First-principles study of negative thermal expansion mechanism in A-site-ordered perovskite SrCu₃Fe₄O₁₂

Abstract

Negative thermal expansion (NTE) materials offer a tremendous opportunity for fundamental as well as applied research, yet the origin remains difficult to understand. Here we perform a systematic first-principles calculation to investigate electrical and magnetic properties of an A-site-ordered perovskite SrCu₃Fe₄O₁₂ and clarify its NTE mechanism. We find that SrCu₃Fe₄O₁₂ is an antiferromagnetic metal, and its magnetic ordering can be demonstrated as C-type within Fe ions of mixed valence at the B-site and paramagnetic Cu³⁺ at the A-site. Electronic structure analysis reveals that there occurs temperature-induced Cu–Fe intersite charge transfer, which is mediated by the corner-sharing O atoms. Meanwhile, the magnetic interaction is found to undergo a transition from antiferromagnetism to ferrimagnetism. Further phonon calculations demonstrate that the SrCu₃Fe₄O₁₂ is thermodynamically stable both at low and high temperature, and that there appear degenerated phonon branches, indicating that it is easy to transfer energy between these modes. We also find that the large NTE of SrCu₃Fe₄O₁₂ originates from intermetallic charge transfer induced by temperature, which relaxes the Sr–O and Fe–O bonding units in the oxide.

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Introduction

Negative thermal expansion (NTE) materials, which exhibit volume contraction upon heating, have aroused extensive attention, largely because their unique thermal properties are relevant for many practical applications such as elasticity-tuned sensors and switching devices. Moreover, they can be mixed with positive thermal expansion materials so as to tune the thermal expansion coefficient of materials. To date, several NTE materials with a large linear thermal expansion coefficient (α) of an order of 10⁻⁵ k⁻¹, have been reported,^1–3 for instance, the Ge-doped anti-perovskite manganese nitrides Mn₃AN (A = Cu, Zn, Ga) show a giant α of up to −2.5 × 10⁻⁵ k⁻¹.¹ In addition to their thermal property, NTE materials can often simultaneously show intriguing electronic and physical properties, rendering them promising candidates for many technological applications.

Much effort has been devoted recently to the study of the NTE phenomena in the A-site-ordered perovskites A′A₃B₄O₁₂ due to their unique structures and for their wide range of intriguing physical properties. For instance, LaCu₃Fe₄O₁₂ and BiCu₃Fe₄O₁₂ are reported to show temperature-induced Cu–Fe intermetallic charge transfer (CT) in the form of 3Cu³⁺ + 4Fe³⁺ → 3Cu²⁺ + 4Fe^3.75+ from low-temperature La³⁺Cu₃³⁺Fe₄³⁺O₁₂ (Bi³⁺Cu₃³⁺Fe₄³⁺O₁₂) with Cu³⁺ at the A-site to high-temperature La³⁺Cu₃²⁺Fe₄^3.75+O₁₂ (Bi³⁺Cu₃²⁺Fe₄^3.75+O₁₂) with Fe^3.75+ at the B-site, which is accompanied by a first-order isostructural transition from antiferromagnetic (AFM) insulator to paramagnetic metal with a remarkable volume shrinkage.^4–6 In contrast, perovskite YCu₃Fe₄O₁₂ shows a vastly different behavior: the instability of its high-valence Fe^3.75+ atoms can be relieved by a charge disproportionation (CD) via the form of 8Fe^3.75+ → 5Fe³⁺ + 3Fe⁵⁺, resulting in a charge ordering and a ferrimagnetic (FIM) ordering at low temperature without any NTE transition.⁷ To investigate the mutual interaction between strain and electronic phases, Yamada et al.⁸ conducted an systematic study of the LnCu₃Fe₄O₁₂ (Ln: lanthanide) by adjusting A′-site ion size via choosing different lanthanides, and found that the oxides with a large Ln ion size show the intersite CT and isostructural NTE transition, while that those with a small Ln ion size show the CD. These findings indicate that both the bond strain and the amount of charges at the A-site play an important role in triggering the intersite CT or CD. Theoretically, the strength of crystal-field splitting and relative energy ordering between Cu 3d_xy and Fe 3d states are reported to be key parameters in triggering the intersite CT and CD.⁹

