A material-agnostic platform to probe spin-phonon interactions using high-overtone bulk acoustic wave resonators

Abstract

Spin-phonon interactions have a dual role in emerging spin-based quantum technologies. While they can be a limitation to device performance through decoherence, they also serve as a critical resource for coherent spin control, detection, and the realization of spin-based quantum networks. However, their direct characterization remains a challenge and is usually material-dependent. Here, we introduce a technique to probe spin-phonon coupling at millikelvin temperatures and gigahertz frequencies, using high-overtone bulk acoustic wave resonators (HBARs) integrated with arbitrary crystals via visco-elastic transfer of thin-film lithium niobate transducers. By tuning the Larmor frequency of dilute spin ensembles into resonance with HBAR modes, we extract the anisotropy and strength of spin-phonon interactions from acoustic dispersion and dissipation measurements. We demonstrate this approach in calcium tungstate (CaWO4) and yttrium orthosilicate (Y2SiO5), achieving cooperativities up to 0.5 for erbium dopant ensembles. Our method enables the study of spin-phonon interactions in complex crystalline materials, with minimal fabrication constraints. These results will facilitate the design of hybrid quantum systems and the quest for ion-matrix combination with enhanced spin-phonon coupling.

Figures (14)

• Figure 1: Manufacturing High-Overtone bulk Acoustic wave Resonators (HBARs) in arbitrary crystals.a, The fabrication of the piezoelectric transducer starts from thin films of LiNbO$_3$ on Si. b, The piezoelectric transducer, patterned in LiNbO$_3$, is fitted with top and bottom metallic electrodes, which are respectively connected to the signal and ground pads of a coplanar waveguide (CPW). The entire structure (transducer and CPW) is free standing and attached to the carrier Si substrate by LiNbO$_3$ tethers. c, We use a PDMS stamp to pick up the entire structure from the Si substrate. d, A target crystal (hosting spins) must have two parallel faces polished. e. After spin-coating a thin layer of PMMA ($\approx$ 60 nm) on the crystal, we heat it up to 150 ° C and we transfer the piezoelectric structure onto it. f, We retract the PDMS stamp and leave the piezoelectric structure bonded onto the crystal. g, We excite and detect the acoustic modes in the crystal via the bonded piezoelectric transducer. h, False-colored optical micrograph of a transducer bonded onto a transparent crystal, showing regions where the bottom electrode is connected to the electrical ground of the CPW.
• Figure 1: Manufacturing HBAR with large external coupling $\kappa_\text{ext}$a, Microwave reflection $S_{11}$ (magnitude and phase) and extracted external coupling $\kappa_\text{ext}$ for two HBARs realized on Si [100] and measured at low temperature. The frequencies of operation are larger here than for the HBAR presented in the main text because the transducers used on these samples where made with aluminum electrodes, instead of gold. b, Microwave reflection $S_{11}$ and extracted external coupling $\kappa_\text{ext}$ for an HBAR realized on glass (Borofloat).
• Figure 2: Acoustic electron paramagnetic resonance in calcium tungstate (CaWO$_4$) using an HBAR.a, Unit cell of the tetragonal lattice of CaWO$_4$, with one Er$^{3+}$ dopant. Oxygen atoms are omitted for clariry. b, Microwave reflection $S_{11}$ (magnitude and phase) of a CaWO$_4$ HBAR at low temperature and large microwave power ($\approx -72$ dBm at the HBAR input). c, Microwave reflection of a critically-coupled HBAR mode, at $f_m=4.441$ GHz. d, Spherical coordinates for the external magnetic field, with amplitude $B_0$ and orientation given by $\theta$ and $\varphi$ with respect to the crystal axes of CaWO$_4$. e, Relative phase shift of the microwave reflection measured on the HBAR resonance shown in c (color scale), as a function of the external magnetic field amplitude $B_0$ and angle $\theta$ (at $\phi=0\degree)$. The main paramagnetic resonance signal for erbium, yterbium and manganese ions are indicated. The secondary lines with weaker contrast correspond to hyperfine resonances, see Extended Data Fig. \ref{['Fig:ZoomCaWO$_4$-c-axis']} for more details.
• Figure 2: External coupling $\kappa_\text{ext}$ for the CaWO$_4$ sample shown in Fig. \ref{['Fig:CaWO$_4$']}
• Figure 3: Acoustic electron paramagnetic resonance in ytrium silicate (YSO) using an HBAR.a, Unit cell of the monoclinic lattice of YSO. Oxygen atoms are omitted for clarity. Two erbium dopants are represented, at the two independent lattice sites for substitution. The mutually perpendicular optical extinction axes (b, D1, D2), conventionally used for YSO, are represented. b, Microwave reflection $S_{11}$ (magnitude and phase) of an HBAR mode in YSO at low temperature. c, Microwave reflection of a critically-coupled HBAR mode, at $f_m=4.754$ GHz. Various parasitic modes can be seen, in particular to the left of the main acoustic resonance. d, Spherical coordinates for the external magnetic field, with amplitude $B_0$ and orientation given by $\theta$ and $\varphi$ with respect to the (b, D1, D2) cartesian coordinates. e, Relative phase shift of the microwave reflection measured on the HBAR resonance shown in c (color scale), as a function of the external magnetic field amplitude $B_0$ and angle $\phi$ at $\theta=90\degree$ (D1-D2 plane). f,g APR signal, taken as in e but in the b-D1 and b-D2 planes.