Spin Relaxometry with Solid-State Defects: Theory, Platforms, and Applications

TL;DR

Spin relaxometry uses solid-state defects to convert environmental magnetic fluctuations into measurable spin-relaxation rates, enabling local, spectrally selective probing of dynamical processes. The paper synthesizes theory and experiment through a minimal NV Hamiltonian and a filter-function framework that links relaxation rates to environmental noise spectra, and surveys platforms (NV in diamond, hBN defects, SiC defects) and cross-relaxometry/NMR applications. It discusses practical challenges—surface and charge noise, geometry, and the inverse problem of inferring S_B(ω)—and outlines opportunities in high-field operation, device integration, and standardized benchmarking. Overall, relaxometry is positioned as a versatile metrology for quantum materials and biological systems, with potential for quantitative noise tomography and multiplexed sensing at the nanoscale.

Abstract

Spin relaxometry using solid-state spin defects, such as the diamond nitrogen-vacancy (NV) center, probes dynamical processes by measuring how environmental fluctuations enhance the spin relaxation rate. In the weak-coupling limit, relaxation rates sample the transverse magnetic-noise power spectral density through a sensor-specific filter function, turning the defect into a local, frequency-selective noise spectrometer. This review bridges theory and experiment, clarifying how measured relaxation rates map onto noise spectra and how near-field geometry shapes the response. We highlight representative applications across condensed-matter physics, chemical and biological sensing, and relaxometry-based magnetic-resonance spectroscopy. We conclude with emerging opportunities and key challenges.

Figures (5)

• Figure 1: Experimental platforms for spin relaxometry. (a) Principle of spin relaxometry as frequency-selective noise detection: Optical pumping initializes the defect spin (e.g., NV) and photoluminescence readout monitors its population dynamics. Longitudinal relaxation ($T_1$) is enhanced by transverse magnetic noise with spectral weight resonant with the spin transition (tunable via bias field and, when used, microwave control), enabling spectroscopy of external targets through resonant energy exchange with the environment. (b) NV-based spin relaxometry modalities and hardware geometries: Schematic illustrations of (from left to right) shallow near-surface NV centers in bulk diamond, scanning NV tips, wide-field NV ensembles, NV centers under high pressure in a diamond anvil cell (DAC), and fluorescent nanodiamonds in solution for relaxometric sensing in diverse environments. (c) Hexagonal boron nitride (hBN), as a two-dimensional spin-relaxometry platform, enables intrinsically small sensor--environment standoff distances, which is particularly advantageous in van der Waals heterostructures where hBN can be stacked directly with other 2D materials that host spin and charge noise. (d) Silicon carbide (SiC) is a promising host for chip-integrated spin relaxometry, leveraging wafer-scale processing, mature device fabrication, and defect spins that are compatible with on-chip photonic and electronic integration.
• Figure 2: (a) Schematic of overlap between power spectral density of sample (blue) with that of the spin defect (red). Center (ODMR) frequency of spin defect is represented by the vertical gray dashed line. (b) Schematic of a single spin sensor experiencing magnetic field fluctuations (blue gradient/squiggly arrows) above a sample of fluctuating spins. The sensor spin is sensitive to a sample volume illustrated by the concentric green hemispheres, with stronger coupling to spins near the center (dark green) and falling off as $r^{-6}$. The distance $h$ sets the spatial resolution of the sensor.
• Figure 3: Experimental applications in condensed matter systems. (a) Probing Johnson noise in metal using single NV centers. A layer of SiO$_2$ is grown on the diamond surface with gradually increasing thickness, followed by a 60 nm silver film. The NV relaxation rate $\Gamma_1$ is measured as a function of distance from the silver film, scaling inversely with distance. Adapted from Ref. kolkowitz2015probing. (b) Investigating non-equilibrium dynamics in graphene. A hBN-encapsulated graphene device on diamond substrate (upper panel). The local magnetic noise, probed by the NV relaxation rate, is measured as a function of distance from the drain, consistent with the exponential growth of phonons (lower panel). Adapted from Ref. andersen2019electron. (c) Imaging domain walls in a synthetic antiferromagnet. The relaxation time $T_1$ of the NV center decreases dramatically when engaged on a domain wall, compared to on domain or retracted. Adapted from Ref. finco2021imaging. (d) Imaging the spin fluctuations in a van der Waals ferromagnet with boron vacancy centers in hBN. A Fe$_3$GeTe$_2$(FGT)/hBN van der Waals heterostructure is transferred on a gold microwave stripline (left panel). The temperature-dependent relaxation rate exhibits a peak amplitude at the phase transition temperature $T_c = 200$ K (right panel). Adapted from Ref. huang2022wide. (e) Probing superconducting dynamics in a thin film Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO). The relaxation rate $\Gamma_1$ of NV on BSCCO is measured as a function of temperature. In the absence of magnetic field, it reveals three distinct regimes: Johnson noise in metallic phase, nodal quasiparticles excitations deep in superconducting phase, and critical fluctuations near the phase transition. Adapted from Ref. liu2025quantum.
• Figure 4: Experimental applications in biological systems. (a) Intracellular radical dynamics. Targeted fluorescent nanodiamonds enable nanoscale $T_1$ relaxometry inside living cells, allowing spatially and temporally resolved readout of radical-driven spin noise at specific intracellular locations, including bacterial surfaces, mitochondria, and lysosomes. (b) Chip-scale biomolecular assays. Planar diamond substrates with shallow near-surface NV ensembles provide quantitative relaxometry of paramagnetic biomolecules in controlled assay environments. (c) Integrated and scalable platforms. Microfluidic and fiber-integrated relaxometry platforms address throughput and accessibility by enabling signal modulation, background suppression, and remote sensing in complex biological fluids.
• Figure 5: Experimental applications in spin dynamics. (a) Defect density map of boron vacancies obtained using scanning NV cross-relaxometry. Inset: The profile of ${\rm V}_{\rm B}^-$ density as a function of position, over the line indicated by the white dashed line. Adapted from Ref. melendez2025probing. (b) Comparison of Hahn echo coherence times ($T_{2,\text{echo}}$) as a function of NV depth. The high-temperature and oxygen-annealed sample (colored markers) exhibits significantly improved coherence times at the same depths compared to those under a standard triacid-cleaned surface (grey markers). Adapted from Ref. sangtawesin2019origins. (c)-(d) Representative spectra from poly(methyl methacrylate) (PMMA) measured with a single $^{14}NV$ center using (c) microwave-free $T_1$ relaxometry and (d) an XY8-N dynamical-decoupling sequence (N=256 microwave $\pi-$pulses). The corresponding pulse sequences are shown schematically, with laser pulses in green and microwave pulses in red ($0^\circ$ phase) or blue ($90^\circ$ phase). Adapted from Ref. wood2017microwave.