Acoustic Spin Resonance

• Acoustic spin resonance is the phenomenon where time-dependent mechanical fields drive coherent spin transitions, enabling precise control in various nanosystems.
• It leverages mechanisms like spin–strain coupling, magnetoelastic excitation, and optically assisted protocols to achieve high-fidelity control in platforms such as SiC defects and semiconductor quantum dots.
• This approach offers submicron-scale wavelength advantages over conventional ESR, paving the way for integrated quantum devices and advanced spintronic applications.

Searching arXiv for recent and foundational work on acoustic spin resonance to ground the article in the literature. Acoustic spin resonance denotes resonant spin dynamics driven by time-dependent mechanical fields—most commonly strain, elastic rotation, or phonons—rather than by an oscillating microwave magnetic field. In the contemporary literature, the term covers several closely related regimes: direct spin–strain driving in localized defects, magnetoelastic excitation of magnons and spin pumping in ferro- and antiferromagnets, spin–vorticity or spin-rotation driving by surface acoustic waves, strain-induced spin flips in spin–orbit-coupled electronic bands, and optically assisted schemes in which acoustic modulation acts through an intermediate excited state (Hernández-Mínguez et al., 2020, Kuniej et al., 16 Dec 2025, Puebla et al., 2020).

1. Definition and conceptual scope

In its most general form, acoustic spin resonance is the coherent driving of spin transitions by a periodic elastic perturbation whose frequency matches a spin-level splitting. For localized electronic spins, the acoustic field acts through a spin–strain Hamiltonian, often quadratic in spin operators, so the resonance condition is set by the matching of an acoustic frequency to a Zeeman or zero-field splitting. In this usage, ASR is explicitly contrasted with conventional electron spin resonance, where an oscillating magnetic field $B_1$ drives the transition through Zeeman coupling (Hernández-Mínguez et al., 2020).

In magnetic films and resonators, the same concept appears as acoustic ferromagnetic resonance or, more broadly, acoustically driven spin-wave resonance. There the elastic wave does not usually address a single spin transition; instead it excites collective precession through magnetoelastic coupling, and the principal observables are acoustic absorption, spin-wave generation, cavity back-action, and spin pumping into an adjacent metal (Puebla et al., 2020). In antiferromagnets, the same logic applies to magnetoelastic modes of the Néel order, including ultrasonic resonances far below the bare antiferromagnetic resonance scale (Gabrielyan et al., 28 May 2025).

The term also extends beyond direct strain coupling. In semiconductor quantum dots, mechanical coupling to a single electron spin is intrinsically weak, so a hybrid acousto-optical protocol can make the acoustic field act on an optically admixed spin manifold and thereby realize effective acoustic spin rotation (Kuniej et al., 16 Dec 2025). In nuclear systems, the relevant interaction may be spin-rotation coupling rather than conventional magnetoelasticity, with the acoustic wave producing an effective Barnett field (Usami et al., 2020). Across these examples, ASR is therefore best regarded as a family of resonance phenomena unified by mechanical driving of spin dynamics rather than by a single microscopic mechanism.

2. Microscopic mechanisms and model Hamiltonians

A central microscopic route is direct spin–strain coupling. For the silicon-vacancy $V_{\mathrm{Si}}$ center in 4H-SiC, treated as a half-integer $S=3/2$ system, the effective Hamiltonian is written as

$H = H_B + H_{\mathrm{def}},$

with

$$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$

and

$$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$

Because $H_{\mathrm{def}}$ is quadratic in spin, it contains both $\Delta m = \pm 1$ and $\Delta m = \pm 2$ channels, which is why purely acoustic driving can access single- and double-quantum transitions in SiC (Hernández-Mínguez et al., 2020).

A symmetry-refined treatment of the same defect replaces the spherical approximation by the full $C_{3v}$-allowed spin–strain Hamiltonian

$V_{\mathrm{Si}}$0

with

$V_{\mathrm{Si}}$1

In that description, the five independent couplings $V_{\mathrm{Si}}$2 control how the strain doublets project onto spin quadrupoles, so the angular dependence of ASR becomes a direct probe of deviations from spherical symmetry (Koga et al., 2024).

