Filtering and Imaging of Frequency-Degenerate Spin Waves Using Nanopositioning of a Single-Spin Sensor

Nano Lett. 22, 9198-9204 (2022) · DOI: 10.1021/acs.nanolett.2c02791

License: CC BY 4.0.

Abstract

Nitrogen-vacancy (NV) magnetometry is a new technique for imaging spin waves in magnetic materials. It detects spin waves by their microwave magnetic stray fields, which decay evanescently on the scale of the spin-wavelength. Here, we use nanoscale control of a single-NV sensor as a wavelength filter to characterize frequency-degenerate spin waves excited by a microstrip in a thin-film magnetic insulator. With the NV probe in contact with the magnet, we observe an incoherent mixture of thermal and microwave-driven spin waves. By retracting the tip, we progressively suppress the small-wavelength modes until a single coherent mode emerges from the mixture. In-contact scans at low drive power surprisingly show occupation of the entire isofrequency contour of the two-dimensional spin-wave dispersion despite our one-dimensional microstrip geometry. Our distance-tunable filter sheds light on the spin-wave band occupation under microwave excitation and opens opportunities for imaging magnon condensates and other coherent spin-wave modes.

Figures

33 panels with data across 4 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

• panel (b-1): Top plot of (b): calculated dispersion of backward-volume spin waves ($\vec{k} \parallel \vec{m}$): frequency above the band minimum $f-f_{\mathrm{min}}$ (GHz) against wavenumber $k_x$ ($\mu$m$^{-1}$), red line. The print draws the axes without tick values and adds the two NV frequencies $f_-$ as dashed lines with the modes $k_1$, $k_2$ marked; these are not hosted. data.csv
• panel (b-2): Bottom plot of (b): calculated isofrequency contours of the two-dimensional spin-wave dispersion at the NV frequency $f_-$ for $B_0 = 34$ mT (light blue) and 40 mT (dark blue): $k_y$ against $k_x$ ($\mu$m$^{-1}$). The print draws the axes without tick values. data.csv
• panel (c): NV photoluminescence under microwave drive normalized to that without drive, PL/PL$_0$, against bias field $B_0$ (mT) and drive frequency (GHz), tip in contact at about 30 $\mu$m from the stripline, 1 mW drive. The print's dashed lines for the calculated $f_\mathrm{B}$ and $2f_\mathrm{B}$ are not hosted. data.csv

