The appearance of a plateau in the magnetization of a quantum spin system subject to continuously varying magnetic field invites the identification of a topological quantization. Indeed, the magnetization plateaus at $1/8$ and $1/2$ of saturation in ${\mathrm{TmB}}_4$ have been suggested to be intrinsic, resulting from such a topological quantization, or, alternatively, to be metastable phases. By means of neutron- and x-ray-scattering experiments and magnetization measurements, we show that the 1/8 plateau is metastable, arising because the spin dynamics are frozen below $T\approx 4.5$ K. Our experiments show that in this part of the phase diagram of ${\mathrm{TmB}}_4$, many long-ranged orders with different propagation vectors may appear and coexist, particularly as the applied field drives the system from one plateau to another. The magnetic structures accommodating a magnetization of $\approx 1/8$ seem to be particularly favorable, but still only appear if the system has sufficient dynamics to reorganize into a superstructure as it is driven toward the expected plateau. This work demonstrates that ${\mathrm{TmB}}_4$ represents a model material for the study of slow dynamics, in and out of equilibrium.

• Received 18 October 2019
• Accepted 24 June 2020

DOI:https://doi.org/10.1103/PhysRevB.102.060407