Tunneling-Induced Relaxometry in Quantum Systems

• Tunneling-induced relaxometry signals are observables where quantum state decay is enhanced by tunneling-assisted energy exchange with nearby systems.
• These signals are measured via cross-relaxation, RF-driven tunneling, and cotunneling methods, yielding nanoscale spectral information across various platforms.
• Accurate interpretation demands disentangling intrinsic relaxation from measurement artifacts to reliably infer underlying coupling mechanisms and rates.

Searching arXiv for papers on tunneling-induced relaxometry and closely related spin-relaxometry mechanisms. Tunneling-induced relaxometry signals are relaxation-based observables in which the measured decay of a localized quantum degree of freedom is controlled by excitation transfer, electron tunneling, cotunneling, or tunneling-assisted coupling to an environment. Across current implementations, the signal is not defined by a single hardware platform but by a common operational structure: a probe state acquires an additional relaxation channel when it can exchange energy or population with nearby spins, itinerant electrons, a quasiparticle continuum, or another localized state. In this sense, the literature spans dipolar cross-relaxation between solid-state spins, tunneling-electron-induced decay in ESR-STM, relaxation-limited transport through Shiba states, cotunneling-driven spin relaxation in quantum dots, and charge-conversion artifacts in NV relaxometry that are plausibly mediated by carrier capture through traps or surface states (Melendez et al., 13 Apr 2025).

1. Definition and conceptual boundaries

In the narrowest usage, tunneling-induced relaxometry refers to situations in which a measured relaxation observable is generated by a tunneling-like process in the underlying Hilbert space. The clearest example is the hybrid NV–hBN system, where the NV $|m_s=0\rangle \leftrightarrow |m_s=+1\rangle$ excitation can be transferred to a nearby $\mathrm{V}_\mathrm{B}^-$ transition through dipolar flip-flop terms. The experimentally observed consequence is a shortening of the NV longitudinal relaxation time $T_1$, or equivalently an increase in $1/T_1$, when the two transitions are tuned into resonance (Melendez et al., 13 Apr 2025).

A broader usage appears in ESR-STM and mesoscopic transport. In ESR-STM, the applied RF voltage simultaneously drives spin transitions, generates spin-dependent tunneling current, and adds relaxation and decoherence channels because the extra RF-induced electrons scatter inelastically from the spin. Under those conditions, an echo-like decay can be dominated by tunneling-induced relaxometry rather than intrinsic phase coherence (Greule et al., 27 Mar 2026). In superconducting STM on Shiba states, single-electron current through a localized subgap state requires relaxation between the Shiba state and the quasiparticle continuum; the dependence of subgap transport on those relaxation rates turns the tunneling experiment into a relaxometry protocol (Ruby et al., 2015).

The concept also includes spin relaxometry in quantum-dot hybrids. In a GaAs/AlGaAs double quantum dot coupled to a lead, first-order tunneling induces both charge and spin relaxation, while deep in Coulomb blockade second-order cotunneling flips the spin without changing the charge state. The measured singlet probability thereby becomes a direct probe of higher-order tunneling processes (Otsuka et al., 2016). In self-assembled quantum-dot molecules, phonon-assisted interdot tunneling can itself carry a spin-flip probability, so tunneling contributes directly to $T_1$-type dynamics even at zero magnetic field (Gawełczyk et al., 2019).

A common misconception is that relaxometry necessarily measures an intrinsic relaxation constant of the probed object. The current literature instead shows that the observed decay may be a composite of intrinsic relaxation, environment-induced noise, measurement backaction, population transfer through tunneling channels, or charge conversion (Greule et al., 27 Mar 2026).

2. Microscopic mechanisms

The microscopic mechanisms differ across platforms, but they share a common structure: a localized degree of freedom couples to another subsystem through a matrix element that opens an additional decay path.

