Comparison of the dielectric and magnetocaloric properties of bulk and film of GdFe_0.5Cr_0.5O₃

Magnetocaloric cooling is environment friendly¹ and has potential to be a highly energy-efficient alternative to the conventional vapor compression/expansion-based cooling technology that contributes toward ozone depletion and global warming.^2,3 Magnetic refrigeration (MR) is a cooling technology based on the magnetocaloric effect (MCE), which was the first method to be used for cooling below 0.3 K (temperature attainable by ³He refrigeration). The MCE is a phenomenon of temperature change of a material induced by the magnetization and demagnetization of a magnetic material in a varying magnetic field.⁴ The physical origin of MCE is the field-dependent entropy of a material.⁵ When the magnetic field is adiabatically applied to a magnetic material, the magnetic entropy is reduced by magnetic-spin ordering that must be compensated by the rising lattice entropy (increase of temperature) since the total entropy is conserved under adiabatic conditions.^5,6 The magnetic material cools when the external magnetic field is removed adiabatically. The efficiency of magnetic refrigeration is estimated to be 30%–60% of the Carnot cycle, which is higher than 5%–10% of the Carnot cycle of gas compression refrigeration.⁷ There is great interest in developing new materials for magnetic refrigeration with a large change in magnetic entropy (ΔS, which is a material cooling power) and adiabatic temperature change (ΔT_ad) induced by a small change in the applied magnetic field (ΔH).⁸ Adequate ΔT_ad is required to move the heat. Device-related studies demonstrated that other material properties to consider are hysteresis (zero or low), heat capacity (moderate), thermal conductivity (large), and chemical/mechanical stability (high), among a couple of others. Different figures of merit have been utilized as an early indicator of the material's suitability for magnetic refrigeration. Some of those are coefficient of refrigerant performance (CRP),⁹ relative cooling power,¹⁰ maximum energetic cooling power,¹¹ and temperature-averaged entropy change (TEC)¹² to name some.

Zimm et al. demonstrated magnetic refrigerator using elemental Gd [with second-order transition, sizeable magnetic moment (7.55 μ_B), soft ferromagnet with low losses, Tc = 294 K] at 5 T, indicating the possibility of an extremely efficient refrigeration process (−ΔS/ΔH: 1.7–4.1 J kg⁻¹K⁻¹T⁻¹).^13,14 Efforts have been made to synthesize various materials, including alloys of rare earth (R), with high peak values of the magnetic entropy change (ΔS), among which Gd, Gd₅(Si_1−xGe_x)₄, La(Fe_13−xSi_x), and the manganites (R_1−xM_xMnO₃, where M = Ca, Sr, and Ba) have been studied for their applications near room temperature.^15–18 

The material systems exhibiting large MCE at low temperatures (<30 K) are also intriguing for basic research and low-temperature refrigeration. For example, in recent years, many investigations have focused on the rare earth–based ABO₃ type perovskite oxide materials, such as RMnO₃, RCrO₃, and RFeO₃ (R with a large total angular momentum) because of their large spontaneous magnetization and large change in magnetization around the order–disorder, i.e., phase transition temperature (<20 K), thereby leading to large ΔS.^19–21 Due to unique properties of Gd, Gd-based oxides have been considered of great interest, and largest relative adiabatic temperature change (=ΔT_ad/ΔH) and isothermal magnetic entropy change (ΔS/ΔH) have been obtained in GdCrO₃ (GCO) and GdFeO₃ (GFO), which renders these as the potential oxide materials as low-temperature refrigerants.^19,22–30 The magnetic entropy of GCO and GFO were reported to be −31.6 J/kg K in a field change of 7 T and −52.5 J/kg K in a field change of 9 T, respectively.^19,31 GdCrO₃ is one of the interesting orthochromites having a magnetic rare earth ion with an orthorhombic crystal structure and G-type antiferromagnetic behavior, which goes through interesting magnetic reversal due to the antiparallel alignment of Gd³⁺ moments with that of the weak ferromagnetic (FM) components of Cr³⁺ ions due to spin canting. In addition, GCO also exhibits rich magnetic properties like multiferroicity^32,33 (with magnetic and electric orders) due to temperature-dependent magnetic Gd³⁺–Gd³⁺, Gd³⁺–Cr³⁺, and Cr³⁺–Cr³⁺ interactions and leading to magnetoelectric multiferroic behavior in the material. Furthermore, it was proposed that the presence of magnetoelectric coupling in multiferroic materials would lead to enhanced magnetocaloric properties.^34,35

