)ReO₆, Sr₂Fe_1+xRe_1−xO₆) are a particularly intriguing class owing to their high magnetic Curie temperatures, diverse electrical behaviors, huge magnetic anisotropy, and large carrier spin polarizations.^23–25 Moreover, the Re-based DP compounds containing 3d and 5d transition metal ions at the B′ and B″ sites have rich electronic structures and complex magnetic structures, which are ascribed to the strong interactions between strongly localized 3d electrons and more delocalized 5d electrons with strong spin–orbit coupling. Thus, the involved physics in the Re-based DP compounds is much more complex than expected. Therefore, there are many issues related to the couplings among the charge, spin, and orbitals, which need to be addressed in the Re-based DP compounds.^23–25 In the past decade, many attempts have been made to study the structural chemistry, microstructure, and metal-to-insulator (MIT) transition via orbital ordering, cationic ordering, and electrical, magnetic, and magneto-transport properties of Re-based DP oxides, forming rich literature in the experimental and theoretical aspects. However, we note that only a few review articles of these compounds have been published. For example, Serrate et al. reviewed the FeMo-based and Re-based DP compounds with a focus on their magnetic properties and MIT behaviors,¹⁹ whereas Karppinen and Yamauchi discussed their chemical aspects with emphasis on oxygen stoichiometry, cation ordering, and redox chemistry.²⁶ In this Review, a comprehensive review of the recent advances in Re-based DP oxides is provided, which includes their syntheses, physical and structural characterizations, and advanced applications of Re-based DP oxides. Theoretical investigations of the electronic and structural aspects of Re-based DP oxides are also summarized. Finally, the summary and outlook of Re-based DP oxides are presented. It is expected that this Review will attract more interest in Re-based DP oxides and more researchers to enter this emerging field.

In the Re-based DP oxides of A₂MReO₆ (A = alkaline earth metals such as Ba, Sr, Ca; M = transition metals such as Sc, Cr, Mn, Fe, Co, Ni, Zn), their rich substitutional properties are advantageous for fabricating DP oxide compounds in the form of bulk single crystals, polycrystalline ceramics, thin films, or nanocrystals. In this section, we will elaborate some methods used for synthesis of Re-based DP oxides.

Re-based DP bulk oxides can be simply obtained by direct annealing the mixture of corresponding metal oxides at high temperatures, where the solid powders undergo both physical and chemical reactions to enable the thermal diffusion of ions or molecules. The solid-state reaction method is widely utilized to fabricate Re-based DP bulk oxides, which is environmentally friendly owing to without releasing toxic gases during the synthesized process. However, it has some disadvantages such as the final products often with impurities and poor chemical homogeneity, non-distributed particle sizes, long reaction time required, and high annealing temperature (e.g., over 1000 °C). These issues can be alleviated by modifying the processing parameters of the solid-state reaction method (e.g., repeatedly grinding the starting materials; increasing annealing temperature and reaction time). For example, Kato et al.²⁷ synthesized the polycrystalline Re-based DP oxides such as Sr₂MReO₆ and Ca₂MReO₆ (M being transition metals) by solid-state reactions, where SrO, CaO, MO_x, Re₂O₇, and Re powders were used as the raw materials. The synthesized samples were almost of pure phase despite a small amount of impurities (less than 2% in fraction) except Ca₂NiReO₆ (about 8%). In another case of the Sr_2−xLa_xFe_1+x/2Re_1−x/2O₆ (x = 0.0–1.8) compounds, they were synthesized by the solid-state reaction method under an inert atmosphere, where La₂O₃, SrCO₃, Fe₂O₃, ReO₃, and Re were used as the starting materials. They were weighted based on the designed ReO₃/Re ratio to the theoretical chemical valence (5+) of Re and calcined at 1100 °C for 2 h in a stream of Ar gas.²⁸ To obtain a single-phase structure, the mixed powders were repeatedly sintered at 1200 °C for 3 h several times in the same atmosphere. To increase the density of bulk ceramics of Re-based DP oxides, Lim et al.²⁹ utilized the spark plasma sintering method to fabricate the bulk ceramic samples (e.g., Sr₂FeReO₆ and Sr₂CrReO₆). Spark plasma sintering technique is a high speed consolidation of the powders by using uniaxial pressure and pulsed electrical current under low atmospheric pressure.^30,31 The remarkable features of the spark plasma sintering method make it suitable for fabricating Re-based DP ceramic oxides with high densification.

In recent years, Re-based DP thin films have attracted much attention owing to their high T_c value, large spin polarization, and half-metallicity, which have promising applications in spin electronic devices. However, to date, only a few works reported on Re-based DP thin films, unlike their bulk counterpart. Recently, Sohn et al.²⁵ grew epitaxial Sr₂Fe_1+xRe_1−xO₆ (−0.2 ≤ x ≤ 0.2) thin films on single-crystal (001) SrTiO₃ substrates by pulsed laser deposition (PLD). They demonstrated that the compositional ratio and cation ordering of the Sr₂Fe_1+xRe_1−xO₆ thin films were closely related to the oxygen pressure (⁠$PO2$⁠). The thin films exhibited a ferromagnetic insulator (FMI) state with high-T_c ferromagnetism and high saturation magnetization (M_S ≈ 1.8 µ_B/f.u.). In addition, their room-T sheet resistance was about three order larger as compared with that of metallic films. The stable FMI state was found in the cation-ordered Fe-rich films due to the formation of extra Fe³⁺–Fe³⁺ and Fe³⁺–Re⁶⁺ bonding states. In another study, highly ordered epitaxial Sr₂CrReO₆ thin films were also deposited on single-crystal (001) SrTiO₃ substrates with an epitaxial buffer layer of Sr₂CrNbO₆ (30 nm–48 nm in thickness) by off-axis magnetron sputtering.³² The Sr₂CrReO₆ films had 99% Cr/Re ordering and high-quality crystallinity. Their electrical resistivity was strongly sensitive to the oxygen partial pressure. 18 000% modulation in electrical resistivity was achieved at a temperature of 7 K (60% modulation at 300 K) as the oxygen partial pressure had 1% modulation during film growth. The results indicate that the electrical properties of Sr₂CrReO₆ thin films are closely related to the content of oxygen vacancies. Orna et al.³³ also grew epitaxial Sr₂CrReO₆ films by PLD, which exhibited high crystallinity and large cationic ordering. Their M_S value at 300 K was ∼1.0 µ_B/f.u. and the electrical resistivity (ρ) was 2.8 mΩ cm at 300 K, similar to those reported previously for the sputtered epitaxial Sr₂CrReO₆ films.

Large magnetoresistances are reported in the polycrystalline Re-based DP oxides such as Sr₂FeReO₆ and Sr₂CrReO₆, which resulted from the intergrain tunneling magnetoresistance (ITMR) effect controlled by the grain boundary magnetization.³⁴ It is also reported that the formation of nanosized particles can significantly enhance the ITMR effect in Re-based DP powders.^35–37 However, the synthesis of Re-based DP powders with high-purity and homogeneity is proven to be challenging due to the strong refractive nature of the reduced rhenates (i.e., Re⁵⁺/Re⁶⁺). Recently, molten salt synthesis (MSS) is used to synthesize Re-based DP oxide nanoparticles (e.g., Sr₂FeReO₆, Ba₂FeReO₆, and Sr₂CrReO₆), and the eutectic mixture of NaCl–KCl salts acted as the reaction medium. Fuoco et al.³⁷ reported the influence of annealing temperature, holding time, cooling rates, and molten salt fluxes on the particle sizes, ordering degree at the B′/B″ site, and the physical properties of Sr₂FeReO₆, Ba₂FeReO₆, and Sr₂CrReO₆ powders. They found that high purity and homogeneity were achieved in the Re-based DP oxide powders (e.g., Sr₂FeReO₆, Ba₂FeReO₆, and Sr₂CrReO₆) synthesized by the MSS method. The particle sizes of the Re-based DP powders were in the range from ∼50 nm to >1 µm, which were dependent upon the different synthesized conditions and the compositions of DP oxides. Generally, small-sized particles were synthesized under short reaction time, which had much large concentrations of grain boundaries, leading to strong temperature dependent resistivity. This new synthetic route allows one to deeply investigate the effects of the particle size and the ordered degree at the B′/B″ site on the magnetic properties of Re-based DP powders.