In semiconductor quantum dots, the mechanism is different. A Voigt-geometry magnetic field defines the spin doublet, a detuned $V_{\mathrm{Si}}$3 continuous-wave laser couples both spin states to a common trion, and a coherent acoustic modulation shifts the trion energy. After adiabatic elimination of the trion, the effective spin Hamiltonian becomes

$V_{\mathrm{Si}}$4

The resonance condition is $V_{\mathrm{Si}}$5 for the dominant single-phonon process, while the acoustic phase $V_{\mathrm{Si}}$6 sets the azimuth of the rotation axis and $V_{\mathrm{Si}}$7 sets its inclination (Kuniej et al., 16 Dec 2025).

For itinerant carriers in monolayer MoS$V_{\mathrm{Si}}$8, the acoustic field enters through spin–orbit-coupled band structure. The low-energy theory uses

$V_{\mathrm{Si}}$9

together with the intrinsic spin–orbit term

$S=3/2$0

A Rayleigh wave then produces an effective in-plane oscillatory magnetic field through strain gradients, leading to spin-flip absorption and acoustoelectric current near a finite-momentum crossing of the spin-split conduction subbands (Sonowal et al., 2022).

In magnetically ordered media, the starting point is usually the magnetoelastic energy density. For a cubic ferromagnet,

$S=3/2$1

and the effective drive field is $S=3/2$2. This formulation underlies acoustic ferromagnetic resonance, surface-acoustic-wave spin pumping, and related cavity magnomechanical descriptions (Puebla et al., 2020).

A distinct limiting case is spin-rotation coupling. For nuclear spins in a surface-acoustic-wave cavity, the local interaction density is

$S=3/2$3

which is equivalently written as

$S=3/2$4

Here the acoustic wave drives resonance through the vorticity field rather than through a conventional spin–strain tensor (Usami et al., 2020).

3. Material platforms and experimental realizations

The present literature spans localized defects, semiconductor nanostructures, collective magnonic systems, molecular triplets, two-dimensional semiconductors, nuclear ensembles, and driven-dissipative bosonic condensates. The table summarizes representative platforms and characteristic observables.

Platform	Acoustic mechanism	Representative result
III–V quantum dots	Hybrid acousto-optical trion-assisted spin rotation	$S=3/2$5 fidelity at $S=3/2$6 GHz with $S=3/2$7 ns
4H-SiC silicon vacancies	Direct spin–strain driving of $S=3/2$8 levels	Purely acoustic $S=3/2$9 and $H = H_B + H_{\mathrm{def}},$0 resonances
Ferromagnetic thin films and SAW devices	Magnetoelastic FMR and spin pumping	Resonant ISHE voltage and cavity-enhanced absorption
YIG composite resonators	Thickness-mode-driven linear and parametric ASR	Shear modes linear; shear and longitudinal modes parametric
Monolayer MoS$H = H_B + H_{\mathrm{def}},$1	SOC-mediated strain-induced effective field	GHz valley spin-acoustic resonance near finite-$H = H_B + H_{\mathrm{def}},$2 crossing
Pentacene thin films	Zero-field triplet-ZFS modulation by high-$H = H_B + H_{\mathrm{def}},$3 SAW	Acoustic Rabi oscillations near $H = H_B + H_{\mathrm{def}},$4 MHz
Nuclear SAW cavities	Spin-rotation/Barnett-field driving	Proposed NSAR with $H = H_B + H_{\mathrm{def}},$5 and mode volume $H = H_B + H_{\mathrm{def}},$6 mm$H = H_B + H_{\mathrm{def}},$7

In semiconductor quantum dots, the hybrid protocol is explicitly designed to circumvent the weak direct phonon–spin coupling of III–V nanostructures. Numerical simulations use $H = H_B + H_{\mathrm{def}},$8 meV ($H = H_B + H_{\mathrm{def}},$9 GHz), $$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$0 meV, $$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$1eV, and $$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$2 meV, with a two-pulse $$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$3 gate taking about $$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$4 ns and reaching $$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$5 fidelity when $$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$6 ns (Kuniej et al., 16 Dec 2025).

