Theoretical Study on the Negative Thermal Expansion Perovskite

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Theoretical Study on the Negative Thermal Expansion Perovskite LaCu3Fe4O12: Pressure-Triggered Transition of Magnetism, Charge, and Spin State Junling Meng,† Lifang Zhang,†,‡ Fen Yao,†,§ Xiong Zhang,†,§ Wenwen Zhang,†,‡ Xiaojuan Liu,*,† Jian Meng,† and Hongjie Zhang† †

State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China ‡ University of Science and Technology of China, Hefei 230026, People’s Republic of China § University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China S Supporting Information *

ABSTRACT: The A-site ordered negative thermal expansion material LaCu3Fe4O12 (LaCFO) was comprehensively investigated by using firstprinciples calculations. A pressure-triggered crystal structural phase transition from space group Im3̅ (No. 204) to Pn3̅ (No. 201) and magnetic transformation from a G-type antiferromagnetic (G_AFM) ground state to ferrimagnetic (FerriM) coupling were observed in LaCFO via gradual compression of the equilibrium volume. Correspondingly, the Fe−Cu intersite charge transfer from Fe to Cu 3dxy orbital, expressed as 4Fe3+ + 3Cu3+ → 4Fe3.75+ + 3Cu2+, was simulated along with the magnetic phase transformation from the G_AFM configuration to the FerriM state. Intriguingly, the Fe charge disproportionation, formulated as 8Fe3.75+ → 5Fe3+ + 3Fe5+, appeared and was attributed to the strong hybridization between Fe 3d and O 2p orbitals in the FerriM state when the volumes were substantially compressed up to less than or equal to 80%V. Meanwhile, the external hydrostatic pressure also leads to a spin flip from a highspin Fe3+ antiferromagnetically arranged LaCu3+3Fe3+4O12 Mott insulator at low pressure and goes through a FerriM LaCu2+3Fe3.75+4O12 half-metal to a low-spin FerriM coupled LaCu2+3Fe3+5/2Fe5+3/2O12 metal at high pressure. Therefore, the crossover from high spin to low spin is responsible for the charge disproportionation in LaCFO. Essentially, the charge transfer and spin flip originate from the discontinuous changes of metal−oxygen bond lengths and angles in the compressed atomic structure. Finally, the negative thermal expansion behavior and mechanism of LaCFO were theoretically examined and clearly revealed.

1. INTRODUCTION A-site-ordered quadruple perovskite-type ACu 3 Fe 4 O 12 (ACFOs) have attracted considerable attention owning to their rich variety of remarkable properties. Antiferromagnetism, ferrimagnetism, negative thermal expansion, and other peculiar properties are intertwined in ACFO oxides and are strongly sensitive to external parameters such as temperature, pressure, chemical composition, and applied fields.1−5 Essentially, discriminative physical and chemical properties are consequences of charge transfer/disproportionation and spin-state transition of Cu and Fe ions in rather different ACFO oxides. A prototypical example is the temperature-induced intersite charge transfer (3Cu3+ + 4Fe3+ → 3Cu2+ + 4Fe3.75+) in LaCFO6,7 and BiCu3Fe4O12 (BiCFO)8,9 oxides, giving rise to antiferromagnetic to paramagnetic phase transitions accompanied by sudden volume or metal−oxygen bond length mutations. Actually, such discontinuous changes are generally induced by a small external stimulus. It therefore would be desirable to be able to control the temperature or pressure at © XXXX American Chemical Society

the point at which the abrupt transition takes place and to have an idea of the mechanism governing the transitions. The aim of this study is to give exactly a specific description of the pressure-driven electronic structure and spin-state transitions and their relationship to the magnetic property and negative thermal expansion behavior. Similar to the case for temperature, pressure can also affect the valence states or magnetic properties in such a way as to induce phase transitions. Experimentally, Seda and Hearne have found a pressure-induced intervalence charge transfer of Fe2+ + Ti4+ → Fe3+ + Ti3+ in ilmenite FeTiO3.10 In addition, the Fe3+/ Fe2+ ratio displayed a rapid increase under pressures from ambient up to ∼2 GPa. For ACFO-type oxides, so far, temperature- and pressure-driven phase transformations have been determined in CaCu3Fe4O12 (CaCFO),11,12 SrCu3Fe4O12 (SrCFO),3,13 LnCu3Fe4O12 (LnCFO, Ln = rare-earth ions),14,15 Received: February 20, 2017

A

DOI: 10.1021/acs.inorgchem.7b00458 Inorg. Chem. XXXX, XXX, XXX−XXX

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ions. The Brillouin zone was sampled using a 7 × 7 × 7 Monkhorst− Pack k mesh, and each crystal structure was fully relaxed with a planewave energy cutoff of 550 eV under the conduction of residual force ≤0.05 eV/Å. The electronic structure and magnetic properties were further performed by a full-potential linear augmented plane wave plus local orbital (LAPW+LO) method28,29 as implemented in the WIEN2K30,31 code. As mentioned above, the GGA-PBEsol approach and the identical U parameters were also employed in the WIEN2k program. In addition, the plane wave expansion cutoffs are 7.0 for expanding the wave function (RKMAX) and 12 for expanding the densities and potential (GMAX) in all calculations. Meanwhile, the 7 × 7 × 7 grids of k points in the complete Brillouin zone were also adopted, and the Brillouin zone integration was carried out with a modified tetrahedron method.19 Finally, the self-consistent calculations were considered to be converged when the charge convergence was less than 10−4 e. Phonon calculations were performed by density functional perturbation theory (DFPT)32,33 and implemented in the VASP code. The phonon dispersions were calculated by using the PHONOPY code,34,35 which used the force constant matrix to calculate the phonon spectra and phonon DOS. In this work, we also employed the quasi-harmonic approximation (QHA)36 to simulate the thermal properties of LaCFO.

