Six-fold clock anisotropy in easy-plane honeycomb CoTiO₃ probed by single-crystal torque magnetometry

We report torque measurements to probe the angular dependence of the magnetic anisotropy in the easy-plane honeycomb magnet CoTiO₃, proposed to display order-by-disorder physics, where the ground state magnetic structure is selected via quantum fluctuations out of a manifold of many classically-degenerate states. Previous experiments observed a finite energy gap, which implies a finite energy cost to rotate spins in-plane away from a set of six symmetry-equivalent energy-preferred directions. The origin of the in-plane anisotropy is non-trivial as it cannot come from single-ion physics, or from two-spin interactions treated in a mean-field approximation, and has been attributed to a quantum zero-point energy contribution to the ground state energy and/or contribution from higher-order spin-orbital exchange [1]. To characterize the magnetic anisotropy directly we have performed single-crystal piezo-cantilever torque measurements as a function of field orientation. Below the magnetic ordering temperature, we have observed a clear six-fold angular dependence of the torque upon rotating the field orientation in the ab plane. We have characterized the dependence of the six-fold signal upon increasing the applied field magnitude from low-field, when adjacent honeycomb layers are spontaneously antiferromagnetically aligned, all the way to high field, when spins in adjacent layers are polarized by the applied field. We discuss the observed behaviour in the context of models for the six-fold in-plane clock anisotropy. [1] M. Elliot, P.A. McClarty, D. Prabhakaran, R.D. Johnson, H.C. Walker, P. Manuel, R. Coldea, Nat. Comm. 12, 3936 (2021).