Local Noise Magnetometry

A spin placed near a material can detect fluctuations even when there is no deliberately applied alternating field. Its relaxation rate depends on the magnetic noise at the spin's transition frequency and on the polarization it can absorb. Agarwal and collaborators use this connection to turn local spin sensors into probes of transport and correlations. The key advance is not simply improved sensitivity: it is a calculable relation between sensor geometry, noise polarization, and the response of the material.

Figure to read

Opposite sensor spin initializations couple to magnetic fluctuations of opposite handedness. Figure 1 in the source paper. De, Suman Jyoti; Pereg-Barnea, Tami; Agarwal, Kartiek. Nanoscale Defects as Probes of Time-Reversal Symmetry Breaking, Physical Review X 16, 011001 (2026). Paper. CC BY 4.0. Original manuscript graphic; no alterations.

The two drawn sensors represent alternative initializations of the same sensor, not a required pair of defects. The important signal is the difference between relaxation channels; its relation to Hall response depends on the sample and geometry.

Distance is a filter, not a perfect wavevector selector

Magnetic fields generated by short-wavelength current patterns decay rapidly away from a conducting surface. A sensor at height $z$ therefore samples a broad range of momenta with characteristic scale of order $1/z$. Varying height changes that distribution. In the two-dimensional theory developed by Agarwal and collaborators, the resulting noise is related primarily to transverse current response under the screening and frequency assumptions analyzed. 1

This is often summarized as measuring a momentum-dependent conductivity, but the experiment measures a weighted integral. Extracting a response function from that integral is an inverse problem. Finite height uncertainty, limited distance range, and background noise can make different response functions difficult to distinguish. The kernel should be included in fitting the data, rather than replacing it automatically with a delta function at a single wavevector.

Which transport regime is visible?

Ballistic, diffusive, and hydrodynamic behavior involve different relations among length scales. Momentum-conserving electron-electron collisions can establish a fluid-like regime before momentum is lost to disorder or phonons. By changing the distance from the sample, a local sensor can weight wavelengths on different sides of those crossover scales. The paper's schematic height dependence is therefore a guide to which regimes might be resolvable, not a universal curve for every conductor. 1

The one-dimensional work by Rodriguez-Nieva, Agarwal, and collaborators develops a related approach for wires and edge states. Sensor orientation and temperature dependence can help separate spin and charge correlations and distinguish scattering mechanisms. Dimensionality changes the electromagnetic kernel and the electronic theory; a formula derived for a two-dimensional sheet should not simply be reused for a narrow edge channel. 2

Handed fluctuations reveal broken time reversal

De, Pereg-Barnea, and Agarwal consider a further information channel: magnetic fluctuations of opposite circular polarization can have different spectra in a time-reversal-breaking material. Initializing the sensor in different spin states changes which fluctuations drive its relaxation. Comparing those rates can isolate response information lost in an unpolarized scalar noise measurement. Their theory relates the asymmetry to Hall-related response under the specified geometry and approximations. 3

This is especially interesting for chiral superconductors and quantum Hall systems, where the sign and wavevector structure of transverse response may distinguish competing states. The proposed access to Hall viscosity and other quantities is conditional on the model, frequency window, and experimental control. It should be presented as a route to discriminating measurements, not as a claim that any measured relaxation asymmetry uniquely identifies a particular topological phase.

What the experimental comparison requires

General quantum-sensing theory distinguishes relaxation measurements from phase-accumulation and dynamical-decoupling sequences. Each sequence has a different spectral response and sensitivity to technical noise. The NV-magnetometry literature also identifies practical constraints from defect depth, surface noise, optical readout, and sample integration. These are parts of a quantitative experiment, rather than corrections to consider only after the material theory is complete. 4 5

A useful protocol would vary height, frequency, temperature, and spin polarization wherever possible. A common material model should explain all those dependences with compatible parameters and a separately characterized background. A field reversal or comparison of opposite sensor initializations can be particularly valuable because it tests symmetry rather than just amplitude. The next pages connect this framework to graphene and Corbino measurements and the original two-dimensional paper. The open challenge is to make the inference robust enough that a distinctive noise signal becomes a credible measurement of an otherwise inaccessible response.

References

1. Agarwal, Kartiek; Schmidt, Richard; Halperin, Bertrand; Oganesyan, Vadim; Zaránd, Gergely; Lukin, Mikhail D.; Demler, Eugene. Magnetic noise spectroscopy as a probe of local electronic correlations in two-dimensional systems. Phys. Rev. B 95, 155107 (2017). Open manuscript.
2. Rodriguez-Nieva, Joaquin F.; Agarwal, Kartiek; Giamarchi, Thierry; Halperin, Bertrand I.; Lukin, Mikhail D.; Demler, Eugene. Probing one-dimensional systems via noise magnetometry with single spin qubits. Phys. Rev. B 98, 195433 (2018). Open manuscript.
3. De, Suman Jyoti; Pereg-Barnea, Tami; Agarwal, Kartiek. Nanoscale Defects as Probes of Time-Reversal Symmetry Breaking. Physical Review X 16, 011001 (2026). Open manuscript.
4. Degen, C. L.; Reinhard, F.; Cappellaro, P.. Quantum sensing. Reviews of Modern Physics 89, 035002 (2017). Open manuscript.
5. Casola, Francesco; van der Sar, Toeno; Yacoby, Amir. Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond. Nature Reviews Materials 3, 17088 (2018). Open manuscript.

Independent research synthesis. Literature checked 5 September 2026; preprints are identified in the references.