and BiCFO2,8 quadruple perovskites. However, a very rare theoretical study of the mechanism of valence or magnetic transitions has been reported by applying pressure in ACFO oxides, specifically in LaCFO perovskite. It is thus constructive and meaningful to examine the effect of pressure on the charge transfer and spin-state transitions in LaCFO by the way of theoretical calculations. LaCFO experimentally undergoes a simultaneous first-order transition including insulator−metal, antiferromagnetic−paramagnetic, and isostructural phase transitions at the Néel temperature (TN = 393 K), where a discontinuous volume change is presented as a negative thermal expansive behavior occurring at the same time.1,16 These observations suggested that the inherent magnetic long-range order of Fe spin in LaCFO cannot be the driving force for the magnetic and charge transitions, but the temperature. Analogously, pressure can also stimulate charge transfer and spin flip in LaCFO oxides. In order to determine the mechanism behind the phase transition by applying pressure, Yamada et al. recently systematically synthesized a series of LnCFO (Ln = rare-earth ion) perovskites.14 It is noteworthy that the substitution of rareearth ions in LnCFO can be seen as chemical pressure is applied in the LaCFO lattice due to the lanthanide contraction. Therefore, the observed phase transformation after applied chemical pressure in LaCFO at 100 K is derived from different pressure-induced mechanisms between compounds with light and heavy lanthanides. Theoretically, Rezaei et al. subsequently investigated the mechanism of charge transfer/disproportionation in the LnCFO series by using density functional theory (DFT) calculations,17 and they revealed that the change in the spin state is responsible for the intersite charge transfer (charge disproportionation) in the light (heavy) Ln compounds. Recently, Shimakawa and his group have devoted their efforts to investigate the LaCFO oxide.1,18 Intriguingly, a pressureinduced charge transfer from a low-pressure LaCu3+3Fe3+4O12 to a high-pressure LaCu2+3Fe3.75+4O12 phenomenon came into being,18 accompanied by an antiferromagnetic insulator to a paramagnetic metallic transformation at ambient temperature. However, the evolution of electronic density for the charge transfer/disproportionation and spin-flip process with applied external pressure still remains unknown. In this work, we are primarily interested in the pressuredriven ground state properties of quadruple LaCFO perovskite, drawing on the calculations for total energies, crystal structure, charge density, electronic density of states (DOS), and magnetic properties. In this pursuit, we performed systematic first-principles calculations based on DFT to mainly investigate the effect of pressure on the charge transfer/disproportionation and spin-state transition of LaCFO oxides. In addition, phonon correlation calculations were also adopted to determine the stability of the structural phase and negative thermal expansion behavior of LaCFO.

3. RESULTS AND DISCUSSION 3.1. Crystal and Magnetic Structure. For LaCFO, in order to confirm the magnetic structure at the ground state, we relaxed the crystal structure based on the experimental cubic space group In3̅ (No. 204) and sampled a number of magnetic configurations (see Table 1). The active 3d shells in Cu and Fe Table 1. Difference of Total Energies of LaCFO in Different Magnetic Structuresa at Six Pairs of U Values Obtained by Subtracting the Total Energy of LaCFO in G_AFM Configuration at UFe = 4.0 eV and UCu = 5.0 eV UFe, UCu (eV) ΔEPM (eV) ΔEFM (eV) ΔEG_AFM (eV) ΔEA_AFM (eV) ΔEC_AFM (eV) ΔEFerriM (eV) aG_AFM (Å)

4.0, 5.0

4.0, 6.0

4.0, 7.0

5.0, 6.0

5.0, 7.0

6.0, 7.0

14.00 2.05 0 0.96 0.46 1.04 7.37

15.75 2.39 1.81 2.69 2.61 2.39 7.36

17.50 3.64 3.55 4.09 4.16 3.64 7.36

22.31 5.77 4.39 5.23 4.79 5.99 7.36

24.02 7.49 6.13 7.21 6.53 7.23 7.35

30.13 9.53 8.38 9.10 8.72 9.52 7.35

a

Magnetic structures of PM, FM, G_AFM, A_AFM, C_AFM, and FerriM are the abbreviations for paramagnetic, ferromagnetic, G-type antiferromagnetic, A-type antiferromagnetic, C-type antiferromagnetic, and ferrimagnetic, respectively.

ions suggest a possible character of electron correlation in LaCFO perovskite. It is advisibly necessary here to use the GGA+U approach in this context as an approximate parametrized self-interaction correction for the specific orbital shells. In comparison to other more refined but timeconsuming calculating methods, GGA+U may not be especially satisfactory but has the advantage of computational simplicity and is quite sufficient. In the present work, a series of U values are chosen for 3d orbitals of Cu and Fe ions. The difference in total energies at different magnetic structures, which are obtained by subtracting the G-AFM energy at UFe = 4 eV and UCu = 5 eV, are given in Table 1. As can be seen in Table 1, the G_AFM spin arrangement for Fe atoms is energetically favorable and is the magnetic ground state of LaCFO, which agrees well with the experimental and theoretical results.14,37,38