Recently, multiferroicity in GFO–GCO solid solutions (GdFe_1−xCr_xO₃) has attracted much attention due to its potential multiferroic behavior near room temperature.³⁶ The composition with a Fe/Cr = 1 at the B-site in this system is of particular interest as multiferroicity and magnetoelectric coupling are observed in similar systems like DyFe_0.5Cr_0.5O₃ and YFe_0.5Cr_0.5O₃.^37,38 The ordering on the B-site affects not only the magnetic but also the electrical and dielectric properties of the oxides.³⁹ In addition, in these oxides, electrical, magnetic, and structural properties are strongly correlated. Mutual coupling exists between electric and magnetic ordering through spin–phonon interaction.⁴⁰ In DyFe_0.5Cr_0.5O₃, the MCE and magnetization values were observed to be enhanced by magnetoelectric coupling.³⁸ For HoFe_0.5Cr_0.5O₃, studies show large MCE along with the presence of nonlinear magneto-dielectric behavior.^40,41

Following these examples, investigations of magnetic, magnetocaloric, and dielectric properties of GdFe_0.5Cr_0.5O₃ (hereafter listed as GFCO for brevity) would be of great interest, and this is the focus of our research, results of which are presented in this paper. Two samples of GFCO were investigated: (i) a bulk sample prepared by the citrate route and (ii) a 960 thick film synthesized on a platinized silicon substrate by chemical solution deposition and spin-coating methods. Comparison of the properties of the bulk and thin film of GFCO is important, since development of the magnetocaloric films is necessary with regard to the miniaturization for devices, such as on-chip cooling of sensors.⁴² It may be that a material with a high MCE in a bulk form may show only a modest MCE after it has been shaped into a heat exchanger with sub-millimeter channels.^43,44 There are only a few reports on the magnetocaloric properties of materials (alloys) at reduced dimensions, such as in films,⁴⁵ nanocrystalline materials,^46–50 and ribbons forms,⁵¹ among which, the confinement effects, strain, and/or high surface-to-volume ratio have been found to affect the properties. The results presented here on the comparison between the properties of the bulk and film of GFCO bring into focus the role of reduced dimensionality of thin films on their magnetic, magnetocaloric, and dielectric properties.

In order to prepare 50% Fe-substituted GdCrO₃ (i.e., GdFe_0.5Cr_0.5O₃ or GFCO) film, stoichiometric ratios of Gd(NO₃)₃, Fe(NO₃)₃, and CrCl₃ were dissolved and mixed in acetic acid to get a coating solution of 0.2M concentration. Subsequently, the solution was spin coated on 1 × 1 cm² Pt (111)/TiO₂/SiO₂/Si (100) (from now on written as Pt/Si substrate) followed by pyrolysis at 600 °C for 5 min. The spin-coating and pyrolysis steps were repeated 12 times followed by annealing and crystallization of the film at 700 °C in oxygen atmosphere for 2 h to get the GFCO film. The bulk GFCO was prepared by the citrate solution route, where the stoichiometric ratios of Gd(NO₃)₃, Fe(NO₃)₃, and CrCl₃ were dissolved in citric acid. The solution was then heated, dried, and annealed at 900 °C for 2 h to obtain the bulk GFCO. The crystal structure and phase purity of this GFCO film and bulk were examined by X-ray powder diffractometer (XRD; Bruker D2 Phaser) with Cu Kα radiation (λ = 1.54 Å). The morphology and thickness of the film were analyzed using a field-emission scanning electron microscope (FEI Nova NanoSEM 450 with Oxford AZtecEnergy Microanalysis System). To check the cross section of the film, it was cut using a diamond cutter pen. X-ray photoelectron spectroscopy (XPS) data were recorded on a PHI model 590 spectrometer with multiprobes (Φ Physical Electronics Industries Inc.) using Al Kα radiation (λ = 1486.6 eV) operated at 250 W. The magnetic properties were measured using a vibrating sample magnetometer (VSM) attached to an Evercool Physical Property Measurement System (Quantum Design Inc.). For the electrical measurements, the top circular Pt electrodes of ∼300 μm were deposited using the dc sputtering method. The capacitance measurements were conducted using an LCR meter (Agilent E4980A) connected to a cryostat (from MMR Tech.) where the sample was placed in the vacuum. The electric field–dependent polarization was measured by the ferroelectric tester (RT66B, Radiant Technologies Inc.).

