Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models

TL;DR

This paper explores magnetic interactions in Mott insulators with strong spin-orbit coupling, revealing a spectrum of models from Heisenberg to Kitaev, and explains anomalous ferromagnetism in Sr$_2$IrO$_4$.

Contribution

It introduces a unified framework for understanding magnetic interactions in spin-orbit coupled Mott insulators, connecting various models and explaining experimental phenomena.

Findings

Derivation of low-energy Hamiltonians from Heisenberg to quantum compass models

Proposal of exactly solvable Kitaev spin models in Mott insulators

Explanation of weak ferromagnetism in Sr$_2$IrO$_4$

Abstract

We study the magnetic interactions in Mott-Hubbard systems with partially filled $t_{2g}$-levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to "engineer" in such Mott insulators an exactly solvable spin model by Kitaev relevant for quantum computation. We, finally, explain "weak" ferromagnetism, with an anomalously large ferromagnetic moment, in Sr$_2$IrO$_4$.