For dipolar cross-relaxation, the NV–$\mathrm{V}_\mathrm{B}^-$ system is the canonical example. The coupling is described by the magnetic dipole-dipole Hamiltonian

$$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$

In the secular approximation it contains flip-flop terms that exchange spin excitations. When

$$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$

the transfer becomes resonant, and the cross-relaxation rate is modeled as

$$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$

with $W_d$ the effective dipolar coupling, $\mathrm{V}_\mathrm{B}^-$0, and $\mathrm{V}_\mathrm{B}^-$1 the detuning. The Lorentzian dependence on $\mathrm{V}_\mathrm{B}^-$2 makes the tunneling interpretation explicit: $\mathrm{V}_\mathrm{B}^-$3 acts as a tunneling matrix element, while $\mathrm{V}_\mathrm{B}^-$4 sets the resonance width (Melendez et al., 13 Apr 2025).

In ESR-STM, the relevant mechanism is different but conceptually analogous. The time-dependent bias $\mathrm{V}_\mathrm{B}^-$5 produces a coherent drive term and, simultaneously, a stream of tunneling electrons that probe and relax the spin. The rate of tunneling events is $\mathrm{V}_\mathrm{B}^-$6, and the extracted probability of decoherence per electron for FePc on MgO/Ag(001) is $\mathrm{V}_\mathrm{B}^-$7. Here the relaxometry signal is not a passive response of the spin to an external bath; it is measurement-induced decay caused by the same RF voltage that nominally implements coherent control (Greule et al., 27 Mar 2026).

For Shiba states in a superconducting tunnel junction, the key point is that single-electron tunneling changes the occupation of a localized subgap state. A steady current is possible only if the Shiba level can relax to or from the quasiparticle continuum with rates $\mathrm{V}_\mathrm{B}^-$8 and $\mathrm{V}_\mathrm{B}^-$9. The total current splits into a single-particle contribution $T_1$0 and an Andreev contribution $T_1$1, and the former is explicitly proportional to the relaxation processes that empty or refill the Shiba state. Without those rates, the single-electron current vanishes even if the tunnel coupling is finite (Ruby et al., 2015).

In quantum-dot hybrids, two mechanisms are distinguished. Near a charge transition, first-order sequential tunneling changes both charge and spin. Deep in Coulomb blockade, inelastic spin-flip cotunneling remains active and is described by

$T_1$2

This process changes the spin state while leaving the charge unchanged, which is why spin readout can detect higher-order tunneling events that are invisible in the charge signal (Otsuka et al., 2016).

In self-assembled InAs/GaAs quantum-dot molecules, the mechanism is phonon-assisted interdot tunneling in the presence of spin mixing. The calculated spin-flip tunneling rate can be as high as $T_1$3 of the spin-conserving one, with the main contribution identified as Dresselhaus spin-orbit interaction. At magnetic fields above $T_1$4 T, that contribution is surpassed by mechanisms due to structural shear strain (Gawełczyk et al., 2019).

3. Signal formation and mathematical descriptions

The measured signal in relaxometry is ordinarily a decay constant, a spectral line shape, a current, or a spatial map. What unifies these observables is that they encode an overlap between the probe dynamics and the spectral properties of the coupled environment.

For NV $T_1$5 relaxometry, the basic relation is

$T_1$6

In the NV–hBN hybrid system, the explicit cross-relaxation contribution $T_1$7 is equivalent to a Lorentzian peak in the transverse magnetic noise spectral density centered at the $T_1$8 resonance. The amplitude depends on $T_1$9, on the number or density of $1/T_1$0 spins within the sensing volume, and on their decoherence through $1/T_1$1 (Melendez et al., 13 Apr 2025).

The same spectral-overlap logic appears in scanning-probe NV measurements of superparamagnetic magnetite nanoparticles. Schmid-Lorch et al. model the nanoparticle magnetization fluctuations as an Ornstein-Uhlenbeck process with

$1/T_1$2

leading to

$1/T_1$3

The external decoherence is then

$1/T_1$4

with $1/T_1$5 the filter function of the chosen protocol. The paper does not explicitly model quantum tunneling of magnetization, but it states that the formalism is generic and that tunneling-induced fluctuations would enter through the same spectral-density framework (Schmid-Lorch et al., 2015).