The field-emission scanning electron microscopy (FE-SEM) images from the top surface and film-substrate cross section of the GFCO film are shown in Figs. 1(a) and 1(b), respectively. The top-view FE-SEM image in Fig. 1(a) reveals the surface nanostructure in the film that seems to be well crystallized and dense. As shown in Fig. 1(a), each grain is a conglomerate of several smaller grains that are formed without sharp boundaries. Grain-growth during the heat treatment and strain in the film plays a dominant role in defining these microstructural characteristics.⁵² The grain size distribution from the top surface of the present GFCO film is shown in the inset of Fig. 1(a), in which the data were collected from around 100 grains with relatively clear grain boundaries visible at the top surface. The histogram in the inset was fitted with the lognormal distribution function, which yielded an average intrinsic crystallite size (ICS) of ∼50 nm on the surface of the film. The cross-section FE-SEM image in Fig. 1(b) clearly exhibits multilayered granular structure (as the film was prepared by 12 coatings, each followed by pyrolysis before the final annealing after 12 layers). The total thickness of the deposited GFCO film was estimated to be ∼960 nm. Thus, the average thickness of each granular layer, defined as single-layer thickness (SLT), is 80 nm. In the spin-coated films with this much thickness of each layer, extensive shrinkage of the initial film takes place at room temperature because of capillary forces, during removal of organics (pyrolysis), and through the volume change that accompanies crystallization. The empirical number q (defined as q = ICS/SLT) was found to be ∼0.625. Therefore, according to Schuler et al., microstructure of the solution grown film is a layer-type film microstructure (for 0.42 < q < 1), which can be clearly noticed in Fig. 1(b).⁵³ In the present film fabrication process, homogeneous nucleation is believed to take place leading to such granular microstructures of the film. From the cross section of the film, semi-quantitative composition of different elements was characterized by energy-dispersive x-ray spectroscopy (EDS) to identify the GFCO layer, as presented in Fig. 1(c). Pt, TiO₂, SiO₂/Si, and GFCO layers are labeled in Fig. 1(b) according to the EDS analysis. This clearly reveals a diffusive film–Pt interface (with traces of Pt detected in the GFCO layer), and the film was of uniform distribution (no clearly visible dead layer or elemental segregation or another phase was observed) as reported in the nanocomposite film, where secondary phase can be clearly identified.^54,55

The XRD pattern of the GFCO film on the Pt/Si substrate is shown in Fig. 2(a). Some major peaks of the GFCO film were indexed with Miller indices (hkl) based on JCPDS Card No. 25-1056 for the orthorhombic GdCrO₃ system associated with the space group Pbnm and JCPDS Card No. 47-0067 for GdFeO₃ with the same structure.^56,57 All the peaks in the XRD pattern were found to be either from the substrate or the GFCO film, indicating the absence of any other impurity, and thus, a phase-pure GFCO film. The film was found to be polycrystalline in nature as no preferred orientation was detected. The lattice parameters of the film were roughly estimated by using the d-spacing formula for the orthorhombic structure and the Bragg's law, results of which are summarized in Table I.²⁹ In Fe-substituted samples, Fe³⁺ and Cr³⁺ have been considered to have a coordination number of 6. The volume of the unit cell of the GFCO film is found to be in between that of GCO and GFO (reported in the literature), which is attributed to the substitution of the larger radii Fe³⁺ (0.645 Å) into the Cr³⁺ (0.615 Å) site in GdCrO₃. In solution grown films, film shrinkage may generate an extrinsic biaxial stress parallel to the plane of the film during heat treatment due to a mismatch of thermal expansion coefficients between the substrate and the oxide film and distributed defects (such as vacancies). Stresses can also develop due to island coalescence and other processes occurring at the grain boundaries. In the present film, in-plane lattice parameters were found to be slightly smaller and out-of-plane lattice parameters were slightly larger than lattice parameters of its bulk obtained from Rietveld refinement, as shown in Fig. 2(b) and Table I. This could indicate minuscule in-plane compressive stress (negative lattice strain, −0.7%, obtained by comparing the average in-plane lattice parameters between film and bulk GFCO powder presented in this study) and out-of-plane tensile stress (positive lattice strain, 0.8%, obtained by comparing the out-of-plane lattice parameters between GFCO film and bulk powder). These are only a rough estimate of the strains as it is known that lattice parameters even in bulk powder could be different due to nonuniform chemical contributions or the presence of instrumental errors, which can deviate even the strain-free lattice constant from its true value. With the increase in film thickness, strain imposed by the substrates generally reduces or disappears; however, internal stress due to the grain boundary may still be present.⁵⁸ It is noted that the distribution of stresses in polycrystalline films is complex and can be estimated using other techniques,^58–60 which is beyond the scope of this work.

As evident in Table I, the volume of the unit cell for the bulk GFCO (226.3 ų) is slightly larger than that for bulk GdCrO₃ (222.6 ų). A similar increase in unit cell volume was also observed with Fe substituting in NdCrO₃ and HoCrO₃, which can be understood due to the larger ionic size of Fe³⁺ compared to Cr³⁺.⁶¹ Another observation is that the unit cell for the bulk GFCO is also larger than that for the GFCO film (224.8 ų), which is likely due to strain in the film. The structural distortion of the unit cell from cubic symmetry, as quantified by the orthorhombic strain factor s⁶² 

is also in between that of two end members of the solid solutions as presented in Table I. Thus, the substitution of Fe in GdCrO₃ resulted in a more distorted structure than that of pure GdCrO₃ but slightly less than that of GdFeO₃. These results also show that s is about 10% larger in the GFCO film as compared to that in bulk GFCO.