Moreover, A-site-ordered perovskites with divalent alkaline-earth metals can also be successfully prepared and exhibit interesting properties. For instance, CaCu₃Fe₄O₁₂ undergoes a phase transition to CD (2Fe^IIIL → Fe^III + Fe^IIIL²) accompanied by a volume contraction at ∼210 K, and its ferrimagnetism has been found to originate from the AFM coupling of the Cu and Fe sublattices.¹⁰ On the contrary, SrCu₃Fe₄O₁₂ is an antiferromagnet with T_N of 180 K, and exhibits a large NTE with a linear expansion coefficient of −2.26 × 10⁻⁵ K⁻¹.^11,12 Furthermore, it has been reported that a partial replacement of Ca²⁺ with Sr²⁺ in CaCu₃Fe₄O₁₂ can alter significantly its electrical and magnetic properties. To understand the origins of the magnetic coupling interactions and the large NTE, here, we investigate systematically the electronic and magnetic properties of SrCu₃Fe₄O₁₂ by first-principles calculations, and demonstrate that this oxide is intrinsically an AFM metal. The large NTE is identified to originate from the temperature-induced Cu–Fe intersite CT, opening up an additional avenue in clarifying mechanisms of NTE phenomenon in transition-metal oxides.

Computational details

Calculations of energies and electronic structures were performed with the full-potential linearized augmented plane wave plus local orbitals methods, which were implemented in WIEN2K package.^13,14 The generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE)¹⁵ was employed to describe the exchange-correlation functional. The values of atomic sphere radii (R_MT) were chosen to be 2.41, 1.83, 1.93, and 1.62 a.u. for Sr, Cu, Fe and O, respectively. Wave function was expanded using the plane wave with a cutoff of 7.0 and the density and potential a value of 14. Sampling of irreducible Brillouin zone was performed with k points of 1000 using the modified tetrahedron method.¹⁶ Self consistence was achieved once the total energy was converged to less than 10⁻⁵ Ry/f.u. Electron correlation effect was taken into account by the effective Hubbard parameter U_eff = U − J,¹⁷ where U and J are the on-site Coulomb repulsion and Hund exchange constant, respectively. For simplicity, the U is used hereafter to represent the effective parameter U_eff. A series of U values were chosen from 2.0 to 7.0 eV for Cu (U_Cu) and from 1.0 to 5.0 eV for Fe (U_Fe). The spin–orbital coupling was also taken in account due to the significant orbital contribution in CaCu₃Fe₄O₁₂,¹⁸ yet was found to impose negligible influence on our calculated results. In addition, the phonon properties were calculated using the PHONOPY package¹⁹ combined with Vienna Ab initio Simulation Package (VASP).²⁰ The cut-off energy of plane wave was set to be 400 eV and the finite displacement method was adopted. The geometrical structures were fully relaxed until the change in total energy was less than 10⁻⁸ eV per atom.

Results and discussion

Crystal structure of SrCu₃Fe₄O₁₂

SrCu₃Fe₄O₁₂ crystallizes in the Im3̄ cubic lattice (shown in Fig. 1),¹¹ in which the FeO₆ octahedra are fairly rigid yet markedly tilted, transforming the original twelvefold coordinated A-site Cu ions to square-coordinated CuO₄ units that are perpendicular to each other. Its structure falls in three ranges (listed in Table 1): an ordinary positive thermal expansion range when temperature is either lower than 170 K (range 1) or higher than 270 K (range 3), and a large NTE range when temperature is in between 170 and 270 K (range 2). In ranges 1 and 3, its lattice constant and bond length expand with the rise of temperature, while in range 2, the Fe–O and Sr–O bonds shrink by ∼0.6% and ∼0.4%, respectively, due to its large NTE. However, the Cu–O distance is elongated significantly by ∼1.4% from 1.878 Å at 170 K to 1.901 Å at 270 K (Table 1). Moreover, its lattice constant relies primarily on the Fe-related parameters, i.e. Fe–O bond length and Fe–O–Fe bond angle, in which the contraction of Fe–O bond contraction is critical to the volume contraction in range 2, albeit that the Fe–O–Fe bond angle is increased by ∼1.5°.