2. COMPUTATIONAL DETAILS The equilibrium geometry and total energies were performed within the context of DFT using the projector-augmented-wave (PAW) pseudopotential19,20 as implemented in the Vienna ab initio simulation package (VASP) (version 5.2.2).21,22 The generalized gradient approximation (GGA) method23 with the Perdew−Burke−Ernzerhof parametrization revised for solids (PBEsol)24 was used for the exchange and correlation functional. Furthermore, Dudarev et al.’s method,25 where only an effective Hubbard parameter Ueff = U − J26,27 enters the Hamiltonian, was used to improve the description of the effective on-site Coulomb interaction of Fe and Cu transition-metal B

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Inorganic Chemistry Interestingly, the G_AFM configuration at UFe = 4 eV and UCu = 5 eV is the most stable state in all pairs of U values, and the corresponding lattice parameter (a) is the closest to the experimental value.18 Therefore, we adopt the G_AFM magnetic structure with UFe = 4 eV and UCu = 5 eV in the following calculations for the ground state properties of LaCFO perovskite. Meanwhile, it is worth noting that that the spin structure of LaCu3Fe4O12 spontaneously changed into space group Pn3̅ (No. 201) due to the opposite spin direction of Bsite Fe ions with G_AFM configuration after geometrical optimization. However the crystal structure space group of LaCu3Fe4O12 is unchanged at Im3̅ (No. 204). Figure 1 shows two kinds of magnetic structures of the cubic LaCFO. The former is a rock-salt-type Feup (spin-up) and Fedn

structure, we must ensure that no phonon imaginary frequency appears in LaCFO.41 Therefore, phonon calculations at the theoretical equilibrium volume were carried out, and the phonon dispersion curves along the high-symmetry direction in the simple cubic Brillouin zone are plotted in the inset of Figure 2. A total of 120 phonon branches were presented in the phonon spectrum, because there are 40 atoms in the LaCFO cell, and the absence of an imaginary phonon branch confirms that the ground state of LaCFO is a stable G_AFM state. Hydrostatic pressure is introduced into the LaCFO lattice via compression of the equilibrium volume (100%V) to 78%V and expansion from 100%V to 110%V. The corresponding changes in volume, lattice constant, pressure, structural symmetry, and magnetic properties are given in Table 2. Intriguingly, LaCFO Table 2. Changes in Volume, Lattice Constant, Pressure, Lattice Space Group, and Magnetic Properties after Expansion and Compression of the Equilibrium Volume (100%V)

Figure 1. Magentic structure of LaCFO quadruple perovskite with (a) G_AFM and (b) FerriM configurations.

(spin-down) G_AFM ordered configuration (see Figure 1a), while the latter is a Feup and Cudn ferrimagnetic (FerriM) coupled alignment (see Figure 1b), which is the same FerriM spin structure as CaCFO.11 In both of the two symmetries, the Fe atom is located at the center of the titled FeO6 octahedra, whereas the Cu atom is coordinated as a square-planar CuO4 unit. We first explore the equilibrium geometry with the G_AFM configuration on the basis of the result of Table 1. The optimal geometry fitted from the Birch−Murnaghan equation39,40 would theoretically give very accurate lattice parameter estimates, and the equilibrium lattice constant of LaCFO obtained by Birch−Murnaghan fitting is 7.3736 Å (see Figure 2). In order to examine the stability of the optimal crystal

volume percent

volume (Å)

lattice param (Å)

hydrostatic pressure (GPa)

110%V 108%V 106%V 104%V 102%V 100%V 98%V 96%V 94%V 92%V 90%V 88%V 86%V 84%V 82%V 80%V 78%V

440.99 432.97 424.95 416.94 408.92 400.90 392.88 384.86 376.85 368.83 360.81 352.79 344.77 336.76 328.74 320.72 312.70

7.61 7.57 7.52 7.47 7.42 7.37 7.32 7.27 7.22 7.17 7.12 7.07 7.01 6.96 6.90 6.85 6.79

−15.36 −12.90 −10.20 −7.38 −3.89 0.00 4.20 8.90 14.11 19.83 26.24 28.07 35.51 43.78 53.77 63.96 75.56

space group Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Im3̅ (No. Pn3̅ (No. Pn3̅ (No.

204) 204) 204) 204) 204) 204) 204) 204) 204) 204) 204) 204) 204) 204) 204) 201) 201)

magnetic property G_AFM G_AFM G_AFM G_AFM G_AFM G_AFM G_AFM G_AFM G_AFM G_AFM G_AFM FerriM FerriM FerriM FerriM FerriM FerriM

undergoes a crystal structure phase transition from space group Im3̅ to a slightly lower Pn3̅ symmetry after compression of the optimal volume to below 82%V at 0 K. In addition, the magnetic transition from the G_AFM to FerriM state takes place when the equilibrium volume is compressed to below 90%V (see Tables S1 and S2 in the Supporting Information). Actually, the FerriM ground state is found for the first time in LaCFO oxide by applying hydrostatic pressure. In addition, there is no phase transition after expansion of the crystal lattice (from 100%V to 110%V); therefore, only lattice compression is considered in the following analysis. During the magnetic transition, fundamentally, the pressure-induced Cu−O and Fe− O bond lengths exhibit clear anomalies. From Figure 3a we can see that the Fe−O bond length (the bond length of Feup is equal to that of Fedn in the G_AFM state) rapidly shrinks at the transition point and then decreases all the way, whereas the Cu−O bond length abruptly expands first and then decreases after the magnetic transition point. This phenomenon is similar to the temperature dependence of Fe−O and Cu−O distances in LaCFO oxide.15 Meanwhile, the changes in bond length can also imply a valence transition, that is, reduction of Cu ions and oxidation of Fe ions, because the relaxation of bond stress on transition-metal−oxygen bonds, which is induced by pressure,

