Charge transfer-tuned magnetism in Nd-substituted Gd₅Si₄

A variety of interesting phenomena such as a giant magnetocaloric effect, giant magnetostriction and large magnetoresistance were observed in Gd₅Si₂Ge₂ near room temperature.^1–3 Those phenomena are related to a magnetostructural transition of this compound from a paramagnetic monoclinic structure to a ferromagnetic orthorhombic structure.⁴ Both crystal structures are built up by stacking of two-dimensional Gd₅T₄ slabs (T = Si or Ge) and the transition between them is controlled by connection or disconnection of interslab T–T bonds.⁵ The ferromagnetism of the orthorhombic structure is established by the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction along Gd–T–T–Gd chains and thus, is sensitive to the connection or disconnection of interslab T–T bonds as well.^6–8 Such an interplay between the crystal structure and magnetism has aroused interest in the electronic structures of Gd₅T₄-type compounds. First principle calculations and X-ray magnetic circular dichroism measurements showed that apart from the interslab T–T bonds, intraslab Gd–T bonds play a crucial role in the RKKY interaction of Gd₅T₄-type compounds.^8–16 The Gd–T bonds comprise hybridization of 5d electrons of Gd atoms with 3p or 4p electrons of T atoms and bring about induced moments of T atoms.^{8,11,12,14,16} As the interslab T–T bonds are connected, the hybridization of Gd with T atoms has enhanced Gd-5d components favoring long-range RKKY interactions between neighboring Gd₅T₄ slabs.^7,8

A similar crystal structure-magnetism interplay was observed in other R₅T₄ compounds (R = rare earth).¹⁷ Many studies were carried out to explore effects of chemical substitutions on the interplay.^18–27 When T atoms are substituted by semimetal or non-metal atoms, the valence electron number and size of substituting T atoms have significant effects on the connection of interslab T–T bonds and therefore on the crystal structure.^{17,21,22,24,26,27} Utilizing those effects, the magnetism of T-substituted R₅T₄ compounds is tunable between ferromagnetism and antiferromagnetism.²⁷ Substitutions of R atoms with another kind of R atoms have a similar effect on the crystal structure of R₅T₄ compounds and allows for tuning of their magnetism as well.^{18–20,23,25} However, the influence of R substitutions on the crystal structure-magnetism interplay of R₅T₄ compounds is complex due to differences in electronic structures of R atoms. Apart from different numbers of 4f electrons, R atoms of different species may have different numbers of 5d electrons. For this latter difference, charge transfer may occur between the base and substituting R atoms and brings about a change of the electronic structure and magnetism of the compounds. This potential effect was hinted at by observations of different magnetism in Eu-substituted Gd₅Ge₄²⁷ and in Gd-substituted Er₅Si₄.²⁰ However, the role of the charge transfer of 5d electrons in tuning of the magnetism is not understood yet. In this paper, we investigated charge transfer of 5d electrons and its influence on the electronic and magnetic structures in Nd-substituted Gd₅Si₄ compounds to unveil this role.

Ingots of Gd_5-xNd_xSi₄ (x = 0, 1 and 2.5) compounds were prepared by arc-melting elements of high purity (99.9% purity or better). The ingots were remelted several times to ensure homogeneity. Each ingot had a mass of about 1.0 g. Their mass losses during melting were compensated for by additions of an excess mass for elemental Gd. The received ingots were milled into fine powders for magnetic and X-ray measurements. Those powders are referred to samples below.

A superconducting quantum interference device was used to measure magnetization of the samples. Temperature-dependent magnetization was measured under a d. c. magnetic field of 0.02 T to determine Curie temperatures and magnetic susceptibility. Isothermal magnetization was measured under magnetic fields of up to 5 T at a temperature of 10 K and near Curie temperatures. The isothermal magnetic entropy changes for a magnetic field change from 0 T to 5 T and the refrigerant capacity power of the samples were calculated from the measured isothermal magnetization using the Maxwell’s relationship.²⁸ The crystal structure of the samples in zero-field cooling from 300 K to 90 K was investigated by high energy X-ray diffraction (HEXRD) using a wavelength of λ = 0.117418 Å at the beamline 11–ID–C of the Advanced Photon Source (APS), Argonne National Laboratory. The lattice parameters of the samples were determined from Rietveld refinement. The X-ray absorption near edge structure (XANES) at Gd L_2,3 and Nd L_2,3 edges were measured in transmission mode at the beamline 20–BM–B of APS. The XANES spectra were fitted and analyzed using the Athena software²⁹ to determine the white line intensities of the L₂ and L₃ edges of Gd and Nd atoms. As explained elsewhere,^30–32 the white line intensity of L₂ edge reflected an electronic transition from 2p_1/2 to 5d_3/2, and that of L₃ edge reflected the transition from 2p_3/2 to 5d_5/2 and 5d_3/2. Thus, a L₃/L₂ branch ratio measured the splitting of 5d_5/2 and 5d_3/2 orbitals.

