Quantum Melting of Magnetic Order due to Orbital Fluctuations

Abstract

We have studied the phase diagram and excitations of the spin-orbital model derived for a three-dimensional perovskite lattice, as in KCuF 3 . The results demonstrate that the orbital degeneracy drastically increases quantum fluctuations and suppresses the classical long-range order near the multicritical point in the mean-field phase diagram. This indicates the presence of a quantum liquid state, and we present explicit evidence for valence bond type correlations in three dimensions. [S0031-9007(97)02824-X] PACS numbers: 71.27.+a, 75.30.Et It is common knowledge that macroscopic ensembles of interacting particles tend to behave classically. This is not always true, however, and the study of collective quantum systems starts to become a prominent theme in condensed matter physics. Central to this pursuit are low-dimensional quantum spin systems (spin chains and ladders [1]), and it proves difficult to achieve quantum melting of magnetic long-range order (LRO) in empirically relevant systems in higher dimensions. Here we suggest a class of systems in which quantum melting occurs even in three dimensions: small spin, orbital degenerate magnetic insulators, and the so-called KugelKhomskii (KK) systems [2]. There might already exist a physical realization of such a three-dimensional (3D) "quantum spin-orbital liquid": LiNiO 2 .Global SU͑2͒ by itself is not symmetric enough to defeat classical order in D . 1, and the pursuit has been open for some time to engineer more fluctuations into these systems. Three (related) strategies to realize quantum melting have proven to be successful: (i) adding zero-dimensional fluctuations as in the bilayer Heisenberg model which leads to an incompressible spin liquid [3,4], (ii) frustrating the system so that the classical sector gets highly degenerate, as in the case of the S 1͞2 square lattice with longer ranged antiferromagnetic (AF) interactions (J 1 -J 2 -J 3 models [5,6]). These systems involve fine-tuning of parameters and are therefore hard to realize by chemistry. (iii) Finally, the third strategy would be to reduce the number of magnetic bonds, as in the 1͞5-depleted square lattice, where the resulting plaquette resonating valence bond (PRVB) state explains the spin gap observed in CaV 4 O 9 [7]. In this Letter we show that orbital degeneracy operates through the same basic mechanisms to produce quantum melting in the KK systems. The novelty is that these systems tend to "self-tune" to (critical) points of high classical degeneracy. There are interactions which may lift the classical degeneracy, but they are usually weak.An interaction of this kind is the electron-phonon coupling-the degeneracy is lifted by a change in crystal structure, the conventional collective Jahn-Teller (JT) instability. However, as was pointed out in the seminal work by Kugel and Khomskii [2], in orbital degenerate Mott-Hubbard insulators one has to consider in the first instance the purely electronic problem. Because of the large local Coulomb interactions (Hubbard U), a low energy Hilbert spa...

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

“…We formulated a general approach to the spectral weights in optical spectroscopy and illustrated it on several examples with different multiplet structure. While a general feature of all the superexchange spin-orbital models is a tendency towards enhanced quantum fluctuations, 9,15 we gave reasons why in many situations such fluctuations are quenched. One then arrives at much simpler reduced models, where certain states with OO allow for a good insight into the mechanisms responsible for the magnetic interactions and for the 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.…”

Orbital ordering and orbital fluctuations in transition metal oxides

“…An interesting situation occurs when d electrons occupy partly degenerate orbital states, and one has to consider orbital degrees of freedom in the SE at equal footing with electron spins [1]. Competition between different states is then possible, holes may couple to orbital excitations [2], and the quantum effects are enhanced already in undoped systems [3]. The first models of SE in such situations were proposed almost three decades ago [4], either by considering the degenerate Hubbard model [5,6], or for realistic situations encountered in cuprates (KCuF3 and K2CuF4) and in V2O3 [7].…”

“…The first models of SE in such situations were proposed almost three decades ago [4], either by considering the degenerate Hubbard model [5,6], or for realistic situations encountered in cuprates (KCuF3 and K2CuF4) and in V2O3 [7]. Then it was realized that the SE which is usually antiferromagnetic (AF) might become ferromagnetic (FM) when Hund's exchange interaction JH is finite, but only in recent years the phenomena which originate from the orbital physics are investigated in a more systematic way.The SE which involves the orbital degrees of freedom is described by the so-called spinorbital models [8], and is typically highly frustrated on a cubic lattice where it might even lead to the collapse of magnetic long-range order by strong spin or orbital fluctuations [3]. 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].…”

Spin–orbital entanglement near quantum phase transitions

“…Status Solidi (b) 244, 2378-2383 (2007 Copyright line will be provided by the publisher Rich magnetic phase diagrams of transition metal oxides and the existence of quite complex magnetic order with coexisting ferromagnetic (FM) and antiferromagnetic (AF) interactions, such as A-AF phase in LaMnO 3 or C-AF phase in LaVO 3 , originate from the intricate interplay between spin and orbital degrees of freedom -alternating orbital (AO) order supports FM interactions, whereas ferro orbital (FO) order supports AF ones [1]. While in many cases the spin and orbital dynamics are independent from each other and such classical concepts apply, the quantum fluctuations are a priori enhanced due to a potential possibility of joint spin-orbital fluctuations, particularly in the vicinity of quantum phase transitions [2]. Such fluctuations are even much stronger in t 2g than in e g systems and may dominate the magnetic and orbital correlations [3], which could then contradict the above classical expectations in certain regimes of parameters.…”