Spintronics is becoming a candidate technology based on the spin of the electron to carry and store information as 0 bits (spin up ↑) and 1 bit (spin down ↓). This new technology has several advantages over the current charge-based technologies.^38–40 To realize the full commercial spintronic devices, the essential components such as half-metallic spin injectors and magnetic semiconductors are highly required.^41–43 However, the main challenge to this new technology is the discovery of suitable candidates that have ferromagnetic ordering and large carrier spin polarizations over room temperature. Re-based DP oxides such as Sr₂CrReO₆ are considered the potential materials for spintronics owing to their high T_c value (∼635 K), half-metallicity, and large M_S (=1.0 μ_B/f.u.).^44–48 Following the successful increase in the T_C value in the Mo-based DP oxides by electron doping, similar research works were also carried out in the Re-based DP oxides.⁴⁹ However, the expected enhancement of T_C with lanthanide addition in the Sr₂CrReO₆ DP oxides was not realized. This means the magnetic interaction strength is decreased with lanthanide doping. The converse electron doping scenarios observed in Sr₂CrReO₆ and Sr₂FeMoO₆ may be ascribed to the presence of secondary phases in the final products of Sr_2-xLn_xCrReO₆ (Ln being La, Nd, or Sm). To confirm this assumption, Blasco et al.⁵⁰ fabricated two sets of polycrystalline Sr_2−xLn_xCrReO₆ and Sr_2−xLn_xCr_1+x/2Re_1−x/2O₆ samples (x = 0.0–0.5; Ln = La, Nd, Sm) by the solid-state reaction method. They found that the synthesis of the Sr_2−xLn_xCrReO₆ (Ln = La, Nd, or Sm) single phase was impossible via conventional synthetic routes because of the formation of competitive Sr_2−xLn_xCr_1+x/2Re_1−x/2O₆ and Sr₁₁Re₄O₂₄ phases. This was the reason why it is significantly hard to synthesize electron-doped DP oxides in the (Cr, Re)-based systems. Single-phase compounds were only obtained with the stoichiometric formula of Sr_2−xLn_xCr_1+x/2Re_1−x/2O₆, which crystallized in a fcc cubic cell with a shrinkage when the sizes of Ln ions were decreased. These samples exhibited spontaneous magnetization and large coercive field at room temperature, and their Curie temperature was weakly affected by Ln addition, whereas the M_S value was decreased owing to the appearance of anti-site (AS) defects. The electronic states of both Cr³+ and Re⁵⁺ ions were not affected by replacing Sr by Ln, as confirmed by x-ray absorption spectroscopy (XAS) at the Cr K edge and Re L_1,2,3 edges. Recently, the first-principles calculations demonstrate that the La-doped Ba_2−xLa_xFeReO₆ (x = 0.0, 0.5, and 1.0) compounds undergo a transition from half-metallic to insulating behavior as the La-doping content (x) is increased up to x = 1.0.⁵¹ The injections of electrons mainly go to Re t_2g orbitals, whereas the Fe 3d orbitals almost remain unchanged when increasing the La-doping content. Therefore, Fe exists as 3+ in doped and un-doped samples, while Re has different chemical states in Ba₂FeReO₆ (5+), Ba_1.5La_0.5FeReO₆ (4.5), and BaLaFeReO₆ (4+) compounds. The remanent magnetization is decreased when increasing the La-doping content.

In the case of homo-valent dopants, polycrystalline Re-based DP Sr₂LnReO₆ (Ln = Y, La, Nd, Sm–Gd, and Dy–Lu) samples are also synthesized by the standard solid-state reaction, where the transition metals such as Fe, Cr were used to replace lanthanide (such as trivalent Y, La, Nd, Sm–Gd, and Dy–Lu) at the B′ site.⁵² It is observed that the Ln³⁺ and Re⁵⁺ ions are orderly distributed at the B′ and B″ sites of the DP structure. The Sr₂LnReO₆ compounds exhibit an antiferromagnetic behavior at 2.6 K–20 K. This can be ascribed to the magnetic interactions between Re⁵⁺ ions. In the Sr₂YbReO₆ compound, the magnetic orderings of Yb³⁺ and Re⁵⁺ ions appear at 20 K, whereas, at around 90 K, Re⁵⁺ ions are magnetically ordered in Sr₂DyReO₆. By furthermore reducing the temperature, Dy moments are ferromagnetically ordered at 5 K.

The structural characterizations of Re-based DP oxides include determinations of crystal structures, chemical compositions, and morphologies. There are several conventional methods for characterizing the crystal structures, which are based on the inactions between the incident x ray (or high-energy electron beam) and the investigated samples. X-ray diffraction (XRD) is a very common method to determine the phase structures of all kinds of matter ranging from fluids, to powders, and crystals. By analyzing the XRD data, the critical features such as crystal structures, crystallite sizes, lattice parameters (a–c), lattice volume, and strain can be determined. Infrared and Raman spectra are two complementary techniques, which provide the characteristic fundamental vibrations used for determination and identification of the crystal structures at a molecular level. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) make use of a fine electron beam to reveal the microstructures of the investigated samples, which work in electron back-scattering and transmission modes, respectively. Two kinds of high-resolution imaging modes named high-resolution TEM (HRTEM) and scanning transmission electron microscopy (STEM) are often used to reveal microstructures (or structural defects) of Re-based DP oxides at an atomic level or even at a sub-Å level. Selected area electron diffraction (SAED) is widely utilized to determine the phase structure of the samples, while convergent beam electron diffraction (CBED) has a unique ability of determining the space group of crystals due to its great advantages of obtaining reliable experimental data from a single-domain area. The spectral analyzed techniques such as energy dispersive x-ray spectroscopy (EDS), electronic energy loss spectroscopy (EELS), and x-ray photoelectron spectroscopy (XPS) are used to determine the chemical compositions and chemical bonding states of the Re-based DP oxide. In this section, we shortly review the recent advantages in the microstructural characterizations of Re-based DP oxides.

To date, many Re-based DP bulk oxides have been synthesized by different methods, and their phase structures are first examined by XRD, from which the lattice parameters (a–c), unit cell volume (V), and density of the sample in theory can be determined. As an example, XRD patterns of Ba₂FeReO₆ and Ca₂FeReO₆ DP compounds synthesized by the solid-state reaction are demonstrated in Fig. 1. As shown in Fig. 1(a), the XRD pattern of Ba₂FeReO₆ can be well indexed based on a cubic cell (Fm3m), and the lattice constant (a) is determined to be about 8.054 Å. Ca₂FeReO₆ [Fig. 1(b)] is found to crystallize in a monoclinic structure with the space group of P2₁/n and lattice parameters of a ≈ 5.396 Å, b ≈ 5.522 Å, c ≈ 7.688 Å, and β = 90.4°.⁵³ It was also noticed that the impurity phase was not observed in the XRD patterns, implying the formation of a pure compound in each case. Figure 2 demonstrates the room temperature XRD patterns of a series of Ca-doped Sr_2−xFeReO₆ (x = 0.0–2.0) samples.⁵⁴ It was observed that the samples with x = 1.5 and 2.0 exhibited a monoclinic structural distortion and crystallized with the space group of P2₁/n, whereas the samples with x = 0.5 and 1.0 had a pseudo-cubic structure. The lattice parameters (a–c) determined from the XRD patterns are displayed in Fig. 3. In order to express the overall behavior of the investigated series, pseudo-cubic parameters, a_ps (=a$2$⁠) and b_ps (=b$2$⁠), are used rather than the lattice parameters (a and b) of the tetragonal and monoclinic samples. To describe the structural changes undergone in the series of Re-based A₂MReO₆ DP compounds (A being Sr, Ca; M being Mg, Sc, Cr, Mn, Fe, Co, Ni, Zn), the tolerance factor (t) is introduced, which is written as

where r_A, r_M, r_Re, and r_O represent the ionic radii of A, M, Re, and O ions, respectively. Figure 4 shows the tolerance factor dependent upon the cell volume, monoclinic structural distortion expressed by ∣β-90°∣ (β, the monoclinic angle), and averaged M-O-Re bond angles of the Re-based A₂MReO₆ compounds.²⁷ It is noticed that the Sr-based compounds (e.g., Sr₂MReO₆) have larger cell volumes and M-O-Re angles (close to 180°) in comparison with the Ca-based compounds (e.g., Ca₂MReO₆). In addition, for each A-site ion, with the decreasing tolerance factor t in the A₂MReO₆ compounds, cell volumes continuously increased, whereas the M-O-Re angles monotonously decreased. For the compounds with t < 0.98, their crystal structures are monoclinically distorted and the distortion degree of ∣β-90°∣increases with the reducing t value.