First principle calculations were performed based on density functional theory implemented in the VASP code. A plane wave basis with a 500 eV kinetic energy cut-off was used while the electron-ion interaction was treated within the projector augmented wave method.³³ The Perdew-Burke-Ernzerhof generalized gradient approximation³⁴ was considered for the exchange-correlation functional. The correlated 4f states of Gd and Nd were treated within the Hubbard-U formalism with the Coulomb parameters U = 7.5 and 6.7 eV, respectively. Hund’s parameter was fixed as 0.7 eV. A 4×2×4 Monkhorst-Pack k-points set was used for geometry optimizations. Densities of states (DOS) calculations were done using a 12×6×12 k-points set. The atomic positions were relaxed until the force on each atom went down to 0.01 eV/Å. The computational unit cell consisted of 20 rare earth atoms and 16 Si atoms. In the Nd-substituted compounds, Nd atoms were assumed to occupy sites for Gd atoms. A total of four random configurations was considered.

As shown in Fig. 1, all samples crystallized into a Gd₅Si₄-type orthorhombic structure (space group Pnma) at room temperature. Impurity phases such as Gd₅Si₃ were not identified in any of the samples. The lattice parameters of the Nd-free sample were determined to be a = 7.483 Å, b = 14.716 Å and c = 7.770 Å. These values agrees well with the literature data.¹⁴ The lattice parameters of the Nd-substituted samples were enlarged compared to those of the Nd-free sample (see Fig. 2). The enlargement is anisotropic and is largest along the b and c axes at x = 1 and 2.5, respectively. This anisotropy is related to different Nd occupation as suggested by the first principle calculations below. In zero-field cooling, the lattices of all samples showed contraction along the b and c axes, but showed little changes along the a axis. There is no evidence for any thermally induced crystallographic transition. Thus, the interslab T–T bonds of the lattice of all samples remained connected, though they were stretched by Nd substitutions.

As shown in Fig. 3a, the measured magnetization showed ferromagnetic ordering of all samples at a temperature of 10 K. Nd substitutions generally increased magnetization responses to low magnetic fields. However, Nd substitutions reduced saturation magnetization of the samples with x = 1 and 2.5 by 19 % and 67 %, respectively. As shown in Fig. 3b, the measured inverse magnetic susceptibility of all samples suggested a ferromagnetic transition. The Curie temperature of the Nd-free sample lies above room temperature and its value of 341 K agrees well with the literature data.¹⁴ Nd substitutions brought about a linear reduction of the Curie temperature. The inverse magnetic susceptibility of the samples also showed a difference in their paramagnetic regions. Unlike a Curie-Weiss law for the samples with x = 0 and 1, a Griffith phase behavior was observed for the sample with x = 2.5. This Griffith behavior provides a sign of short-range ferromagnetic correlations. As shown in Fig. 3c, the samples with x = 0 and 1 showed a maximum magnetic entropy change, 6 J/kg/K, for a magnetic field change from 0 T to 5 T. This result is surprising because the saturation magnetization of the sample with x = 1 is smaller than that of x = 0. More surprisingly, the refrigerant capacity power of the sample with x = 1 was determined to be even larger than that of the sample with x = 0 (184 vs 165 J/kg). The sample with x = 2.5 showed a maximum magnetic entropy change of 3 J/kg/K and refrigerant capacity power of 123 J/kg. Its maximum magnetic entropy is also higher than expected in terms of the 67% reduction of its saturation magnetization. Such abnormally high magnetic entropy changes of the Nd-substituted samples are attributed to the improved magnetization responses to low magnetic fields, which can compensate for an effect of the reduced saturation magnetization. The microscopic mechanism underlying such changes of the magnetic properties was revealed by the XANES measurements and first principles calculations.

