Ferrimagnetism from triple-q order in Na${}_2$Co${}_2$TeO${}_6$

Abstract

The candidate Kitaev magnet Na${}_2$Co${}_2$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-$\Gamma$-${\Gamma }^{\prime }$ 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 Na${}_2$Co${}_2$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-$\Gamma$-${\Gamma }^{\prime }$-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.

12 pages, 6 figures; v2:published version

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Cited by in corpus (9)

• Robust triple-q magnetic order with trainable spin vorticity in Na${}_2$Co${}_2$TeO${}_6$
• On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides
• Spin waves in Na${}_2$Co${}_2$TeO${}_6$ studied by high-frequency/high-field ESR: Successes and failures of the triple-$\mathbf{q}$ model
• Ferrimagnetism from quantum fluctuations in Kitaev materials
• Field-induced magnetic phases in the Kitaev candidate Na${}_3$Co${}_2$SbO${}_6$
• Phenomenological Ginzburg-Landau theory for triple-Q magnetic orders on a hexagonal lattice
• Crystalline water intercalation into the Kitaev honeycomb cobaltate Na${}_2$Co${}_2$TeO${}_6$
• Direct probe of magnetic field effects on phonons by ultrasound propagation in a quasi-two-dimensional honeycomb magnet Na${}_2$Co${}_2$TeO${}_6$
• Dominant Kitaev Interaction and Field-induced Quantum Disordered Phase in the Cobaltate Na${}_2$Co${}_2$TeO${}_6$