In ESR-STM, the directly measured quantity is the current change. For Rabi traces, the signal is modeled as

$1/T_1$6

The term $1/T_1$7 is central because it shows that even at $1/T_1$8, the RF field alone generates a spin-dependent current and therefore probes the spin during the pulse. This same current also relaxes the spin, which is why an echo-like decay can become a relaxometry signal (Greule et al., 27 Mar 2026).

For Shiba transport, the current through the localized subgap state is governed by tunnel rates $1/T_1$9, $T_1$0, and the relaxation rates $T_1$1, $T_1$2. In the weak-tunneling limit the peak heights scale linearly with conductance and satisfy relations such as

$T_1$3

while in the strong-tunneling regime the single-electron current saturates at values of order $T_1$4. Those algebraic relations are what make the STM signal a relaxometry observable rather than only a spectroscopy trace (Ruby et al., 2015).

4. Experimental realizations

These mechanisms have been realized in several distinct architectures. The platforms differ in readout modality and microscopic coupling, but each uses a relaxation observable to infer otherwise inaccessible dynamics.

Platform	Tunneling or transfer channel	Relaxometry observable
NV–hBN hybrid	Dipolar flip-flop cross-relaxation	NV $T_1$5, $T_1$6-MR, iso-$T_1$7 maps
ESR-STM on FePc/MgO/Ag(001)	RF- and DC-driven tunneling electrons	$T_1$8, apparent echo decay
Shiba STM on Mn/Pb(111)	Tip-Shiba tunneling plus relaxation to continuum	$T_1$9, $\mathrm{V}_\mathrm{B}^-$0, saturation currents
GaAs/AlGaAs QD–lead hybrid	Sequential tunneling and cotunneling	singlet probability, charge sensor response
InAs/GaAs QD molecules	Phonon-assisted interdot tunneling	spin-flip tunneling rate, effective $\mathrm{V}_\mathrm{B}^-$1

In the NV–hBN implementation, a single NV is implanted about $\mathrm{V}_\mathrm{B}^-$2 nm below the diamond surface at the apex of a nanopillar, the hBN membrane is $\mathrm{V}_\mathrm{B}^-$3–$\mathrm{V}_\mathrm{B}^-$4 nm thick, and frequency-modulated contact mode keeps the NV–hBN separation around $\mathrm{V}_\mathrm{B}^-$5 nm. At a field direction $\mathrm{V}_\mathrm{B}^-$6 from the NV axis, the NV and $\mathrm{V}_\mathrm{B}^-$7 transitions become degenerate near $\mathrm{V}_\mathrm{B}^-$8 G, and the resulting cross-relaxation sharply reduces $\mathrm{V}_\mathrm{B}^-$9. The reported values are $$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$0 ms without drive and off cross-relaxation, $$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$1s at the cross-relaxation field with no drive, and $$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$2s at the cross-relaxation field with a $$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$3 dBm drive on the $$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$4 $$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$5 transition (Melendez et al., 13 Apr 2025).

In scanning NV relaxometry on a single $$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$6-nm Fe$$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$7O$$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$8 nanoparticle, the shallow NV is about $$H_\mathrm{dip} = \frac{\mu_0}{4\pi} \frac{\gamma_e^2 \hbar^2}{r^3} \left[ \mathbf{S}_\mathrm{NV}\cdot\mathbf{S}_\mathrm{V_B} - 3(\mathbf{S}_\mathrm{NV}\cdot\hat{r})(\mathbf{S}_\mathrm{V_B}\cdot\hat{r}) \right].$$9 nm below the diamond surface, the static field is $$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$0 mT, and combined $$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$1 and $$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$2 imaging yields anisotropic spots whose shapes reflect the different sensitivities to $$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$3 and $$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$4. Joint fitting of multiple contrast images gives $$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$5 nm and $$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$6 nm for the NV-particle geometry (Schmid-Lorch et al., 2015).

In ESR-STM on FePc/MgO/Ag(001), the key scales are $$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$7 ns, a linear $$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$8 relation with slope $$\omega_\text{NV}^{0\leftrightarrow +1}(B) \approx \omega_\mathrm{VB}^{0\leftrightarrow -1}(B),$$9, and apparent one-delay Hahn or Carr-Purcell times that extend far beyond the independently known $$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$0 ns. For Fe–FePc complexes, the refined two-delay protocol yields coherent interference only up to total delay times $$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$1 ns, implying $$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$2 ns (Greule et al., 27 Mar 2026).