To identify the valence states of the Fe, Gd, and Cr ions in the present GFCO film, the XPS spectra of GFCO film were recorded. Figure 3(a) represents the survey scan spectrum obtained from the surface of the GFCO film. The signals around binding energy of 142, 284, 529, 710, 576, and 1187 eV originate from Gd 4d, carbon (C) 1s, O 1s, Cr 2p, Fe 2p, and Gd 3d. The XPS core-level spectrum of Gd 4d is displayed in Fig. 3(b), which was fitted using three peaks, out of which two intense peaks at ∼141.05 and ∼147.05 eV are associated with Gd³⁺:4d_3/2 and 4d_5/2, respectively.⁶⁶ The third peak in the Gd spectrum could be ascribed to an additional multiplet structure due to spin–spin interaction.⁵⁶ The Fe 2p core-level spectrum in Fig. 3(c) exhibits four obvious peaks. The peaks at binding energies of 710.18 and 724.05 eV were attributed to Fe³⁺: 2p_3/2 and 2p_1/2, respectively.⁶⁷ One additional peak at ∼711.80 eV may indicate the presence of Fe²⁺ in the present GFCO film.⁶⁸ The satellite peak that appears at 719.03 eV further confirms the +3 oxidation state of Fe in the GFCO film.⁶⁹ The Cr 2p_3/2 core-level spectrum consist of two peaks as shown in Fig. 3(d). One peak at ∼576.43 eV can be correlated with the presence of Cr³⁺, and the other located at ∼575.30 eV could suggest the presence of Cr⁴⁺ in the film.³⁹ However, no extra peaks from Cr⁴⁺ or Fe²⁺ were identified in the XRD pattern, indicating that the other oxidation state impurities may be minimally present.⁷⁰ 

The capacitance of the bulk and film of GFCO were recorded under various temperatures and frequencies, and dielectric constant vs temperature data, so determined, are shown in Figs. 4(a) and 4(b). Dielectric constant decreases with the increasing frequency, which could be attributed to the dipoles such as space charge being unable to follow the electric field at a high frequency.⁷¹ For the bulk GFCO, it is observed that first, the dielectric constant increases with the increasing temperature from 5 K up to 490 K at 100 Hz, which may be related to the increase of drift mobility of charge carriers with the increase of temperature.⁷² The dielectric constant then decreases by further increasing the temperature (T > 490 K). This anomaly may indicate that the ferroelectric to paraelectric phase transition in the bulk GFCO occurs at the transition temperature, Tc, ≈ 490 K at 100 Hz. The shift of temperature of this dielectric anomaly to higher temperatures with the increasing frequency (640 K at 1 MHz) and the broad transition peaks indicate diffusive or relaxor-type disorder–order behavior. This behavior can be described by the modified Curie–Weiss law as follows:

where ɛ and ɛ_m are dielectric constant and peak dielectric constant at temperature T and T_m, respectively, C is the Curie constant, and γ is the diffusion exponent.³² In order to fit the ɛ(T) data using Eq. (2), $ln(1ε−1εm)$ vs $ln(T−Tm)$ data were fitted as shown in Fig. 4(c), resulting in the γ value of 1.70. This indicates diffuse ferroelectric behavior as the value of γ is between 1 (for normal ferroelectric) and 2 (for ideal relaxor ferroelectric). The relaxor-like behavior may be attributed to either multiple valence states (Cr⁴⁺/Cr³⁺, Fe³⁺/Fe²⁺) caused by oxygen vacancies or the randomness of B-site cations.³² The exact relaxation process is examined by the empirical Vogel–Fulcher (VF) law given by

where τ is the inverse of frequency, τ₀ is the inverse of the limiting response frequency of the dipoles, E_a is the activation energy of local polarization, k_B is Boltzmann's constant, and T_m and T_VF are the temperature of peak dielectric constant and static freezing temperature, respectively.³² The experimental data fit the model in Eq. (3) well, as shown in Fig. 4(d), yielding the following fitting parameters: τ₀∼ 2.02 μs, T_VF ∼ 508.2 K, and E_a∼ 0.03 eV. These results are close to the other reports on RFe_0.5Cr_0.5O₃, such as E_a∼ 0.035 eV and τ₀∼ 0.11 μs in the Yb(Fe_0.5Cr_0.5)O₃ bulk sample.⁷³ However, the activation energy of 0.03 eV of the present bulk GFCO is much smaller than that of the GFCO film (0.11 eV), reported earlier, indicating different relaxation behavior in film and bulk.³² It is noted that T_c observed in the present film is lower than that of the bulk at low frequencies, as shown in Fig. 4(b). Observed variation in dielectric constant could be attributed to the different fabrication conditions (annealing temperature), grain size, and other defects (compositional, stress, oxygen vacancies, lower density in bulk, etc.).⁷⁴ The activation energy of the present GFCO bulk (0.03 eV) suggests that the polar-glassy system has thermally activated polarization fluctuations.^75,76 The kinetics of the fluctuation in the bulk sample is assumed to be controlled by a coupling between nanometer scale clusters,⁷⁶ while the fluctuation in film could be attributed to the hopping electrons along the single-charged oxygen vacancy chain.³² The room temperature electric polarization vs electric field (P–E) hysteresis loops from the bulk and film samples are shown in Fig. 4(e). The plot does not show saturation in electric polarization with the applied electric field (limited by measurement capability), which is typically observed in the case of a leaky dielectric material.⁷⁷ This cigar-shaped loops were also reported in some multiferroic materials due to larger leakage currents, which may result from mixed valence or oxygen vacancies.⁷⁸ 