Figure 2. Birch−Murnaghan fitting of LaCFO to obtain the optimal volume. The phonon spectrum of the optimal lattice is plotted in the inset. C

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lanthanide substituted LnCFO oxides in our theoretical calculations are in the G_AFM configuration without a phase transition at the ground state. It is considered that the pressure introduced by only lanthanide contraction is not strong enough to cause the magnetic phase transition without accounting of temperature. In summation, the message we are trying to get across in this section is that the introduction of hydrostatic pressure can drive a crystal structural phase transition from space group Im3̅ (No. 204) to Pn3̅ (No. 201) and induce a magnetic transformation from the G_AFM to the FerriM phase, which is attributed to the discontinuous changes in metal−oxygen bond lengths and angles in the atomic structure. The FerriM configuration is first found in the LaCFO, and the electronic structure and charge density will be discussed in particular in the next section. 3.2. Pressure-Triggered Charge Transfer/Disproportionation. From the above crystal and magnetic structural analysis, we divided the LaCFO oxide into two classes on the basis of the magnetic phase transition after applied hydrostatic pressure. The first class has a G_AFM configuration via low pressure introduced into the LaCFO lattice in the volume range of 100%V−90%V, whereas the other class is ascribed to a FerriM coupling, corresponding to high pressure applied to the LaCFO lattice from 88%V to 78%V. To clarify the evolution of charge transfer, we examine the charge density of LaCFO from a G_AFM state to a FerriM state by constraining the volume of LaCFO. Figure 4 shows a pressure-driven spin charge density difference of LaCFO under the same scaleplate in the (110) crystal plane, in which all pivotal kinds of elements (La, Cu, and Fe) in LaCFO are included. At equilibrium volume with G_AFM configuration, as can be seen in Figure 4b, Feup and Fedn are orderly arranged in the (110) plane and directly hybridize with an unoccupied Cu 3dxy orbital (four-petal shape) so that the intersite charge transfer would occur when an external stimulus was applied. Comparing Figure 4b with Figure 4a (102%V), we can see that the orbital hybridization between Fe and Cu 3dxy increases when the lattice expands, whereas a scarcely orbital hybridization appears when we further compress the optimal volume to 90%, as shown in Figure 4c (96%V) and Figure 4d (90%V). It is therefore concluded that, in the G_AFM state, Fe and Cu interact

Figure 3. Changes in transition-metal−oxygen (a) bond lengths and (b) bond angles as a function of compressed lattice parameter. The chemical pressure effects on bond lengths and angles are assigned to the purple spheres in the dotted rectangle.

is one of the fundamental causes of the Cu−Fe charge transfer in LaCFO. According to the rapid decrease of the nearest neighbor Fe−O distance observed above, a strong reduction in the FeO6 octahedral distortion can be inferred, reflected by the increased average bond angles of ⟨Fe−O−Fe⟩ as shown in Figure 3b. The G_AFM ordering and FerriM coupling is derived from the changes in ⟨Fe−O−Fe⟩ and ⟨Fe−O−Cu⟩ bond angles and will be discussed in the following section. In addition, the chemical pressure effect induced by La-cation substitution is also considered with a comparison of hydrostatic pressure. As Yamada et al.14 reported in their experiments, we substituted the La with a series of lanthanides (from Ce to Tm) in LaCFO theoretically. It is clear that the chemical pressure effects, which are plotted as purple spheres in the dotted rectangle of Figure 3, cause the the Fe−O bond length to shrink correspondingly, while the Cu−O bond length is almost constant; moreover the ⟨Fe−O−Fe⟩ bond angle slightly increases at the ground state. These tendencies of microscopic atomic structure through theoretical predictions agree well with the experimental reports.14 However, unlike the experimentally observed phase transition in LnCFO at 100 K, all of the

Figure 4. Computed spin charge density differences of LaCFO in the (110) crystal plane for (a) 102%V, (b) 100%V, (c) 96%V, (d) 90%V, (e) 88% V, and (g) 78%V in the same scaleplate. D