During the growth of Re-based double perovskite oxides, AS defects are also formed in Sr₂FeReO₆ (e.g., Fe occupies the normal Re site, Fe_Re, and Re occupies the normal Fe site, Re_Fe) and Sr₂CrReO₆ (e.g., Cr occupies the normal Re, Cr_Re, and Re occupies the normal Cr site, Re_Cr), respectively, which are dependent upon the synthesis conditions (e.g., annealing temperature, holding time, and pressure) in the spark plasma sintering process. The formation of AS defects is harmful to magnetization. Therefore, it is critical to suppress the formation of AS defects during the growth process of the DP samples. In general, diffraction techniques are used to detect the AS defects (quantifying the amount of misplaced magnetic ions) since some specific Bragg peaks such as (111), (113), and (331) diffraction peaks would emerge owing to the cationic ordering formed at the B′ and B″ superlattices.⁵⁵ Recently, local cationic ordering in the pristine and Re-excess Sr₂FeReO₆ samples was comparatively investigated by high-angle annular dark-field (HAADF)-STEM.⁵⁶ It is found that cationic ordering appears not only in the pristine sample but also in the Re-excess 15 mol. % Sr₂FeReO₆ sample. The HAADF-STEM images obtained from the pristine Sr₂FeReO₆ sample taken along [001] and [110] directions are demonstrated in Figs. 5(a) and 5(b), respectively. It is noticed that only the Fe and Re columns (orange sphere) and Sr column (green sphere) are resolved in the [001] projection, whereas, in the [110] projection, the Fe column (yellow sphere), Re column (blue sphere), and Sr column (green sphere) are clearly resolved. This confirms the Fe/Re ordering in the pristine Sr₂FeReO₆ sample. Figure 5(c) displays three kinds of intensity profiles of atomic columns, which are obtained from the pristine Sr₂FeReO₆ sample (marked by a red line), the Re-excess Sr₂FeReO₆ sample (marked by a blue line), and the simulated Sr₂FeReO₆ image (marked by a green line). Thus, the Fe/Re cationic ordering at the B′ and B″ sites in the pristine and Re-excess Sr₂FeReO₆ samples is well confirmed. However, in the pristine Sr₂FeReO₆ sample, AS defects are also found, as revealed in Fig. 6(a). In column intensity profiles, the Re atomic columns with much higher intensities are clearly distinguishable, and between two adjacent Re columns, there are three Fe atomic columns with almost equal intensities, which are indicated by the red arrow. It is noticed that some Fe atomic columns exhibit much lower intensities as compared with their neighbors, which are indicated by the green or yellow arrow. The appearance of Fe atomic columns with unusual strong intensities indicates the formation of AS defects. Figures 6(b)–6(d) present a series of [110] projections of simulated HAADF-STEM images, which have the Fe–Re exchanging ratios at 10%, 15%, and 20%, respectively. It is observed that the intensity profiles of the Fe atomic columns marked by the green and red arrows indicate more AS defects, which match well with the simulated images with 15% and 20% Fe–Re exchanges. Besides the AS defects, the antiphase boundary (APB) was also observed in the Re-excess Sr₂FeReO₆ samples. Figure 7(a) shows the HAADF-STEM image taken from an APB in the [110] direction projection, and Fig. 7(b) displays the intensity profile across the APB boundary. It is observed that the intensity profile in Fig. 7(b) exhibits quite symmetry near the Sr atom, as demonstrated by a red arrow. However, across the APB, the intensities of the Re columns (column nos. 4–7) are found to be reduced gradually, whereas an inverse case appears for the Fe columns (indicated by blue arrows). This means the Fe/Re cationic disordering appears around the APB region due to the formation of strong antiferromagnetic coupling between the magnetic cationic pairs of Fe³⁺/Fe³⁺ near the APB, leading to the reduced magnetic spin of Fe across the APB. Lim et al.²⁹ also reported that adding Re is an effective way to reduce the AS defects in Sr₂FeReO₆ (by 10.4% when increasing the amount of excess Re up to 15 mol. %), but it slightly increases the AS defects (by 0.9% in Sr₂CrReO₆ when increasing the amount of excess Re up to 10 mol. %).²⁹ Such a discrepancy can be ascribed to their different thermodynamic stabilities between Sr₂FeReO₆ and Sr₂CrReO₆ with the excess of Re. The microscopic structures of AS defects in Sr₂FeReO₆ and Sr₂CrReO₆ are also examined by HAADF-STEM images. Figure 8(a) reveals the sequential atomic chains of Re–Sr–Fe–Sr–Re along the [001] direction and Re–Fe–Re along the [110] direction since B-sited atoms (Re and Fe) are arranged along the ⟨110⟩ direction. Figures 8(b)–8(e) show the HAADF-STEM images taken from Sr₂CrReO₆-Re excess 5 mol. %, Sr₂CrReO₆-Re excess 15 mol. %, Sr₂CrReO₆-no excess Re, and Sr₂CrReO₆-Re excess 10 mol. %. In the Sr₂CrReO₆-Re excess 5 mol. % sample [Fig. 8(b)], antiphase-boundary (APB)-like defects were observed, similar to that reported for Sr₂FeReO₆⁵⁶ and Sr₂FeMoO₆.⁵⁷ However, such defect structures were not observed in the sample of Sr₂CrReO₆ with Re excess 15 mol. % [Fig. 8(c)], which was ascribed to the reduced sizes of AS defects with a larger amount of excess Re. In the pure Sr₂CrReO₆ sample [Fig. 8(d)] and Re excess 10 mol. % Sr₂CrReO₆ sample [Fig. 8(e)], the AS defects were not observed due to their wide distribution in the whole samples, similar to the cases in other oxides.^58,59 The Fe/Re cation ordering at the B-sites (B′ and B″) of Sr₂FeReO₆ was also examined by using EDS element mapping formed by the Fe Kα signal at 6.405 keV and Re Kα signal at 8.652 keV, besides the nanodiffraction patterns along ⟨011⟩_pc.⁶⁰ Figure 9(a) is the HAADF-STEM image taken from a perfect region of the Sr₂FeReO₆ sample, and Figs. 9(b)–9(e) show the corresponding atomic-resolution elemental maps and nanodiffraction pattern. The compositional distributions of the Fe element (red) [Fig. 9(b)] and Re element (blue) [Fig. 9(b)] are stacked alternatively in the {111} planes, giving a composite color map, which matches well with the feature of the Z-contrast image shown in Fig. 9(a). The appearance of 1/2{111}_pc super-diffraction spots marked by dotted circles in Fig. 9(e) also confirmed the alternative distributions of Fe and Re atoms in the {111} planes. The quantitative results of EDX spectra demonstrate the Fe/Re ratio of the selected region was 0.51:0.49, close to the statistical measurements. Therefore, the Sr₂FeReO₆ phase can be further written as Sr₂[Fe]_B′[Re]_B″O₆.

The local electronic structures and geometries around the Cr and Re atoms in the double perovskite Sr_2−xLn_xCr_1+x/2Re_1−x/2O₆ doped with Ln (=La, Nd, or Sm) were also investigated by x-ray absorption near edge structure (XANES) and extended x-ray absorption fine structure (EXAFS) spectra.⁵⁰ Figure 10(a) presents the XANES spectra of Sr₂CrReO₆ obtained at the Cr K-edge, where different chemical valences of Cr ions are selected such as the Cr³⁺ ions in LaCrO₃ and Cr₂O₃, Cr⁶⁺ ion in CrO₃, and metallic Cr. It is found that this edge is very sensitive to the local structures of the investigated samples. For example, in the CrO₃ sample, a sharp peak appears in the pre-edge region at 5.993 keV, which resulted from the dipole-forbidden transition from 1s to 3d. This indicates the tetrahedral coordination of Cr⁶⁺ without an inversion center.⁶¹ As shown in Fig. 10(a), the positions of absorption edges are dependent upon the Cr oxidation states, which move to higher energy with increasing chemical valences of Cr ions. It is observed that the rising part of the Sr₂CrReO₆ main edge located at 6.006 keV coincides with that of LaCrO₃ due to both compounds having a similar perovskite structure; thus, the chemical valence of the Cr³⁺ ion is determined for Sr₂CrReO₆. The absorption spectra for the Sr_2−xLn_xCr_1+x/2Re_1−x/2O₆ samples (Ln = Nd or Sm) are identical to those of Sr₂CrReO₆, and their edge positions are also presented [see the inset of Fig. 10(a)], where the parent compound data at 35 K and 295 K are also presented. It is found that the edge positions maintain almost a constant value, indicating the chemical states of Cr ions are stable despite replacing the Sr element by rare earths. This means Cr³⁺ ions exist in all the investigated samples. To accurately understand the physical mechanisms of the pre-edge peaks of the Sr_2−xNd_xCr_1+x/2Re_1−x/2O₆ samples, their pre-edge features are comparatively investigated with those of LaCrO₃, as shown in Fig. 10(b). The small peak denoted A was observed in all samples with nearly the same energy and intensity, which resulted from pure quadrupole transitions that occurred in related oxides, and was much sensitive to the occupied 3d orbital.⁶² In this way, the presence of Cr³⁺ in the double perovskite of Sr_2−xNd_xCr_1+x/2Re_1−x/2O₆ is confirmed. However, the other pre-edges of DP compounds have much difference from those of LaCrO₃. A strong peak (denoted the B peak) was observed in Sr₂CrReO₆, and its intensity was decreased with the increasing rare earth-doping concentration [see the inset of Fig. 10(b) for details]. The electrical conductivities of these samples were reported to be decreased as the Ln-doped concentration was increased.⁶³ This is consistent with the concomitant weak orbital overlapping between the Cr and oxygen atoms. Thus, the intensity of peak B reflects the covalent bond strength of the Cr–O bond. Recently, the sensitivity of the XANES spectra has been used to check the oxidation states of Cr and Re elements. The chemical shift of the Cr K edge in the XANES spectra revealed the presence of Cr³⁺ ions for all compounds [Fig. 11(a)], while the XANES spectra at the Re L_1,2,3 edges confirm the Re⁵⁺ ions exist in all compounds [Fig. 11(b)]. This means the electronic states of both Cr³⁺ and Re⁵⁺ ions are not affected by Sr substitution by Ln elements. The Re–O and Cr–O bond lengths can be deduced from the EXAFS spectra, which fit well with crystallography. These bond lengths do not change along with the Ln-doping concentration, which agrees with the as expected values for Re⁵⁺ and Cr³⁺ oxides. As a consequence, the spectroscopic study confirms that the chemical valences of Cr and Re elements are not changed before and after substituting Sr with Ln elements.