The frequency dependences of imaginary parts of dielectric constant (ɛ″) at 500 K and 520 K for the GFCO film and bulk samples are shown in Figs. 5(a) and 5(b), respectively. ɛ″ decreases drastically with the increase in the frequency. The larger value of ɛ″ at the lowest frequency clearly indicates the presence of DC conductivity in the material, which is also known as interfacial Maxwell–Wagner (MW) polarization.⁷⁹ The variation of ɛ″ as a function of frequency is fitted to the MW polarization model (as shown in Fig. 5) using the following equation:^80,81

where ω is the angular frequency, $C0$ is the capacitance of system, t is the relaxation time, and R₁ and R₂ are resistance of grain and grain boundary, respectively. $ε0$ and $ε∞$ are the permittivity at zero and infinite frequencies, respectively.⁸⁰ The perfect match between the experimental data and the model at a low frequency indicates that the large dielectric constant at a low frequency can be attributed to the MW interfacial polarization. The deviation of the experimental ɛ″ from the model data at high frequencies may be caused by the absence of space charge polarization.⁸⁰ 

To convert measured magnetic moment of a sample to magnetization in units of emu/gm, accurate magnitude of the mass of a sample is needed. For the film, the use of the standard balance method by subtracting the mass of the substrate from the prepared film yielded the mass of the GFCO component of the film as 0.31 mg. However, this method is vulnerable to large errors for film since, in this case, the mass of the substrate is about 100 times larger than the mass of the GFCO component. So, an alternative and more accurate magnitude of mass = 0.228 mg was obtained by using the calculated x-ray density = 7.657 g/cm³ of the film from lattice parameters of the film presented in Table I and volume of the film with its measured dimensions of 0.31 cm × 1 cm × 960 nm. Next, using 85% as the typical reported packing density of some films,⁸² the estimated mass = 0.228 × 0.85 = 0.194 mg of the GFCO component of the film, which is used in the results of magnetic and magnetocaloric properties reported here.

The temperature dependence of the dc magnetic moment of the present GFCO film on the Pt/Si substrate (total) and the bare Pt/Si substrate (sub) in the field-cooled (FC) mode (with dc magnetic field H = 500 Oe applied in the plane of the film) are shown in Fig. 6(a). Although the magnetic moment of the substrate is comparatively negligible, it was subtracted from the magnetic data of the GFCO film on the substrate to get the temperature-dependent magnetic moment data of only the GFCO film (film) in the FC mode as also plotted in Fig. 6(a). The dc magnetic susceptibility (χ) of the present GFCO film in FC and zero field-cooled (ZFC) modes is presented in Fig. 6(b). The d(χT)/dT data of the ZFC component are plotted in the inset of Fig. 6(b), which indicates that the signal-to-noise ratio is very small, may be due to the small mass (0.19 mg) of the film. The small magnitude of the magnetic moment in the film, especially for T > 250 K, is very close to VSM's sensitivity limit (10⁻⁶ emu), which made it very difficult to identify the exact magnetic ordering temperature in the present GFCO film.³² 

The temperature dependence of the ZFC and FC data for the GFCO bulk powder was measured with H = 50 Oe, and this plot is presented in Fig. 6(c). The inset of Fig. 6(c) shows the temperature-dependent d(χT)/dT data of the bulk at 50 Oe, suggesting an ordering temperature of ∼275 K. At higher temperatures for T > 245 K, the data had reduced the signal-to-noise ratio, and the Cr-ordering temperature was not very clear. However, as previously reported,⁸³ the change in the slope was noted by sketching the two solid lines (as shown by the blue color in the inset) and by noting the temperature where the two lines meet, suggesting an ordering temperature of ∼275 K (shown with an arrow). The higher temperature paramagnetic (PM) data were fitted with the Curie–Weiss law, which results in the negative value of the Weiss temperature (θ), indicating an AFM state below the transition temperature (275 K). It should be noted that other RCrO₃ (with a magnetic R-ion) was found to order in the AFM state (mostly G-type) below the Néel temperature (⁠$TNCr$⁠, where Cr³⁺ orders), above which the material is PM.^21,84 End members, GdFeO₃ and GdCrO₃, exhibit Néel temperatures of $TNFe∼657K$ (where Fe³⁺ orders) and $TNCr∼167K$ (where Cr³⁺ orders), respectively. According to rough linear interpolation of the Néel temperatures (T_N) of their solid solutions, $TN$ for GFCO can be predicted to be ∼412 K.⁶⁴ However, $TN$ of the bulk GFCO was reported to be 241 K by Boudad et al.,³⁶ 250 K by Yin et al.,³⁹ and 260 K by Dash et al.⁸⁵ In the work by Orlinski et al., $TN$ of GFCO (substitution of 51% iron) could not be identified in the temperature range of 380–800 K.⁸⁶ The ambiguity in the transition temperature of GFCO could be attributed to the difference in grain size (different fabrication techniques and annealing conditions) or slight Fe/Cr compositional disorder, induced by randomly distributed Fe/Cr. Such a nonuniform distribution of Mn³⁺ and Cr³⁺ was also reported in La_0.7Ca_0.3Mn_1−xCr_xO₃.⁸⁷ 