Fig. 1 Crystal structure of A-site-ordered double perovskite SrCu₃Fe₄O₁₂ with Im3̄ symmetry. A′- and A-site ions are ordered at the ratio of 1 : 3 and B-site ions form a heavily tilted FeO₆ octahedron to optimize Sr–O and Fe–O bond lengths.

Table 1 The structural parameters of SrCu₃Fe₄O₁₂ at the transfer temperature for the three ranges

	Range 1	Range 2		Range 3
	80 K	170 K	270 K	450 K
a (Å)	7.356	7.358	7.348	7.357
Sr–O (Å)	2.615	2.620	2.607	2.601
Fe–O (Å)	1.979	1.979	1.968	1.970
Cu–O (Å)	1.878	1.878	1.901	1.905
Fe–O–Fe (°)	136.676	136.672	138.028	138.048

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Magnetic ground state of SrCu₃Fe₄O₁₂

Two experimentally observed structures of SrCu₃Fe₄O₁₂ are adopted to calculate the magnetic ground state, i.e. 80 and 270 K, the former of which is low-temperature structure below T_N and the latter of which is the most contracted one above T_N.¹¹ We construct several magnetic configurations by taking two likely magnetic sublattices of Cu and Fe into account: ferromagnetism (FM), A-type and G-type AFM within Cu sublattice, and the FM, A-type, C-type and G-type AFM within Fe sublattice. Furthermore, we also consider the Cu–Fe FIM, in which the Cu and Fe sublattices are arranged in an antiparallel manner.

To gain insights into how magnetic structures correlate with electron localization, we perform GGA + U calculations using different U values (2.0 to 7.0 eV for U_Cu and 1.0 to 5.0 eV for U_Fe) as well as GGA calculations for comparison. For the 80 K states, the magnetic moment of Cu is calculated to be nearly zero when magnetic interaction within Fe sublattice is AFM coupled, whichever the GGA or GGA + U method is used. Hence, we mainly analyze the results of the AFM coupling between Fe sublattice and Cu–Fe FIM for comparison. Table 2 lists their relative energies ΔE as a function of U (taking the A-type AFM within Fe sublattice, which hereafter is named AFM-A, as a reference). It is clear that the CC-type AFM (named AFM-C) is energetically favorable than the A-type and G-type AFM within Fe sublattice (named AFM-G), though the energy of AFM-G configuration is lower than that of AFM-C when the U_Cu and U_Fe are adopted as (3.0, 2.0) eV and (4.0, 3.0) eV, respectively. Moreover, the lowest energy state calculated using the GGA is FIM (see Table 2), yet switches to AFM-A when the U_Cu and U_Fe are adopted as 4.0 and 3.0 eV, respectively, consistent with the AFM observations below 180 K.¹¹ In particular, the total energy difference between the AFM-C and FIM configurations is increased markedly with the rise of U (Table 2), implying that the former is affected more severely by the electron correlation. As for the high-temperature structure at 270 K, the FIM configuration is always found to be most stable, despite of the calculation method. In addition, the low-temperature ground state is energetically more preferred than the high-temperature one.

