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 TmMgGaO4, 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 Tc ∼ 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 columnar magnetic neutron reflections below µ0Hc ∼ 2.6 T, with highly anisotropic correlation lengths, ξ ab ≥ 250a in the triangular plane and ξc < 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.

Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4

“…We present in Fig. 2 the calculated thermodynamic quantities and their experimental counterparts 25,26 , where excellent agreements are seen. In Fig Agreements between the experimental curves (taken from various independent measurements [24][25][26] ) and numerical results can be seen in all panels, down to very low temperatures.…”

“…The model parameters in Eq. (1) can be accurately determined through fitting the available experimental data of TMGO [24][25][26] , from which we find J 1 = 0.99 meV, J 2 = 0.05J 1 , Δ = 0.54J 1 and g ∥ = 13.212. We present in Fig.…”

“…In ref. 25 , the authors took the lowest two levels Φ ± j i of Tm 3+ as non-Kramers doublet and construct a classical TLI with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions to account for the absence of zero-point entropy observed in experiments. Substantial randomness was also introduced to explain the smooth magnetization curves even at a very low temperature.…”

“…Experimentally, the triangular-lattice quantum magnets have been synthesized only very recently, including compounds Ba 3 CoSb 2 O 9 [11][12][13][14] , Ba 8 CoNb 6 O 24 15,16 , and a rare-earth oxide YbMgGaO 4 -which has been suggested as a quantum spin liquid candidate [17][18][19][20] -whereas an alternative scenario of glassy and disorder-induced state has also been proposed recently [21][22][23] . On the other hand, an Ising-type triangular antiferromagnet TmMgGaO 4 (TMGO, with Yb 3+ replaced by another rare-earth ion Tm 3+ ) [24][25][26] , as shown in Fig. 1a and explained in details in this study, is the successful material realization of a quantum magnet with strong Ising anisotropy.…”

“…In this work, we construct the microscopic model of TMGO and employ two state-of-the-art quantum many-body simulation approaches: the exponential tensor renormalization group (XTRG) 27 and quantum Monte Carlo (QMC) equipped with stochastic analytic continuation (QMC-SAC) [28][29][30][31][32] , to calculate both the thermodynamic and dynamic properties. By scanning various parameters and fit our simulation results to the existing experimental data [24][25][26] , we find TMGO realizes a triangularlattice transverse-field Ising model and determine accurately its model parameters. Based on this, we conclude that TMGO should host the celebrated KT phase and further predict several prominent features to be observed in TMGO, inspired by the experimental measurements for detecting KT physics in a superfluid thin film 4 .…”