Ferrimagnetism from triple- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi mathvariant="normal">q</mml:mi> </mml:math> order in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Na</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Co</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>TeO</mml:mi> <mml:mn>6</mml:mn> </mml:msub> </mml:mrow> </mml:math>
Niccolò Francini, Lukas Janssen
Abstract
The candidate Kitaev magnet ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ exhibits a characteristic ferrimagnetic response at low temperatures, with a finite residual magnetization that changes sign at a compensation point located at around half the ordering temperature. We argue that the behavior can be naturally understood to arise in this material as a consequence of a noncollinear triple-$\mathbf{q}$ magnetic ground state. Using large-scale classical Monte Carlo simulations, we study the finite-temperature response of the pertinent honeycomb Heisenberg-Kitaev-$\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ model in weak training fields. Our model features all symmetry-allowed nearest-neighbor exchange interactions, as well as sublattice-dependent next-nearest-neighbor interactions, consistent with the reported crystal structure of the material. We also consider a six-spin ring exchange perturbation, which allows us to tune between the two different magnetic long-range orders that have been suggested for this material in the literature, namely, a collinear single-$\mathbf{q}$ zigzag state and a noncollinear triple-$\mathbf{q}$ state. We demonstrate that the experimentally observed ferrimagnetic response of ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ can be well described within our modeling if the magnetic ground state features noncollinear triple-$\mathbf{q}$ order. The observation of a compensation point, where the residual magnetization reverses sign, suggests a sublattice $g$-factor anisotropy, with a larger out-of-plane $g$ factor on the sublattice with stronger antiferromagnetic intrasublattice exchange. By contrast, a classical Heisenberg-Kitaev-$\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$-type model with collinear zigzag ground state is insufficient even in principle to describe the observed behavior. Our results illustrate the unconventional physics of noncollinear magnetic long-range orders hosted by frustrated magnets with bond-dependent interactions.