Table 2 Relative energy difference (in meV per formula unit) between the different magnetic configurations at 80 K. Calculations are conducted using the GGA + U with the U ranging from 0.0 to 7.0 eV for Cu and from 0.0 to 5.0 eV for Fe

	UCu	0.0	2.0	3.0	4.0	5.0	6.0	7.0
	UFe	0.0	1.0	2.0	3.0	4.0	5.0	5.0
AFM-A		0.0	0.0	0.0	0.0	0.0	0.0	0.0
AFM-C		343.4	93.4	−78.7	−79.3	−45.5	−5.1	−10.6
AFM-G		508.3	24.4	−172.2	−88.8	2.23	82.3	88.9
FIM		−684.4	−817.6	−380.0	69.0	330.6	496.9	339.1

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For the 80 K states, the magnetic moment of Fe increases as the U_Fe increases from 2.0 to 4.0 eV, and maintains at ∼4.0 μ_B (Table 3). Meanwhile, the calculated total magnetic moment for each formula unit nearly maintains zero, whichever the GGA or GGA + U method is adopted, confirming the low-temperature AFM phase.¹¹ Similarly, the magnetic moment of Cu or Fe is also increased with the rise of U in the case of 270 K. Based upon these results and our previous studies,²¹ the GGA + U method is adopted with U_Cu = 5.0 eV and U_Fe = 4.0 eV, unless otherwise stated.

Table 3 Calculated total magnetic (M_total) per formula unit and corresponding magnetic moments of Cu (M_Cu) and Fe (M_Fe) ions (in μ_B) for the AFM-C at 80 K and FIM at 270 K. Calculations are conducted using the GGA + U with the U ranging from 0.0 to 7.0 eV for Cu and from 0.0 to 5.0 eV for Fe

	UCu	0.0	2.0	3.0	4.0	5.0	6.0	7.0
	UFe	0.0	1.0	2.0	3.0	4.0	5.0	5.0
AFM-C	MCu	0.00	0.00	0.02	0.01	0.02	0.01	0.02
	MFe	2.64	3.27	3.68	3.84	3.94	4.04	4.03
	Mtotal	0.03	0.05	0.04	0.04	0.02	0.00	0.00
FIM	MCu	−0.21	−0.38	−0.48	−0.54	−0.52	−0.53	−0.67
	MFe	2.72	3.12	3.37	3.54	3.75	3.88	3.82
	Mtotal	11.8	13.0	13.4	13.7	14.9	15.5	14.2

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Comparative analysis of electronic structures of SrCu₃Fe₄O₁₂

To shed light on the relation between magnetic coupling and charge distribution, we conduct a comparative study of electronic structures of AFM-C at 80 K and FIM at 270 K. Fig. 2 shows total density of states (TDOS) and partial density of states (PDOS) for the AFM-C and FIM configurations calculated using both GGA and GGA + U. From the TDOS, a metallic behavior is observed for the two configurations with both spins crossing Fermi level (E_F), independent of the calculation method. This indicates that low-temperature ground state of SrCu₃Fe₄O₁₂ is AFM yet metallic, in sharp contrast to those of a conventional compound showing either the FM ordering with metallicity or AFM ordering with insulating states. Further GGA + U calculations reveal that the 3d orbitals below E_F are pushed to low energy area, while those above the E_F are pushed to the high energy area, indicating that the electron correlation plays an important role in 3d electrons in this system.

Fig. 2 TDOS and PDOS plots of the Cu, Fe and O atom contributions for the AFM-C configuration calculated using the (a) GGA and (b) GGA + U method. The corresponding plots for the FIM configuration calculated using the (c) GGA and (d) GGA + U method. The inset in (b) enlarges the DOS around Fermi level, highlighting the metallic nature. The Fermi level is aligned to zero and indicated by a vertical dashed line.