In the QD–lead hybrid, measured relaxation times separate the sequential and cotunneling regimes. At operation point O$$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$3, the spin relaxation time is approximately $$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$4s while the charge relaxation time is approximately $$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$5s. At O$$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$6, the spin still relaxes with $$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$7s while the charge histogram remains fixed, revealing cotunneling-induced spin decay (Otsuka et al., 2016).

5. Measurement protocols and interpretation pitfalls

The literature repeatedly shows that relaxometry signals can be misidentified if one assumes that any measured decay is a direct estimate of intrinsic $$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$8 or $$\Gamma_1^\text{CR} = \frac{W_d^2}{2\pi} \frac{\Sigma_2}{\Sigma_2^2 + \delta^2},$$9.

The most explicit case is ESR-STM. Standard one-delay Hahn protocols on FePc yield

$W_d$0

and $W_d$1 scales linearly with current. Yet the same exponential decay persists when the sequence is deliberately made non-echo-like, including unequal delays, wrong pulse areas, and pulse trains such as $W_d$2–$W_d$3–$W_d$4 or three equal $W_d$5 pulses. In addition, Carr-Purcell sequences with $W_d$6 refocusing pulses produce an apparent coherence time that grows almost linearly with $W_d$7, reaching $W_d$8 ns at $W_d$9, which exceeds the bound implied by $\mathrm{V}_\mathrm{B}^-$00 ns. The paper concludes that the standard one-delay decay is dominated by tunneling-induced relaxation rather than by intrinsic coherence (Greule et al., 27 Mar 2026).

The recommended diagnostic is a two-delay Hahn protocol,

$\mathrm{V}_\mathrm{B}^-$01

implemented so that lock-in A and B cycles have equal total RF excitation and therefore largely cancel rectification and relaxometry backgrounds. A genuine echo then appears as an interference feature localized near $\mathrm{V}_\mathrm{B}^-$02, whereas a pure relaxometry signal does not exhibit that refocusing condition (Greule et al., 27 Mar 2026).

NV relaxometry has a different but equally important artifact channel: charge conversion. In nanodiamonds excited at $\mathrm{V}_\mathrm{B}^-$03 nm, NV$\mathrm{V}_\mathrm{B}^-$04NV$\mathrm{V}_\mathrm{B}^-$05 ionization during the laser pulse and dark NV$\mathrm{V}_\mathrm{B}^-$06NV$\mathrm{V}_\mathrm{B}^-$07 recharging can distort or even dominate the apparent $\mathrm{V}_\mathrm{B}^-$08 signal. The measured recharging dynamics are biexponential,

$\mathrm{V}_\mathrm{B}^-$09

with $\mathrm{V}_\mathrm{B}^-$10 and $\mathrm{V}_\mathrm{B}^-$11. At $\mathrm{V}_\mathrm{B}^-$12W, the NV$\mathrm{V}_\mathrm{B}^-$13 signal gives $\mathrm{V}_\mathrm{B}^-$14 ms in an all-optical protocol and $\mathrm{V}_\mathrm{B}^-$15 ms in the MW $\mathrm{V}_\mathrm{B}^-$16-pulse protocol, but at higher powers the normalized NV$\mathrm{V}_\mathrm{B}^-$17 fluorescence becomes non-monotonic and can invert because recharging outweighs spin relaxation. The paper therefore recommends low excitation power and fluorescence normalization before the relaxation interval (Barbosa et al., 2023).

A further misconception is that tunneling-induced relaxometry is always a nuisance. The superconducting STM work on Shiba states shows the opposite possibility: when relaxation processes are incorporated into the model, peak ratios and saturation currents become a quantitative route to $\mathrm{V}_\mathrm{B}^-$18 and $\mathrm{V}_\mathrm{B}^-$19, so the backaction channel is the measurement principle rather than an artifact (Ruby et al., 2015).

6. Significance, limits, and directions of extension

The significance of tunneling-induced relaxometry is that it converts relaxation into a nanoscale spectroscopic observable in parameter regimes where direct optical or electrical access to the target subsystem is weak or absent.

