Partial Up-Up-Down Order with the Continuously Distributed Order Parameter in the Triangular Antiferromagnet TmMgGaO4

Abstract

We show that frustrated quasidoublets without time-reversal symmetry can host highly unconventional magnetic structures with continuously distributed order parameters even in a single-phase crystal. Our study comprises a comprehensive thermodynamic and neutron diffraction investigation on the single crystal ofTmMgGaO4, which entails non-KramersTm3+ions arranged on a geometrically perfect triangular lattice. The crystal electric field randomness caused by the site-mixing disorder of the nonmagneticMg2+andGa3+ions merges two lowest-lying crystal electric field singlets ofTm3+into a ground-state quasidoublet. Well belowTc∼0.7K, a small fraction of the antiferromagnetically coupledTm3+Ising quasidoublets with small inner gaps condense into two-dimensional up-up-down magnetic structures with continuously distributed order parameters, and give rise to the columnar magnetic neutron reflections belowμ0Hc∼2.6T, with highly anisotropic correlation lengths,ξab≥250ain the triangular plane andξc<c/12between the planes. The remaining fraction of theTm3+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 ground-state quasidoublets.

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Plain Language Summary

Geometrical frustration describes a collection of spins on some symmetric lattice where not all of the interactions can simultaneously minimize energy. This kind of system cannot achieve conventional low-temperature ordering, where neighboring spins are oriented parallel to one another (ferromagnets) or in opposing directions (antiferromagnets). Specifically, an ideal “triangular-lattice Ising antiferromagnet” (where spins can be oriented only along a special direction, up or down) remains completely disordered even down to absolute zero, retaining a large residual entropy that violates the third law of thermodynamics. However, to date, the relevant real materials are still rare. Recently, researchers synthesized the triangular-lattice Ising antiferromagnetTmMgGaO4. Here, we report on a thorough single-crystal investigation of the low-temperature magnetism ofTmMgGaO4.

Its structural siblingYbMgGaO4was proposed as a quantum spin-liquid candidate. Here, theYb3+ion has an odd number of the4felectrons, and thus the crystal electric field (CEF) always produces the lowest-lying doublet (the effective spin-1/2moment), according to Kramers theorem. However, inTmMgGaO4the situation is different: TheTm3+ion has an even number of the4felectrons, and CEF singlets are expected. Our present work indicates that the inner energy gap between the two lowest-lying singlets is small, and the site-mixing disorder of the nonmagneticMg2+andGa3+ions with different valences distributes that inner gap throughout the crystal. These two lowest-lying CEF singlets are characterized as a “ground-state quasidoublet.”

We observe a very unconventional and complex magnetic order inTmMgGaO4at low temperatures. A similar geometrically frustrated model can be generally applied to other non-Kramers rare-earth magnets with similar disorder-induced ground-state quasidoublets.