For the low-temperature AFM-C configuration, the contribution to the DOS at E_F comes mainly from Fe and O atoms, as shown in inset of Fig. 2(b), implying that they are crucial to realizing the metallicity. Importantly, the PDOSs of Fe, Cu and O span a broad energy range from −7.6 eV to 4.5 eV, indicating a strong hybridization between them. Moreover, the A-site Cu atoms are nonmagnetic as there is a symmetry in the spin-up and spin-down channel (Fig. 2(b)), consistent with the zero magnetic moment (Table 3). Further PDOS analyses reveal that the 3d_xz orbital of Cu is unoccupied in both the spin-up and the spin-down channels, while the other four 3d orbitals are all occupied (Fig. 3(a)), a typical characteristic of d⁸ electronic configuration for the Cu³⁺, similar to what was seen in the low-temperature LaCu₃Fe₄O₁₂ and BiCu₃Fe₄O₁₂.^4,6 On the other hand, the spin-up channel of Fe is almost filled (Fig. 3(b)), while its spin-down channel is utterly empty, demonstrating that it has a high-spin d⁵ electronic configuration. The O atoms show the p⁶ electronic states in view of the nearly full occupation of 2p orbitals (Fig. 3(c)). In light of charge neutrality, one can conclude that the charge combination is Sr²⁺Cu₃³⁺Fe₄^3.25+O₁₂²⁻ at low temperature. This mixed valence for the Fe^3.25+ is close to the experimental ⁵⁷Fe Mössbauer spectrum observation, where the isomer shift of B-site Fe is divided into a pair of components with a ratio of Fe³⁺ : Fe⁵⁺ to 4 : 1.¹¹ This is, however, reasonable because the Fe³⁺ and Fe⁵⁺ cations are randomly distributed in SrCu₃Fe₄O₁₂.

Fig. 3 PDOS plots of the (a) Cu 3d, (b) Fe 3d, and (c) O 2p orbitals for the AFM-C configuration. Corresponding plots for the FIM configuration are given in (d), (e) and (f), respectively. The Fermi level is aligned to zero and indicated by a vertical dashed line.

The Fe, Cu and O atoms all contribute significantly to the electronic states at E_F for the high-temperature FIM configuration (Fig. 2(d)), in sharp contrast to the case of low-temperature AFM-C state. Evidently, the Cu atoms show magnetic nature, and the Cu²⁺ is formed with a d⁹ electronic configuration because its spin-down 3d_xz orbital is shifted to low energy area (Fig. 2(d)). By comparing the d⁹ of Cu²⁺ with d⁸ electronic configuration of Cu³⁺ in low-temperature AFM-C, electrons are introduced to Cu sites. Consequently, B-site Fe atoms release electrons because their energetically degenerate 3d_xz and 3d_yz states are shifted to high energy (Fig. 3(e)). In this respect, the valence states should be Sr²⁺Cu₃²⁺Fe₄⁴⁺O₁₂²⁻ at the high temperature. The temperature-induced intersite CT actually takes place between the Cu and Fe in SrCu₃Fe₄O₁₂ via a form of 3Cu³⁺ + 4Fe^3.25+ → 3Cu²⁺ + 4Fe⁴⁺, in consistence with the experimental observations.¹¹ In addition, the magnetic moment (Table 3) is calculated to be 3.94 μ_B for Fe in the AFM-C, and −0.52 and 3.75 μ_B for Cu and Fe in the FIM, respectively, all of which are somewhat smaller than their respective theoretical values (4.75 μ_B for Fe^3.25+ in AFM-C, and 1 and 4 μ_B for Cu²⁺ and Fe⁴⁺ in FIM, respectively). Such differences can be attributed to the fact that a small amount of magnetic moment is distributed to the O atoms, suggestive of the formation of covalent bonding.

