Relaxation of a single defect spin by the low-frequency gyrotropic mode of a magnetic vortex

At a Glance

Metadata	Details
Publication Date	2021-08-25
Journal	Journal of Applied Physics
Authors	Jeremy Trimble, B. Gould, F. Joseph Heremans, Steven S.-L. Zhang, D. D. Awschalom
Institutions	University of Chicago, Case Western Reserve University
Citations	5
Analysis	Full AI Review Included

Executive Summary

This research demonstrates a novel mechanism for coupling a solid-state spin qubit (Nitrogen-Vacancy, NV center) to the dynamics of a magnetic texture (Permalloy vortex).

Non-Resonant Coupling: Enhanced NV spin relaxation was observed when driving the low-frequency gyrotropic mode (f_g = 0.15 GHz) of a magnetic vortex, despite the NV spin transitions (f₀ ~ 2.87 GHz) being highly detuned from the vortex modes.
Soliton-Like Dynamics: The coupling is attributed to the large-amplitude, soliton-like motion of the vortex core, which generates a highly nonlinear magnetic fringe field spectrum containing significant high-frequency components that overlap with the NV transition frequencies.
Threshold Requirement: Enhanced relaxation only occurs above a critical microwave driving field (b > 0.36 mT_rms), necessary to unpin the vortex core and initiate large-amplitude gyrotropic motion.
Spatial Localization: The strong spin relaxation effect is highly localized, occurring only when the vortex core is within approximately 250 nm of the NV defect.
Mechanism Validation: The high-frequency components generated by the dynamic vortex core act as a source of magnetic field noise, causing random Rabi rotations and subsequent enhanced spin relaxation (depolarization) of the NV spin state.

Technical Specifications

Parameter	Value	Unit	Context
Ferromagnet Material	Ni_0.81Fe_0.19	-	Permalloy disk composition
Disk Geometry	2 µm diameter, 35 nm thick	-	Soft ferromagnetic structure
NV Defect Type	Negatively Charged Nitrogen Vacancy	-	Quantum spin sensor
NV Ground State Transition (f₀)	2.87	GHz	Zero-field splitting
NV Excited State Transition (f_ex)	1.43	GHz	Zero-field splitting
Vortex Gyrotropic Frequency (f_g)	0.15	GHz	Low-frequency mode (experimental)
Vortex Core Half Width	~10	nm	Set by exchange length
Critical Microwave Field (b)	0.36	mT_rms	Threshold for enhanced relaxation
Interaction Distance	~250	nm	Proximity required for strong relaxation
Diamond Growth Method	PECVD	-	Plasma Enhanced Chemical Vapor Deposition
NV Layer Doping	¹⁵N delta-doped	-	Layer depth ~15 nm
Electron Irradiation Dose	1 x 10¹⁴	e/cm²	Used to create vacancies
Annealing Temperature	850	°C	Post-irradiation processing
Simulation Saturation Magnetization (M_s)	8.1 x 10⁵	A/m	Micromagnetic modeling
Simulation Exchange Stiffness (A)	1.05 x 10^-11	J/m	Micromagnetic modeling

Key Methodologies

Diamond Preparation: Isotopically pure ¹²C diamond was grown via PECVD, followed by ¹⁵N₂ gas introduction to create a 15 nm deep delta-doped layer of nitrogen.
NV Creation: Vacancies were created using 2 MeV electron irradiation (1 x 10¹⁴ dose), followed by annealing at 850 °C under forming gas (H₂/Ar) for 2 hours.
Permalloy Disk Fabrication: 2 µm diameter, 35 nm thick Ni_0.81Fe_0.19 disks were fabricated atop the diamond surface using electron beam lithography, evaporation, and liftoff.
Microwave Structure Fabrication: A 125 nm thick gold Co-Planar Waveguide (CPW) was patterned over the disk array using photolithography to deliver the microwave magnetic field (b).
Spin Initialization and Readout: NV spins were initialized and monitored using confocal Optically Detected Magnetic Resonance (ODMR) at room temperature, employing 532 nm laser excitation and Photoluminescence (PL) detection.
Vortex Core Control: An external in-plane static magnetic field (B) was applied using permanent magnets to translate the vortex core position across the disk, allowing spatial mapping of the NV-vortex interaction.
Gyrotropic Mode Excitation: The CPW was driven at the gyrotropic frequency (f_g = 0.15 GHz) to excite the vortex motion, and the resulting NV spin relaxation (PL contrast reduction) was measured as a function of driving amplitude (b).
Micromagnetic Simulation: The Object-Oriented Micromagnetic Framework (OOMMF) was used to simulate the dynamic fringe field generated by the large-amplitude gyrotropic motion, confirming the presence of high-frequency spectral components.

