Probing Thermal Magnon Current Mediated by Coherent Magnon via Nitrogen-Vacancy Centers in Diamond

Currently, thermally excited magnons are being intensively investigated, owing to their potential in computing devices and thermoelectric conversion technologies. We report the detection of a thermal magnon current propagating in a magnetic insulator yttrium iron garnet under a temperature gradient using a quantum sensor: electron spins associated with nitrogen-vacancy (N-V) centers in diamond. A thermal magnon current is observed as modified Rabi-oscillation frequencies of N-V spins hosted in a beam-shaped bulk diamond that is resonantly coupled with coherent magnon propagating over a long distance. Additionally, using a nanodiamond, alteration in N-V spin-relaxation rates, depending on the applied temperature gradient, are observed under nonresonant N-V excitation conditions. The demonstration of probing a thermal magnon current mediated by coherent magnons via N-V spin states serves as a basis for creating a device platform that hybridizes spin caloritronics and spin qubits.

Figure 1

Mechanism of thermal magnon current detection via N-V center. In a magnet, thermal magnon current is created by applying temperature gradient $\mathrm{\nabla }T$, exerting torque ${\tau }_{\mathrm{TM}}$ (with damping torque ${\tau }_d$) to spin wave’s (coherent magnon) precessing magnetization M excited by a microwave ac field. Then, information on thermal magnon current can be probed by N-V center’s spin in diamond near the magnet through the spin wave.

Figure 2

Experimental setup with a diamond beam and mapping of spin waves and N-V spin-resonance spectra. (a) Experimental setup for probing thermally excited magnon current via N-V centers in a diamond beam centered on the upper YIG surface. (b) Schematic model of thermal magnon current spin-transfer torque system with N-V spin (dark blue ball with red arrow) and precessing magnetization M in YIG (red arrow) under magnetic field $B_{\mathrm{ext}}$. Transverse component, m, of M produces ac magnetic field amplitude $b_R^{-}$ that drives N-V spin into its Rabi oscillation. Thermal magnon spin-transfer torque produced by temperature gradient $\mathrm{\nabla }T$ is exerted on M resulting in the modification of $b_R^{-}$. $M_s$ is the saturation magnetization of the YIG. (c) Microwave absorption $(P_{\mathrm{MW}}=1\mathrm{mW)}$ spin-wave resonance spectra as a function of externally applied magnetic field, $+B_{\mathrm{ext}}$ [solid lines indicate upper (red, $m_s=0\leftrightarrow +1$) and lower (yellow, $m_s=0\leftrightarrow -1$) bounds of possible ground-state resonance transitions of N-V spins]. MSSWs are observed at higher frequencies above the Kittel mode (FMR). (d) ODMR spectra of N-V spins in the diamond beam as a function of $+B_{\mathrm{ext}}$ field. Region between two dashed white lines indicates the resonance frequency band of MSSWs. N-V1 to N-V4 indicate four possible N-V spins directed to $⟨111⟩$-symmetrical axes, as shown in (a). (e) Magnified spin-wave resonance spectra at white squares in (c). Dashed white line indicates resonance transitions of N-V3 spins in (d). (f) Magnified ODMR spectra of white squares in (d), showing discretized ODMR resonance line of N-V3, owing to crossing with MSSWs’ resonant frequencies. (g) Line cut of (e) at $+B_{\mathrm{ext}}=19\mathrm{mT}$. (h) Line cut of (f) at $+B_{\mathrm{ext}}=19\mathrm{mT}$. (g),(h) Matching conditions at frequency of 2.58 GHz.

Figure 3

ODMR spectra and Rabi-oscillation frequencies under temperature differences. (a) ODMR spectra with various temperature differences, $\mathrm{\Delta }T$_, applied to the YIG at $+B_{\mathrm{ext}}=19\mathrm{mT}$ and $P_{\mathrm{MW}}=1\mathrm{mW}$. ODMR dip contrast evolves monotonically (solid line) with $\mathrm{\Delta }T$ applied to the YIG. (b) ODMR contrast as a function of $\mathrm{\Delta }T$ applied to the YIG. Error bars are obtained from the standard-deviation error of curve fitting to data in (a) using a single Lorentzian function (not shown here). (c) Measurement protocol to excite Rabi oscillation on the N-V spins. Laser pulse 1 initializes the N-V spins to the $m_s=0$ state followed by a microwaves pulse with duration $\tau$ that drives MSSWs in the YIG, which then excite N-V spins to the $m_s=-1$ state. Laser pulse 2 probes the remaining N-V spin population at the $m_s=0$ state. $\tau$ is varied to produce a stroboscopic oscillation between $m_s=0$ and $m_s=-1$ states. (d) Rabi oscillations at three different $\mathrm{\Delta }T$ applied to the YIG for $+B_{\mathrm{ext}}=19\mathrm{mT}$. Frequency of Rabi oscillation evolves with applied $\mathrm{\Delta }T$. Colored solid lines are damped sinusoidal functions. (e) Variation in Rabi-oscillation frequency, ${\mathrm{\Omega }}_R^{-}/2\pi$, with $\mathrm{\Delta }T$. (f) Calculated Rabi-field amplitude, $b_R^{-}$, inferred from the Rabi frequency in (e) as a function of applied $\mathrm{\Delta }T$. (g)–(i) Rabi oscillations, Rabi frequencies, and Rabi-field amplitudes, respectively, as a function of $\mathrm{\Delta }T$ with $-B_{\mathrm{ext}}=19\mathrm{mT}$. Error bars in (e),(f),(h),(i) are obtained from the standard deviation of curve fitting to data in (d),(g), respectively, with a damped sinusoidal function. Colored solid lines in (e),(f),(h),(i) are fittings to Eq. (1). Shaded red and blue areas in (f),(i) are possible variations in fitting curves based on the uncertainties of fitting parameters in Eq. (1) (see Supplemental Material Note 10 [38]).

Figure 4

Local detection of thermal magnon current using a nanodiamond. (a) Experimental setup for local detection of thermally excited magnon current with a nanodiamond containing several N-V spins. (b) ODMR spectral map of N-V spins in the nanocrystal diamond on the YIG under zero temperature difference, $\mathrm{\Delta }T$ (P_MW= 1 mW). Nonresonant PL quenching is observed beside the straight lines of the N-V spin-resonant transitions, $m_s=0\leftrightarrow -1$. Inset shows a fluorescence image of the nanodiamond used in the measurement. (c) Longitudinal spin-relaxation-rate measurement protocol to detect the thermally excited magnon current, comprising of a polarizing laser pulse followed by a variable duration, τ, pulse of nonresonant N-V spin excitation via MSSWs at a frequency of 2.66 GHz with $\pm B_{\mathrm{ext}}=13\mathrm{mT}$ [dashed black circle in (b)]. (d),(e) N-V spin-relaxation rate, $\mathrm{\Gamma }$, as a function of $\mathrm{\Delta }T$ applied to the YIG for $+B_{\mathrm{ext}}$ [(d)] and $-B_{\mathrm{ext}}$ [(e)]. Solid red line in (d) and blue line in (e) are fitting curves to data with a model in Eq. (2). Error bars in (d),(e) are obtained from the standard deviation of curve fitting to longitudinal spin-relaxation data with a single-exponential function (see Supplemental Material Note 6 [38]). Shaded red and blue areas in (d),(e) are possible variations in fitting curves based on uncertainties of fitting parameters in Eq. (2) (see Supplemental Material Note 10 [38]).