Fig. 2

• panel (a): Filter function $f_k = k\,e^{-kd}$ ($\mu$m$^{-1}$, eq 1) against spin-wavenumber $k$ ($\mu$m$^{-1}$) for NV-sample distances $d$ = 20, 200, 600 and 1000 nm. Computed from eq 1; the deposit does not hold this panel. data.csv
• panel (a-inset): Inset of (a): the filter function $f_k = k\,e^{-kd}$ ($\mu$m$^{-1}$) against $k$ ($\mu$m$^{-1}$) for small wavenumbers, $d$ = 20, 200, 600 and 1000 nm. Computed from eq 1; the deposit does not hold this panel. data.csv
• panel (b): Calculated NV Rabi frequency $\Omega_\mathrm{R}$ from one coherent spin-wave mode with $k = 2$ $\mu$m$^{-1}$ (orange) and NV relaxation rate $\Gamma_-$ from thermal spin waves (blue) against NV-sample distance $d$ ($\mu$m), each normalized to its value at $d = 0$. data.csv
• panel (d): Spin-wave-driven NV spin dynamics: normalized photoluminescence (PL norm.) against microwave pulse duration $\tau$ ($\mu$s) and tip-sample distance $d$ ($\mu$m), at 31 $\mu$m from the stripline, $B_0 = 32$ mT, $f_- = 1.98$ GHz and $P_\mathrm{MW} = 6.3$ mW. Rows sit at the measured distances, which are unevenly spaced. data.csv
• panel (d-inset): Inset of (d): fitted Rabi frequency $\Omega_\mathrm{R}$ (MHz) against tip-sample distance $d$ ($\mu$m), down to 100 nm (dark red dots). data.csv
• panel (e-1): Spatial map of the ESR contrast at $d = 1.7$ $\mu$m ($f_- = 1.89$ GHz, $B_0 = 35$ mT, $P_\mathrm{MW} = 1$ mW) against position $x$, $y$ ($\mu$m). The deposit gives PL/PL$_0$ with each map's mean subtracted, hosted so; the print shows PL/PL$_0$ from 0.7 to 1 with a 5 $\mu$m scale bar. data.csv
• panel (e-2): Spatial map of the ESR contrast at $d = 1.3$ $\mu$m ($f_- = 1.89$ GHz, $B_0 = 35$ mT, $P_\mathrm{MW} = 1$ mW) against position $x$, $y$ ($\mu$m). The deposit gives PL/PL$_0$ with each map's mean subtracted, hosted so; the print shows PL/PL$_0$ from 0.7 to 1 with a 5 $\mu$m scale bar. data.csv
• panel (e-3): Spatial map of the ESR contrast at $d = 0.9$ $\mu$m ($f_- = 1.89$ GHz, $B_0 = 35$ mT, $P_\mathrm{MW} = 1$ mW) against position $x$, $y$ ($\mu$m). The deposit gives PL/PL$_0$ with each map's mean subtracted, hosted so; the print shows PL/PL$_0$ from 0.7 to 1 with a 5 $\mu$m scale bar. data.csv
• panel (e-4): Spatial map of the ESR contrast at $d = 0.5$ $\mu$m ($f_- = 1.89$ GHz, $B_0 = 35$ mT, $P_\mathrm{MW} = 1$ mW) against position $x$, $y$ ($\mu$m). The deposit gives PL/PL$_0$ with each map's mean subtracted, hosted so; the print shows PL/PL$_0$ from 0.7 to 1 with a 5 $\mu$m scale bar. data.csv
• panel (e-5): Spatial map of the ESR contrast at $d = 0.2$ $\mu$m ($f_- = 1.89$ GHz, $B_0 = 35$ mT, $P_\mathrm{MW} = 1$ mW) against position $x$, $y$ ($\mu$m). The deposit gives PL/PL$_0$ with each map's mean subtracted, hosted so; the print shows PL/PL$_0$ from 0.7 to 1 with a 5 $\mu$m scale bar. data.csv
• panel (e-6): Spatial map of the ESR contrast at $d = 0$ $\mu$m ($f_- = 1.89$ GHz, $B_0 = 35$ mT, $P_\mathrm{MW} = 1$ mW) against position $x$, $y$ ($\mu$m). The deposit gives PL/PL$_0$ with each map's mean subtracted, hosted so; the print shows PL/PL$_0$ from 0.7 to 1 with a 5 $\mu$m scale bar. data.csv

Fig. 3

• panel (b-1): Spatial map (1) of the NV ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) at $B_0 = 34$ mT and tip-sample distance $d \approx 1.5$ $\mu$m, showing backward-volume spin waves excited by the stripline; drive power $P_\mathrm{MW} = 4$ mW. data.csv
• panel (b-2): Spatial map (2) of the NV ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) at $B_0 = 35$ mT and tip-sample distance $d \approx 1.0$ $\mu$m, showing backward-volume spin waves excited by the stripline; drive power $P_\mathrm{MW} = 4$ mW. data.csv
• panel (b-3): Spatial map (3) of the NV ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) at $B_0 = 36$ mT and tip-sample distance $d \approx 0.7$ $\mu$m, showing backward-volume spin waves excited by the stripline; drive power $P_\mathrm{MW} = 4$ mW. data.csv
• panel (b-4): Spatial map (4) of the NV ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) at $B_0 = 37$ mT and tip-sample distance $d \approx 0.5$ $\mu$m, showing backward-volume spin waves excited by the stripline; drive power $P_\mathrm{MW} = 4$ mW. data.csv
• panel (b-5): Spatial map (5) of the NV ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) at $B_0 = 38$ mT and tip-sample distance $d \approx 0.4$ $\mu$m, showing backward-volume spin waves excited by the stripline; drive power $P_\mathrm{MW} = 4$ mW. data.csv
• panel (b-6): Spatial map (6) of the NV ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) at $B_0 = 39$ mT and tip-sample distance $d \approx 0.3$ $\mu$m, showing backward-volume spin waves excited by the stripline; drive power $P_\mathrm{MW} = 4$ mW. data.csv
• panel (b-7): Spatial map (7) of the NV ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) at $B_0 = 40$ mT and tip-sample distance $d \approx 0.2$ $\mu$m, showing backward-volume spin waves excited by the stripline; drive power $P_\mathrm{MW} = 4$ mW. data.csv
• panel (b-8): Spatial map (8) of the NV ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) at $B_0 = 41$ mT and tip-sample distance $d \approx 0.2$ $\mu$m, showing backward-volume spin waves excited by the stripline; drive power $P_\mathrm{MW} = 4$ mW. The print marks a dashed analysis box. data.csv
• panel (b-9): Spatial map (9) of the NV ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) at $B_0 = 42$ mT and tip-sample distance $d \approx 0.2$ $\mu$m, showing backward-volume spin waves excited by the stripline; drive power $P_\mathrm{MW} = 4$ mW. data.csv
• panel (c): Spin wavelength $\lambda_\mathrm{SW}$ ($\mu$m) against $B_0$ (mT): wavelengths extracted by fitting the maps of (b) (pink dots, with fit errors smaller than the markers) and calculated from the backward-volume dispersion (red line); right axis, the tip-sample distance $d$ ($\mu$m) used for each scan (blue dots). The print's $\lambda_\mathrm{B}$ line is not hosted. data.csv
• panel (c-inset): Inset of (c): calculated backward-volume dispersion relative to the minimum spin-wave frequency, $f-f_\mathrm{B}$ (GHz) against $k_x$ ($\mu$m$^{-1}$) (red line), with the modes imaged in (b) (pink dots). The print draws the axes without tick values. data.csv

