Angular Modulations in Magnetic Torque Induced by Phase Transitions in the Triangular Supersolid $2H$-AgNiO$_2$
Easy-axis frustrated triangular lattice antiferromagnets provide an important playground for stabilising a wide range of exotic magnetic phases. The delafossite $2H$-AgNiO$_2$ offers a unique model system containing a lattice of localised ($S=1$) moments surrounded by a honeycomb of itinerant electrons. Below $T_{\rm N} =19$ K, the system exhibits collinear stripe antiferromagnetic order, whereas applied magnetic fields induce a cascade of transitions which has been proposed to contain a magnetic supersolid phase. In this study, we perform detailed angular and field-dependent torque measurements in static fields of up to 45~T on single crystal samples. The angular dependence of the torque displays a sawtooth-shaped signal close to the first supersolid phase, while near $T_{\rm N}$, an unexpected additional modulation emerges. On the other hand, the field dependence of the torque indicates the presence of four field-induced anomalies which evolve in distinct ways as a function of field orientation. To understand these complex behaviours and assess the role of local moments, we employ mean-field and Monte-Carlo calculations on a minimal spin model and construct comprehensive polar phase diagrams at different temperatures. We find that the angular dependence of the torque can be understood in terms of crossing different phase boundaries by field rotation, and we identify qualitative similarities between the experimental and theoretical polar phase diagrams. Our study highlights $2H$-AgNiO$_2$ as a rich anisotropic system that provides a robust example of how spin supersolid orders can manifest in angle-dependent magnetic torque.