Re-based DP thin films have promising applications in the near-future spintronics due to their high T_c value, half-metallicity, and large spin polarization. In addition, during the growth process of thin films, the strain, chemical heterogeneity, and artificial structures can be well controlled to realize the novel or enhanced properties, which are much different from those observed in the form of bulk counterparts.^64–68 Recently, Sohn et al.²⁵ grew high-quality epitaxial Sr₂Fe_1+xRe_1-xO₆ (−0.2 ≤ x ≤ 0.2) thin films by PLD. Figure 12(a) demonstrates the XRD patterns of θ–2θ scans for the films grown at 775 °C but with different $PO2,and$ Fig. 12(b) displays the off-axis XRD θ–2θ scans collected near the (111) diffraction peak of Sr₂Fe_1+xRe_1−xO₆, where only the (111) peak is observed in the films grown with $PO2$ ≥ 15 mTorr. The appearance of the (111) diffraction peak confirms the Fe/Re ordering, which is confirmed by the HAADF-STEM image [Fig. 12(c)] taken from the film grown at 20 mTorr in the projection along the [110] direction. In Fig. 12(c), the atomic chains of Re–Sr–Fe–Sr–Re along the [001] direction are clearly distinguishable and the atomic chains of Re–Fe–Re along the [110] direction are also clearly observed, which are sandwiched between two adjacent Sr atomic layers. Such clear atomic ordering is highlighted by the yellow diamond in Fig. 12(c), which is well consistent with the atomic positions in the projected structure of Sr₂FeReO₆ along the [110] direction [Fig. 12(d)]. The Re and Fe atoms are alternatively distributed in the (111) planes, as marked by blue and red lines, respectively. In another work, Hauser et al.⁶⁹ grew (001)-oriented and (111)-oriented Sr₂CrReO₆ epitaxial thin films by magnetron sputtering, which were characterized by XRD, as shown in Fig. 13. Figure 13(a) shows XRD θ–2θ scans of (111)-oriented Sr₂CrReO₆ thin films grown on SrTiO₃ single-crystal substrates, where only the {111} diffraction peaks from the film and substrate are observed, indicating the formation of the pure DP phase. In Fig. 13(b), Laue oscillations near the (004) diffraction peak of (001)-oriented Sr₂CrReO₆ thin films are clearly observed, indicating a perfect interface between the film and the substrate as well as a smooth film surface. The high crystalline quality of the Sr₂CrReO₆ films is reflected by their rocking curves that are shown in Fig. 13(c). The full-width-at-half-maximum (FWHM) of the rocking curve for the Sr₂CrReO₆ (004) peak is only 0.0088°, which is smaller than 0.0093° for the SrTiO₃ (002) peak. For the Sr₂CrReO₆ films grown under optimal conditions, both clear Laue oscillations and sharp rocking curves reveal the high quality of the Sr₂CrReO₆ films.⁷⁰ This is also confirmed by HAADF-STEM images. Figure 14(a) displays a low-magnification HAADF-STEM image of the Sr₂CrReO₆ film taken along the [110] direction, which exhibits flat surface and uniform thickness. The atomic structure of the Sr₂CrReO₆ film is revealed by a high-magnification HAADF-STEM image, which demonstrates the atomic chains of Re–Sr–Fe–Sr–Re along the [001] direction and the atomic chains of Re–Fe–Re along the [110] direction, confirming the clear Laue oscillations observed in Fig. 13(b). Pronounced STEM image contrast is obviously observed in the inset of Fig. 14(b), where three distinct shadows are clearly resolved, which correspond to Sr, Cr, and Re atoms, respectively. This matches well with the crystal projection of the DP lattice in the [110] direction [Fig. 14(c)]. The direct observations on the Cr/Re ordering in the Sr₂CrReO₆ films reveal the high quality of the film. Similarly, epitaxial growth of Sr₂CrReO₆ films on the SrTiO₃ (001) substrate by PLD is also reported by Orna et al.³³ The epitaxial growth relationship between the Sr₂CrReO₆ film and the SrTiO₃ substrate is confirmed by high-resolution XRD patterns and STEM images, which is expressed as Sr₂CrReO₆ (001)[100] || SrTiO₃ (001)[110]. The AS concentration in this epitaxial film was estimated to be 14%, and the Curie temperature (T_C) was determined to be 481 K, smaller than that reported for sputtered samples.⁷¹ 

Recently, the half-metallic A₂FeReO₆ (A = Sr and Ba) and Sr₂CrReO₆ powders were synthesized by the MSS method.³⁷ Figure 15 demonstrates XRD patterns collected from the flux-synthesized and solid-state-synthesized A₂FeReO₆ (A = Sr and Ba) and Sr₂CrReO₆ powders. Rietveld refinements of these XRD data gave the crystal parameters such as unit cell parameters, atomic positions, fractional B′ and B″ site occupancies, and ordering degree. The Fe/Re ordering degree is reflected via the peak intensity of the (111) super-structural reflections in Sr₂FeReO₆ and Sr₂CrReO₆, or the analogous (101) super-structural reflection in Ba₂FeReO₆, and these super-structural reflections are labeled with asterisks in Fig. 15. Morphologies of the flux-prepared A₂FeReO₆ (A = Sr and Ba) and Sr₂CrReO₆ powders under different flux-to-product molar ratios were examined by SEM, and the representative SEM images are shown in Figs. 16 and 17. Aggregated block-like particles were observed in the SEM images, and their sizes changed from about 50 nm to over 1.0 µm, which were dependent upon the particular DP oxide compositions and the flux-synthesized conditions. Generally, smaller particles could be synthesized under the larger flux-to-product molar ratio and faster cooling process, or shorter reaction time. Strong temperature dependence of magnetoresistivity was found in the flux-synthesized A₂FeReO₆ (A = Sr and Ba) and Sr₂CrReO₆ powders, which are ascribed to the higher concentrations of grain boundaries present, as compared to the solid-state-synthesized samples.

The magnetic properties of Re-based DP bulk oxides are strongly related to the ordering of the B-site ions. Their net magnetizations are decreased owing to the existence of B-site disorder. The possible reasons can be classified as follows: (i) the B-site disorder destroys the spin arrangements in the B′ and B″ sublattices but has no influence on each magnetic moment at B′ and B″ sites and/or (ii) each magnetic moment at B′ and B″ sites decreased because of cation disorder, but the nature of the spin order at the B′ and B″ sublattices is not affected. Since the magnetic properties of Re-based DP oxides have promising applications in spintronics, therefore, their fundamental magnetic properties have received much attention in the past decades, which have been investigated by the superconducting quantum interference device (SQUID), a Quantum Design Physical Property Measurement System (PPMS) with a vibrating sample magnetometer (VSM). For example, under a static magnetic field increasing up to 30 T, high-field magnetizations of Re-based DP bulk oxides of A₂FeReO₆ (A = Ca, Sr, BaSr) and Sr₂CrReO₆ were measured, which are shown in Fig. 18.⁴⁷ It is found that the magnetizations of BaSrFeReO₆, Sr₂FeReO₆, and Ca₂FeReO₆ compounds measured at 4 K under 5 T are 2.98, 2.81, and 2.25 μ_B/f.u., respectively. At the maximum magnetic field of 30 T, the magnetization of BaSrFeReO₆ [Fig. 18(a)] was measured to be 3.27 μ_B/f.u. This approached the saturated magnetization (M_s) since this compound was nearly saturated under 30 T, as observed in the inset of this figure. To evaluate the M_s value of this compound, the following expression is used:^72,73

where M_s (expt.) represents the saturated magnetization measured experimentally and M_s represents the saturated magnetization without AS. In the present case, the AS value is 0.5% and M_s (expt.) is 3.27 μ_B/f.u.; therefore, the M_s value for the BaSrFeReO₆ compound is determined to be 3.30 μ_B/f.u. The M–H loop of the BaSrFeReO₆ compound was measured by a SQUID magnetometer up to 5 T, which is shown as an inset of Fig. 18(a) at the upper left corner. Magnetic field dependence of the magnetization of the BaSrFeReO₆ compound measured at 4 K and 100 K is shown as an inset of Fig. 18(a) at the lower right corner. The magnetization is expected to be increased when decreasing the temperature, which is confirmed by the slightly increased magnetization at 4 K as compared with that at 100 K, which allows one to ignore any kind of spurious paramagnetic contribution to the measurement at 4 K. The magnetization of the BaSrFeReO₆ compound was measured to be 3.21 μ_B/f.u. at 100 K and under the maximum field of 30 T, which was still much higher than the assumed value of 3.0 μ_B/f.u. The magnetic data for the Sr₂FeReO₆ compound are displayed in Fig. 18(b), which are similar to the case of BaSrFeReO₆ composition. The magnetizations of the Sr₂FeReO₆ compound under the maximum field of 30 T were measured to be 3.23 μ_B/f.u. @4 K and 3.17 μ_B/f.u. @100 K, respectively, which exhibits a less saturated tendency than BaSrFeReO₆ does. It is much more evident that the Ca₂FeReO₆ sample does not achieve magnetic saturation under 30 T, as demonstrated in Fig. 18(c). Its magnetizations under the maximum field of 30 T were about 3.12 μ_B/f.u. @ 4 K and 100 K. It is also noticed that the M_S value @ 4 K is smaller than that @ 110 K across the magnetic field of 12 T–30 T, which can be ascribed to a structural transition undergone between the two monoclinic crystallographic structures in this compound below 120 K.^74–76 The above experimental results clearly demonstrate that the magnetic saturation of these materials can be only achieved by much high magnetic fields. In general, the higher magnetic field required for magnetic saturation and larger coercive fields are, the larger magnetic anisotropy is the compound possesses. Therefore, Re-based double perovskites exhibit a large coercive field and saturation field, which are comparable to those observed in permanent magnets, indicating a high magneto-crystalline anisotropy. In order to understand why the highest Curie temperature (T_C ≈ 635 K) is observed in the Sr₂CrReO₆ compound, recently x-ray magnetic circular dichroism (XMCD), an element-specific magnetic measurement technique based on synchrotron radiation, has been utilized to directly measure each magnetic moment at the B′ and B″ sublattices since XMCD technique has some advantages such as element-specific selectivity and the ability to extract the magnetic contributions from spin and orbital magnetic moments in complex magnetic materials using the magneto-optical sum rules.^77,78 As an example, the XMCD signal of Sr₂CrReO₆ measured as a function of the applied magnetic field at the Re L₂ absorption edge and 10 K is displayed in Fig. 19,⁷⁹ from which the coercive field was determined to be 1.27 T. The intensity of the XMCD signal matches well with the M–H loop obtained by a SQUID at 5 K (see the inset of Fig. 19) and other measurements.²⁷ The M_S value was measured to be 0.89 μ_B/f.u., which is consistent with the theoretical value of 1.0 μ_B calculated based on a simple ionic model with Cr³⁺ and Re⁵⁺ ion antiferromagnetic coupling. In terms of the data of XMCD at the L_2,3 edges and sum rules, the magnetic moments of Re 5d spin and orbital moments in the Sr₂CrReO₆ compound were determined to be −0.68 μ_B and +0.25 μ_B, respectively. The experimental results demonstrate that the Curie temperature of the A₂B′B″O₆ DPs scales with the magnetic moments of the non-magnetic 3d or 5d transitional metal ions at the B″ site.

