Observation of low-temperature magnetomechanic effects in crystalline resonant phonon cavities

We observe magnetic effects in ultrahigh-quality factor crystalline quartz bulk acoustic wave resonators at milli-Kelvin temperature. The study reveals the existence of hysteresis loops, jumps, and memory effects of acoustical resonance frequencies. These loops arise as a response to the external magnetic field, and they span a few Hertz for modes with linewidths of about $25\mathrm{mHz}$, which constitute a frequency shift of order 60 linewidths. The effects are broadband but get stronger toward higher frequencies where both nonlinear effects and losses are limited by two-level systems. This suggests that the observed effects are due to the ferromagnet-like phase of a spin ensemble coupled to mechanical modes. The observed coupling between mechanical and spin degrees of freedom in the ultralow-loss regime brings about new possibilities for the emerging class of quantum hybrid systems.

Figure 1

Experimental setup for measuring the frequency response of BAW cavity with acoustic modes standing along $\vec{k}$ as a function of external magnetic field that is parallel (${\vec{B}}_p$) or normal (${\vec{B}}_n$) to the resonator plate.

Figure 2

Frequency deviation as a function of external magnetic field parallel to the crystal plate for a sweeping magnetic field up and down for the 37th OT of the longitudinal mode.

Figure 3

Frequency deviation as a function of an external magnetic field normal to the crystal plate for a sweeping magnetic field up and down for the 33st (a) and 37th OTs (b) of the longitudinal mode.

Figure 4

Frequency deviation as a function of an external magnetic field normal to the crystal plate in the strong signal regime. Indices in boxes denote OT numbers and types of vibration: A, longitudinal; B, fast shear; C, slow shear.