A Fiber-Coupled Scanning Magnetometer with Nitrogen-Vacancy Spins in a Diamond Nanobeam

Magnetic imaging with nitrogen-vacancy (NV) spins in diamond is becoming an established tool for studying nanoscale physics in condensed matter systems. However, the optical access required for NV spin readout remains an important hurdle for operation in challenging environments such as millikelvin cryostats or biological systems. Here, we demonstrate a scanning-NV sensor consisting of a diamond nanobeam that is optically coupled to a tapered optical fiber. This nanobeam sensor combines a natural scanning-probe geometry with high-efficiency through-fiber optical excitation and readout of the NV spins. We demonstrate through-fiber optically interrogated electron spin resonance and proof-of-principle magnetometry operation by imaging spin waves in an yttrium-iron-garnet thin film. Our scanning-nanobeam sensor can be combined with nanophotonic structuring to control the light–matter interaction strength and has potential for applications that benefit from all-fiber sensor access, such as millikelvin systems.


Estimating the Collection Efficiency through Absorption Cross Section
Consider a single NV center inside a diamond nanobeam. If the area of the optical mode cross section inside the beam is approximately the cross section of the nanobeam itself A beam , then the probability for an NV center to absorb a single photon and trigger an excitation will be where σ = 3.1(8)×10 −21 m 2 is the absorption cross section of the NV center. 1 Therefore when a total of N ph photons enter a beam containing N NV NVs, the total number of excitations (thus total number of emitted photons) will be Note that the effect of saturation discussed in the main text is not taken into account here, thus the optical power needs to stay well below saturation for this equation to hold.
Now consider a power of P being sent into the fiber with a fiber-coupling efficiency of η f .
The rate of excitation photons that eventually end up in the beam mode will then be where η nf is the coupling efficiency at the fiber-nanobeam interface. Thus the photoluminescence rate will be and the measured photon rate is (assuming coupling efficiency at the fiber-nanobeam inter-face is equal for both directions) where η D is the fraction of photons exiting the fiber that are eventually detected by the APD. Figure S1: Overview of the efficiencies involved in our measurement. Γ exc : Photon rate of excitation laser. η f : Efficiency of free-space excitation laser coupling into the fiber. η nf : Efficiency of adiabatic light coupling at the fiber-nanobeam interface. Γ NV : Photoluminescence rate of NV centers inside the nanobeam. η D : fraction of total photons exiting the fiber that are eventually detected by the APD, consisting of losses in free space optics (e.g. on mirrors and filters), fiber coupling efficiency at the APD input and the detection efficiency of the APD.
Therefore from eq. (5) one can estimate η nf from P and R meas , both of which are measured experimentally. For the device mentioned in the main text, we measured Γ meas = 1.08 × 10 6 s −1 at P = 30 nW. For the efficiencies, fig. S1 shows a simplified overview of the measurement setup and the efficiencies involved. To experimentally determine η f , we connect a non-tapered fiber (same model as the tapered one) to the fiber coupler (A), send in a green laser with power P in measured in front of the coupler, measure the power at the output (B) of the fiber P out and determine η f = P out /P in ≈ 0.35. For η D , we send in a red laser from B, measure the power at fiber output (A) and the APD fiber input (C and D), and determine η D ≈ 0.035 (including the efficiency of the free-space optical components η A→C ≈ 0.5, APD fiber coupling efficiency η C→D ≈ 0.1 and APD detection efficiency η APD = 0.7). Substituting all the numbers into eq. (5), we can calculate the coupling efficiency at the interface Additional Characterization of Fiber-Nanobeam Devices  the ESR dips in the absence of external field, indicating that this is intrinsic to the specific diamond we use rather than the nanobeam geometry. Figure S5 shows the spectrum of the photoluminescence measured from our device. A shift towards the NV 0 spectrum is visible for excitation power above around 1 µW, indicating minimal NV 0 contribution in our low-power ESR measurements.

Imaging the Spin Waves in YIG with NV centers
Spin waves can be excited in the YIG thin film with the AC magnetic field we apply through the stripline. To model the spin dynamics, we consider our YIG layer as an infinite film parallel to the xy plane, infinite in x and y, and with a thickness t in z direction. We can calculate the dispersion of the spin waves using the Landau-Lifshitz-Gilbert (LLG) equation Figure S4: ESR spectrum measured on the bulk of the same diamond. Free space laser excitation of 350 nW is focused on the surface of the diamond via a 50× microscope objective in a confocal microscope, and NV photoluminescence is also collected using the same objective.
where m ⊥ = m x ′x ′ + m y ′ŷ ′ is the transverse components of the magnetization vector, with the magnetic frame (x ′ , y ′ , z ′ ) defined such that m(r) =ẑ ′ in equilibrium. B AC,⊥ = B AC,x ′x ′ +B AC,y ′ŷ ′ is the transverse drive field in the magnetic frame, and χ is the transverse susceptibility. Following the formalism by Rustagi et al., 2 we can find χ by solving the LLG equation in k-space, and determine the spin wave dispersion ω sw (k) by finding the singularity of χ, which eventually gives us: where k = (k x , k y ) is the in-plane wave vector. Parameters ω 1 ∼ ω 3 are in general functions of the angle between the z and z ′ axes, the direction of k, effective static field and the film thickness. 2 In our measurements, we apply the external magnetic field in-plane, and we excite and detect spin waves in the Damon-Eshbach (DE) regime where the spin wave wave vector k is perpendicular to the external magnetic field B 0 . Under these conditions, ω 1 ∼ ω 3 are reduced to: where we defined ω B = γB 0 , ω D = γD/M s with D being the spin stiffness that characterizes the exchange interaction between spins, ω M = γµ 0 M s , f = 1 − (1 − e −kt )/kt with t being the film thickness.
The spin waves generate an AC magnetic field at the spin wave frequency ω sw , and the amplitude of the field varies in space according to the wave number k. In our system we use a stripline to excite spin waves traveling in x-direction with a planar wave front, which can be written as This field can then drive the NV-ESR transitions when the spin wave frequency matches the ESR frequency. In order to image the spatial variation of B sw , we apply a homogeneous reference field with the same frequency B ref (t) = B ref,0 e iωswt through a bonding wire located above the sample. This creates a spatial variation in the field amplitude at the spin wave wavelength: This results in a spatially varying Rabi frequency of the NV-ESR transition which directly determines the NV-ESR contrast C = (PL − PL 0 )/PL 0 (defined in the main text) through the relation 3 where the parameter ∆ is determined by the optical excitation power of NV centers, therefore remains constant in our measurement scheme. As a result, the measured ESR contrast along the spin wave propagation direction has the same periodicity as the spin wave itself, allowing the imaging of spin wave through measuring ESR contrast.
Furthermore, from the ESR frequency one can determine both the detected spin wave frequency (as they should be exactly the same) and the external magnetic field strength, and theoretically determine the wavelength of the measured spin wave through eq. (9). This gives us λ ∼ 6 µm for our measurement in fig. 4 of the main text, which agrees reasonably well with our measurement given the imperfect alignment of both the nanobeam and the external magnetic field.

Uncertainty Evaluation of Spin Wave Imaging
In the 1D spin wave imaging measurement shown in fig. 4(c) of the main text, the photoluminescence from the fiber-coupled nanobeam is measured both at the NV ESR frequency