Order from disorder: Quantum spin gap in magnon spectra of LaTiO_3

A theory of the anisotropic superexchange and low energy spin excitations in a Mott insulator with t_{2g} orbital degeneracy is presented. We observe that the spin-orbit coupling induces frustrating Ising-like anisotropy terms in the spin Hamiltonian, which invalidate noninteracting spin wave theory. The frustration of classical states is resolved by an order from disorder mechanism, which selects a particular direction of the staggered moment and generates a quantum spin gap. The theory explains well the observed magnon gaps in LaTiO_3. As a test case, a specific prediction is made on the splitting of magnon branches at certain momentum directions.Comment: 5 pages, 2 figures, final versio

Entropy Driven Dimerization in a One-Dimensional Spin-Orbital Model

We study a new version of the one-dimensional spin-orbital model with spins S=1 relevant to cubic vanadates. At small Hund's coupling J_H we discover dimerization in a pure electronic system solely due to a dynamical spin-orbital coupling. Above a critical value J_H, a uniform ferromagnetic state is stabilized at zero temperature. More surprisingly, we observe a temperature driven dimerization of the ferrochain, which occurs due to a large entropy released by dimer states. This dynamical dimerization seems to be the mechanism driving the peculiar intermediate phase of YVO_3.Comment: 5 pages, 4 figure

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. [{\it Published in Phys. Rev. Lett. {\bf 96}, 147205 (2006).}]Comment: 4 pages, 2 figure

Orbital liquid in three dimensional Mott insulator: LaTiO3LaTiO_3

We present a theory of spin and orbital states in Mott insulator $LaTiO_3$. The spin-orbital superexchange interaction between $d^1(t_{2g})$ ions in cubic crystal suffers from a pathological degeneracy of orbital states at classical level. Quantum effects remove this degeneracy and result in the formation of the coherent ground state, in which the orbital moment of $t_{2g}$ level is fully quenched. We find a finite gap for orbital excitations. Such a disordered state of local degrees of freedom on unfrustrated, simple cubic lattice is highly unusual. Orbital liquid state naturally explains observed anomalies of $LaTiO_3$.Comment: 5 pages, 3 figure

Spin-orbital excitation continuum and anomalous electron-phonon interaction in the Mott insulator LaTiO3_3

Raman scattering experiments on stoichiometric, Mott-insulating LaTiO$_3$ over a wide range of excitation energies reveal a broad electronic continuum which is featureless in the paramagnetic state, but develops a gap of $\sim 800$ cm$^{-1}$ upon cooling below the N\'eel temperature $T_N = 146$ K. In the antiferromagnetic state, the spectral weight below the gap is transferred to well-defined spectral features due to spin and orbital excitations. Low-energy phonons exhibit pronounced Fano anomalies indicative of strong interaction with the electron system for $T > T_N$, but become sharp and symmetric for $T < T_N$. The electronic continuum and the marked renormalization of the phonon lifetime by the onset of magnetic order are highly unusual for Mott insulators and indicate liquid-like correlations between spins and orbitals.Comment: to appear in Phys. Rev. Let

Theory of orbital state and spin interactions in ferromagnetic titanates

A spin-orbital superexchange Hamiltonian in a Mott insulator with $t_{2g}$ orbital degeneracy is investigated. More specifically, we focus on a spin ferromagnetic state of the model and study a collective behavior of orbital angular momentum. Orbital order in the model occurs in a nontrivial way -- it is stabilized exclusively by quantum effects through the order-from-disorder mechanism. Several energetically equivalent orbital orderings are identified. Some of them are specified by a quadrupole ordering and have no unquenched angular momentum at low energy. Other states correspond to a noncollinear ordering of the orbital angular momentum and show the magnetic Bragg peaks at specific positions. Order parameters are unusually small because of strong quantum fluctuations. Orbital contribution to the resonant x-ray scattering is discussed. The dynamical magnetic structure factor in different ordered states is calculated. Predictions made should help to observe elementary excitations of orbitals and also to identify the type of the orbital order in ferromagnetic titanates. Including further a relativistic spin-orbital coupling, we derive an effective low-energy spin Hamiltonian and calculate a spin-wave spectrum, which is in good agreement with recent experimental observations in YTiO$_3$.Comment: 25 pages, 17 figure

Impurity-induced spin polarization and NMR line broadening in underdoped cuprates

We present a theory of magnetic (S=1) Ni and nonmagnetic Zn impurities in underdoped cuprates. Both types of impurities are shown to induce S=1/2 moments on Cu sites in the proximity of the impurity, a process which is intimately related to the spin gap phenomenon in cuprates. Below a characteristic Kondo temperature, the Ni spin is partially screened by the Cu moments, resulting in an effective impurity spin S=1/2. We further analyze the Ruderman-Kittel-Kasiya-Yosida-type response of planar Cu spins to a polarization of the effective impurity moments and derive expressions for the corresponding ^{17}O NMR line broadening. The peculiar aspects of recent experimental NMR data can be traced back to different spatial characteristics of Ni and Zn moments as well as to an inherent temperature dependence of local antiferromagnetic correlations.Comment: PRB B1 01June9

One-dimensional orbital fluctuations and the exotic magnetic properties of YVO3_3

Starting from the Mott insulator picture for cubic vanadates, we derive and investigate the model of superexchange interactions between V$^{3+}$ ions, with nearly degenerate $t_{2g}$ orbitals occupied by two electrons each. The superexchange interactions are strongly frustrated and demonstrate a strong interrelation between possible types of magnetic and orbital order. We elucidate the prominent role played by fluctuations of $yz$ and $xz$ orbitals which generate ferromagnetic superexchange interactions even in the absence of Hund's exchange. In this limit we find orbital valence bond state which is replaced either by $C$-type antiferromagnetic order with weak $G$-type orbital order at increasing Hund's exchange, or instead by $G$-type antiferromagnetic order when the lattice distortions stabilize $C$-type orbital order. Both phases are observed in YVO$_3$ and we argue that a dimerized $C$-type antiferromagnetic phase with stronger and weaker FM bonds alternating along the c axis may be stabilized by large spin-orbital entropy at finite temperature. This suggests a scenario which explains the origin of the exotic $C$-AF order observed in YVO$_3$ in the regime of intermediate temperatures and allows one to specify the necessary ingredients of a more complete future theory.Comment: 23 pages, 15 figure