Partial up-up-down order with the continuously distributed order parameter in the triangular antiferromagnet TmMgGaO4

Abstract

Frustrated quasidoublets without time-reversal symmetry can host highly unconventional magnetic structures with continuously distributed order parameters even in a single-phase crystal. Here, we report the comprehensive thermodynamic and neutron diffraction investigation on the single crystal of TmMgGaO${}_4$, which entails non-Kramers Tm${}^{3+}$ ions arranged on a geometrically perfect triangular lattice. The crystal electric field (CEF) randomness caused by the site-mixing disorder of the nonmagnetic Mg${}^{2+}$ and Ga${}^{3+}$ ions, merges two lowest-lying CEF singlets of Tm${}^{3+}$ into a ground-state (GS) quasidoublet. Well below $T_c$ $\sim$ 0.7 K, a small fraction of the antiferromagnetically coupled Tm${}^{3+}$ Ising quasidoublets with small inner gaps condense into two-dimensional (2D) up-up-down magnetic structures with continuously distributed order parameters, and give rise to the \emph{columnar} magnetic neutron reflections below $\hat{I}{¼}_0{H}_c$ $\sim$ 2.6 T, with highly anisotropic correlation lengths, $\hat{I}{¾}_{ab}$ $\ge$ 250$a$ in the triangular plane and $\hat{I}{¾}_c$ $<$ $c$/12 between the planes. The remaining fraction of the Tm${}^{3+}$ ions remain nonmagnetic at 0 T and become uniformly polarized by the applied longitudinal field at low temperatures. We argue that the similar model can be generally applied to other compounds of non-Kramers rare-earth ions with correlated GS quasidoublets.

Accepted in Physical Review X. The present manuscript is significantly different from the earlier preprint, arXiv:1804.00696, in the analysis, results, and contains additional neutron diffraction data