Proximity to quantum criticality in the Ising ferromagnet TbV$_6$Sn$_6$

Abstract: TbV$_6$Sn$_6$ is a topological metal where ferromagnetic Tb ions with strong uniaxial magnetic anisotropy interact with V kagome layers. Inelastic neutron scattering measurements show that the Tb ions adopt an Ising doublet ground state. Here, we consider whether a transverse magnetic field can drive TbV$_6$Sn$_6$ towards a quantum critical point, providing a rare example of transverse-field Ising criticality in a metallic compound. High-field magnetization measurements suggest that this quantum criticality is avoided and reveal a first-order-like spin-reorientation transition at 25.6 T due to an excited-state level crossing. Theoretical analysis shows that small changes in the local Hamiltonian can restore the quantum criticality for some in-plane field directions, suggesting that TbV$_6$Sn$_6$ is close to a novel quantum tricritical point induced by in-plane magnetic anisotropy.