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90%V (Figure 5), 88%V (Figure S5 in the Supporting Information), and 78%V (Figure 6) for Fe 3d and Cu 3d

directly and the charge transfer between them is slightly enhanced as the hydrostatic pressure is decreased, rather than being weakened as the hydrostatic pressure is increased. For the FerriM state, the orbital interaction between Fe 3d and O 2p surmounts the hybridization between Fe 3d and Cu 3dxy, resulting in a completely different bonding property, as shown in Figure 4e−g. Previous studies have reported that in ACFO oxides the generation of ligand holes stemmed from the strong hybridization between Fe 3d and O 2p orbitals,42,43 which was also the reason for the production of ligand holes in our present work, because the PDOS of Fe 3d and O 2p are energetically degenerate and exhibit similar character in the FerriM configuration (see Figure S1 in the Supporting Information). Meanwhile, from Figure S1 we can clearly see that a competition of orbital hybridization between Fe(3d)−Cu(3d) and Fe(3d)−O(2p) exists in LaCFO during compression of the lattice volume. The orbital hybridization in the G_AFM state is mainly between Fe 3d and Cu 3d orbitals, whereas in the FerriM state the hybridization is primarily between Fe 3d and O 2p orbitals and is gradually strengthened as the hydrostatic pressure is increased. Furthermore, a charge-disproportionated state appeared when sufficient hydrostatic pressure was exerted. This distinct charge behavior is regarded as a redistribution and a localization of ligand holes near the Fe site. Figure 4g exhibits a rock-salt-type charge ordering of Fe ions in the (110) plane when the volume is restrained to 78%V. Considering the fact that Cu normally prefers to be in the Cu2+ state and Fe generally favors the Fe3+ state, on this basis, we can further deduce that, as the pressure is increased, the Cu2+ state remains unaffected, whereas partial Fe3+ ions transform to higher oxidation states, involving a charge ordering of Fe ions in the (110) plane. However, the rock-salt-type charge ordering is not tolerated in other crystal planes; actually, it exhibits a further deviation from 1:1 because of the high oxidation state of Fe ions randomly distributed in the LaCFO lattice after continuous compression of the optimal volume to 80%V and 78%V. For 78%V, the high valence state of Fe rock-salt ions is distributed in the (110) plane (see Figure 4g), whereas, for 80% V, the high-valent Fe states are arranged adjacently in the (010) plane. The charge density pictures of LaCFO with 80%V in (010), (110), and (011) crystal planes are shown in Figure S2 in the Supporting Information, in which the charge disproportionation can be distinctly observed. Therefore, as mentioned above, the intersite charge transfer of Fe−Cu and charge disproportionation of Fe ions emerging once alter the external pressure and are accompanied by the antiferromagnetic−ferrimagnetic phase transition in LaCFO. In order to further explore the mechanism of pressure-driven electronic behavior in LaCFO, we next discuss the electronic DOS after hydrostatic pressure is exerted. For the G_AFM class, the calculated DOS of LaCFO indicated that this group is really a typical G_AFM chargetransfer-type Mott insulator at the ground state. A number of total DOS from 100%V to 90%V are displayed in Figure S3 in the Supporting Information, in which the band gap of equilibrium volume is about 0.82 eV, which is well in line with the nonmetallic character. Interestingly, the band gaps shrink as the pressure is increased by compressing the optimal volume to 90%V, demonstrating a degradation of nonmetallic features after application of hydrostatic pressure. In order to understand the evolution of electronic structure in LaCFO from a G_AFM to a FerriM state, we examine the partial DOS (PDOS) of 100%V (Figure S4 in the Supporting Information),

Figure 5. Calculated PDOS of LaCFO for 90%V: (a) split Fe 3d orbitals; (b) split Cu 3d orbitals. The Fermi level is set to 0 eV and presented as a red dashed line.

Figure 6. Computed PDOS of LaCFO for 78%V: (a) split Fe 3d orbitals with low valence state; (b) split Fe 3d orbitals with high oxidation state; (c) split Cu 3d orbitals. The Fermi level is set to 0 eV and presented as a red dashed line.

orbitals. In the G_AFM state, as can be seen in Figure S4a and Figure 5a, the shapes of DOS for Fe ions in the two antiparallel spin directions (Feup and Fedn) are similar, and it is therefore enough to analyze only one spin alignment. It is obvious that, taking Feup as an example, all of its 3d orbitals are occupied below the Fermi level (EF) in the majority spin direction and are empty in the minority spin direction. Similarly, all of the 3d orbitals of Cu are occupied in both the majority and minority spin directions except for the Cu 3dxy orbitals, which are empty in the two spin orientations (see Figure 5b). Therefore, Fe3+ with a 3d5 configuration and Cu3+ with a peculiar 3d8 configuration are confirmed in the G_AFM state. This result is consistent with the previous experimental and theoretical reports.17,18 For the FerriM state, a half-metal behavior with an antiparallel Fe−Cu spin alignment is presented in Figure S5 in the Supporting Information (88%V). It is interesting that a half-metal to metal transition appeared along with a charge E

