Frustrated Ising magnetism of TmMgGaO${}_4$

Motivated by the interesting spin-liquid physics of the triangular antiferromagnet YbMgGaO${}_4$, we studied its Tm-based analog. Unlike Yb${}^{3+}$, Tm${}^{3+}$ is a non-Kramers ion that would normally feature non-magnetic singlet as the crystal-field ground state. However, random crystal electric field (CEF) caused by the random distribution of Mg and Ga in the structure mixes two lowest-lying CEF singlets into a quasidoublet that gives rise to Ising-like pseudospins with $g_{\parallel }$ $\simeq$ 13.2 and $g_{\perp }$ $\simeq$ 0. Low-temperature thermodynamic measurements indicate three field-induced phase transitions that can be broadly understood within the J${}_1^{zz}$ - J${}_2^{zz}$ Ising model on the triangular lattice, albeit with a distribution of the critical fields and underlying exchange couplings. Interestingly, only one ordered state, the 1/3-plateau below 2.5 T, shows long-range order confirmed by neutron diffraction, whereas other ordered states expected in the J${}_1^{zz}$ - J${}_2^{zz}$ triangular Ising antiferromagnet seem to be only short-range in nature. Moreover, no zero-point entropy is observed.