Andrzej M. Oleś

Fingerprints of spin-orbital entanglement in transition metal oxides.

The concept of spin-orbital entanglement on superexchange bonds in transition metal oxides is introduced and explained on several examples. It is shown that spin-orbital entanglement in superexchange models destabilizes the long-range (spin and orbital) order and may lead either to a disordered spin-liquid state or to novel phases at low temperature which arise from strongly frustrated interactions. Such novel ground states cannot be described within the conventionally used mean field theory which separates spin and orbital degrees of freedom. Even in cases where the ground states are disentangled, spin-orbital entanglement occurs in excited states and may become crucial for a correct description of physical properties at finite temperature. As an important example of this behaviour we present spin-orbital entanglement in the RV O(3) perovskites, with R = La,Pr,…,Y b,Lu, where the finite temperature properties of these compounds can be understood only using entangled states: (i) the thermal evolution of the optical spectral weights, (ii) the dependence of the transition temperatures for the onset of orbital and magnetic order on the ionic radius in the phase diagram of the RV O(3) perovskites, and (iii) the dimerization observed in the magnon spectra for the C-type antiferromagnetic phase of Y V O(3). Finally, it is shown that joint spin-orbital excitations in an ordered phase with coexisting antiferromagnetic and alternating orbital order introduce topological constraints for the hole propagation and will thus radically modify the transport properties in doped Mott insulators where hole motion implies simultaneous spin and orbital excitations.

Mechanism of the Verwey transition in magnetite.

By combining ab initio results for the electronic structure and phonon spectrum with the group theory, we establish the origin of the Verwey transition in Fe3O4. Two primary order parameters with X3 and Delta5 symmetries are identified. They induce the phase transformation from the high-temperature cubic to the low-temperature monoclinic structure. The on-site Coulomb interaction U between 3d electrons at Fe ions plays a crucial role in this transition--it amplifies the coupling of phonons to conduction electrons and thus opens a gap at the Fermi energy.

Spin-orbital entanglement and violation of the Goodenough-Kanamori rules.

We point out that large composite spin-orbital fluctuations in Mott insulators with t(2g) orbital degeneracy are a manifestation of quantum entanglement of spin and orbital variables. This results in a dynamical nature of the spin superexchange interactions, which fluctuate over positive and negative values, and leads to an apparent violation of the Goodenough-Kanamori rules.

Thermally activated Peierls dimerization in ferromagnetic spin chains

We demonstrate that a Peierls dimerization can occur in ferromagnetic spin chains activated by thermal fluctuations. The dimer order parameter and entanglement measures are studied as functions of the modulation of the magnetic exchange interaction and temperature, using a spin-wave theory and the density-matrix renormalization group. We discuss the case where a periodic modulation is caused by spin-phonon coupling and the case where electronic states effectively induce such a modulation. The importance of the latter for a number of transition metal oxides is highlighted.

Anharmonicity due to Electron-Phonon Coupling in Magnetite

We present the results of inelastic x-ray scattering for magnetite and analyze the energies and widths of the phonon modes with different symmetries in a broad range of temperature 125 < T < 293 K. The phonon modes with X(4) and Δ(5) symmetries broaden in a nonlinear way with decreasing T when the Verwey transition is approached. It is found that the maxima of phonon widths occur away from high-symmetry points, which suggests the incommensurate character of critical fluctuations. Strong phonon anharmonicity induced by electron-phonon coupling is discovered by a combination of these experimental results with ab initio calculations which take into account local Coulomb interactions at Fe ions. It (i) explains observed anomalous phonon broadening and (ii) demonstrates that the Verwey transition is a cooperative phenomenon which involves a wide spectrum of phonons coupled to the electron charge fluctuations condensing in the low-symmetry phase.

Absence of hole confinement in transition-metal oxides with orbital degeneracy.

We investigate the spectral properties of a hole moving in a two-dimensional Hubbard model for strongly correlated t(2g) electrons. Although superexchange interactions are Ising-like, a quasi-one-dimensional coherent hole motion arises due to effective three-site terms. This mechanism is fundamentally different from the hole motion via quantum fluctuations in the conventional spin model with SU(2) symmetry. The orbital model describes also propagation of a hole in some e(g) compounds, and we argue that orbital degeneracy alone does not lead to hole self-localization.

Noncollinear magnetic order stabilized by entangled spin-orbital fluctuations.

Quantum phase transitions in the two-dimensional Kugel-Khomskii model on a square lattice are studied using the plaquette mean field theory and the entanglement renormalization Ansatz. When 3z(2)-r(2) orbitals are favored by the crystal field and Hunds exchange is finite, both methods give a noncollinear exotic magnetic order that consists of four sublattices with mutually orthogonal nearest-neighbor and antiferromagnetic second-neighbor spins. We derive an effective frustrated spin model with second- and third-neighbor spin interactions which stabilize this phase and follow from spin-orbital quantum fluctuations involving spin singlets entangled with orbital excitations.

Magnetic properties of nanoscale compass-Heisenberg planar clusters

We study a model of spins 1/2 on a square lattice, generalizing the quantum compass model via the addition of perturbing Heisenberg interactions between nearest neighbors, and investigate its phase diagram and magnetic excitations. This model has motivations both from the field of strongly correlated systems with orbital degeneracy and from that of solid-state based devices proposed for quantum computing. We find that the high degeneracy of ground states of the compass model is fragile and changes into twofold degenerate ground states for any finite amplitude of Heisenberg coupling. By computing the spin structure factors of finite clusters with Lanczos diagonalization, we evidence a rich variety of phases characterized by Z2 symmetry, that are either ferromagnetic, C-type antiferromagnetic, or of Neel type, and analyze the effects of quantum fluctuations on phase boundaries. In the ordered phases the anisotropy of compass interactions leads to a finite excitation gap to spin waves. We show that for small nanoscale clusters with large anisotropy gap the lowest excitations are column-flip excitations that emerge due to Heisenberg perturbations from the manifold of degenerate ground states of the compass model. We derive an effective one-dimensional XYZ model which faithfully reproduces the exact structure of these excited states and elucidates their microscopic origin. The low energy column-flip or compass-type excitations are robust against decoherence processes and are therefore well designed for storing information in quantum computing. We also point out that the dipolar interactions between nitrogen-vacancy centers forming a rectangular lattice in a diamond matrix may permit a solid-state realization of the anisotropic compass-Heisenberg model.

Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects

We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: Neel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.

Short-Range Correlations in Magnetite above the Verwey Temperature

Magnetite, Fe