Field-driven phases in a three-dimensional twisted Kitaev model for CoNb$_2$O$_6$: Interplay of frustration and spin-orbit coupling

TL;DR

This study models the complex magnetic phases of CoNb$_2$O$_6$ considering twisted Kitaev interactions and frustration, revealing a highly sensitive phase diagram influenced by magnetic field orientation.

Contribution

It introduces a three-dimensional model incorporating Kitaev physics and frustration, providing detailed phase diagrams and spectra for CoNb$_2$O$_6$ under magnetic fields.

Findings

Multiple field-driven phases with commensurate and incommensurate order

Phase diagram highly sensitive to field angle due to spin-orbit coupling

Computed spectra match experimental observations

Abstract

The Ising chain in a transverse field stands out as a paradigmatic example for a quantum phase transition. CoNb$_2$O$_6$ has been discussed as a material realization of this physics, but it was later realized that its magnetic exchange couplings are more complicated, taking the form of twisted Kitaev chains. Here we study a three-dimensional model for CoNb$_2$O$_6$, taking into account both Kitaev physics and frustrated inter-chain coupling, in applied magnetic field. Using semiclassical techniques at zero temperature, we map out the sequence of field-driven phases for arbitrary field direction; these include phases with commensurate and incommensurate inter-chain order. As a result of spin-orbit coupling, the phase diagram is extremely sensitive to small changes in the field angle. We compute static observables as well as magnetic excitation spectra in the various phases and connect our results to existing experimental data.