Fig. 4

• panel (a-1): Spatial map (1) of the ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) with the tip in contact with the sample at low drive power (6.3 $\mu$W), $B_0 = 34$ mT. The print marks the region enlarged in a-4. data.csv
• panel (a-2): Spatial map (2) of the ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) with the tip in contact with the sample at low drive power (6.3 $\mu$W), $B_0 = 37$ mT. data.csv
• panel (a-3): Spatial map (3) of the ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) with the tip in contact with the sample at low drive power (6.3 $\mu$W), $B_0 = 40$ mT. data.csv
• panel (a-4): Zoom into map (1) of (a), $B_0 = 34$ mT: ESR contrast PL/PL$_0$ against position $x$, $y$ ($\mu$m) inside the box the print draws on (1), where 360 nm spin waves are visible (the print marks them with black bars, not hosted). data.csv
• panel (b-1): Absolute value of the two-dimensional Fourier transform (FFT) of map (1) of (a), $B_0 = 34$ mT, against wavevector components $k_x$, $k_y$ ($\mu$m$^{-1}$), revealing the wavevectors in the spin-wave pattern. The hosted range is the printed crop; the full transform is in the data. data.csv
• panel (b-2): Absolute value of the two-dimensional Fourier transform (FFT) of map (2) of (a), $B_0 = 37$ mT, against wavevector components $k_x$, $k_y$ ($\mu$m$^{-1}$), revealing the wavevectors in the spin-wave pattern. The hosted range is the printed crop; the full transform is in the data. data.csv
• panel (b-3): Absolute value of the two-dimensional Fourier transform (FFT) of map (3) of (a), $B_0 = 40$ mT, against wavevector components $k_x$, $k_y$ ($\mu$m$^{-1}$), revealing the wavevectors in the spin-wave pattern. The hosted range is the printed crop; the full transform is in the data. data.csv
• panel (b-4): Line trace of the 34 mT Fourier map (b-1) along $k_y$ ($\mu$m$^{-1}$, vertical) at the dashed line the print draws, labelled $k_x = 15$ $\mu$m$^{-1}$ (the column at $k_x = -15.3$ $\mu$m$^{-1}$ of the hosted map): FFT amplitude, blue dots joined by a line. The print's fitted peak (yellow) is not hosted. data.csv

Cite

Brecht G. Simon, Samer Kurdi, Joris J. Carmiggelt, Michael Borst, Allard J. Katan, Toeno van der Sar. Filtering and Imaging of Frequency-Degenerate Spin Waves Using Nanopositioning of a Single-Spin Sensor. Nano Lett. 22, 9198-9204 (2022). https://doi.org/10.1021/acs.nanolett.2c02791

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