Generalized model of magnon kinetics and subgap magnetic noise

At a Glance

Metadata	Details
Publication Date	2022-05-09
Journal	Physical review. B./Physical review. B
Authors	Haocheng Fang, Shu Zhang, Yaroslav Tserkovnyak
Institutions	University of California, Los Angeles
Citations	5
Analysis	Full AI Review Included

Technical Documentation & Analysis: Magnon Kinetics Probing via NV Centers

Executive Summary

This research develops a generalized theoretical framework for two-dimensional (2D) magnon transport, successfully bridging the ballistic, intermediate, and diffusive regimes. The methodology relies critically on the use of Nitrogen-Vacancy (NV) centers in diamond as a noninvasive, high-sensitivity magnetic noise probe.

Generalized Transport Model: A unified theory based on the Boltzmann equation and generalized Lindhard function describes magnon transport across length scales ranging from the mean free path ($l \approx 100 \text{ nm}$) to the diffusion length ($l_s \approx 1.2 \text{ µm}$).
NV Center Application: NV relaxometry is confirmed as a powerful tool for probing subgap magnetic noise, offering high frequency resolution (GHz scale) and tunable distance control (nanometers to micrometers).
Predicted Scaling Laws: The NV transition rate ($\Gamma$) exhibits distinct power-law scaling with NV-material distance ($d$), transitioning from $\Gamma \sim d^{-2}$ (ballistic limit, $d \ll l$) to $\Gamma \sim d^{-6}$ or $\Gamma \sim d^{-4}$ (diffusive limits, $d \gg l_s$).
Material Requirement: The precision of the NV probe necessitates ultra-high purity Single Crystal Diamond (SCD) substrates with atomically flat surfaces for accurate nanoscale placement relative to the magnetic thin film.
Key Findings: The transport in 2D magnetic insulators is dominated by low-energy (infrared) magnons, rather than thermal magnons, highlighting the importance of precise material parameters (e.g., Gilbert damping $\alpha=10^{-4}$).

Technical Specifications

The following hard data points and material parameters were used or derived in the analysis of 2D magnon transport at $T=100 \text{ K}$.

Parameter	Value	Unit	Context
NV Resonance Frequency ($\omega/2\pi$)	2.87	GHz	Zero-field default
Magnon Gap ($\Delta/k_B$)	1	K	Energy scale
Temperature ($T$)	100	K	Operating temperature
Spin Stiffness ($A$)	10^-39	J·m²	Magnetic material property
Gilbert Damping ($\alpha$)	10^-4	Dimensionless	Magnetic dissipation
Magnon Mean Free Path ($l$)	100	nm	Crossover length scale
Spin Diffusion Length ($l_s$)	1.2	µm	$\sqrt{D\tau}$
Spin Diffusion Constant ($D$)	1.8 x 10^-4	m²·s^-1	Transport coefficient
Spin Conductivity ($\sigma$)	1.4 x 10³⁶	J^-1·s^-1	Transport coefficient
Spin Relaxation Time ($\tau$)	8.3	ns	Transport coefficient
Characteristic NV Distance ($d$)	80 to 1000	nm	Probing distance range

Key Methodologies

The theoretical and experimental approach combines advanced kinetic modeling with nanoscale quantum sensing techniques:

Kinetic Modeling: The Boltzmann equation is used to describe the dynamics of the magnon wave packet, incorporating relaxation-time approximation (RTA) for both spin-conserving ($\tau_c$) and spin-nonconserving ($\tau_r$) scattering processes.
Dynamic Susceptibility Derivation: The longitudinal dynamic spin susceptibility ($\chi”$) is derived in a generalized Lindhard form, applicable across all transport regimes (ballistic, intermediate, diffusive).
NV Relaxometry Principle: The NV transition rate ($\Gamma$, or $1/T_1$) is calculated by applying the fluctuation-dissipation theorem, relating the magnetic noise at the NV position to the derived dynamic spin susceptibility $\chi” (q, \omega)$.
Length Scale Probing: By varying the NV-material distance ($d$) from nanometers (ballistic regime, $d \ll l$) to micrometers (diffusive regime, $d \gg l$), the experiment maps the transition between different magnon transport kinetics.
Parameter Extraction: Effective transport coefficients (spin diffusion constant $D$, spin conductivity $\sigma$, and spin relaxation time $\tau$) are extracted from the diffusive limit of the generalized model, allowing for comparison with microscopic material parameters.

6CCVD Solutions & Capabilities

This research demonstrates the critical role of high-quality diamond substrates in enabling fundamental spintronics research. 6CCVD is uniquely positioned to supply the necessary materials and engineering precision required to replicate and advance these NV-based magnon studies.

Research Requirement	6CCVD Solution & Value Proposition
High-Purity Diamond Substrate for NV Centers	Optical Grade Single Crystal Diamond (SCD): Essential for creating stable, high-coherence NV centers required for GHz-scale relaxometry. Our MPCVD SCD ensures superior purity, low nitrogen content, and minimal strain, maximizing NV coherence time.
Precise NV-Material Distance Control (80 nm to 1 µm)	Ultra-Low Roughness Polishing (Ra < 1 nm): Achieving nanoscale proximity ($d$) requires atomically flat surfaces to minimize geometric uncertainty. 6CCVD guarantees Ra < 1 nm on SCD wafers, critical for probing the ballistic regime ($d \approx 100 \text{ nm}$).
Integration with 2D Magnetic Thin Films	Custom Dimensions and Thickness Control: We provide SCD plates/wafers up to 125mm in diameter, with thickness control for SCD ranging from 0.1 µm to 500 µm, facilitating seamless integration with complex 2D material stacks.
Future Integration of Electrical Readout	In-House Custom Metalization: While this study is noninvasive, future experiments may require integrated microwave or DC circuitry. We offer custom deposition of Au, Pt, Pd, Ti, W, and Cu directly onto the diamond surface.
Replication/Extension of Magnon Transport Studies	Engineering Support: 6CCVD’s in-house PhD team specializes in material science for quantum and spintronic applications. We can assist researchers with material selection, orientation (e.g., [100] or [111] SCD), and surface preparation for similar NV-based Magnon Transport projects.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Magnetic noise spectroscopy provides a noninvasive probe of spin dynamics in\nmagnetic materials. We consider two-dimensional magnetically ordered insulators\nwith magnon excitations, especially those supporting long-distance magnon\ntransport, where nitrogen-vacancy (NV) centers enable the access to (nearly)\nballistic transport regime of magnons. We develop a generalized theory to\ndescribe the magnon transport across a wide range of length scales. The\nlongitudinal dynamic spin susceptibility is derived from the Boltzmann equation\nand extended to a Lindhard form, which is modified by both the spin-conserving\nmagnon collisions and spin relaxation. Our result is consistent with the\ndiffusive (ballistic) model for the length scale much larger (smaller) than the\nmagnon mean free path, and provides a description for the intermediate regime.\nWe also give a prediction for the NV transition rate in different magnon\ntransport regimes.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.105.184406