Canted antiferromagnetic order and spin dynamics in the honeycomb-lattice Tb2Ir3Ga9

Single crystal neutron diffraction, inelastic neutron scattering, bulk magnetization measurements, and first-principles calculations are used to investigate the magnetic properties of the honeycomb lattice $\rm Tb_2Ir_3Ga_9$. While the $R\ln2$ magnetic contribution to the low-temperature entropy indicates a $\rm J_{eff}=1/2$ moment for the lowest-energy crystal-field doublet, the Tb$^{3+}$ ions form a canted antiferromagnetic structure below 12.5 K. Due to the Dzyalloshinskii-Moriya interactions, the Tb moments in the $ab$ plane are slightly canted towards $b$ by $6^\circ$ with a canted moment of 1.22 $\mu_{\rm B} $ per formula unit. A minimal $xxz$ spin Hamiltonian is used to simultaneously fit the spin-wave frequencies along the high symmetry directions and the field dependence of the magnetization along the three crystallographic axes. Long-range magnetic interactions for both in-plane and out-of-plane couplings up to the second nearest neighbors are needed to account for the observed static and dynamic properties. The $z$ component of the exchange interactions between Tb moments are larger than the $x$ and $y$ components. This compound also exhibits bond-dependent exchange with negligible nearest exchange coupling between moments parallel and perpendicular to the 4$f$ orbitals. Despite the $J_{{\rm eff}}=1/2$ moments, the spin Hamiltonian is denominated by a large in-plane anisotropy $K_z \sim -1$ meV. DFT calculations confirm the antiferromagnetic ground state and the substantial inter-plane coupling at larger Tb-Tb distances.