As shown in Figs. 4a–4d, Nd substitutions increased the L₃ white line intensity of Gd by 17.0 % and 26.1 % for x = 1 and x = 2.5, respectively, and likewise the L₂ white line intensity by 5.1 % and 5.5 %, respectively. The L₃ and L₂ white line intensities of Nd showed opposing trends with increasing x. Such observations suggested that 5d electrons are significantly transferred from Gd to Nd in the Nd-substituted samples. This charge transfer had a critical consequence on the spin-orbital coupling (SOC) of Nd and Gd. As shown in Fig. 4e, neither of the L₃/L₂ branch ratios of Gd and Nd was equal to 2, suggesting the presence of non-zero SOC in all samples.^30,31 However, the L₃/L₂ branch ratio of Gd rose close to 2 with increasing x, suggesting a continuous weakening of the SOC of Gd. In contrast, the L₃/L₂ branch ratio of Nd declined from 2.15 for x = 1 to 1.85 for x = 2.5. The two values had a positive and a negative deviation from the statistical value of 2, respectively. Such opposite deviations meant a change of the sign of the spin-orbital interaction of 5d electrons of Nd at a larger x. Thus, it is suggested that the increased magnetization responses of the substituted samples is more closely related to the weakening of the SOC of Gd than to the strengthening of the SOC of Nd.

First principle calculations suggested that the preferred occupation of Gd₃ sites (see Fig. 1a) for Nd at x = 1 minimizes the total lattice energy. However, the calculations did not suggest any preferred occupation for Nd at x = 2.5. Such predictions of the preferred and random Nd occupation can account for the observations of the largest linear expansion along different primary axes with rising x (see Fig. 1). The stable magnetic structures of the samples were determined by several trial tests assuming different magnetic couplings of Nd and Gd. Agreeing with the early calculations,¹⁴ a ferromagnetic structure is energetically favored at x = 0. This ferromagnetic structure is also stable at x = 1. However, a ferrimagnetic structure is stabilized at x = 2.5. It comprises an antiparallel arrangement of magnetic moments of Nd and Gd. Its stabilization can be correlated to the change of the sign of the spin-orbital interaction of 5d electrons of Nd. The observations of the Griffiths phase behavior of the sample with x = 2.5 suggested that the spatial distribution of Gd and Nd in the orthorhombic lattice may not be uniform. Although this non-uniform distribution of atoms was not dealt with, the first principle calculations provided a microscopic explanation of the reduced magnetization and the lowering of Curie temperature.

As listed in Table I, a total magnetic moment of 36.5μ_B per chemical formula was predicted for the Nd-free compound. This value agrees with an earlier calculation.¹⁴ With respect to it, the predicted value for the Nd-substituted compounds showed a reduction by 12.3% and 71.5 % at x = 1 and 2.5, respectively. Such reductions agree reasonably with the observed changes of saturation magnetization (see Fig. 2a). An underestimation of 6.7% at x = 1 is attributed to a non-zero orbital moment of Nd, which was neglected in the present calculations. This orbital contribution, however, became negligible at x = 2.5. The larger reduction of the total magnetic moment at x = 2.5 can be attributed mainly to the antiparallel arrangement of the 4f moments. The magnitude of 4f moments of Gd is little changed by the Nd substitutions. This result is consistent with highly localized nature of 4f electrons. However, the mean 5d moments showed a reduction by 26.5% and 81.3% at x = 1 and 2.5, respectively. The larger reduction predicted at x = 2.5 again can be attributed to the ferrimagnetic structure. Assuming that 5d moments of Gd is proportional to their remaining numbers of 5d electrons in the Nd-substituted compounds, it is estimated that Gd atoms transferred 25 % and 13% of their 5d electrons to Nd atoms at x = 1 and 2.5, respectively. The smaller percentage of the transferred charge at x = 2.5 is probably due to the reversal of the sign of the SOC of Nd. Under such assumptions, the effects of the SOC of Gd and Nd on the RKKY interaction can be evaluated. A weighted ratio of 4f and 5d moments for Gd and Nd is defined by dividing their 4f moments by their 5d moments per 5d electron. It was found that the weighted 4f-5d ratio for Nd is by a factor of 2.5 and 9.0 larger than that for Gd in the Nd-substituted compounds with x = 1 and 2.5, respectively. Such large factors highlighted that a unit 4f moment of Nd is more efficient in polarizing the 5d electrons than a unit 4f moment of Gd. This difference meant promotion of the RKKY interaction by the Nd substitutions and provided a microscopic interpretation of the increase of the magnetization responses of the substituted compounds to low magnetic fields. The induced 3p moments of Si are always antiparallel to those of 5d moments of Gd. The mean 3p moments of the substituted compounds showed a reduction by about 3% and 83% at x = 1 and 2.5, respectively. The larger decrease at x = 2.5 is attributed again to the antiparallel arrangement of 5d moments because the 5d–3p hybridization is little changed as shown below.