In the NV–hBN system, the method eliminates the need for optical excitation or fluorescence detection of $\mathrm{V}_\mathrm{B}^-$20, resolves hyperfine splitting in isotopically enriched h$\mathrm{V}_\mathrm{B}^-$21B$\mathrm{V}_\mathrm{B}^-$22N, and yields $\mathrm{V}_\mathrm{B}^-$23-MR spectra with a linewidth of $\mathrm{V}_\mathrm{B}^-$24 MHz and contrast of $\mathrm{V}_\mathrm{B}^-$25, compared with $\mathrm{V}_\mathrm{B}^-$26 MHz and $\mathrm{V}_\mathrm{B}^-$27 for $\mathrm{V}_\mathrm{B}^-$28 ODMR under the reported conditions. A plausible implication is that tunneling-like cross-relaxation can function as a general route to nanoscale spectroscopy of spin systems that are difficult to read out directly (Melendez et al., 13 Apr 2025).

In superconducting STM on Mn/Pb(111), tunneling spectroscopy into a localized subgap state extracts absolute relaxation rates. At $\mathrm{V}_\mathrm{B}^-$29 K the extracted values are $\mathrm{V}_\mathrm{B}^-$30 and $\mathrm{V}_\mathrm{B}^-$31, corresponding to $\mathrm{V}_\mathrm{B}^-$32 ns and $\mathrm{V}_\mathrm{B}^-$33 ns; a cross-check gives $\mathrm{V}_\mathrm{B}^-$34. At $\mathrm{V}_\mathrm{B}^-$35 K, $\mathrm{V}_\mathrm{B}^-$36, consistent with a strong thermal enhancement of relaxation. The data are more consistent with cascaded relaxation via higher-energy Shiba states than with direct Shiba-continuum transitions using standard phonon-assisted formulas (Ruby et al., 2015).

In tunnel-coupled quantum-dot systems, the consequences extend beyond individual tunneling events. Phonon-assisted spin-flip tunneling in self-assembled quantum-dot molecules remains active at zero magnetic field, misalignment can enhance the relaxation rate by over an order of magnitude, and virtual tunneling at nonzero temperature provides a Zeeman-doublet relaxation channel even without the magnetic field. Near resonance, the effective $\mathrm{V}_\mathrm{B}^-$37 for a stationary electron can be shortened to $\mathrm{V}_\mathrm{B}^-$38 ms at $\mathrm{V}_\mathrm{B}^-$39 K and to $\mathrm{V}_\mathrm{B}^-$40s at $\mathrm{V}_\mathrm{B}^-$41 K in the reported calculations (Gawełczyk et al., 2019).

The principal limitations are also system-dependent. In the NV–hBN study, relaxometry is slower than CW-ODMR by about $\mathrm{V}_\mathrm{B}^-$42 in acquisition time, though the paper notes possible improvements from NV ensembles, optimized NV depth, and lower temperature (Melendez et al., 13 Apr 2025). In ESR-STM, direct tunneling readout intertwines driving, probing, and relaxation so strongly that extracting intrinsic $\mathrm{V}_\mathrm{B}^-$43 requires deliberately balanced pulse protocols or alternative readout architectures (Greule et al., 27 Mar 2026). In NV nanodiamond relaxometry, optical power itself alters the charge-state population, so any quantitative interpretation of $\mathrm{V}_\mathrm{B}^-$44 requires simultaneous control of charge conversion (Barbosa et al., 2023).

Taken together, these results suggest that tunneling-induced relaxometry is best understood not as a single technique but as a family of measurements in which relaxation acts as a reporter of microscopic transfer channels. Depending on platform, the relevant transfer may be dipolar excitation exchange, RF-driven tunneling current, relaxation-limited occupation of a localized subgap state, cotunneling with an electronic reservoir, or phonon-assisted interdot transfer. The unifying lesson is that the measured decay encodes the coupling pathway itself, and that rigorous interpretation depends on identifying whether the observed relaxation is the target observable, a controlled readout resource, or a measurement-induced artifact.