Generalized model of magnon kinetics and subgap magnetic noise
At a Glance
Section titled “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 |
Executive Summary
Section titled “Executive Summary”This research presents a generalized theoretical framework for understanding magnon transport in two-dimensional (2D) magnetic insulators, specifically tailored for noninvasive probing using Nitrogen-Vacancy (NV) center relaxometry.
- Unified Transport Model: A generalized dynamic spin susceptibility (modified Lindhard form) is derived from the Boltzmann equation, unifying the description of magnon transport across ballistic, intermediate, and diffusive regimes.
- NV Center Application: The theory provides a quantitative prediction for the NV transition rate (Gamma) as a function of the NV-sample distance (d) and resonance frequency (omega).
- Regime Crossover Prediction: The model accurately captures the transition between the ballistic regime (d < l, where l is the mean free path) and the diffusive regime (d >> l), predicting distinct power-law scalings for the magnetic noise (e.g., Gamma scales as d-4 or d-6 in the diffusive limit).
- Subgap Noise Focus: The analysis focuses on the subgap regime (NV frequency is much less than the magnon gap), where longitudinal spin dynamics dominate the noise, reflecting the magnon population distribution and scattering effects.
- Low-Energy Magnon Dominance: The results emphasize that spin transport in 2D systems is primarily contributed by low-energy (infrared) magnons, rather than high-energy thermal magnons, due to the energy dependence of the collision time.
- Extraction of Coefficients: The model allows for the extraction of effective transport coefficients, such as the spin diffusion constant (D) and spin conductivity (sigma), directly from the microscopic parameters of the magnon dispersion.
Technical Specifications
Section titled “Technical Specifications”The following parameters were used for the numerical estimation and plotting of the NV transition rate (Gamma) in the predictive model, based on typical values for magnetic insulators like Yttrium Iron Garnet (YIG).
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Spin Stiffness (A) | 10-39 | J·m2 | Used in the quadratic magnon dispersion relation. |
| Magnon Gap (Delta/kB) | 1 | K | Assumed gap energy relative to Boltzmann constant. |
| Temperature (T) | 100 | K | Operating temperature, satisfying h*omega << Delta << kBT. |
| Gilbert Damping (alpha) | 10-4 | Dimensionless | Low damping coefficient assumed for clean systems. |
| NV Resonance Frequency (omega/2pi) | 2.87 | GHz | Zero-field NV electron spin resonance frequency (Fig. 1). |
| Magnon Mean Free Path (l) | 100 | nm | Characteristic length scale for ballistic transport. |
| Spin Diffusion Constant (D) | ~1.8 x 10-4 | m2·s-1 | Estimated value in the diffusive limit. |
| Spin Relaxation Time (tau) | ~8.3 | ns | Estimated value for spin non-conserving processes. |
| Spin Diffusion Length (ls) | ~1.2 | µm | Calculated as sqrt(D*tau). |
| Thermal Magnon Wavelength (lambdaT) | ~5.3 | nm | Wavelength of magnons with energy kBT. |
| Characteristic Wavelength (lambda) | ~34 | nm | Wavelength related to the magnetic healing length (4*sqrt(A/Delta)). |
Key Methodologies
Section titled “Key Methodologies”The theoretical framework relies on solving the Boltzmann transport equation for magnons under the relaxation-time approximation (RTA), incorporating both spin-conserving and spin-non-conserving scattering mechanisms.
- Hamiltonian Definition: The magnon gas is described by a Hamiltonian H = H0 + H1, where H0 defines the magnon dispersion (epsilonk) and H1 is the perturbing potential h(r,t) conjugate to the local magnon density.
- Boltzmann Equation Formulation: The dynamics of the magnon distribution function fk(r,t) in phase space are governed by the Boltzmann equation, including drift terms (group velocity Vk) and collision terms.
- Relaxation-Time Approximation (RTA): Two distinct relaxation times are introduced:
- tauc (Collision Time): For spin-conserving scattering (thermalization, momentum redistribution).
- taur (Relaxation Time): For spin-non-conserving scattering (magnon decay, spin relaxation).
- Local Chemical Potential (µ) Implementation: To satisfy the conservation of local magnon number during spin-conserving collisions, a local magnon chemical potential µ(r,t) is introduced. This potential drives the system toward a local equilibrium distribution gk.
- Self-Consistent Solution: The chemical potential µ is determined self-consistently by requiring that the integral of the spin-conserving collision term over all wavevectors vanishes.
- Dynamic Spin Susceptibility Derivation: The full dynamic spin susceptibility (chiF) is derived by solving the linearized Boltzmann equation in momentum space, resulting in a modified Lindhard function that incorporates both tauc and taur.
- NV Transition Rate Calculation: The NV transition rate (Gamma) is calculated using the fluctuation-dissipation theorem, relating Gamma to the imaginary part of the susceptibility (chi”) integrated over wavevector q, weighted by the demagnetization kernel (q3e-2qd).
Commercial Applications
Section titled “Commercial Applications”This theoretical work provides the foundation necessary for engineering and characterizing next-generation spintronic and quantum sensing devices based on magnetic insulators.
| Application Area | Relevance to Magnon Kinetics |
|---|---|
| Magnonics and Low-Power Computing | Provides crucial parameters (D, sigma) for designing magnonic circuits where information is carried by spin waves. Understanding the ballistic regime is essential for minimizing dissipation in ultra-clean devices. |
| Quantum Sensing and Metrology | Enables quantitative interpretation of NV relaxometry data, allowing engineers to noninvasively map intrinsic spin transport properties (l, ls) in magnetic films with high spatial (nanometer) and frequency (GHz) resolution. |
| Advanced Materials Characterization | Offers a systematic method to characterize novel 2D magnetic materials (e.g., magnetic van der Waals materials) where long-distance, potentially ballistic, spin transport is expected. |
| Thermal Spintronics | The model is foundational for future work exploring coupled spin and heat transport (spin Seebeck effect), relevant for energy harvesting and thermal management in magnetic nanostructures. |
| Hydrodynamic Spin Transport | Motivates the search for and study of hydrodynamic regimes in ultra-clean magnetic materials, where collective magnon behavior dominates over individual particle scattering. |
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