Quantum Sensing of Spin Fluctuations of Magnetic Insulator Films with Perpendicular Anisotropy

Nitrogen-vacancy (N-V) centers, optically active atomic defects in diamond, have been widely applied to emerging quantum sensing, imaging, and network efforts, showing unprecedented field sensitivity and nanoscale spatial resolution. Many of these advantages derive from their excellent quantum-coherence, single-spin addressability, and remarkable functionality over a broad temperature range, enabling opportunities to outperform their classical counterparts. To date, N-V measurements of spin fluctuations have mainly focused on systems with in-plane magnetization, but applications to material systems with a spontaneous out-of-plane magnetization remain largely unexplored despite their technological importance. Here, we report N-V sensing of intrinsic spin fluctuations of magnetic insulator ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ thin films with perpendicular magnetic anisotropy. The measured field dependence of N-V relaxation rates is well correlated to the variation of magnon density and band structure of the magnetic samples, which are challenging to access by the conventional magnetometry methods. Our results highlight the significant opportunities offered by N-V centers in diagnosing the noise environment of functional magnetic elements, providing valuable information to develop next-generation, high-density, and scalable spintronic devices.

Figure 1

(a) X-ray diffraction θ-2θ scan of 8-nm-, 10-nm-, 12-nm-, and 30-nm-thick YIG films grown on GSGG (111) substrates. The XRD data of a substrate is also shown for comparison. The curves are offset for clarity. (b) Out-of-plane magnetic hysteresis loops for YIG(8 nm)/GSGG and YIG(12 nm)/GSGG samples. (c) Atomic force microscopy image of an 8-nm-thick YIG film grown on GSGG (111) over an area of 5 µm × 5 µm, showing a surface roughness of 0.12 nm.

Figure 2

(a) Two representative FMR spectra (in arbitrary unit) at a frequency f = 10 GHz for the 8-nm-thick YIG film grown GSGG (111). The red and blue curves correspond to in-plane and out-of-plane magnetic field geometries, respectively. (b) Angular dependence of the obtained FMR resonant field H_res for YIG(8 nm)/GSGG (blue points) and YIG(12 nm)/GSGG (red points). The curves are fittings to extract the effective magnetization. (c) Frequency dependence of H_res for YIG(8 nm)/GSGG (dots) and YIG(12 nm)/GSGG (squares) measured in both in-plane (red color) and out-of-plane (blue color) field geometries. The red and blue curves are fittings to Kittel equations. (d) Frequency dependence of FMR linewidth ΔH_FMR for 8-nm (blue points) and 12-nm (red points) PMA YIG films. The red and blue curves are linear fittings to extract Gilbert damping and inhomogeneous contribution to ΔH_FMR.

Figure 3

(a) Schematic of a single N-V spin contained in a patterned diamond nanobeam locally probing the spin fluctuations of a PMA YIG thin-film grown on a GSGG substrate. (b) PL image showing individually addressable N-V spins positioned on top of the sample surface. (c) Top panel: optical and microwave sequence for N-V relaxometry measurements. Bottom panel: two sets of N-V relaxation data measured with H = 345 and 459 Oe for an 8-nm-thick YIG film grown GSGG. (d) N-V spin-relaxation rate Γ₊ (blue points) and Γ₋ (red points) measured as a function of H. The solid lines are fitting to Eq. (2), which gives the N-V-to-sample distance of 239 ± 11 nm. (e) Sketch of the magnon density of the YIG (8 nm)/GSGG sample and the N-V ESR frequencies f_± as a function of H.

Figure 4

(a), (b) Two sets of N-V relaxation data measured with H = 548 and 736 Oe for a 12-nm-thick YIG film grown a GSGG substrate. (c) N-V spin-relaxation rate Γ₊ (blue points) and Γ₋ (red points) measured as a function of H. The solid lines are fitting to Eq. (2), which gives the N-V-to-sample distance of 114 ± 10 nm. (d) Sketch of the magnon density of the YIG(12 nm)/GSGG sample and the N-V ESR frequencies f_± as a function of H.

Figure 5

The coordinate system used for the analysis of the magnon dispersion relationship of a YIG thin-film grown on a GSGG substrate.

Figure 6

(a) Energy diagram of a N-V spin as a function of an external field H applied along the N-V axis. (b) Schematic to illustrate the spin relaxation in a three-level quantum system.

Figure 7

Calculated magnon dispersion ω/2π (red curve) for the 8-nm-thick PMA YIG thin film at H = 477 Oe and θ_H = 72°. The green dashed line plots the “filter function” as a function of wave vector k and the blue dashed line marks the lower branch of the N-V ESR frequency f₋= 1.53 GHz.

Figure 8

Normalized N-V relaxation rate [Γ₋/Γ₋ (f = 1.46 GHz)] measured as a function of the microwave frequency. The external magnetic field H is fixed at 455 Oe. The blue dashed line indicates the FMR frequency f_FMR of the 8-nm-thick PMA YIG thin film grown on the GSGG substrate.