In GFCO, three competing magnetic interactions are expected from the three clusters: Fe-rich (Fe³⁺–O²⁻–Fe³⁺), Cr-rich (Cr³⁺–O²⁻–Cr³⁺), and Fe/Cr compositional disordered (Cr³⁺–O²⁻–Fe³⁺), as have been reported previously.^88,89 Orlinski et al. suggested that the substitution of Fe at the Cr-site in GdCrO₃ could weaken its canted AFM ordering and may even destroy it when the substitution ratio is close to 50%.⁸⁸ It is obvious that these magnetic interactions make the magnetic behavior in GCO–GFO solid solution slightly different compared to that in the parent GdCrO₃. For example, temperature-induced magnetization reversal observed in GdCrO₃ did not occur in the present bulk and the previously reported GFCO.^31,63 In general, three types of magnetic interactions dominate in RCrO₃: (i) Cr–Cr interactions (dominate above 100 K and below $TN$⁠), (ii) R–Cr interactions (below 100 K), and (iii) R–R interactions (close to rare earth ordering, which is ∼2.4 K for Gd in the present case).^90,91 In the present GFCO film and the bulk χ(T) data, a sharp increase in the magnetization value (ZFC and FC) was observed when the temperature decreases below ∼25 K, which may be due to the dominant paramagnetic susceptibility of Gd³⁺ in that temperature range compared to the magnetic contribution of canted Cr³⁺/Fe³⁺. The d(χT)/dT data of the bulk GFCO also indicate another transition ∼11 K, which could be due to the Gd–Fe/Cr magnetic interactions as reported in Gd-doped DyFe_0.5Cr_0.5O₃.⁹² However, this transition was not reported in the other GdFe_1−xCr_xO₃ study.⁷⁷ 

Isothermal magnetization vs applied magnetic field (M vs H) loops between applied −4 T and +4 T were measured for the GFCO film and bulk in the temperature range of 5–150 K. The AFM ordering of Gd³⁺ (2–3 K) was not observed at low temperatures, and Fe³⁺/Cr³⁺ ordering temperature (canted AFM–PM) is probably beyond 270 K for both film and bulk. Thus, in the measured temperature range, the magnetic behavior is expected to have only two intrinsic contributions: (i) the weak ferromagnetic contribution that can be attributed to the canting of the AFM order of the transition metal (Fe³⁺ or Cr³⁺) and (ii) the strong paramagnetic contribution from the Gd³⁺ sublattice. Therefore, to better reveal the hysteresis properties of the present GFCO bulk and film, the M vs H curves were corrected so that the linear component of magnetization containing the AFM component from Fe³⁺/Cr³⁺ sublattice and paramagnetic component from Gd³⁺ ions is subtracted from the data for the GFCO bulk and film.^90,93 This is expressed by $M=MFM+(χH)$⁠, where M is the total magnetization, M_FM is the FM contribution, and χ is the dc susceptibility containing contributions of AFM susceptibility of Fe³⁺/Cr³⁺ as well as paramagnetic susceptibility of the Gd³⁺.⁹⁰ Hence, the corrected hysteresis magnetization data $MFM=M−(χH)$ should contain only the FM contribution due to spin canting of the Fe³⁺/Cr³⁺ moments. The corrected isothermal magnetic hysteresis loops are shown in Fig. 7 for both bulk (a) and film (b) measured at different temperatures and a comparison of hysteresis loops at room temperature (c). The temperature-dependent remnant magnetization (M_R) and coercive magnetic field (H_C) values were extracted from the data given in Fig. 7 and are presented in Figs. 8(a) and 8(b), respectively. The presence of H_C observed at low temperatures clearly indicate that the GFCO exhibits canted antiferromagnetism at low temperatures in which the canting of magnetic spins (at least of Cr³⁺ spins) results in the uncompensated magnetic moment, leading to a weak FM behavior similar to that observed in other RCrO₃ bulk samples.⁹⁴ Such canted AFM behaviors have been reported to depend on the magnetic moment of the rare earth ion⁹⁰ or the particle size in RCrO₃.⁴⁸ Figure 6(c) shows the hysteresis curves recorded at room temperature. The bulk sample exhibits almost zero H_C and M_R, indicating paramagnetic behavior. However, the film sample shows nonzero H_C and M_R, suggesting slight FM behavior even at room temperature. The presence of FM order at 300 K for film may be attributed to the canted Fe³⁺/Cr³⁺ AFM order, indicating that the Néel temperature in the present film may be higher than 300 K. The difference of magnetic properties between the film and the bulk may be extrinsic due to the sample morphology, dimensionality effects, difference in Fe/Cr compositional disorder, and the stress state.^95,96 At 10 K, H_C and M_R of the present GFCO film were ∼298 Oe and 0.28 emu/g, respectively. The hysteresis losses in the present GFCO film were estimated by the enclosed area of M–H curves and roughly calculated using H_C× M_R⁹⁷ to be ∼83 Oe emu/g. These values of Hc and hysteresis loss of film are way smaller compared to those of the GFCO bulk (H_C = 1011 Oe, hysteresis loss ∼1476 Oe emu/g, and M_R = 1.46 emu/g at 10 K).³¹ At 5 K, Hc of 350 Oe for the present GFCO film was smaller than 1030 Oe for the present bulk GFCO. As mentioned earlier, this could be due to the difference in the particle size, stress, disorder/defects between bulk and film, or other factors, such as large disordered surface and interface spins in the film.⁹⁸ 