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compare the two competing magnetic models, one of which is Fe3+(3d5)Cu3+(3d8) and the other is Fe3.75+(3d4.25)Cu2+(3d9). In the G_AFM state, because the Cu3+ ions do not contribute to the magnetization, the magnetic ordering is therefore ascribed to the Fe3+−O−Fe3+ antiferromagnetic superexchange interactions, which is mainly governed by the ⟨Fe−O−Fe⟩ bond angles. As can be seen from Figure 3b, the gradually increasing ⟨Fe−O−Fe⟩ bond angles demonstrate increasing Fe3+−O−Fe3+ antiferromagnetic superexchange interactions in the G_AFM state. However, in the FerriM state, in fact, there are two magnetically coupled models. One is a antiferromagnetic-like Feup−Cudn ferrimagnetic coupling with residual magnetic moment. Obviously, the almost invariable ⟨Fe−O− Cu⟩ bond angles (see Figure 3b) indicate that a Feup−Cudn ferrimagnetic interaction is always present in the FerriM configuration. Meanwhile, the other magnetically coupled model is a ferromagnetic-like Fe3+−O−Fe5+ interaction. This interaction arises from the aforementioned charge-disproportionated Fe ions; in this case the randomly distributed Fe5+ ions disorder the antiferromagnetic superexchange interactions in the Fe3+−O−Fe3+ pathway, resulting in small-scale and localized ferromagnetic-like Fe3+−O−Fe5+ double-exchange interactions. Therefore, the changes in ⟨Fe−O−Fe⟩ and ⟨Fe− O−Cu⟩ bond angles, caused by application of hydrostatic pressure, determined the magnetic transition between G_AFM and FerriM. This conclusion is similar to the previous argument that the transition-metal−oxygen bond angles play a decisive role in the magnetic transformation.45 In combination with the above electronic structure and magnetization analysis, the antiferromagnetically arranged Fe3+ (S = 5/2) with high-spin configuration causes the low-pressure LaCu3+3Fe3+4O12 phase to be a Mott insulator; subsequently, the ferrimagnetically coupled Fe3.75+ (spin-up) and Cu2+ (S = 1/2, spin-down) cause the LaCu2+3Fe3.75+4O12 phase to be a half-metal; finally, the charge-disproportionated Fe3+ (S = 5/2) and Fe5+ (S = 3/2) with low-spin configuration cause the highpressure LaCu2+3Fe3+5/2Fe5+3/2O12 phase to be a metal. Therefore, hydrostatic pressure can drive a spin flip in LaCFO oxides. As shown in Figure 8, at the high-spin state, Fe and Cu ions prefer a 3d5 and an unusual 3d8 configuration, respectively, while they retreat to a average Fe 3d4.25 and a normal Cu 3d9 configuration through a charge transfer from Fe to the Cu 3dxy orbital as the pressure is increased, whereas, at the low-spin state, Fe3+ and Fe5+ are disproportionally

disproportionation of Fe ions when the volume was continuously compressed to 80%V and 78%V. Comparing Figure 6a with Figure 6b, one can clearly observe that there are two kinds of charged Fe in 78%V LaCFO. With the assumption that Fe is +3 valence in Figure 6a, the Fe in Figure 6b is thus prone to have +5 valence because two spin-up electrons, at dz2 and dx2−y2 orbitals, move up to cross EF and are lost. Therefore, in combination with the above charge density analysis, the charge disproportionation can be expressed as 8Fe3.75+ → 5Fe3+ + 3Fe5+ with an optimal volume of less than or equal to 80%V, which is consistent with the above crystal structure phase transition (see Table 2). Similarly, this deviation of Fe3+:Fe5+ = 5:3 from the ideal abundance ratio for rock-salt-type charge ordering is also observed in YCFO oxide, which has a FerriM configuration as well.44 Meanwhile, valence modification also took place in the Cu site, where all of the Cu 3d orbitals are occupied except for a spin-up Cu 3dxy orbital. Therefore, Cu2+ with a normal 3d9 configuration is determined in the FerriM state. The electronic DOS analysis is consistent with the above charge density pictures and the changes in transition-metal− oxygen bond lengths. Therefore, the intersite charge transfer from the G_AFM state to the FerriM configuration with an increase in hydrostatic pressure can be expressed as 4Fe3+ + 3Cu3+ → 4Fe3.75+ + 3Cu2+, and subsequently, a charge disproportionation formulated as 8Fe3.75+ → 5Fe3+ + 3Fe5+ emerges when we further compress the volume up to 80%V and 78%V. 3.3. Pressure-Induced Spin-State Transitions. As mentioned above, pressure-driven structural and magnetic phase transitions appeared, giving rise to intersite charge transfer (4Fe3+ + 3Cu3+ → 4Fe3.75+ + 3Cu2+) and charge disproportionation (8Fe3.75+ → 5Fe3+ + 3Fe5+). A noteworthy point is how the magnetization and spin state are affected with an increase in hydrostatic pressure. Figure 7 shows the changes

Figure 7. Changes in average magnetization of Fe and Cu ions as a function of compressed lattice constant. The corresponding magnetic structures are also exhibited in the inset.

in average magnetization as a function of lattice parameters, which corresponds to the compressed volumes (see Table 2). As shown in Figure 7, the average magnetization of Fe displays a slow decline in the G_AFM state and then exhibits a sudden decrease on conversion to the FerriM state. However, for Cu ions, the vanishing Cu moments are the best validation of an unusual nonmagnetic Cu 3d8 configuration in the G_AFM state, whereas a gradually decreased spin-down magnetization of Cu emerges in the FerriM state. Therefore, it is interesting to

Figure 8. Spin-state transformation of LaCFO in the low-pressure LaCu3+3Fe3+4O12 phase and high-pressure LaCu2+3Fe3.75+4O12 and LaCu2+3Fe3+5/2Fe5+3/2O12 states. F