The physical pressure also has an impact on the magnetic properties of Re-based DP bulk oxides such as A₂FeReO₆ (A = Ca, Ba). For example, at room temperature, the Ba₂FeReO₆ compound with a larger Ba cation at the A-site has a cubic crystal structure and exhibits both metallicity and magnetism, whereas the Ca₂FeReO₆ compound with a small Ca cation at the A-site has a monoclinic structure and exhibits insulating behavior.^80–82 The higher T_c (=540 K) and magnetic coercive field (H_c = 9 kOe) are observed in the Ca₂FeReO₆ compound, indicating the co-existence of stronger exchange interactions and larger magnetic anisotropy in this compound. In Ca₂FeReO₆ with a monoclinic structure, the rotations of FeO₆ and ReO₆ octahedra around b and c axes are favorable, resulting in a smaller Fe–O–Re bonding angle of 156°.^83,84 Thus, the pdπ hopping that controls the transport behavior in the un-rotated structure is decreased, resulting in the observed insulating behavior.⁸⁵ The distorted monoclinic structure with a lower symmetry makes the ReO₆ octahedra be a tetragonal distortion and leads to an enhanced magnetic anisotropy as compared with the Ba compound. Escanhoela et al.⁸⁶ investigated the physical pressure dependence of the magnetic properties of ferrimagnetic A₂FeReO₆ DP oxides with A = Ca or Ba by using XAS at the Re L_2,3 edge and powder diffraction technique. Figures 20(a) and 20(b) show the XMCD hysteresis loops of A₂FeReO₆ (A = Ba, Ca) DP oxides measured at 10 K with different pressures. It was found that the Ba₂FeReO₆ and Ca₂FeReO₆ compounds became magnetically harder when increasing the pressure. The coercive field of Ba₂FeReO₆ increased from 0.2 T to 1.55 T as the pressure was changed from 1.5 GPa to 22 GPa, and that of Ca₂FeReO₆ also increased about threefold under the pressure of 25 GPa. The pressure-dependent coercive field (H_c) is shown in Fig. 20(c) for both compounds. It is noticed that Ca₂FeReO₆ is under a pre-compressed state owing to the chemical pressure. Therefore, its coercive field change is smaller than that of the Ba₂FeReO₆ compound for a given physical pressure. It was also found that the volume compression dramatically increased the magnetic coercive field of these two polycrystalline samples at a rate of ΔH_c/ΔV ∼ 150 Oe/ų–200 Oe/ų.

Hauser et al.⁶⁹ grew Sr₂CrReO₆ films by the magnetron sputtering method and measured their magnetic properties. Figure 21(a) shows the M–H loop of Sr₂CrReO₆ (001) films at 5 K, from which the M_s was measured to be 1.29 μ_B/f.u., which is larger than the theoretical value of 1.0 μ_B/f.u. obtained from ferrimagnetic ionic alignments of Cr³⁺ (3d³↑) and Re⁵⁺ (5d²↓) ions. However, the present M_S value is well consistent with the calculated value of 1.28 μ_B/f.u. that considers the contribution of spin–orbit coupling.⁸⁷ This means strong spin–orbit coupling should exist in Sr₂CrReO₆ thin films. The coercive field (H_C) of the Sr₂CrReO₆ (001) film at 5 K was measured to be 1.05 T, which means the Sr₂CrReO₆ thin film is a hard ferrimagnet at low temperature. However, at 300 K, the H_C is reduced to be 890 Oe, indicating that the Sr₂CrReO₆ thin film is suitable for magneto-electronic applications at room temperature. Orna et al.⁷¹ also measured the magnetic properties of Sr₂CrReO₆ thin films grown by the PLD method. Figure 21(b) shows the saturation magnetization (M_s) dependence of the substrate temperature and the partial oxygen pressure. The M_s had the largest value ∼1.0 μ_B/f.u. when the substrate temperature was between 700 °C and 800 °C and the partial oxygen pressure was 2.6 × 10⁻⁴ Torr (open red squares), which is related to the AS fraction of the films. The AS concentration in the thin films was estimated to be in the order of 14%. The inset illustrates the room temperature M–H loops of the Sr₂CrReO₆ films grown at different temperatures. The coercive fields of all the Sr₂CrReO₆ films are found to be very small (H_C ∼ 120 Oe) [see the inset of Fig. 21(b)]; however, the coercive field of bulk Sr₂CrReO₆ is as high as 3.1 kOe at 300 K.⁷³ Under high partial oxygen pressure $PO2$⁠, the M_s value of Sr₂CrReO₆ films can be larger than that of bulk Sr₂CrReO₆. This is ascribed to the CrO_x oxide segregation at the film surface, and a similar case was reported in the Sr₂FeMoO₆ films.⁸⁸ 

The magnetic properties of Sr₂FeReO₆, Ba₂FeReO₆, and Sr₂CrReO₆ powders synthesized by the molten salt method under different synthesized conditions were reported by Fuoco et al.³⁷ Their M–H loops are displayed in Fig. 22, which indicate the magnetization saturation is not fully achieved for these compounds under 7 T. Previously, it was reported that these materials could only achieve the magnetic saturation under magnetic field as high as 30 T.^47,89 In Fig. 22(a), the magnetizations for the flux-prepared Sr₂FeReO₆ powders under different flux-to-product molar ratios and reaction time are measured to be in the range of 1.57–2.17 μ_B under 7 T, which was lower than the theoretical value of 3.0 μ_B obtained with the antiparallel spin alignments for the Fe³⁺ and Re⁵⁺ ions. Such smaller magnetizations are also bound up with the disordering degree at B′ and B″ sites.^54,90 As for the flux-prepared Ba₂FeReO₆ powders [Fig. 22(b)], they exhibit a lower H_c and larger M_s (from 2.10 to 2.40 μ_B) due to a higher ordering degree of the Fe/Re site, as compared to Sr₂FeReO₆. The spontaneous magnetizations of the flux-prepared Sr₂CrReO₆ powders are in the range of 0.74–0.80 μ_B, lower than the expected value of 1.0 μ_B under the antiparallel spin alignments of the Cr³⁺ and Re⁵⁺ ions. It is found that the higher the ordering degree at the Cr/Re site is, the larger the values of M_s and M_r are in the flux-prepared Sr₂CrReO₆ powders. As a rule of thumb, the coercive field of the Sr₂CrReO₆ powders is much larger than that of either Sr₂FeReO₆ or Ba₂FeReO₆.

Transport property measurements of the Re-based DP oxides were performed by the four-probe method in conjunction with a Quantum Design PPMS system. With a constant applied magnetic field, the temperature dependence of resistivity can be measured. Prellier et al.⁵³ reported the electrical properties of ferrimagnetic A₂FeReO₆ DP oxides with A = Ba and Ca. Figure 23(a) demonstrates the resistivity (ρ) of the Ba₂FeReO₆ ceramics vs the temperature under different magnetic fields (e.g., 0 kOe, 2 kOe, and 50 kOe). A metallic behavior was observed in the Ba₂FeReO₆ ceramics below 300 K. The inset of Fig. 23(a) presents the resistivity measured up to 385 K under no applied magnetic field, and the metallic behavior is still kept within this temperature region. On the contrary, Ca₂FeReO₆ exhibited a semiconducting behavior across 5 K–300 K, as depicted in Fig. 23(b). The observed metallic behavior in the Ba₂FeReO₆ compound is ascribed to the direct interaction between R e t_2g and Re t_2g, whereas the semiconducting behavior observed in the Ca₂FeReO₆ compound is attributed to the disrupted interaction between R e t_2g and Re t_2g by the monoclinic structural distortion (the degeneracy of t_2g states is lifted). To investigate the magnetoresistance (MR) effects in the Sr₂FeReO₆ and Ba₂FeReO₆ compounds, the magnetic field dependent upon the MR ratios measured at different temperatures is demonstrated in Figs. 23(c) and 23(d), respectively. Here, the MR value is defined as

where H_peak is the magnetic field corresponding to the maximal value of resistivity (ρ). It should be noticed that both Sr₂FeReO₆ and Ba₂FeReO₆ exhibit negative MR behavior, and their MR values increase fast at low fields but slowly at high fields. This effect becomes much apparent at low temperatures, whereas it becomes less evident at room temperature (300 K); thus, the MR is much smaller. This is the typical characteristic of intergrain MR.⁹¹ It is also noticed that Sr₂FeReO₆ has a significantly larger MR than Ba₂FeReO₆ under comparable conditions, which can be ascribed to the metal–insulator boundaries in the metallic Ba-based compound.⁹² The appearance of metallic or insulating behavior in the isoelectronic series of A₂B′B″O₆ DP compounds dependent upon the A-site cation would enable them useful in magnetic devices.