The PDOSs of Cu, Fe and O atoms span a broad energy range and are almost in the same energy region with a similar intensity. In particular, the O 2p_x and 2p_y share the energy range with the Cu 3d_xz orbital and the O 2p_z share the energy range with the degenerate Fe 3d_xz and 3d_yz orbitals, indicating a strong covalent hybridization between them. Consequently, the Cu³⁺ prefers the d⁹L (L: a ligand oxygen hole) rather than the d⁸ electronic configuration, while the Fe^3.25+ and Fe⁴⁺ have the d⁵L^0.25 and d⁵L electronic configuration, respectively. The Cu–Fe intersite CT in SrCu₃Fe₄O₁₂ can be expressed as 3d⁹L + 4d⁵L^0.25 → 3d⁹ + 4d⁵L, which can be realized by the redistribution of ligand holes from Fe–O to Cu–O bonds. The Cu–Fe intersite CT is, however, not energetically expensive because all the FeO₆ octahedra and CuO₄ square-planar units are linked by the corner-sharing O atoms in SrCu₃Fe₄O₁₂. Meanwhile, holes are found to be injected into the O 2p_z orbital (Fig. 3(f)), as confirmed by upshift of its spin-up channel. The Cu–Fe intersite CT is thus mediated by O 2p orbitals via the form of Cu 3d_xz → O 2p_x, 2p_y → O 2p_z → Fe 3d_xz + 3d_yz. To test this scenario, we present the charge density difference (CDD) plots near E_F for both the AFM-C and FIM (Fig. 4). There is no CDD distributed around Cu in the AFM-C (Fig. 4(a)), whereas the 3d_xz orbital of Cu is occupied in the spin-down channel (Fig. 4(b)) in the FIM state. The 2p_z orbital of O atom spatially expands to its neighboring Fe in the AFM-C state, while the 2p_x and 2p_y orbitals of O expand to its nearest Cu in the FIM state. These verify that the temperature-induced intersite CT occurs through the form of Cu 3d_xz → O 2p_x, 2p_y → O 2p_z → Fe 3d_xz + 3d_yz when the magnetic configuration varies from the low-temperature AFM-C to the high-temperature FIM.

Fig. 4 Three-dimensional CDD plots for the (a) AFM-C and (b) FIM configurations of SrCu₃Fe₄O₁₂ calculated using the GGA + U method. The spin-up and spin-down electrons are indicated in red and blue, respectively.

Comparative analysis of phonon property of SrCu₃Fe₄O₁₂

Since vibrating properties are important for evaluating its thermal and dynamical stability, we also conducted the phonon calculations of SrCu₃Fe₄O₁₂. The calculated phonon dispersion curves along the high symmetry lines in the Brillouin zone and the corresponding total phonon DOS are shown in Fig. 5 and 6, respectively. Obviously, there is no soft mode, i.e. negative frequencies in the phonon dispersion relations, at any wave vectors both in the low-temperature (Fig. 5(a)) and in high-temperature (Fig. 5(b)) states, confirming the dynamical stabilities of SrCu₃Fe₄O₁₂. It is noteworthy that the phonon spectra can be divided into three intervals with the wide band gaps in the low-temperature SrCu₃Fe₄O₁₂, which is mainly attributed to the large mass difference between these atoms. However, for the high-temperature structure, the high-frequency and mid-frequency phonon bands are practically disappeared and merged in the low-frequency region, which is also confirmed in its phonon DOS plot (shown in Fig. 6). These phonon spectrums transfer should be ascribed to the weakening of chemical bonding between the corresponding cations and anions under the higher-temperature circumstance.²² Furthermore, one can notice from Fig. 5 that the phonon branches are severely degenerated at the high-symmetry R and G points, whereas at the adjacent M and X points all the phonon modes are not degenerate. The closeness between the frequencies of the intensive phonon modes suggests that the phonon–phonon coupling turns stronger, which should benefit the realization of its metallic nature. In addition, the frequencies of some optical modes are close to those of some acoustic modes, suggesting that it is not hard to transfer energy between these modes.

Fig. 5 Phonon dispersion curves along the high symmetry directions for SrCu₃Fe₄O₁₂ at (a) 80 K and (b) 270 K.

Fig. 6 Total phonon DOS for SrCu₃Fe₄O₁₂ at 80 K and 270 K.

