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 an external field in an arbitrary direction. We find that the Kasteleyn transition known for [001] fields appears also for general field directions and we 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 toward $T_K$, 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.

• Received 8 April 2022
• Revised 4 July 2022
• Accepted 18 July 2022

DOI:https://doi.org/10.1103/PhysRevB.106.054437

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society