Both H_C and M_R were found to decrease with the increasing temperature for film as can be seen in Fig. 8. This behavior can be understood by the weakening of the FM signal from the canted Fe³⁺/Cr³⁺ sublattice when the temperature increases. At $TN$⁠, typically, such canted AFM material depicts an AFM to PM transition; thus, no magnetic hysteresis behavior is expected above $TN$⁠. For the GFCO film, M_R approached zero; however, Hc was still ∼120 Oe at 150 K (measured temperature range). It should be noted that M(T) results of the film [Fig. 5(b)] indicated that the AFM–PM transition could be higher than that in the GFCO bulk. The data for the bulk GFCO clearly show H_C and M_R approaching zero with the increase in temperature. The initial increase of H_C with the decreasing temperature of the bulk could be explained by the well-known Stoner–Wohlfarth (SW) model, where H_C is proportional to the magnetocrystalline anisotropy constant (K_A). However, the reduction of H_C of the bulk at lower temperatures (below anomaly) is related to another mechanism.⁹⁰ The R³⁺–Cr³⁺ exchange coupling becomes operative due to lowering thermal energy at low temperatures and the moment of rare earth can rotate with the Cr³⁺ moment, leading to a decrease in H_C with the decreasing temperature.⁹⁰ 

The M vs H curves from 0 to 7 T fields were recorded at different temperatures from 5 to 150 K for the GFCO bulk and film. Figure 9 shows the representative isothermal M vs H curves for the GFCO film. It is observed that, at any fixed temperature, magnetization increases with the increasing applied magnetic field. The maximum M (86.5 emu/g) was recorded at 7 and 5 K. From the isothermal M(H) curves, four important parameters for the initial assessment of the materials for magnetic refrigeration, viz., the magnetic entropy change (−ΔS), relative cooling power (RCP), TEC, and adiabatic temperature change (ΔT_ad), can be obtained based on the following equations. The change in entropy, ΔS, is evaluated based on the thermodynamic Maxwell relation by the following formula:⁹⁹ 

It could be interpreted that the change in entropy of a material is directly related to the slope of M vs T at a certain applied field.⁹³ The adiabatic temperature change could be assessed by adding $TCp$ to Eq. (5) as follows:

where C_p is the specific heat of material. The RCP is often estimated based on ΔS using the following equation:

where T₁ and T₂ are temperatures of the cold and hot sources and taken here as 5 and 150 K, respectively.⁹⁴ 

The TEC is calculated using the following equation:

where ΔS(T,H) is from Eq. (5), $ΔTlift$ is the desired lift temperature of the device $(ΔTlift=10K)$⁠, and T_mid is the temperature at the center of TEC and is chosen to maximize TEC.¹⁰⁰ 

The calculated −ΔS and RCP values for the GFCO film and bulk are plotted in Figs. 10(a) and 10(b), respectively. It is evident that the maximum (−ΔS) value enhances with the increasing applied magnetic field. This is expected since larger magnetization induced by a stronger field, which is favorable for sharper slope of M vs T curve. At 5 and 7 T, the −ΔS curve attains a maximum value of 18.8 J/kg K for the GFCO film and 32.9 J/kg K for the bulk GFCO. The maximum value of −ΔS of the GFCO film is smaller than that (30∼40 J/kg K) of bulk GdCrO₃ or GdFeO₃ as well as of the present bulk GFCO. To estimate ΔT_ad, the heat capacity of pure GdCrO₃ (9.72 J/kg K at 6 K, 1 T)²² was used as the heat capacity of GFCO at the same temperature and the heat capacity is assumed to be magnetic field independent. The estimated ΔT_ad for the present GFCO bulk is 7.7 K at 6 K and 3 T, and ΔT_ad = 5 K for film at 7 K and 3 T. The RCP value estimated from Fig. 10(a) based on Eq. (7) as plotted in Fig. 10(b) can also be used to assess the viability of the GFCO film and bulk for magnetic refrigeration. It is evident that the RCP value increases with the increasing magnetic field. The RCP value of 228.2 J/kg at 5 T of film is comparable to that of the well-known Gd₅(Si,Ge)₄ alloy.¹⁰¹ However, it is smaller than the RCP value of the bulk GFCO 343.5 J/kg. Since ΔS(T,H) is decreasing monotonically with the increasing temperature, T_mid could be easily chosen as 10 K to maximize the TEC (10 K) at the measured temperature range of 5–150 K. The calculated TEC (10 K) is 1.0 J/kg K for bulk and 0.6 J/kg K for film under a field change of 1 T. $TEC(10K)$ increases to 25.0 J/kg K for bulk and 15.0 J/kg K for film when the field change is 7 T. Furthermore, −ΔS/ΔH values for the present film and bulk were 2.68 J kg⁻¹K⁻¹T⁻¹ at 7 K and 4.7 J kg⁻¹K⁻¹T⁻¹ at 5 K, respectively. These values are comparable to that of pure Gd around room temperature, indicating good cooling efficiency.¹⁴ Moreover, the higher surface-to-volume ratio of the film sample is favorable for high heat exchange efficiency and cycling frequency.¹⁰¹ 

