Pressure-Induced Restoration of the Reversed Crystal-Field Splitting in α -Sr 2 CrO 4
Ryo Takahashi, Tomoki Yamaguchi, Koudai Sugimoto, Touru Yamauchi, Hiroya Sakurai, Yukinori Ohta
aa r X i v : . [ c ond - m a t . s t r- e l ] F e b Pressure-Induced Restoration of the ReversedCrystal-Field Splitting in α -Sr CrO Ryo
Takahashi , Tomoki Yamaguchi , Koudai Sugimoto , , Touru Yamauchi , Hiroya Sakurai , and Yukinori Ohta Department of Physics, Chiba University, Chiba 263-8522 , Japan Center for Frontier Science, Chiba University, Chiba 263-8522, Japan Department of Physics , Keio University, Yokohama 223-8522, Japan Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan National Institute for Materials Science, Tsukuba 305-0044, JapanE-mail: [email protected] (Received August 29, 2019)Motivated by an experimental finding that the successive phase transitions in α -Sr CrO observed at ambient pressure ceases to exist under high pressures, we carry out the density-functional-theory-based electronic structure calculations and demonstrate that the reversalof the crystal-field splitting reported previously is restored under high pressures, so that theorbital degrees of freedom disappears, resulting in the single phase transition that dividesthe system into high-temperature Mott insulating and low-temperature antiferromagneticinsulating phases. KEYWORDS: Sr CrO , crystal field splitting, orbital ordering, pressure effect
1. Introduction
The orbital degrees of freedom in transition-metal compounds have long been one of themajor themes in the physics of strongly correlated electron systems [1]. One of the recentexamples is the origin of successive phase transitions observed in a layered perovskite α -Sr CrO [2]. This material is a Mott insulator, having the K NiF -type crystal structure withCrO octahedra elongated along the c -axis of the lattice and with a 3 d electron configuration[3, 4]. Therefore, one would naturally expect that two electrons occupy the lowest doublydegenerate t g orbitals forming an S = 1 spin due to Hund’s rule coupling, so that onlythe antiferromagnetic N´eel ordering of S = 1 spins occurs below the N´eel temperature T N ,without any orbital ordering. However, a recent experimental study [2] revealed that twophase transitions occur successively at 112 and 140 K, releasing nearly the same amountof entropy. The lower-temperature phase transition (denoted as T N ) was ascribed to N´eelordering by magnetic measurement, but the cause of the higher-temperature one (denotedas T S ) remained a mystery from the experiment [2, 5, 6].Then, using the density-functional-theory (DFT) based electronic structure calculations,Ishikawa et al. [7] have shown that the crystal field level of nondegenerate 3 d xy orbitals of r ion is in fact lower in energy than that of doubly degenerate 3 d yz and 3 d xz orbitals,giving rise to the orbital degrees of freedom in the system with a 3 d electron configuration.Thereby, they have argued that the higher (lower) temperature phase transition is causedby the ordering of the orbital (spin) degrees of freedom of the system. Because the CrO octahedron is elongated along the c -axis of the crystal structure, this result offers a rareexample of the reversal of the crystal-field splitting in transition-metal compounds.A natural question that arises in this respect would then be what occurs if externalpressures are applied to this system. Recently, Yamauchi et al. [8] reported that the suc-cessive phase transitions disappear at a high pressure above a few GPa, leaving only onephase transition that divides the system into two phases, a high-temperature paramagneticinsulating phase and a low-temperature antiferromagnetic insulating phase. This result canreadily be understood if we assume that the reversal of the crystal-field splitting ceases tooccur under high pressures, so that the lowest doubly degenerate t g orbitals are occupiedby two electrons, forming an S = 1 spin due to Hund’s rule coupling, which leads to theantiferromagnetic N´eel ordering of S = 1 spins at T N , without any orbital ordering.In this paper, to check the validity of this assumption, we apply the DFT-based electronicstructure calculations using the generalized gradient approximation (GGA); in particular, weuse the GGA+ U method for a better description of electron correlations. We thus show thatthe reversed crystal-field splitting in α -Sr CrO is actually restored under high pressures,resulting in the elimination of the orbital degrees of freedom of the system.