SiC hosts two experimentally distinct ASR implementations. In a ZnO/SiC surface-acoustic-wave cavity, the negatively charged silicon vacancy in the V2 configuration exhibits room-temperature purely acoustic resonances at $$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$7 MHz, with features at $$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$8 mT for $$H_B = g \mu_B \mathbf{S}\cdot \mathbf{B} + D \left(S_z^2 - 5/4\right),$$9 and $$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$0 mT for $$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$1 (Hernández-Mínguez et al., 2020). In a high-$$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$2 lateral overtone bulk acoustic resonator fabricated directly from semi-insulating 4H-SiC, optically detected spin-acoustic resonance resolves magnetically forbidden $$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$3 transitions, linewidth narrowing toward the acoustic linewidth on the resonator wings, and room-temperature coherent population oscillations with $$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$4 MHz on the wings and $$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$5 MHz under the transducer at $$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$6 MHz (Dietz et al., 2022).

Collective-spin realizations are equally diverse. A Co(10 nm)/Pt(7 nm) bilayer on LiNbO$$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$7 shows time-resolved acoustic spin pumping under a $$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$8 GHz Rayleigh pulse, with $$H_{\mathrm{def}} = \Xi \sum_{\alpha\beta} u_{\alpha\beta} S_\alpha S_\beta.$$9V at resonance and no detectable off-resonant signal within $H_{\mathrm{def}}$0V (Weiler et al., 2011). A planar Ni surface-acoustic-wave cavity magnomechanical system reaches more than $H_{\mathrm{def}}$1 acoustic power absorption, a coupling rate $H_{\mathrm{def}}$2 MHz, and cooperativity $H_{\mathrm{def}}$3 at room temperature (Hatanaka et al., 2021). In a distributed-Bragg-reflector SAW cavity with a Ni/Cu/Bi$H_{\mathrm{def}}$4O$H_{\mathrm{def}}$5 trilayer, the cavity enhances SAW power absorption by $H_{\mathrm{def}}$6 and spin-current generation by up to $H_{\mathrm{def}}$7 in the low-power regime (Hwang et al., 2020).

Other platforms broaden the scope of ASR rather than merely reproducing the same mechanism. Theory for monolayer MoS$H_{\mathrm{def}}$8 identifies a conduction-band crossing that brings the relevant spin splitting into the $H_{\mathrm{def}}$9–$\Delta m = \pm 1$0 GHz range at electron densities of $\Delta m = \pm 1$1–$\Delta m = \pm 1$2 cm$\Delta m = \pm 1$3, allowing valley-resolved acoustic spin resonance and acoustoelectric current under millitesla-scale magnetic fields (Sonowal et al., 2022). In a pentacene:$\Delta m = \pm 1$4-terphenyl thin film on a high-$\Delta m = \pm 1$5 LiNbO$\Delta m = \pm 1$6 SAW resonator, heterogeneous optically detected spin-acoustic resonance drives zero-field triplet transitions near $\Delta m = \pm 1$7 MHz with reported cavity quality factors $\Delta m = \pm 1$8, $\Delta m = \pm 1$9, and $\Delta m = \pm 2$0 and with Rabi frequency proportional to $\Delta m = \pm 2$1 (Chen et al., 9 Feb 2026). In hematite, acoustic resonance occurs at ultrasonic frequencies: a representative mode has $\Delta m = \pm 2$2 kHz, yet it still generates ISHE-detectable spin pumping in Pt because strong magnetoelastic coupling converts large elastic amplitudes into large magnetic oscillations (Gabrielyan et al., 28 May 2025).

