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The transverse-field Ising model on the triangular lattice is expected tohost an intermediate finite-temperature Kosterlitz-Thouless (KT) phase througha mapping of the spins on each triangular unit to a complex order parameter.TmMgGaO$_4$ is a candidate material to realize such physics due to thenon-Kramers nature of Tm$^{3+}$ ion and the resulting two-singlet single-ionground state. Using inelastic neutron scattering, we confirm this picture bydetermining the leading parameters of the low-energy effective Hamiltonian ofTmMgGaO$_4$. Subsequently, we track the predicted KT phase and relatedtransitions by inspecting the field and temperature dependence of the acsusceptibility. We further probe the spin correlations in both reciprocal spaceand real space via single crystal neutron diffraction and magnetic totalscattering techniques, respectively. Magnetic pair distribution functionanalysis provides evidence for the formation of vortex-antivortex pairs thatcharacterize the proposed KT phase around 5~K. Although structural disorderinfluences the field-induced behavior of TmMgGaO$_4$, the magnetism in zerofield appears relatively free from these effects. These results positionTmMgGaO$_4$ as a strong candidate for a solid-state realization of KT physicsin a dense spin system.

Neutron scattering investigation of proposed Kosterlitz-Thouless transitions in the triangular-lattice Ising antiferromagnet TmMgGaO4