The origin of successive phase transitions observed in the layered perovskite α-Sr2CrO4 is studied by the density-functional-theory-based electronic structure calculation and mean-field analysis of the proposed low-energy effective model. We find that, despite the fact that the CrO6 octahedron is elongated along the c-axis of the crystal structure, the crystal-field level of nondegenerate 3dxy orbitals of the Cr ion is lower in energy than that of doubly degenerate 3dyz and 3dxz orbitals, giving rise to the orbital degrees of freedom in the system with a 3d 2 electron configuration. We show that the higher (lower) temperature phase transition is caused by the ordering of the orbital (spin) degrees of freedom.The orbital degrees of freedom in transition-metal compounds have long been one of the major themes in the physics of strongly correlated electron systems.
1-3)The simplest example is the cubic perovskite structure, where the transition-metal ion surrounded by six ligand ions forms an octahedron and the corresponding crystal field splits the energy levels of the five d orbitals into triply degenerate t 2g orbitals and doubly degenerate e g orbitals. Moreover, in a layered perovskite with the K 2 NiF 4 -type crystal structure, the octahedron is elongated along the c-axis and the triply degenerate t 2g levels further split into low-energy doubly degenerate d xz and d yz orbitals and the high-energy nondegenerate d xy orbital.4) No one would have doubted this simple law of the crystal field theory.In this paper, we show that a serious deviation from this simple law occurs in the Mott insulator α-Sr 2 CrO 4 . This material has the K 2 NiF 4 -type crystal structure with CrO 6 octahedra elongated along the c-axis and with a 3d 2 electron configuration. 5, 6) Therefore, one would naturally expect that two electrons occupy the lowest doubly degenerate t 2g orbitals forming an S = 1 spin due to Hund's rule coupling, so that only the antiferromagnetic Néel ordering of S = 1 spins occurs at the Néel temperature T N , without any orbital ordering.6) Surprisingly, however, a recent experimental study 7) revealed that two phase transitions occur successively at 112 and 140 K, releasing nearly the same amount of entropy. The lower-temperature phase transition was ascribed to Néel ordering by magnetic measurement, but the cause of the higher-temperature one (denoted as T S ) remains a mystery from the experiment.
7, 8)In what follows, using the density-functional-theory (DFT)-based electronic structure calculations, we will * ohta@faculty. chiba-u.jp show that, in α-Sr 2 CrO 4 , the crystal-field level of nondegenerate 3d xy orbitals of the Cr ion is in fact lower in energy than that of doubly degenerate 3d yz and 3d xz orbitals. Therefore, in this system with the 3d 2 electron configuration, the orbital degrees of freedom are indeed active. More precisely, this system can be modeled as the Kugel-Khomskii-type spin-orbital subsystem 9,10) consisting of the d xz and d yz orbitals of the Cr ion, which couples to the antife...