Spin ice in a general applied magnetic field: Kasteleyn transition, magnetic torque and rotational magnetocaloric effect

Spin ice is a paradigmatic frustrated system famous for the emergence of magnetic monopoles and a large magnetic entropy at low temperatures. It exhibits unusual behavior in the presence of an external magnetic field as a result of the competition between the spin ice entropy and the Zeeman energy. Studies of this have generally focused on fields applied along high symmetry directions: [111], [001], and [110]. Here we consider a model of spin ice with external field in an arbitrary direction. We find that the Kasteleyn transition known for $[001]$ fields, appears also for general field directions and calculate the associated Kasteleyn temperature $T_K$ as a function of field direction. $T_K$ is found to vanish, with a logarithmic dependence on field angle, approaching certain lines of special field directions. We further investigate the thermodynamic properties of spin ice for $T>T_K$, using a Husimi cactus approximation. As the system is cooled towards $T_K$ a large magnetic torque appears, tending to align the $[001]$ crystal axis with the external field. The model also exhibits a rotational magnetocaloric effect: significant temperature changes can be obtained by adabiatically rotating the crystal relative to a fixed field.