Figure 5 shows the calculated spin-polarized DOS for the ground state structures of the three compounds. In the compound with x = 1, the total DOS showed a new and positive peak at an energy of about 5.5 eV below the Fermi energy, E_F, due to the increased densities of the occupied spin-up 4f states of Gd. This new peak confirmed that the Nd substitutions weaken the SOC of Gd via the charge transfer of 5d electrons. The unoccupied and occupied 4f states showed a shift left with reduced peak densities due to the change in the 4f states of Nd. A change more relevant to the magnetism is a reduction of the total exchange splitting of 5d electrons at E_F. This reduction is mainly due to a reduction of the spin-up 5d states of Gd. Nevertheless, the densities of the spin-up 5d states are still higher than those of the spin-down 5d states. As a result, the ferromagnetic coupling between the magnetic moments of Gd is still favored. The DOS of the compound with x = 2.5 showed changes more influential on the magnetism. A striking change is a broad extension of unoccupied states above E_F. This extension is mainly related to the unoccupied 5d states of Gd. A second change is the reduced peak densities of the occupied and unoccupied 4f states in the total DOS. Such changes in the 4f and 5d states highlighted significant and intercorrelated changes of the SOC of Gd and Nd and are in an excellent agreement with the XANES measurements.

The variations of the partial DOS of the 5d and 3p electrons with rising x were examined to have insight into the 5d–3p hybridization between rare earth and Si. As shown in Fig. 6, the 5d and 3p bands of all three compounds showed a large and similar overlapping. This result suggested that the strong 5d–3p hybridization is preserved in the Nd-substituted compounds, though 5d electrons are diluted. An analysis of the hybridization function confirmed this (not shown here). The preservation of the strong 5d–3p hybridization is not surprising because the interslab Si–Si bonds were not broken and the elongation of R–Si bonds were small (see Figs. 1 and 2). Because of the indirect character of the RKKY interaction, the Curie temperature of the substituted compounds cannot be estimated in terms of the exchange splittings of 5d and 3p states at E_F only. Rather, its lowering with rising x follows well a declining tendency in the integrated DOS below E_F. This correlation is understood because the 4f, 5d and 3p electrons all play a role in the RKKY interaction of Gd₅Si₄^8–16 and jointly determine the stability of the long-range magnetic ordering against thermal fluctuations.

The XANES measurements and first principles calculations have unveiled a charge transfer mechanism in tuning of the magnetism of the Nd-substituted Gd_5-xNd_xSi₄ compounds. It has been shown that the charge transfer of 5d electrons from Gd to Nd weakens the SOC of Gd while it strengthens SOC of Nd. Such opposite effects of the charge transfer on the SOC of Gd and Nd improve the magnetization responses to low magnetic fields and help preserve the large magnetic entropy change of Gd₅Si₄ in the compound with x = 1. More critically, the charge transfer stabilizes a ferromagnetic and a ferrimagnetic structure in the Nd-substituted compounds with x = 1 and x = 2.5, respectively. However, the charge transfer does not change the 5d–3p hybridization significantly. It has been suggested that such a charge transfer mechanism may occur in other rare earth-substituted Gd₅Si₄ compounds and allows for tuning of their magnetism in a similar way.

The authors thank R. Mathiesen and A. Shahani for reading the manuscript. JG and RHK are grateful to financial support by the National Basic Research Program of the Ministry of Science and Technology, China (2012CB619405). RHK is indebted to the China Scholarship Council for a visiting PhD fellowship. Use of the facilities of the Advanced Photon Source and the Center for Nanoscale Materials, Argonne National Laboratory was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357.