2. Computational details
We employ the WIEN2k code [9] based on the full-potential linearized augmented-plane-wave method for our DFT calculations. Here, we present results obtained in the GGA forelectron correlations using the exchange-correlation potential of Ref. [10]. To improve thedescription of electron correlations in the Cr 3 d orbitals, we also use the rotationally invariantversion of the GGA+ U method with the double-counting correction in the fully localizedlimit [11, 12]. In particular, we examine the U dependence of the crystal-field splitting. Thespin polarization is not allowed in the present calculations. The spin-orbit interaction isnot taken into account. We use the crystal structure measured at high pressures [8], whichhas the tetragonal symmetry (space group I /mmm ) with one (two) crystallographicallyinequivalent Cr (O) ions, but we apply the local structural relaxations keeping the measuredlattice constants unchanged. We assume the high-temperature metallic phase, allowing for noantiferromagnetic spin polarizations. In the self-consistent calculations, we use 99 k -points inthe irreducible part of the Brillouin zone. Muffin-tin radii ( R MT ) of ∼ ∼ ∼ K max = 8 . /R MT is assumed.
3. Results of calculation
The calculated energy dispersions of the three bands near the Fermi level are fitted bythe tight-binding bands of the three molecular orbitals obtained as the maximally localizedWannier functions [13, 14]. The energy-level splittings of the maximally localized Wannier = 3 eV U = 2 eV U = 1 eV U = 0 eV Fig. 1.
Calculated splitting ∆ E xy − yz = E ( d xy ) − E ( d yz ) of the energy levels of the maximallylocalized Wannier orbitals as a function of applied pressure P , where several U values are assumed inthe GGA+ U calculations. orbitals are thus determined as a function of the applied pressure.Then, our calculated results for the crystal-field splitting are given in Fig. 1, where wepresent the pressure dependence of the difference in the energy levels between the nonde-generate 3 d xy orbital and the doubly degenerate 3 d yz and 3 d xz orbitals of a Cr ion, i.e.,∆ E xy − yz = E ( d xy ) − E ( d yz ). Here, we first confirm that the reversal of the crystal-field split-ting, E ( d xy ) < E ( d yz ) = E ( d xz ), actually occurs at ambient pressure, as was found in Ref. [7].Then, under high pressures P & E ( d xy ) > E ( d yz ) = E ( d xz ), in particular when we assume the standard valueof U = 3 eV for Cr ion. We should note that the restoration of the reversed crystal-fieldsplitting occurs only for larger values of U ( & U is essential. Thus, the effectof strong electron correlations is suggested to be important in α -Sr CrO , as was noticed inRef. [7]. More precisely, the repulsive interaction U in the GGA+ U type of approximationsin general works to lower (raise) the energy of the occupied (unoccupied) orbitals [12, 15]. Inthe present case, the interaction U works to stabilize the state where the doubly degenerateorbitals ( d yz and d xz ) are occupied by two electrons, in comparison with the state where thenondegenerate d xy orbital is occupied by two electrons.Thus, we have shown that the reversed crystal-field splitting in α -Sr CrO is actuallyrestored under high pressures, resulting in the elimination of the orbital degrees of free-dom of the system, which naturally leads to the single phase transition that divides thesystem into two phases, a high-temperature paramagnetic Mott insulating phase and a low-temperature antiferromagnetic insulating phase, in agreement with experiment [8]. Note that,in the present calculation, the paramagnetic metallic state without antiferromagnetic spinpolarization is assumed for extracting the values of the crystal-field splitting because theparamagnetic Mott insulating state cannot be obtained in the GGA+ U type of calculations. owever, the present assumption is usually sufficient for extracting the values because theyare not strongly affected by the spin polarization of the system [7].
4. Summary
In our previous paper [7], we have shown that the successive phase transitions observed ina layered perovskite α -Sr CrO at ambient pressure are ascribed to the active orbital degreesof freedom of the system caused by the reversal of the crystal-field splitting of the system.However, a recent high-pressure experiment [8] has shown that the successive phase transi-tions disappear under high pressures, leaving only one phase transition dividing the systeminto two phases, a high-temperature paramagnetic insulating phase and a low-temperatureantiferromagnetic insulating phase.Motivated by this experimental finding, we have made the DFT-based electronic structurecalculations for α -Sr CrO under high pressures in the GGA+ U method and have demon-strated that the reversal of the crystal-field splitting is actually restored under high pressures,so that the orbital degrees of freedom of this system disappears, resulting in the single anti-ferromagnetic phase transition.Our result for α -Sr CrO on the one hand provides an interesting example of the pressureeffects in strongly-correlated transition-metal compounds, but on the other hand reinforcesthe idea that the reversal of the crystal-field splitting found in α -Sr CrO is a rare and fragilephenomenon easily destroyed by the external perturbation. Acknowledgments
This work was supported in part by Grants-in-Aid for Scientific Research from JSPS (ProjectsNo. JP17K05521, No. JP17K05530, No. JP19K14644, and No. JP19J10805), by a JST MiraiProgram (JPMJMI18A3), and by Keio University Academic Development Funds for Individ-ual Research.
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