Charge transfer and negative thermal expansion mechanism in SrCu₃Fe₄O₁₂

As discussed above, the electrical and magnetic properties of SrCu₃Fe₄O₁₂ differ from those of its analogue CaCu₃Fe₄O₁₂.^4,6 The discrepancy can primarily be ascribed to the large difference in bond strain arising from the different ionic size between Sr²⁺ and Ca²⁺ (1.44 Å for Sr²⁺ and 1.34 Å for Ca²⁺), as in the case of the LnCu₃Fe₄O₁₂ compounds.⁸ This also implies that the difference in bond strain might be responsible for the remarkable electronic phase transitions. In addition, the difference can also be observed in iron-based perovskites CaFeO₃ and SrFeO₃, for example, there occurs the CD of 2Fe⁴⁺ → Fe⁵⁺ + Fe³⁺ (2Fe³⁺L → Fe³⁺L² + Fe³⁺) in CaFeO₃,²³ while metallic conductivity and cubic symmetry are preserved in SrFeO₃ even at low temperatures,²⁴ which are amazingly similar to those shown in CaCu₃Fe₄O₁₂ and SrCu₃Fe₄O₁₂.^10,11 In view of the fact that CuO₄ square-planar units are spatially isolated from each other, electrical property of this system is dominated by the corner-sharing FeO₆ octahedral networks. In this sense, A-site-ordered perovskite BaCu₃Fe₄O₁₂ is believed to have a similar electrical behavior as the perovskite BaFeO₃.²⁵

Structurally, an obvious lattice expansion is seen owing to the larger ionic size of Sr²⁺ as compared to that of Ca²⁺. Meanwhile, Fe–O bonds are elongated from 1.979 Å in SrCu₃Fe₄O₁₂ to 1.970 and 1.893 Å in CaCu₃Fe₄O₁₂, which is accompanied by the elongation of the Sr–O bonds as well (from 2.620 Å in SrCu₃Fe₄O₁₂ to 2.585 Å in CaCu₃Fe₄O₁₂). As a result, the CD is not preferred because not only the compression stress of Sr–O and Fe–O bonds should be overcome, but also the crystal symmetry is lowered due to the distortion of FeO₆ octahedra. Consequently, the intermetallic CT should account for the relief of its structural instability and the structural linkage of the FeO₆ octahedra and the CuO₄ square-planar units by the corner sharing is critical to the charge distribution. In addition, the Cu–O bond is very sensitive to temperature, showing an unexpected elongation in the range of NTE, which indicates that the Cu²⁺ is prone to be formed because the ionic radius of Cu²⁺ is larger than that of Cu³⁺. This also implies that once the Cu–O bonds are elongated to a certain level, the Cu³⁺ can be transformed to Cu²⁺ by electron gain from B-site Fe as Fe has a variable valence state, leading to the shrinking of the Fe–O bonds. The O atoms hence play an important role in mediating active charge in this system. The unusual NTE of SrCu₃Fe₄O₁₂ originates from the intersite CT, which relaxes the compression of Sr–O and Fe–O bonding units.

Conclusions

We have conducted a first-principles calculation to investigate the electrical and magnetic properties of A-site-ordered perovskite SrCu₃Fe₄O₁₂, aimed at clarifying its NTE mechanism. Our calculations demonstrate that SrCu₃Fe₄O₁₂ is intrinsically an AFM metal with an C-type magnetic configuration for Fe ions of mixed valence at the B-site and paramagnetic Cu³⁺ at the A-site. Electronic structure analysis reveals that there occurs temperature-induced intersite CT between the Cu and Fe in this oxide in the form of Cu 3d_xz → O 2p_x, 2p_y → O 2p_z → Fe 3d_xz + 3d_yz. The unusual NTE is found to originate from the temperature-induced intermetallic CT, which relaxes the Sr–O and Fe–O bonding units, opening up thereby an additional avenue to understand origins of the NTE in transition-metal oxides.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) under grant no. 21301075 and 51372244, Specialized Research Fund for the Doctoral Program of Higher Education under grant no. 20133227120003, the Open Project of State Key Laboratory of Rare Earth Resources Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences (CAS) (grant no. RERU2014006), the Natural Science Foundation of Jiangsu Province (grant no. BK20140551) and Research Foundation for Advanced Talents of Jiangsu University (grant no. 12JDG096). Z.W. appreciates the financial supports from the Grant-in-Aid for Young Scientists (A) (grant no. 24686069), the NSFC (grant no. 11332013), the JSPS and CAS under the Japan-China Scientific Cooperation Program, and the Murata Science Foundation.

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