The transport properties of Re-based ordered DPs such as A₂MReO₆, where A is Sr, Ca and M is Mg, Sc, Cr, Mn, Fe, Co, Ni, Zn, are also reported by Kato et al.²⁷ The temperature dependence of resistivities (ρ) is shown in Fig. 24. It is noticed that the A₂MReO₆ compounds with A = Sr exhibit higher conductivity than the Ca-based ones. Insulating nature was observed in all the compounds except for the two compounds of Sr₂FeReO₆ and Sr₂CrReO₆, which are fallen into the classification of half-metals.^91,93 It is observed in Fig. 24(a) that at room temperature, the resistivities of a series Sr₂MReO₆ DPs (M being Mg, Sc, Mn, Ni, and Zn) are in the order of kΩ⋅cm, which has nothing to do with A-site ions. However, the Sr₂MReO₆ DPs with M = Co, Cr, and Fe have relatively low resistivity. In the case of Ca₂FeReO₆ compound, a temperature-driven metal–insulator transition appeared around 150 K, which was reflected by a turning point in the resistivity curve marked by a triangle in Fig. 24(b), similar to that reported previously.⁷⁴ Figure 25 demonstrates the temperature dependent magnetizations of A₂MReO₆ (A being Sr, Ca; M being Cr, Mn, Fe, and Ni) DPs, which were measured under 1 T. The M_s values of Sr₂MnReO₆ and Sr₂NiReO₆ compounds were measured to be 2.0 and 1.0 μ_B/f.u., respectively, which matched well with the expected values obtained from the antiferromagnetic coupling of Mn²⁺ (or Ni²⁺) and Re⁶⁺ ions. However, the measured magnetizations of Ca₂MnReO₆ and Ca₂NiReO₆ at 1 T were much smaller than the calculated values from the antiferromagnetic coupling between Mn²⁺ (or Ni²⁺) and Re⁶⁺ ions. This may be ascribed to the large coercive fields of these two compounds (e.g., 4.0 T for Ca₂MnReO₆ and 2.8 T for Ca₂NiReO₆, respectively) and the insulating nature as well as relatively low magnetic transition temperature (T_c < 150 K). On the other hand, Sr₂CrReO₆ and Sr₂FeReO₆ compounds exhibit metallic behavior and have high magnetic transition temperatures (T_c = 635 K and 400 K). This can be ascribed to that the exchange interactions between M (= Cr, Fe) and Re spins are not disturbed and there is no gap around the Fermi level. The saturation magnetizations of Sr₂CrReO₆ and Sr₂FeReO₆ compounds were measured to be 0.56 and 2.2 μ_B/f.u., respectively, lower than their theoretical values of 1.0 and 3.0 μ_B/f.u. calculated based on the electronic configurations of Cr³⁺ (or Fe³⁺) and Re⁵⁺ ions within a simplest ionic model. Similarly, the Ca₂MReO₆ (M being Cr, Mn, Fe, and Ni) DPs possess comparable saturation magnetization and higher magnetic T_C, as compared with the corresponding Sr-based compounds. A metal–insulator transition is observed in the ordered A₂MReO₆ DPs (A being Sr, Ca; M being Cr, Mn, Fe, and Ni). This phenomenon can be ascribed to the formation of the half-metallic conduction band due to the hybridization between the down-spin t_2g bands of Re and M (=Cr, Fe) Cr³⁺ around the Fermi level. This intuitive interpretation is proven by theoretical electronic calculations of Sr₂FeReO₆.⁹¹ 

In the cases of Ca₂FeReO₆ and Ca₂CrReO₆ compounds, their small structural distortion drives the one-electron bandwidth to be narrower than that in their Sr-based analogs, leading a Mott transition in these compounds. For the Sr₂MnReO₆ and Sr₂NiReO₆ compounds, their highest occupied states are the up-spin e_g states for Mn²⁺ and Ni²⁺ ions, respectively. To virtually excite the M³⁺–Re⁵⁺ state, the up-spin e_g electrons of M²⁺ ions are required to move toward the down-spin t_2g states of Re⁶⁺ ions. Due to the lack of mixing states between t_2g and e_g at the adjacent sites in a perfect cubic perovskite, the above electronic transferring process is nearly prohibited in ordered DPs, which makes the Sr₂MnReO₆ and Sr₂NiReO₆ compounds exhibit insulating behavior and used as Mott insulators.

The transport properties of the Sr₂CrReO₆ films were reported. Figure 26(a) shows the magnetization ratio of M/M(5 K) vs temperature, which is measured under 8 kOe. The inverse magnetic susceptibility (χ⁻¹) vs temperature is demonstrated in the inset, showing two magnetic transition temperatures (T_C = 508 K for the majority phase and T_C = 595 K for a secondary phase). In comparison, the T_C for bulk Sr₂CrReO₆ is reported to be 620 K–635 K^24,91 and 481 K for Sr₂CrReO₆ films.³³ The observed higher T_C may be contributed from the local regions around a small number of APBs, where there exists a stronger exchange interaction, enhancing the T_C value. Figure 26(b) demonstrates the semi-log plots of the electrical resistivity of bulk Sr₂CrReO₆ and thin films vs temperature. The room temperature bulk resistivity was measured to be 2.1 mΩ cm. With the decreasing temperature, the electrical resistivity increases, as reported by Kato et al.⁹³ In the Sr₂CrReO₆ film, the resistivity was increased more than two orders of magnitude (from 16.2 mΩ cm to 5.05 Ω cm) as the temperature was decreased from 300 K to 2 K. Such a behavior is the feature of a semiconductor (or insulator) with a gap at the Fermi level. The ln ρ vs 1000/T plot across the temperature range of 90 K–200 K is shown in the inset of Fig. 26(b), which exhibits nearly perfect linear fitting. Such temperature dependence of resistivity is frequently observed in semiconductors owing to their thermal activation,^94,95 which is given by

where ρ₀ is the prefactor and E_a is the activation energy. The E_a value was determined to be 9.4 meV from the linear fitting of the ln ρ vs 1000/T plot across the temperature range of 90 K–200 K. However, at temperatures below 90 K, the ln ρ vs 1000/T plot does not exhibit a linear behavior; instead, a good linear fitting is found for ln ρ vs (1000/T)^0.25 across a temperature range of 55 K–90 K, and for ln ρ vs (1000/T)^0.20 from 6 K to 25 K. This indicates a variable-range hopping model is appropriate in the whole temperature range (6 K–200 K), similar to those reported in the doped-semiconductors at low temperatures.⁹⁶ Sohn et al.²⁵ reported the transport properties of cation-ordered Sr₂Fe_1+xRe_1−xO₆ DP films. Figure 27(a) displays the magnetization (M) vs T curves measured under 1000 Oe for the Sr₂Fe_1+xRe_1−xO₆ films with different stoichiometric ratios, and Fig. 27(b) shows the corresponding temperature-dependent sheet resistance R_S. It was found that the ferromagnetic ground state existed in the Fe-rich/ordered films, but it fully vanished in the Re-rich/disordered films. In addition, the metallic ground state was more vulnerable in the films with excess Fe ions than that with excess Re ions. The Fe-rich/ordered films (blue lines) underwent a magnetic transition around 400 K, but it completely disappeared in the Re-rich/disordered films (red lines). This was confirmed by the magnetization exhibiting no temperature dependence. The disappearance of long-range magnetic ordering in the Re-rich films was attributed to the cation disordering at the B-site, which substantially influenced the magnetic properties of DP oxides. In contrast to the magnetism, the Re-rich/disordered films exhibit the metallic ground state, as evident by the R_S(T) curve in Fig. 27(b). However, the Fe-rich films behave like an insulator, and their room-T resistivity is about three orders of magnitude larger than that of the stoichiometric or Re-rich samples. Therefore, in the present Sr₂Fe_1+xRe_1−xO₆ single-crystalline films, a metal–insulator transition is observed, which exhibits much more dramatic phenomena than that reported for polycrystalline Sr₂Fe_1+xRe_1−xO₆ ceramics.⁹⁷ The reason can be ascribed to the existence of many metallic grain boundaries in polycrystalline films but absence in the present films. Figure 27(c) summarizes the measured results for the M_s and R_s values of the Sr₂Fe_1+xRe_1−xO₆ DP films; based on them, the Sr₂Fe_1+xRe_1−xO₆ single-crystalline films can be classified as paramagnetic metal (PMM, x < 0), ferromagnetic metal (FMM, x ≈ 0), and room-temperature ferromagnetic insulator (FMI, x > 0) catalogs.

Fuoco et al.³⁷ reported the transport properties of Sr₂FeReO₆, Ba₂FeReO₆, and Sr₂CrReO₆ powders synthesized by the MSS method, which were measured by polycrystalline pellets formed by pressing the powders but no annealing. Figure 28(a) shows their temperature dependent resistivity. A semiconducting-type behavior was observed in all the samples, which is consistent with previous reports. A stronger temperature dependence of resistivity is observed in the flux-prepared Sr₂FeReO₆ samples, which have resistivity about three times higher than that of the sample synthesized by the solid-state reaction. The flux-prepared Ba₂FeReO₆ powders had a resistivity in the range of ∼0.07 Ω cm to 0.1 Ω cm across 300 K–550 K, and the Sr₂CrReO₆ powders had a higher resistivity (∼13 Ω cm to 3 Ω cm). Figure 28(b) demonstrates the temperature dependent resistivity of Sr₂FeReO₆ powders synthesized by the solid-state method and flux-synthetic route, which was measured under magnetic fields of 0 T and 0.3 T across temperatures of 300 K–550 K. It was found that the flux-prepared Sr₂FeReO₆ powders had larger resistivity, which also exhibited much evident magnetic field-dependence of resistivity. This phenomenon can be attributed to the high concentrations of insulating grain boundaries in the flux-prepared Sr₂FeReO₆ powders. At room temperature, both Sr₂CrReO₆ and Ba₂FeReO₆ powders exhibit a similarly large intergrain tunneling magnetoresistance (ITMR) of up to ∼70% and ∼65%, respectively, whose details are shown in Figs. 29(a) and 29(b), respectively. Such polycrystalline MR at low magnetic field is larger than that reported previously for Sr₂FeMoO₆ (ITMR of ∼20% to 30% at 0.4 T) prepared from nanoscale particles of ∼29 nm to 45 nm.³⁴ 

The optical behaviors of the Re-based DP oxides have promising applications in various optical devices. It is reported that the optical properties of Re-based DP oxides are controlled by their inter-band transitions between the B-site (B′ or B″) transition metal cations and the oxygen anions, which reflect the electronic states’ energy distribution in valence/conduction bands.^98–100 Jeon et al.¹⁰¹ measured the reflectance spectra of Ba₂FeReO₆ and Ca₂FeReO₆ polycrystalline samples at 300 K across the energy range of 5.0 meV–6.0 eV, as shown in Fig. 30(a), from which the optical conductivity spectra σ(ω) of the Ba₂FeReO₆ and Ca₂FeReO₆ samples can be obtained by the Kramers–Kronig (KK) transformation, which is shown in Fig. 30(b). Two spectral peaks are clearly observed in these two samples, which are marked by α and β for Ba₂FeReO₆ and A, B for Ca₂FeReO₆. It is noticed that the intensities of the peaks (β and B) appearing on the higher energy side are much larger than those of the peaks (α and A) located on the lower energy side. It is reported that the higher energy (β and B) peaks resulted from the electric dipole allowed charge transitions from the O 2p to the Re 5d or Fe 3d orbital states, whereas the lower energy (α and A) peaks are contributed from the d–d electronic transition between the Re 5d and/or Fe 3d states.¹⁰² It is also noticed that the position of the B peak in Ca₂FeReO₆ has a chemical shift (∼0.5 eV) toward higher energy as compared with that of Ba₂FeReO₆, as marked by the arrow in Fig. 30(b). This indicates the projected density of states (DOS) of the unoccupied Re t_2g bands in Ca₂FeReO₆ is higher than that in Ba₂FeReO₆. The dc conductivity data of Ba₂FeReO₆ and Ca₂FeReO₆ polycrystalline samples are also given in Fig. 30(b), as marked by black and red squares. At low-frequency, σ(ω) exhibits much differences between the two samples. However, as the photon energy was beyond 2.0 eV, the σ(ω) of Ca₂FeReO₆ became much suppressed as compared with that of the metallic Ba₂FeReO₆, but the σ(ω) still had a finite Drude component at room temperature. To solve this issue, low temperature (10 K) conductivity spectra of Ca₂FeReO₆ were measured in comparison with those at 300 K, as shown in Fig. 30(c). The low-frequency σ(ω) became more suppressed, the spectral peak was much narrow, and a gap opened at 10 K.¹⁰³ Such gap opening indicates the existence of an insulating ground state in the present Ca₂FeReO₆ sample.

