Spin Order due to Orbital Fluctuations: Cubic Vanadates

Abstract

We investigate the highly frustrated spin and orbital superexchange interactions in cubic vanadates. The fluctuations of t2g orbitals trigger a novel mechanism of ferromagnetic interactions between spins S = 1 of V 3+ ions along one of the cubic directions which operates already in the absence of Hund's rule exchange JH , and leads to the C-type antiferromagnetic phase in LaVO3. The Jahn-Teller effect can stabilize the orbital ordering and the G-type antiferromagnetic phase at low temperatures, but large entropy due to orbital fluctuations favors again the C-phase at higher temperatures, as observed in YVO3.PACS numbers: 75.30. Vn, 71.27.+a, 75.30.Et, Large Coulomb interactions play a crucial role in transition metal oxides, and are responsible for the collective behavior of strongly correlated d electrons which localize in Mott-Hubbard (or charge-transfer) insulators [1]. Such localized electrons may occupy degenerate orbital states which makes it necessary to consider orbital degrees of freedom at equal footing with electron spins, and leads to the effective (superexchange) spin-orbital models to describe the low-energy physics [2][3][4]. A remarkable feature of these models is that the superexchange interaction is highly frustrated on a cubic lattice, which was recognized as the origin of novel quantum effects in transition metal oxides [5]. In case of e g orbital systems this frustration is likely removed by orbital order due to order-out-ofdisorder mechanism, which maximizes the energy gain from quantum spin fluctuations [6]. Moreover, quantum effects among e g orbitals are largely suppressed by the Jahn-Teller (JT) effect in real systems, which together with superexchange often leads to structural phase transitions accompanied by a certain ordering of occupied orbitals, supporting particular magnetic structures. Some well known examples are systems with degenerate e g orbitals filled either by one hole (KCuF 3 ), or by one electron (LaMnO 3 ), which order antiferromagnetically well below the structural transition.The transition metal oxides with partly filled t 2g orbitals exhibit different and more interesting phenomena. This occurs due to the relative weakness of the JT coupling in this case, and due to the higher degeneracy and additional symmetry of t 2g orbitals [7]. As a result, the orbitals may form the coherent orbital-liquid ground state stabilized by quantum effects, as observed in the spin S = 1/2 Mott-insulator LaTiO 3 [8]. It is puzzling what happens when the t 2g orbitals are filled by two electrons, as in vanadium oxides. On one hand, the occupied t 2g orbitals are known to order in non-cubic vanadium compounds, such as LiVO 2 [9] and V 2 O 3 [10]. In fact, the first spin-orbital model for V 2 O 3 with spins s = 1/2 was proposed over twenty years ago [11], but later it was realized that J H at V 3+ (d 2 ) ions is large [12], and the relevant model has to involve S = 1 spins [10]. On the other hand, the situation in cubic systems might be very different as all the bonds are a priori magnetica...

Fingerprints of spin-orbital physics in cubic Mott insulators: Magnetic exchange interactions and optical spectral weights

“…6 At orbital degeneracy the superexchange interactions have a rather rich structure, represented by the so-called spin-orbital models, discovered three decades ago, 7,8 and extensively studied in recent years. [9][10][11][12][13][14][15][16][17][18] Although this field is already quite mature, and the first textbooks have already appeared, 3,4,19 it has been realized only recently that the magnetic and the optical properties of such correlated insulators with partly filled d orbitals are intimately related to each other, being just different experimental manifestations of the same underlying spin-orbital physics. 20,21 While it is clear that the low-energy effective superexchange Hamiltonian decides about the magnetic interactions, it is not immediately obvious that the high-energy optical excitations and their partial sum rules have the same roots and may be described by the superexchange as well.…”

“…91 Here we shall consider in more detail G-type OO, relevant for the case of LaVO 3 . We will show in particular that the superexchange spin-orbital model 16 allows one to understand the microscopic reasons behind the C-AF phase observed in LaVO 3 , and predicts that ͉J c ͉ϳJ ab , as actually observed. 92 The comparable size of FM and AF exchange constants J c and J ab , respectively, is unexpected when considering the Goodenough-KanamoriAnderson rules, 34 which would suggest that ͉J c ͉ is by a factor J H / U smaller.…”

“…9-11͒ and for t 2g systems. 15,16 This frustration is partly removed in anisotropic AF phases, which break the cubic symmetry and effectively may lead to dimensionality changes, such as in A-type AF phase realized in LaMnO 3 , or in C-type AF phase in LaVO 3 .…”

“…The spin-orbital models have been derived before in several cases, and we refer for these derivations to the original literature. 11,13,15,16 6 at U ӷ t-thus the resulting superexchange interactions will be called U terms. The essential difference which makes it necessary to analyze the excitation energies in each case separately is caused by the existence of several different excitations.…”

“…͑5.3͒ and Table I͔. 39 The excitation spectrum which leads to the superexchange model includes three states: 16 ͑i͒ a highspin state 4 A 2 at energy U −3J H , ͑ii͒ two degenerate low-spin states 2 T 1 and 2 E at energy U, and ͑iii͒ a 2 T 2 low-spin state at energy U +2J H ͑Fig. 1͒.…”