The possibility of experimental observation of the ultrasonic attenuation in the ferromagnet $\mathrm{LuCo}{}_3$ near the low-spin-high-spin crossover is discussed. We show that ultrasound propagation gives rise to transitions between states of the magnon band due to absorption of phonons, and this process is highly sensitive to the value of magnetization. The high magnetic field, which governs the crossover, alters the ultrasound propagation regime from off-resonant to resonant and we formulate a criterion of the change. Calculated temperature and field dependences of the ultrasonic wave number and attenuation clearly demonstrate anomalies in these characteristics in the vicinity of the crossover at intermediate temperatures far below the Curie temperature.

• Received 19 May 2022
• Accepted 4 August 2022

DOI:https://doi.org/10.1103/PhysRevB.106.054417