4. Selection rules, symmetry, and wave polarization

Selection rules are a defining feature of acoustic spin resonance, because the acoustic field couples through tensors whose symmetry can differ sharply from that of magnetic-dipole driving. In the SiC $\Delta m = \pm 2$3 vacancy, the quadratic operator structure of $\Delta m = \pm 2$4 makes both $\Delta m = \pm 2$5 and $\Delta m = \pm 2$6 resonances accessible. Experimentally, the angular dependence is not a trivial Zeeman effect: the resonance fields are independent of the in-plane field angle $\Delta m = \pm 2$7, but the amplitudes vary strongly with $\Delta m = \pm 2$8, producing a “butterfly-like” pattern for $\Delta m = \pm 2$9 and a “cocoon-like” pattern for $C_{3v}$0 in a standing-wave cavity (Hernández-Mínguez et al., 2020).

The beyond-spherical $C_{3v}$1 theory sharpens this point by showing that the anisotropy itself contains materials information. In the $C_{3v}$2-quantized basis, $C_{3v}$3 drive $C_{3v}$4 and $C_{3v}$5 drive $C_{3v}$6. The theory predicts that standing and traveling SAWs, together with field rotation in the $C_{3v}$7 and $C_{3v}$8 planes, allow extraction of the coupling ratios $C_{3v}$9 and $V_{\mathrm{Si}}$00. It also predicts a sixfold modulation with SAW tilt $V_{\mathrm{Si}}$01, with odd-in-$V_{\mathrm{Si}}$02 terms proportional to $V_{\mathrm{Si}}$03, a signature that cannot be reproduced by the spherical model (Koga et al., 2024).

Wave polarization is equally decisive in magnetic films. In a composite ZnO–YIG–GGG–YIG/Pt high-overtone bulk acoustic resonator, only shear thickness modes linearly excite acoustic spin waves, whereas longitudinal modes do not couple in the linear regime and appear only through parametric pumping. For a representative acoustic mode at $V_{\mathrm{Si}}$04 GHz, the paper identifies $V_{\mathrm{Si}}$05 Oe, $V_{\mathrm{Si}}$06 Oe, $V_{\mathrm{Si}}$07 Oe, and $V_{\mathrm{Si}}$08 Oe as the field scales delimiting linear and parametric regimes (Alekseev et al., 2024).

Surface-wave polarization can also change the dominant coupling channel from magnetoelasticity to spin–vorticity. In Cu/Ni$V_{\mathrm{Si}}$09Fe$V_{\mathrm{Si}}$10 on ST-cut quartz, a shear-horizontal SAW generates strong $V_{\mathrm{Si}}$11 and $V_{\mathrm{Si}}$12 components, whereas an idealized Rayleigh SAW yields mainly $V_{\mathrm{Si}}$13. Because the SH mode generates an in-plane effective spin-transfer torque in the ferromagnet, the measured power absorption is four orders of magnitude higher than for Rayleigh SAW at the same wavelength, and the normalized absorption reaches $V_{\mathrm{Si}}$14 at $V_{\mathrm{Si}}$15 GHz (Huang et al., 2023).

Strain-field engineering at the transducer level modifies the same symmetry logic. Focused interdigital transducers on LiNbO$V_{\mathrm{Si}}$16 introduce finite $V_{\mathrm{Si}}$17, $V_{\mathrm{Si}}$18, and $V_{\mathrm{Si}}$19 components in addition to the usual Rayleigh terms. In Ni, this rotates and reshapes the angular absorption lobes and raises the linear-regime absorption contrast from $V_{\mathrm{Si}}$20 dB/mm for straight IDTs to $V_{\mathrm{Si}}$21 dB/mm for $V_{\mathrm{Si}}$22 focused IDTs at sub-GHz frequencies (Shah et al., 2023).

Finally, in spin–orbit-coupled itinerant systems, selection rules are tied to band symmetry rather than to localized-spin matrix elements. In monolayer MoS$V_{\mathrm{Si}}$23, the acoustic wave produces an effective in-plane field polarized along $V_{\mathrm{Si}}$24, so the relevant spin-flip matrix element is proportional to $V_{\mathrm{Si}}$25, momentum is conserved up to $V_{\mathrm{Si}}$26, and an out-of-plane magnetic field splits the valley-degenerate ASR into $V_{\mathrm{Si}}$27- and $V_{\mathrm{Si}}$28-resolved resonances (Sonowal et al., 2022).