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Inorganic Chemistry distributed in LaCFO. As a result, these data tell us the transformation from high spin to low spin is responsible for the charge disproportionation in LaCFO. 3.4. Negative Thermal Expansion Behavior. Experimentally, it has been reported that LaCFO undergoes a temperature-induced negative thermal expansion at the Néel temperature (TN = 393 K),1 accompanied by a phase transition from an antiferromagnetic insulating state at low temperature to a paramagnetic metallic state above the TN. In the present work, we provide a theoretical calculation to verify the thermal behavior by using the PHONOPY code. Once the phonon DOS has been computed, the thermal properties of LaCFO can be evaluated straightforwardly. The specific calculation steps are given below.46 First, the phonon DOS is calculated for several volumes around the equilibrium volume. Subsequently, the total Helmholtz free energies are calculated for these respective volumes with the same temperature ranges and same temperature steps. After the free energies have been calculated, the minimum Helmholtz free energy gives the corresponding optimal volume at the considered temperature; meanwhile, each temperature step corresponds to an optimal volume. Finally, thermal expansion properties can be obtained by using the PHONOPY-QHA script under the quasi-harmonic approximation. We first adopted a series of volumes from the G_AFM ground state to FerriM state of LaCFO to calculate their phonon DOS and estimated the stability of different phases. The absence of an imaginary frequency demonstrates that these phases are stable (see Figure S6 in the Supporting Information). Meanwhile, we also built a basic model of the paramagnetic structure of LaCFO that allowed us to examine its negative thermal expansive character. It is well-known that the paramagnetic structure employs an Im3̅ (No. 204) symmetry; the stable equilibrium volume of paramagnetic LaCFO is obtained by Birch−Murnaghan fitting and examined by phonon spectrum calculations, which are shown in Figure S7 in the Supporting Information. In order to calculate the thermal expansion properties of paramagnetic LaCFO, the optimal volume was compressed and enlarged from 85%V to 115%V, and no phonon imaginary frequency emerged for these different volumes (see Figure S8 in the Supporting Information). The calculated Helmholtz free energy as functions of volumes and temperatures are displayed in Figure 9, in which each black line corresponds to a constant temperature. As can be seen in Figure 9, the simulation, in the temperature range 0−800 K with an interval of 10 K, is divided into two parts with 390 K as the segmentation point, assuming that 390 K is the first-order-type transition temperature (TN) in the present calculations. The first part is in the low-temperature range from 0 to 390 K (see Figure 9a), where both G_AFM and FerriM magnetic structures are presented. The minimum Helmholtz free energies, plotted as blue spheres, correspond to the optimal volumes from 0 to 390 K. The second part is in the hightemperature region from 390 to 800 K (see Figure 9c), in which the paramagnetic phase is simulated and the optimal volumes are indicated as red spheres at each temperature line. Figure 9b presents the incorporation of these optimal volumes in the two graphs. Clearly, the volume gradually increased as the temperature was increased below and above TN. However, an abrupt and drastic reduction in optimal volume at TN appears, presented as a experimentally reported negative thermal expansion like volume contraction. It is interesting

Figure 9. Computed negative thermal expansion properties of LaCFO: (a) Helmholtz free energy as a function of lattice volume in G_AFM and FerriM configurations in the temperature range 0−390 K; (b) change in optimal volumes as the temperature is increased; (c) Helmholtz free energy as a function of lattice volume in the paramagnetic state in the temperature range 390−800 K.

that the slope of the volume curve below TN in the G_AFM configuration is smaller than that of the paramagnetic state above TN. Although the volume is slightly smaller than that reported in previous research because the actual lattice volume depends strongly on the method used to do the counting, the volume slope is similar to that in the literature.1,14 Therefore, the negative thermal expansion properties of LaCFO are confirmed from G_AFM to the paramagnetic configuration at TN in our present work.

4. CONCLUSION For A-site-ordered LaCu3Fe4O12 quadruple perovskite, we first theoretically observed a pressure-driven crystal structural transition from space group Im3̅ (No. 204) to Pn3̅ (No. 201) and a magnetic transformation from the G_AFM ground state to FerriM coupling, which was first found in LaCFO oxide by applying hydrostatic pressure. Essentially, the fundamental reason for the magnetic transition was the change in internal atomic structure, such as metal−oxygen bond lengths and angles, induced by compressing the equilibrium volume continuously. Meanwhile, the magnetic transition from the low-pressure G_AFM configuration to the high-pressure FerriM state initiated an intersite charge transfer between the A-site Cu and B-site Fe ions, which can be expressed as 4Fe3+ + 3Cu3+ → 4Fe3.75+ + 3Cu2+. Interestingly, a charge disproportionation formulated as 8Fe3.75+ → 5Fe3+ + 3Fe5+ came into being when the volume was continuously compressed to less than or equal to 80%V. Actually, the charge disproportionation was attributed to the strong hybridization between Fe 3d and O 2p orbitals in the FerriM state. In addition, the external hydrostatic pressure also impelled a spin flip from the high-spin Fe3+ antiferromagnetically arranged LaCu3+3Fe3+4O12 phase at low pressure to the low-spin ferrimagnetically coupled LaCu2+3Fe3.75+4O12 and LaCu2+3Fe3+5/2Fe5+3/2O12 states at high pressure. Finally, the negative thermal expansion of LaCFO from the G_AFM state to the paramagnetic configuration was examined by phonon calculations. G