Sohn et al.²⁵ measured the real part of optical conductivities σ₁(ω) of the Sr₂Fe_1+xRe_1−xO₆ films by a spectroscopic ellipsometer across the energy of 1.2 eV–5 eV, as shown in Fig. 31(a). The inset shows the local density of states (DOS) for three bonding types (Fe³⁺–Re⁵⁺, Fe³⁺–Fe³⁺, Fe³⁺–Re⁶⁺) in Fe-rich films based on the density functional theoretical calculations.^104–106 For the original Re⁵⁺–Fe³⁺ bonding of stoichiometric Sr₂FeReO₆, two types of optical transitions can be expected: (i) d–d optical transition from Re 5d to Fe 3d orbitals [indicated by A in the inset of Fig. 31(a)] and (ii) p–d optical transition from O 2p to Re/Fe d orbitals [indicated by B in the inset of Fig. 31(a)]. As expected, two apparent spectral features are observed, one is a broad spectral band located below 2.5 eV (denoted A) and another one is a strong spectra peak located near 4.0 eV (denoted B) in the σ₁(ω) of a stoichiometric film (green line, FMM film), which is consistent with the previous bulk data.¹⁰¹ However, in the Fe-rich film (blue line, FMI film), a new spectral peak C appeared at the expense of weights of A and B peaks. Peak C could be originated from the optical transition from O 2p to Fe 3d orbitals in the Fe³⁺–Fe³⁺ bonding, similar to the case of La³⁺Fe³⁺O₃.¹⁰⁷ However, any absorption peak expected from the Re⁶⁺–Fe³⁺ bonding, i.e., optical transition from O 2p to Re/Fe d orbitals, is not observed in the present energy regime. This is attributed to that the O 2p states of the Fe³⁺–Re⁶⁺ bonding are much far away from E_F than those of other two bonding states with strong O 2p–Re 5d¹ hybridization; thus, the corresponding optical transition requires higher energy than the present energy regime. Hauser et al.³² measured the FTIR transmission spectra of a 200-nm thick Sr₂CrReO₆ (001) film deposited on the SrTiO₃ substrate. Its Tauc’s plot of (αE)² vs E is shown in Fig. 31(b), where α is the absorption coefficient and E is the incident photon energy.¹⁰⁸ A linear fitting of the Tauc plot and its intercept of the extension of the linear part on the x axis clearly indicate that the direct bandgap (E_g) of the Sr₂CrReO₆ film is 0.21 eV. These features observed below 0.17 eV likely resulted from phonon modes. The noise appearing around 0.29 eV and in the energy range of 0.44 eV–0.50 eV contributes to water vapor and CO₂ present in the FTIR chamber. The present FTIR spectrum indicates that Sr₂CrReO₆ is a semiconductor rather than a metal. Therefore, high temperature ferrimagnetism and semi-conductivity of the Sr₂CrReO₆ thin films enable them to find promising applications in the fields of spin filters, magnetic proximity switches, and energy efficient quantum electronic devices.

In parallel with experimental investigations of Re-based DP oxides, theoretical calculations have also been carried out, allowing one to study electronic structures and structural aspects of Re-based DP oxides in theory. So far, several ab initio calculations such as the full potential linearized augmented plane-wave (FP-LAPW) method that is based on generalized gradient approximation (GGA),^91,109–111 local density approximation (LDA), LDA + U (the Hubbard U term), and LAD + U + SOC (spin–orbital coupling) calculations,¹⁰¹ local spin density approximation (LSDA) and LSDA + U methods,¹¹² and density functional theory (DFT) + U calculations¹¹³ are developed to investigate electronic, optical, mechanical, structural, and thermodynamic properties of Re-based DP oxides. As an example, the DOS of Sr₂FeReO₆ calculated by the FP-LAPW method based on GGA is shown in Fig. 32.⁹¹ It is found that at the Fermi level (E_F), the DOS exists only in the down-spin band, whereas there is no DOS in the up-spin band. In another word, there exists an energy gap (∼1 eV) between the occupied Fe e_g band and the unoccupied Re t_2g band in the up-spin state [see the middle part of Fig. 32]. The nature of half-metallicity means the carriers in half-metals are completely spin-polarized charge carriers in the ground state. In an ideal ferromagnetic half-metal, at the Fermi level between the two spin (up and down) bands, only one spin band is partially occupied, while the other does not have DOS across the Fermi level. Thus, the electrical conduction is controlled only by one spin direction of the carriers. In the half-metal Sr₂FeReO₆ compound, theoretical calculations demonstrated that in the occupied up-spin band just below the E_F, there mainly exist the Fe 3d electrons with the localized spins on the Fe sites, whereas, in the down-spin band around E_F, there mainly exist the hybridized Re 5d t_2g and Fe 3d t_2g states. In addition, at the Fermi level, the partial DOS of Re (t_2g) is 3–4 times larger than that of Fe (t_2g). This implies the electrical conduction of the Sr₂FeReO₆ compound is dominated by the 5d conduction electrons (Re⁵⁺ = 5d²). In order to understand the importance of the on-site Coulomb interaction energy U (4.0 eV–5.0 eV), the crystal-field splitting energy, Δ (2.0 eV–3.0 eV), and the SOC (spin–orbit coupling, 0.3 eV–0.4 eV) in the electronic structures of the A₂FeReO₆ DP oxides with A = Ca and Ba, the total energy and electronic band structures of the A₂FeReO₆ DP oxides with A = Ca and Ba were calculated by LDA, LDA + U, and LAD + U + SOC methods.¹⁰¹ Figures 33(a) and 33(b) show the calculated results for Ba₂FeReO₆ by LDA and LDA + U methods, respectively. Different electronic structures are observed due to the different spin directions. It is found that a finite DOS exists at the Fermi energy in the down-spin bands (marked by red dashed lines), whereas, in the up-spin bands, a gap near the Fermi level is observed (marked by black solid lines). This indicates the characteristic electronic feature of a half-metal.⁵ Similar results calculated by the LDA + U method were reported for Sr₂FeMoO₆.^114,115 However, when the SOC becomes much strong in the Re-based DP oxides, the mixture of spin states and the half-metallicity can be neglected.^116,117 Figure 33(c) shows the calculated electronic structure of Ba₂FeReO₆ by using the LDA + U + SOC method. It is noticed that the SOC term leads to much changes in the electronic structure. In comparison with Fig. 33(b), great changes in the electronic states are observed in Fig. 33(c), especially that two bands are nearly parallel to each other around the Fermi energy, as indicated by blue and magenta lines. Therefore, the SOC plays a crucial role in determining the electronic structures of Ba₂FeReO₆. Similarly, band structures of Ca₂FeReO₆ with lattice distortion are also calculated by LDA, LDA + U, and LAD + U + SOC methods, which are shown in Figs. 34(a)–34(c).¹⁰¹ In Fig. 34(b), the LDA + U calculation predicts a semi-metallic ground state in Ca₂FeReO₆, in which the conduction band and valence band just get in touch with the Fermi level. Figure 34(c) shows the calculated electronic structure of Ca₂FeReO₆ by using the LDA + U + SOC method. However, no significant change is observed in the band dispersion as the SOC term is included. This means the U term is crucial, whereas the SOC term is less important in determining the electronic structure of Ca₂FeReO₆. To understand the role of lattice distortion in the electronic structure of Ca₂FeReO₆, theoretical calculations are also carried out by assuming that the bond angle of the Fe–O-Re bond in the Ca₂FeReO₆ compound is equal to 180° rather than the experimental value of 153°. Figures 34(d)–34(f) show the calculated band structures of Ca₂FeReO₆ by LDA, LDA + U, and LAD + U + SOC methods without considering lattice distortion. It is noticed that the band dispersions of Ca₂FeReO₆ are almost the same as those of Ba₂FeReO₆ [see Figs. 33(a)–33(c)]. Such a similarity indicates that the lattice distortion has a great influence on the electronic structure of a real Ca₂FeReO₆ compound. Therefore, in the real Ca₂FeReO₆ compound, the lattice distortion plays an important role in determining the electronic structure. In contrast, there is very little lattice distortion in Ba₂FeReO₆, and its electronic structure is mainly controlled by electron correlation and SOC. Similar conclusions are also drawn in the A₂FeReO₆ (A = Ca, Sr, and Ba) oxides based on the calculations by the LSDA and LSDA + U methods.¹¹² To understand the correlation effects on the Re site, the partial DOSs of the Re 5d orbital in the A₂FeReO₆ (A = Ca, Sr, and Ba) oxides are calculated based on fully relativistic Dirac approximation, as shown in Fig. 35. It is found that Ca₂FeReO₆ has a much smaller Re bandwidth than the two compounds, A₂FeReO₆ (A = Sr and Ba). Therefore, a strong electron correlation should exist in the Re 5d bands in the Ca₂FeReO₆ oxide, leading to much narrow bands near the Fermi level with pseudo-gaps just above it. These bands separate from almost disconnect states that are dominated by Fe contributions above the Fermi level. A similar case happens for the Fe 3d energy bands. It is found that the Fe t_2g bandwidth is decreased by about 25% from Sr₂FeReO₆ to Ca₂FeReO₆ compounds. The Fe and Re d bandwidths are different among the A₂FeReO₆ (A being Ca, Sr, and Ba) compounds, which can be ascribed to their different crystal distortions. The John–Teller distortions are increased in the series of A₂FeReO₆ (A = Ba, Sr, and Ca) oxides. The bond angle of the Fe–O–Re bond in the monoclinic Ca₂FeReO₆ is about 156°,⁹² which is much smaller than 180° in the cubic Ba₂FeReO₆ and tetragonal Sr₂FeReO₆. Such low bond angle makes the Fe–Re bond overlapping decrease and the t_2g bandwidths become narrowed. In addition, the monoclinic structural distortion in the Ca₂FeReO₆ oxide lifts the degeneracy of the t_2g levels on the Fe and Re sites. The above two factors result in more narrow energy bands for Fe and Re t_2g in the Ca₂FeReO₆ oxides, as compared with the A₂FeReO₆ (A = Sr and Ba) oxides. Thus, the Fe and Re t_2g electrons become much more localized and Ca₂FeReO₆ undergoes a Mott transition. To understand the electronic, magnetic, and structural properties of the A₂FeReO₆ (A being Ba, Sr, and Ca) oxides, x-ray absorption spectra (XAS) and x-ray magnetic circular dichroism (XMCD) spectra are theoretically investigated at the Re, Fe, and Ba L_2,3 and Fe, Ca, and O K edges by the LSDA + U method. Figure 36 shows the calculated XAS and XMCD spectra at the Re L_2,3 edges from the A₂FeReO₆ (A = Ba, Sr, and Ca) oxides and their corresponding experimental spectra.^118,119 It is observed that the Re L₃ spectra (contributed from 2p_3/2 → 5d_3/2,5/2 transition) have almost the same similarity and exhibit two peaks with the same edge energy position in A₂FeReO₆ (A being Ba, Sr, and Ca) oxides. The first peak appeared at about 10 540.1 eV, and the stronger one appeared at 10 543.6 eV. The split energy is attributed to the crystal-field splitting of d orbitals into t_2g and e_g states.¹²⁰ The Re L₂ XAS are composed of two peaks, and the low-energy peak exhibits relatively stronger intensity than the high-energy one. Theoretical calculations demonstrate an inverse peak relative intensity for the L₃ and L₂ XAS. The experimental dichroic L₂ lines of the A₂FeReO₆ (A being Ba, Sr, and Ca) oxides exhibit an asymmetric negative peak with a shoulder appearing on the higher energy side. Three peaks are found in the dichroic lines at the L₃ edge, which are two positive peaks with high energy and a negative one with low energy. This negative peak observed in Ba₂FeReO₆ and Sr₂FeReO₆ compounds embodies as a shoulder at low energy, but it exhibits a much large intensity in Ca₂FeReO₆. The dichroism at the L₂ edge exhibits much stronger intensity than that at the L₃ edge in all three compounds. The XMCD spectra can be qualitatively interpreted by analyzing the corresponding selection rules, orbital character, and occupation numbers of individual 5d orbitals.¹¹² The theoretical calculations match relatively well with the experimental XAS and XMCD spectra in the A₂FeReO₆ (A = Ba, Sr, and Ca) oxides in both the spectral shape and relative intensities. Indeed, theoretical calculated techniques now allow one to fundamentally understand the physical properties and structural aspects of Re-based DP oxides, and now, they become important and complementary methods to the experimental probes; in particular in some cases, the physical properties of Re-based DP oxides are only directly obtained by some theoretical calculations. In parallel with much advances in theoretical computational models, the experimental scientists can grow Re-based DP oxide films by the laser-MBE method with the film growth controlled at the atomic scale and measure local physical properties at the nanoscale. It is expected, in the near future, the two trends have more chance to perform a lively theoretical–experimental dialog.

