Superconducting meander-line surface coil for NMR spectroscopy of nanoscale thin films

TL;DR

The paper addresses the challenge of performing NMR on nanoscale thin films where conventional coils suffer from low filling factors and limited sensitivity. It introduces a lithographic NbN meander-line surface coil designed to maximize inductive coupling to thin samples, supported by a reciprocity-based model that uses excitation and detection efficiencies $m_{xy}$ and $\beta_{\mathrm{det.}}$. The authors demonstrate detection of $^{11}$B NMR in a $150\,\mathrm{nm}$ boron film ($n_s \approx 2\times 10^{16}$ spins) with both FID and spin-echo measurements, achieving a normalized limit of detection $nLOD_f \approx 80\,\mu\mathrm{mol\,Hz^{1/2}}$ (effective $\sim 250\,\mu\mathrm{mol\,Hz^{1/2}}$ under hydrogen-like normalization). They identify the dominant role of the superconductor's critical current density $j_c$ in limiting sensitivity and outline a path to higher performance by adopting high-$T_c$ materials (e.g., YBCO) to approach monolayer NMR in atomically thin materials and 2D systems.

Abstract

Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique to study local magnetism in a variety of materials. However, the inherently low sensitivity of conventional inductively detected solid state NMR typically requires a large number of spins, reducing its applicability to two-dimensional (2D) materials and nanoscale thin films. To overcome this experimental challenge, we introduce a novel probe based on a superconducting meander-line surface coil that significantly enhances the NMR sensitivity for thin samples. Using a NbN meander with an optimized geometry, we demonstrate the sensitivity of this technique by detecting the NMR signal of a 150-nm-thick boron film containing only $\sim 2\times10^{16}$ $^{11}$B nuclear spins. Spin-echo measurements and theoretical modeling offer insight into the parameters limiting the coil's performance. This work lays the foundation for developing highly sensitive NMR probes, potentially unlocking new opportunities for studying atomically thin materials.

Figures (3)

• Figure 1: a A schematic (not to scale) of the meander-line inductance used in this work, showing the device parameters, the sample position and the orientation of the magnetic field $\vec{B}_0$. b The detection efficiency $\beta_\mathrm{det.}$, c the transverse magnetization $m_{xy}$ (or excitation efficiency) and d the product $\beta_\mathrm{det.} m_{xy}$, calculated as a function of wire thickness $t$ and meander period $a$. The star indicates the geometry used in our measurements. e Critical current density $j_c$ measured on a NbN stripe with width $w = 3.5~\mu$m and thickness $t=1~\mu$m.
• Figure 2: a Optical image of the the meander-line surface coil fabricated with NbN sputtered on sapphire. b, c RF field per unit of current $b_1$ in the vicinity of the meander calculated assuming a uniform current distribution. The values used for this calculation correspond to those of the meander shown in a. d Exponential decrease of $b_1$ as a function of distance from the sample $x$. The solid curve is the calculated average RF field as a function of $x$ and the dotted line is calculated using the equation $b_1 = \frac{\mu_0 }{8\lambda} e^{-x/\lambda}$ with $\lambda = a/2\pi$ and $a= 24$$\mu$m.
• Figure 3: $^{11}$B NMR signal measured from a 150-nm-thick boron thin film with an area of 1.5 mm$^2$ at $T_s =4.2$ K in a static magnetic field of 5.6 T. a Magnitude of the free induction decay (FID). This measurement was obtained after $4.4\times 10^5$ scans, with $N = 1024$ data points per scan and a dwell time of 300 ns (receiver bandwidth $\Delta f = 3.33$ MHz). An exponential fit provides a crude estimate of $T_2^\ast$. b Fourier transform following a single pulse. c Spin-echo signal and corresponding fit. d Integrated spin-echo signal as a function of $\tau$, with an exponential fit used to extract the value of $T_2$.