Quantum melting of magnetic long-range order near orbital degeneracy: Classical phases and Gaussian fluctuations

Abstract

We address the role played by orbital degeneracy in strongly correlated transition-metal compounds. Specifically, we study the effective spin-orbital model derived for the d 9 ions in a three-dimensional perovskite lattice, as in KCuF 3 , where at each site the doubly degenerate e g orbitals contain a single hole. The model describes the superexchange interactions that depend on the pattern of orbitals occupied and shows a nontrivial coupling between spin and orbital variables at nearest-neighbor sites. We present the ground-state properties of this model, depending on the splitting between the e g orbitals E z , and the Hund's rule coupling in the excited d 8 states, J H . The classical phase diagram consists of six magnetic phases which all have different orbital ordering: two antiferromagnetic ͑AF͒ phases with G-AF order and either x 2 Ϫy 2 or 3z 2 Ϫr 2 orbitals occupied, two phases with mixed orbital ͑MO͒ patterns and A-AF order, and two other MO phases with either C-AF or G-AF order. All of them become degenerate at the multicritical point M ϵ(E z ,J H )ϭ(0,0). Using a generalization of linear spin-wave theory we study both the transverse excitations which are spin waves and spin-andorbital waves, as well as the longitudinal ͑orbital͒ excitations. The transverse modes couple to each other, providing a possibility of measuring the new spin-and-orbital excitations in inelastic neutron spectroscopy. As the latter excitation turns into a soft mode near the M point, quantum corrections to the long-range-order parameter are drastically increased near the orbital degeneracy, and classical order is suppressed in a crossover regime between the G-AF and A-AF phases in the (E z ,J H ) plane. This behavior is reminiscent of that found in frustrated spin models, and we conclude that orbital degeneracy provides a different and physically realizable mechanism which stabilizes a spin liquid ground state due to inherent frustration of magnetic interactions. We also point out that such a disordered magnetic phase is likely to be realized at low J H and low electronphonon coupling, as in LiNiO 2 . I. NOVEL MECHANISM OF FRUSTRATION NEAR ORBITAL DEGENERACYQuite generally, strongly correlated electron systems involve orbitally degenerate states, 1 such as 3d(4d) states in transition metal compounds, and 4 f (5 f ) states in rare-earth compounds. Yet, the orbital degrees of freedom are ignored in most situations and the common approach is to consider a single correlated orbital per atom which leads to spin degeneracy alone. Indeed, most of the current studies of strongly correlated electrons deal with models of nondegenerate orbitals. The problems discussed recently include mechanisms of ferromagnetism in the Hubbard model, 2 hole propagation and quasiparticles in the t-J model, 3 and magnetic states of the Kondo lattice.4 Of course, in many actually existing compounds the orbital degeneracy is removed by the crystal field, and a single-orbital approach is valid per se. Also, from a fundamental point of view it is often possible ...

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.…”

“…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.…”

Orbital ordering and orbital fluctuations in transition metal oxides

“…However, in real eg systems such quantum phenomena are usually quenched by finite JH which induces a structural phase transition and thus helps to stabilize a particular ordering of occupied orbitals which supports A-type AF order, as observed when degenerate orbitals are filled either by one hole (KCuF3) [9], or by one electron (LaMnO3) [10]. The coupling to the lattice due to the Jahn-Teller (JT) effect also helps to stabilize the orbital ordering, and quantitative models of the structural transition have to include both these effects [10].…”

“…It is important to use the accurate form of the electron-electron interactions [5,9], and for this reason some early work led to inaccurate expressions [4,6]. Note that spin interactions have SU(2) symmetry, while the orbital interactions are anisotropic.…”

“…1(a)], with the excitation energies derived from Eq. (1): ε( 3 A2) = U − 3JH , ε( 1 E) = U − JH , and ε( 1 A1) = U + JH [9]. The SE Hamiltonian derived from Eq.…”