Owing to the diverse electrical behaviors and huge magnetic anisotropy, Re-based DP oxides have promising applications in oxide spintronics, nonvolatile data memory devices, and multiferroic devices. For example, at room temperature, some A₂FeReO₆ oxides exhibit half-metallic ferromagnetism, which can be utilized as electrodes for fabricating the magnetic tunnel junctions (MTJs). In the MTJ structure, the tunneling current is dependent upon the relative orientation of the magnetization of two ferromagnetic electrodes, and it is modified by applying a magnetic field.^121,122 Therefore, the MTJs constructed with Sr₂FeReO₆ and Sr₂FeMoO₆ as ferromagnetic electrodes would exhibit high TMR ratios due to the larger magneto-crystalline anisotropy because of the Re ion. Furthermore, the Re-based and Mo-based DP oxides such as Sr₂FeReO₆ and Sr₂FeMoO₆ exhibit much different coercive fields; thus, in the MTJs, the Sr₂FeReO₆ electrode with high coercive field may act as a pinned layer, while the Sr₂FeMoO₆ electrode with low coercive field acts as a free layer. The magnetization of Sr₂FeMoO₆ (free layer) can be rotated concerning the pinned layer (Sr₂FeReO₆) through a barrier in MTJs. As a consequence, it is possible to obtain different states of resistance, and each state can be functioned as a specific degree of spin, while, at the same time, the number of states can be applied in the storage or data processing system. Due to the two ferromagnetic electrodes (Sr₂FeReO₆ and Sr₂FeMoO₆) having almost the same lattice parameters, epitaxial growth of such heterostructured MTJs can be easily achieved in different crystallographic directions. This allows one to investigate electron tunneling as functions of not only the spin direction but also the orbital symmetry. It is expected that this direction will become an exciting topic in oxide spintronics. In an epitaxy bilayer of Ca₂FeMoO₆/Ca₂FeReO₆, as the insulating phase of Ca₂FeReO₆ appears at low temperature, the tunneling electrons across the insulator Ca₂FeMoO₆ layer and the counter-electrode have strongly exchanged split sub-bands. Based on this phenomenon, spin-filtering devices can be developed. Furthermore, such an epitaxial heterostructure provides easier manipulating of the spin filtering than the other systems such as Al/EuS/Al or La_2/3Sr_1/3MnO₃/NiFe₂O₄ reported previously.^123,124 As the important components used for dissipationless electronic and spintronic devices, ferromagnetic insulators (FMIs) can filter the electronic charges to produce pure spin currents, manipulating spins within nonmagnetic layers via the magnetic proximity effect,^125–127 creating the quantum anomalous Hall effect in conjunction with topological insulators.^128,129 For example, the cation-ordered DP Sr₂Fe_1+xRe_1−xO₆ thin films exhibit a FMI state and have high Curie temperature (400 K) and large M_s value (1.8 µ_B/f.u.). This enables them to be used in spin filters, magnetic proximity, and quantum anomalous Hall effects. Such new FMIs also find promising applications in spintronic, electronic, and energy efficient quantum devices. Another promising application of Re-based compounds is the development of multiferroic devices based on the magnetoelastic coupling. The resistance modulations in the Re-based thin films can be induced by the strain, which is generated by a piezoelectric layer beneath the DP Re-based thin film. At present, the advanced applications of Re-based DP oxides are still at their embryonic stage, and many issues need to be resolved and some technical challenges lie ahead. As a consequence, there is a long journey before accomplishing the commercialization of Re-based DP oxides.

Here, we present a comprehensive overview of the recent advances in the Re-based DP oxides, focusing on their syntheses, structural characterizations, physical properties, advanced applications, and theoretical studies on their electronic and structural aspects. The characteristic features of Re-based DP oxides such as metallic-like, half-metallic, or insulating behavior, high Curie temperature, and large carrier spin polarization enable them to find promising applications in oxide spintronic devices, multiferroic devices, and energy efficient quantum electronic devices. From the viewpoint of applications, the epitaxial growth of Re-based DP oxide thin films with high quality is highly required although the epitaxial growth of Re-based DP oxide thin films has become an emerging research field. It is expected that in the near future, remarkable advances will be achieved in the epitaxial growth of Re-based DP oxide thin films by the laser-MBE method with growth control at the atomic scale and enhanced properties. With the development of the aberration corrector (or Cs-corrector), the new generation HRTEM/STEM facility equipped with the Cs-corrector allows one to achieve a spatial resolution better than sub-Å and an energy resolution better than sub-eV, thereby making the structural characterizations of Re-based DP compounds at sub-Å available. Although the advanced applications of Re-based DP oxides are promising, they still remain in their early stage; a long journey lies ahead before the commercialization of Re-based DP oxides. However, the scientific and technical potentials of Re-based DP oxides are, for sure, great, and the future research in this field is very bright. It is hoped that this Review could attract renewed interest in the fundamental research of Re-based DP compounds, encouraging the scientific community to enter this impressive area.

K.L. collected the references and prepared the manuscript. Q.T., Y.W., L.Y., and Y.X. participated in sequence alignment. X.Z. designed the structure and modified the manuscript. All authors contributed to data interpretation and discussion and read and approved this manuscript.

The authors are grateful for financial support from the National Natural Science Foundation of China (Grant Nos. 11674161 and 11174122), the Natural Science Foundation of Jiangsu Province (Grant No. BK20181250), and undergraduate teaching reform projects from Nanjing University (Grant Nos. X20191028402 and 202010284036X).

The authors declare that they have no conflict of interest.

Data sharing is not applicable to this article as no new data were created or analyzed in this study.