Commercial Applications

This technology, which leverages the nonlinear dynamics of magnetic textures for quantum control, is relevant to several high-tech engineering fields:

Quantum Sensing and Metrology: Using NV centers as highly localized, broadband sensors to map complex, dynamic magnetic fields generated by magnetic textures (e.g., domain walls, skyrmions) in spintronic devices.
Hybrid Quantum Systems: Developing novel architectures for quantum information processing where spin qubits are coupled to magnonic systems, utilizing non-resonant coupling mechanisms for fast, localized control and entanglement.
Spintronics and Magnonics: Characterizing the fundamental dynamic properties of confined magnetic elements, particularly understanding pinning effects and the spectral content of soliton-like excitations for use in magnonic circuits.
Non-Volatile Memory: Probing the stability and dynamics of magnetic vortex cores, which are candidates for high-density, non-volatile memory elements (e.g., MRAM), especially concerning pinning and depinning thresholds.
Materials Science Research: Providing a nanoscale probe for studying magnetic noise and relaxation mechanisms in novel ferromagnetic and ferrimagnetic materials.

View Original Abstract

We excite the gyrotropic mode of a magnetic vortex and observe the resulting effect on the spin state of a nearby nitrogen-vacancy (NV) defect in diamond. Thin permalloy disks fabricated on a diamond sample are magnetized in a vortex state in which the magnetization curls around a central core. The magnetization dynamics of this configuration are described by a discrete spectrum of confined magnon modes as well as a low-frequency gyrotropic mode in which the vortex core precesses about its equilibrium position. Despite the spin transition frequencies being far-detuned from the modes of the ferromagnet, we observe enhanced relaxation of the NV spin when driving the gyrotropic mode. Moreover, we map the spatial dependence of the interaction between the vortex and the spin by translating the vortex core within the disk with an applied magnetic field, resulting in steplike motion as the vortex is pinned and de-pinned. Strong spin relaxation is observed when the vortex core is within approximately 250 nm of the NV center defect. We attribute this effect to the higher frequencies in the spectrum of the magnetic fringe field arising from the soliton-like nature of the gyrotropic mode when driven with sufficiently large amplitude.

Tech Support

Original Source

DOI: https://doi.org/10.1063/5.0055595

References

2013 - Long-distance entanglement of spin qubits via ferromagnet [Crossref]
2016 - Fast nanoscale addressability of nitrogen-vacancy spins via coupling to a dynamic ferromagnetic vortex [Crossref]
2016 - Exploiting bistable pinning of a ferromagnetic vortex for nitrogen-vacancy spin control [Crossref]
2017 - Long-range spin wave mediated control of defect qubits in nanodiamonds [Crossref]
2017 - Strong driving of a single coherent spin by a proximal chiral ferromagnet [Crossref]
2018 - Single-nitrogen-vacancy-center quantum memory for a superconducting flux qubit mediated by a ferromagnet [Crossref]
2020 - Predicted strong coupling of solid-state spins via a single magnon mode [Crossref]
2015 - Nanometre-scale probing of spin waves using single-electron spins [Crossref]
2016 - Spatially resolved detection of complex ferromagnetic dynamics using optically detected nitrogen-vacancy spins [Crossref]