5. Coherent control, fidelity, and dissipation

The most explicit gate-level control protocol currently described for ASR is the hybrid quantum-dot scheme. Under the effective Hamiltonian

$V_{\mathrm{Si}}$29

two flat-top acoustic pulses with opposite azimuths implement a naive $V_{\mathrm{Si}}$30 gate. With $V_{\mathrm{Si}}$31 meV, $V_{\mathrm{Si}}$32 meV, $V_{\mathrm{Si}}$33eV, and $V_{\mathrm{Si}}$34 meV, each $V_{\mathrm{Si}}$35 rotation takes about $V_{\mathrm{Si}}$36 ns, so the two-pulse $V_{\mathrm{Si}}$37 gate takes about $V_{\mathrm{Si}}$38 ns. Under cooled nuclear-spin conditions, the Overhauser-limited infidelity remains below about $V_{\mathrm{Si}}$39 for GaAs/AlGaAs droplet QDs and about $V_{\mathrm{Si}}$40 for InAs/GaAs self-assembled dots; with $V_{\mathrm{Si}}$41 ns and $V_{\mathrm{Si}}$42 GHz, the total gate infidelity is about $V_{\mathrm{Si}}$43, i.e. about $V_{\mathrm{Si}}$44 fidelity. An optimized seven-pulse phase-only sequence reduces the average longitudinal-noise infidelity below $V_{\mathrm{Si}}$45 already for $V_{\mathrm{Si}}$46 ns (Kuniej et al., 16 Dec 2025).

Coherent room-temperature control has also been demonstrated in defect and molecular systems. In the 4H-SiC lateral overtone bulk acoustic resonator, pulsed acoustic driving at $V_{\mathrm{Si}}$47 MHz produces optically detected coherent population oscillations, with the faster decay on the resonator wings attributed to inhomogeneous stress distribution through the confocal depth slice (Dietz et al., 2022). In pentacene thin films, pulsed SAW excitation at the strongest mode near $V_{\mathrm{Si}}$48 MHz yields Rabi oscillations fit by

$V_{\mathrm{Si}}$49

with the experimentally reported scaling $V_{\mathrm{Si}}$50, consistent with a linearly transduced acoustic drive (Chen et al., 9 Feb 2026).

In collective-spin systems, dissipation enters both through magnetic linewidths and through the acoustic cavity itself. In the planar SAW cavity magnomechanical Ni device, the acoustic response is modified by the magnon self-energy,

$V_{\mathrm{Si}}$51

which shifts the cavity frequency and damping. The measured $V_{\mathrm{Si}}$52 MHz and $V_{\mathrm{Si}}$53 place the device in the regime $V_{\mathrm{Si}}$54, so normal-mode splitting is not yet resolved but coherent interaction is already inferred from the cooperativity exceeding unity (Hatanaka et al., 2021).

Time-resolved acoustic spin pumping gives another operational metric: signal appears only under resonant elastic excitation. In Co/Pt, the SAW arrival time produces both a resonant attenuation in transmitted power and a synchronous ISHE signal of about $V_{\mathrm{Si}}$55V, with sign reversal under magnetic-field reversal and no detectable off-resonant spin current within the reported $V_{\mathrm{Si}}$56V resolution (Weiler et al., 2011). In cavity-enhanced SAW pumping through a Ni/Cu/Bi$V_{\mathrm{Si}}$57O$V_{\mathrm{Si}}$58 interface, the scaling of both acoustic absorption and inverse Edelstein signal with cavity build-up shows directly that the limiting factor is not merely magnetic susceptibility but also local acoustic field intensity (Hwang et al., 2020).

Antiferromagnetic acoustic spin pumping in hematite adds a low-frequency limit to this picture. There, the spin current is predicted to scale as

$V_{\mathrm{Si}}$59

so the very large ultrasonic response follows from the product of strong magnetoelastic coupling and high mechanical quality factor rather than from proximity to a high-frequency intrinsic magnetic mode (Gabrielyan et al., 28 May 2025).

