Theory of orbital state and spin interactions in ferromagnetic titanates

TL;DR

This paper investigates the quantum-driven orbital order and spin interactions in ferromagnetic titanates, providing theoretical predictions for orbital excitations and spin-wave spectra that align with experimental data.

Contribution

It introduces a quantum-mechanically stabilized orbital order in a spin-orbital model and derives an effective spin Hamiltonian including relativistic effects, matching experimental observations.

Findings

Orbital order is stabilized by quantum fluctuations via order-from-disorder.

Multiple orbital ordering patterns, including quadrupole and noncollinear types, are identified.

Calculated spin-wave spectra agree with experimental results in YTiO$_3$.

Abstract

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$_3$.