According to Eq. (7), RCP also depends on the choice of T₁ and T₂ in addition to its dependence on H. In the aforementioned analysis, T₁ = 5 K and T₂ = 150 K were chosen, since these are the lowest and highest temperature, respectively, for which we have the M vs H data, and H = 7 T is the highest magnetic field available to us (Fig. 9). However, we have also calculated RCP for other values of T₂ for which M vs H data for the film are shown in Fig. 9, with similar data for the bulk sample (not shown here). The plots of RCP vs (T₂–T₁) with fixed value of T₁= 5 K and using various values of T₂ as well as H = 7 T are shown in Fig. 11 for both the GFCO bulk and the film. Slopes of these plots suggest that for these systems, cooling efficiency will be most effective for T < 30 K, where the slopes of the plots are the highest. Also, the ratio of RCP(film)/RCP(bulk) ∼0.65 (which is nearly equal to the ratio of their magnetization) is effectively independent of (T₂–T₁).

In general, the magnetocaloric properties of film are found to be inferior to the corresponding bulk.^62,102 This could be due to several factors, such as suppression of magnetic moment at interfaces (magnetic dead layer) and broadening of the phase transition interval.¹⁰² A large change in entropy or ΔT_ad at a low applied magnetic field is crucial for commercializing magnetic refrigeration. The estimated ΔT_ad is 1.0 K for the present GFCO bulk at 6 K and 1 T, and 0.7 K for film at 7 K and 1 T. The measured −ΔS of the present film and bulk are 0.9 J/kg K and 1.2 J/kg K, respectively, for a field change of 1 T. The value of −ΔS is 7.1 J/kg K at 3 T of GFCO film, which is comparable to some of Gd-based thin films studied for room temperature applications, such as 3.4 J/kg K at 3 T for Gd/W thin films.¹⁰³ 

In this paper, comparison of the dielectric, magnetic, and magnetocaloric properties of samples of bulk pellet GdFe_0.5Cr_0.5O₃ (GFCO) with those of 960 nm thick film of GFCO on a platinized-silicon substrate are presented. X-ray diffraction studies showed comparatively higher level of orthorhombic structural distortion in the film, which has an average grain size of about 50 nm as revealed by the FE-SEM. Temperature dependence of the dielectric properties of the two samples indicates that the ferroelectric to paraelectric transition at ∼525 K in the present GFCO bulk is lowered to ∼440 K in the GFCO film, which is likely due to the reduced dimensionality of the film. Temperature and magnetic field dependence of the magnetization also shows reduced magnetization (emu/g) of the film vis-à-vis the bulk sample under similar conditions of temperature and magnetic field. This reduction in the magnetization is likely related to the reduced magnetism of the surface atoms and other inhomogeneities in the present film. This reduced magnetization in the GFCO film leads to reduced values of its magnetocaloric parameters whose magnitudes are about 60% of the corresponding values in the present GFCO bulk sample. The maximum magnetic entropy change and the relative cooling power (RCP) for the GFCO film are 18.8 J/kg K and 377.7 J/kg, respectively, compared to 32.9 J/kg K and 566.5 J/kg, respectively, for the GFCO bulk sample. Since magnetocaloric properties scale with the magnetization, improvements in the overall quality and homogeneity of the films are likely to improve both their magnetic and magnetocaloric properties. Variation of RCP with temperature shows that for these samples, magnetic cooling will be most effective for temperatures < 30 K.

Support for this project was provided through the UCONN IMS Interdisciplinary Multi-Investigator Materials Proposal (IMMP) program. The scanning electron microscopy work was performed in part at the Biosciences Electron Microscopy Facility of the University of Connecticut. For microscopy and x-ray photoemission characterization, S.L.S. acknowledges the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, Division of Chemical, Biological and Geological Sciences under Grant No. DE-FG02-86ER13622.

The data that support the findings of this study are available within the article.