Anisotropic susceptibilities in the honeycomb Kitaev system $alpha$-RuCl$_{3}$

The magnetic insulator $alpha$-RuCl$_{3}$ is a promising candidate to realize Kitaev interactions on a quasi-2D honeycomb lattice. We perform extensive susceptibility measurements on single crystals of $alpha$-RuCl$_{3}$, including angle-dependence of the in-plane longitudinal and transverse susceptibilities, which reveal a unidirectional anisotropy within the honeycomb plane. By comparing the experimental results to a high-temperature expansion of a Kitaev-Heisenberg-$Gamma$ spin Hamiltonian with bond anisotropy, we find excellent agreement with the observed phase shift and periodicity of the angle-resolved susceptibilities. Within this model, we show that the pronounced difference between in-plane and out-of-plane susceptibilities as well as the finite transverse susceptibility are rooted in strong symmetric off-diagonal $Gamma$ spin exchange. The $Gamma$ couplings and relationships between other terms in the model Hamiltonian are quantified by extracting relevant Curie-Weiss intercepts from the experimental data.