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Inorganic Chemistry

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(8) Long, Y. W.; Shimakawa, Y. Intermetallic Charge Transfer between A-Site Cu and B-Site Fe in A-Site-Ordered Double Perovskites. New J. Phys. 2010, 12, 063029−063045. (9) Li, H.; Lv, Sh.; Liu, X.; Meng, J. First-Principles Investigation of A-B Intersite Charge Transfer and Correlated Electrical and Magnetic Properties in BiCu3Fe4O12. J. Comput. Chem. 2011, 32, 1235−1240. (10) Seda, T.; Hearne, G. R. Pressure Induced Fe2+ + Ti4+ → Fe3+ + Ti3+ Intervalence Charge Transfer and the Fe3+/Fe2+ Ratio in Nature Ilmenite (FeTiO3) Minerals. J. Phys.: Condens. Matter 2004, 16, 2707− 2718. (11) Yamada, I.; Takata, K.; Hayashi, N.; Shinohara, S.; Azuma, M.; Mori, S.; Muranaka, S.; Shimakawa, Y.; Takano, M. A Perovskite Containing Quadrivalent Iron as a Charge-Disproportionated Ferrimagnet. Angew. Chem., Int. Ed. 2008, 47, 7032−7035. (12) Yamada, I.; Murakami, M.; Hayashi, N.; Mori, S. Inverse Charge Transfer in the Quadruple Perovskite CaCu3Fe4O12. Inorg. Chem. 2016, 55, 1715−1719. (13) Yamada, I.; Shiro, K.; Etani, H.; Marukawa, S.; Hayashi, N.; Mizumaki, M.; Kusano, Y.; Ueda, S.; Abe, H.; Irifune, T. Valence Transitions in Negative Thermal Expansion Material SrCu3Fe4O12. Inorg. Chem. 2014, 53, 10563−10569. (14) Yamada, I.; Etani, H.; Tsuchida, K.; Marukawa, S.; Hayashi, N.; Kawakami, T.; Mizumaki, M.; Ohgushi, K.; Kusano, Y.; Kim, J.; Tsuji, N.; Takahashi, R.; Nishiyama, N.; Inoue, T.; Irifune, T.; Takano, M. Control of Bond-Strain-Induced Electronic Phase Transition in Iron Perovskites. Inorg. Chem. 2013, 52, 13751−13761. (15) Shimakawa, Y. Crystal and Magnetic Structure of CaCu3Fe4O12 and LaCu3Fe4O12: Distinct Charge Transition of Unusual High Valence Fe. J. Phys. D: Appl. Phys. 2015, 48, 504006−504018. (16) Yamada, I.; Marukawa, S.; Murakami, M.; Mori, S. ″True″ Negavite Thermal Expansion in Mn-Doped LaCu3Fe4O12 Perovskite Oxides. Appl. Phys. Lett. 2014, 105, 231906−231909. (17) Rezaei, N.; Hansmann, P.; Bahramy, M. S.; Arita, R. Mechanism of Charge Transfer/Disproportionation in LnCu3Fe4O12 (Ln = Lanthanides). Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 125125. (18) Long, Y. W.; Kawakami, T.; Chen, W. T.; Saito, T.; Watanuki, T.; Nakakura, Y.; Liu, Q. Q.; Jin, C. Q.; Shimakawa, Y. Pressure Effect on Intersite Charge Transfer in A-Site-Ordered Double-PerovskiteStructure Oxide. Chem. Mater. 2012, 24, 2235−2239. (19) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (20) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758−1775. (21) Kresse, G.; Hafner, J. Abinitio Molecular-Dynamics for LiquidMetals. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558−561. (22) Kresse, G.; Furthmuller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (23) Anisimov, V.; Aryasetiawan, F.; Lichtenstein, A. First-Principles Calculations of the Electronic Structure and Spectra of Strongly Correlated Systems: The LDA+U Method. J. Phys.: Condens. Matter 1997, 9, 767−808. (24) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (25) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron-Energy-Loss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 1505−1509. (26) Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. DensityFunctional Theory and Strong-Interactions - Orbital Ordering in Mott-Hubbard Insulators. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 52, R5467−R5470. (27) Petukhov, A. G.; Mazin, I. I.; Chioncel, L.; Lichtenstein, A. I. Correlated Metals and the LDA+U Method. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 67, 153106. (28) Andersen, O. K. Linear Method in Band Theory. Phys. Rev. B 1975, 12, 3060−3083.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b00458. Calculated total energy of LaCFO with different magnetic structures, electron PDOS of LaCFO from 100%V to 78%V, difference in spin charge density of 80% V in the (010), (110), and (011) crystal planes, total electron DOS of LaCFO from 100%V to 90%V, PDOS for 3d orbitals of Fe and Cu at 100%V and 88%V, phonon DOS of LaCFO from 100% to 78%V, Birch− Murnaghan fitting curves and phonon spectrum for the paramagnetic structure of LaCFO, phonon DOS of paramagnetic LaCFO, and total energies of LaCFO from 100%V to 78%V at different magnetic structures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*X.L.: tel, +86-431-85262415; fax, +86-431-85698041; e-mail, [email protected]. ORCID

Xiaojuan Liu: 0000-0002-1232-5043 Hongjie Zhang: 0000-0001-5433-8611 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China under grant nos. 21571174, 51372244, and 21521092, the Major Program of the National Natural Science Foundation of China under grant no. 21590794, and a Project Funded by the China Postdoctoral Science Foundation under grant no. 2016LH00025.

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REFERENCES

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