6. Applications, open problems, and contested claims

The primary attraction of ASR is architectural. Acoustic wavelengths at tens of GHz are microns to submicrons, four orders of magnitude shorter than the free-space microwaves that would produce the same frequency, which favors local addressability, on-chip routing, and dense integration (Kuniej et al., 16 Dec 2025). In quantum-dot proposals, this makes ASR a candidate interface for state transfer and transduction among acoustic, optical, and microwave domains. In SiC, it supports all-acoustic control of multilevel spin defects at room temperature and naturally integrates with photonics and NEMS (Hernández-Mínguez et al., 2020). In bulk acoustic SiC resonators, the same physics already functions as stress metrology, revealing stress concentration in tethers and near etch asperities (Dietz et al., 2022).

Several current research directions follow directly from the reviewed results. One is chirality and nonreciprocity: traveling-wave SAWs in SiC are predicted to produce ASR amplitudes that change under $V_{\mathrm{Si}}$60 or under reversal of the SAW propagation direction, but the reported room-temperature experiment was performed in a standing-wave cavity, so dedicated traveling-wave devices remain to be realized (Hernández-Mínguez et al., 2020). Another is single- or few-spin scaling. In molecular HODSAR, the present measurements are ensemble-based and do not yet calibrate the absolute strain susceptibility, but the combination of high-$V_{\mathrm{Si}}$61 SAW confinement and zero-field triplet transitions suggests a path toward mechanically addressable molecular spin control (Chen et al., 9 Feb 2026). In nuclear systems, SAW-cavity NSAR was proposed specifically as a route to detecting a single flake of an atomically thin semiconductor; the estimate relies on $V_{\mathrm{Si}}$62, mode volume $V_{\mathrm{Si}}$63 mm$V_{\mathrm{Si}}$64, and the favorable planar overlap of the Barnett field with a near-surface specimen (Usami et al., 2020).

A broader implication is that ASR is not limited to spin-$V_{\mathrm{Si}}$65 or to equilibrium magnetic matter. In monolayer MoS$V_{\mathrm{Si}}$66, it points toward valley-resolved acoustospintronics once the Fermi level is tuned near the finite-$V_{\mathrm{Si}}$67 crossing of the conduction subbands (Sonowal et al., 2022). In spinor polariton condensates, theory predicts that an acoustic effective magnetic field transverse to the static in-plane splitting should produce nonlinear resonance, amplitude hysteresis, and resonant switching between bifurcated circular-polarization states, with a Zeeman splitting providing an additional conservative tuning knob (Saltykova et al., 15 May 2026).

The literature also contains a markedly different and more controversial usage of the term. In anthracite samples studied by stationary ESR, ASR is defined as an emission process driven by a coherent reservoir of resonance phonons created in situ under strong spin–photon–phonon coupling. That work reports an acoustic Rabi frequency $V_{\mathrm{Si}}$68 kHz, linewidth narrowing to $V_{\mathrm{Si}}$69 G in a nonlinear regime, a phonon coherence time exceeding $V_{\mathrm{Si}}$70 minutes at room temperature, and claims of superconductivity-like behavior under ESR conditions. The same paper also states that independent corroboration with time-domain ESR/EPR, ultrasound transduction, microwave cavity ringdown, dc transport, and magnetic susceptibility would be valuable, and that direct measurements of zero resistance, Meissner effect, or Josephson-like $V_{\mathrm{Si}}$71–$V_{\mathrm{Si}}$72 characteristics would be decisive (Yerchuck et al., 2011).

Taken together, the present record shows that acoustic spin resonance is no longer a niche variant of ESR. It is a heterogeneous research domain in which mechanical waves address spins through rank-2 spin–strain operators, optically assisted excited states, magnetoelastic torques, spin–vorticity coupling, or Barnett fields, depending on the platform. The common theme is the replacement of electromagnetic drive by a mechanically structured field whose symmetry, momentum, and confinement can be engineered with unusual precision.