AC magnetometry in the strong drive regime with NV centers in diamond

TL;DR

This work addresses the limitation of NV AC magnetometry under strong drive fields by introducing SIPHT, a phase-tuning protocol that cancels drive-induced detuning and preserves sensitivity to the out-of-phase AC response signal. The method phase-modulates MW pulses so that the rotating-frame phase from the drive is nulled, enabling direct readout of the response field $B_S$ and its phase delay $\delta$ even when $B_D$ is large. The authors derive the NV phase accumulation $\phi_{NV}$ under SIPHT and demonstrate substantial contrast preservation and accurate $\delta$ extraction in experiments, including measurements of eddy-current fields from Cu, Al, and Ti disks. By enabling strong-drive NV AC magnetometry, SIPHT expands applications in magnetic hyperthermia and nondestructive testing, with implications for probing dissipation, conductivity, and interparticle dynamics in complex materials.

Abstract

Magnetic response measurements in the presence of AC drive fields provide critical insight into the properties of magnetic and conductive materials, such as phase transitions in two-dimensional van der Waals magnets, the heating efficiency of magnetic nanoparticles in biological environments, and the integrity of metals in eddy current testing. Nitrogen-vacancy (NV) centers in diamond are a commonly-used platform for such studies, due to their high spatial resolution and sensitivity, but are typically limited to weak-drive conditions, i.e., AC drive fields well below the NV microwave (MW) pulse Rabi strength. Once the AC drive field grows comparable to or larger than the Rabi strength, the induced MW pulse detuning suppresses NV sensitivity to the out-of-phase magnetic response, which encodes dissipation and conductivity in materials of interest. Here, we introduce a phase modulation protocol that cancels MW pulse detuning to leading order, and extends NV AC magnetometry into the strong drive field regime. The protocol, termed SIPHT (Signal Isolation through PHase Tuning), is experimentally demonstrated using an NV ensemble. By directly comparing SIPHT to the conventional Hahn echo AC sensing protocol, we quantify the preservation of NV magnetometry contrast for an out-of-phase signal. We further showcase SIPHT by detecting eddy current-induced magnetic fields from Cu, Al, and Ti samples, with the measured response field phase delays reflecting their distinct conductivities. SIPHT extends NV AC magnetometry to regimes inaccessible to standard dynamical decoupling measurement protocols, unlocking novel utility, e.g., in the study of magnetic hyperthermia and nondestructive testing of conductors.

Figures (5)

• Figure 1: SIPHT dynamical decoupling (DD) for AC magnetometry of magnetic response signals in the strong drive regime. a) Experimental schematic for an AC response measurement with NV centers in diamond. A strong AC drive field ($B_D$) generated by a coil induces an AC response field ($B_S$) from a sample (with examples shown in the shaded inset), sensed by an NV ensemble. MW pulses for NV spin control during DD-based AC magnetometry measurements are generated by an $\Omega$-shaped waveguide. The static bias magnetic field and AC drive field are aligned to the probed NV axis. b) NV electronic spin phase accumulation in conventional and SIPHT DD. In conventional DD, NV spins precess around $\Delta/\gamma=(B_D+B_S)$ in rotating frame RF$_0$ and accumulate phase due to both $B_D$ and $B_S$, highlighted by the green and orange areas in the Bloch plane. In SIPHT DD, rotating frame RF$_{\text{mod}}$ has a tunable phase modulation, which can be chosen to match the NV phase accumulation due to $B_D$ in RF$_0$. When this condition is satisfied, the SIPHT DD sequence effectively isolates the signal field $B_S$ by rejecting all contributions from $B_D$ to NV phase accumulation.
• Figure 2: NV AC signal measurement contrast for a Hahn echo sequence in the presence of a coil generated field at $f_D$ = 152 kHz, consisting of a drive field $B_D \approx$ 100 $\mu$T and a response field $B_S \approx$ 4 $\mu$T at a known phase delay $\delta=0.065\cdot 2\pi$ ($\approx 23\degree$). NV AC measurements are made under SIPHT ($B_D'=B_D$) and conventional ($B_D'=0$) DD conditions for a relatively modest and large normalized drive field $\gamma B_D/\Omega$ in a) and b) respectively. For conventional DD conditions, NV spin phase accumulation due to $B_D$ induces large oscillations in the contrast as a function of the phase offset $p$ of the MW pulse train used to control the NV spins. Under SIPHT conditions, phase accumulation is solely due to $B_S$ and the phase delay $\delta$ of the response field can be read out directly from the contrast data at values of $p$ where the contrast is symmetric (red stars in a) and b)). For large normalized drive fields $\gamma B_D/\Omega$, contrast is reduced for conventional DD around values where $|B_D|$ is maximum. SIPHT preserves contrast in the strong drive field regime.
• Figure 3: a) First period of the measured out-of-phase response ($p=\pi/2$) NV AC magnetometry curve generated by sweeping $B_S'$ for a drive field of $B_D\approx$ 97 $\mu$T at $f_D$ = 149 kHz, and MW pulse Rabi strength of 3.32 MHz ($\gamma B_D/\Omega \approx 0.81$). b) Relative contrast of SIPHT Hahn echo ($B_D'=B_D$) with respect to conventional Hahn echo ($B_D'=0$) for out-of-phase response NV AC magnetometry measurements ($p=\pi/2$), as a function of normalized drive field amplitude $\gamma B_D/\Omega$. Significant contrast loss is observed for conventional DD compared to SIPHT DD at larger $\gamma B_D/\Omega$.
• Figure 4: a) Experimental demonstration of effective drive field rejection through MW phase modulation in SIPTH DD. The phase offset $p$ of the MW pulse train is swept for 3 different conditions: a reference measurement in the absence of a drive field (orange line), a comparison measurement in the presence of a drive field without SIPHT conditions (green pentagons), and a demonstration measurement in the presence of a drive field under SIPHT conditions (blue triangles). SIPHT DD rejects $>$ 99.9% of the drive field-induced phase for $B_D\approx102$$\mu$T at $f_D=$ 152 kHz. b) Extraction of response field phase delay $\delta$ from an NV SIPHT Hahn echo measurement of coil-generated fields $B_S\approx$ 2 and 7 $\mu$T together with drive fields $B_D \approx$ 78 and 75 $\mu$T, respectively, at $f_D=$ 160 kHz. Good agreement is found with independent measurements performed with an inductive pickup coil over the full range of phase delays $\delta$, with residuals to a linear fit of the two measurement methods shown in the inset.
• Figure 5: NV measurement of the eddy current-induced response field from Cu, Al, and Ti disks using a SIPHT Hahn echo. a) Measurement contrast as a function of the phase offset $p$ of the MW pulse train. NV spin phase accumulation is solely due to the response field induced by the eddy currents; and the phase delay $\delta$ of the response field can be directly read out from the contrast, as indicated by the red stars. b) Amplitudes $B_S$ of the eddy current-induced response fields for each metal disk (shown in inset), extracted from the fits in a), as a function of relative distance of the disk center from the NV-diamond sensor. The observed trend follows an inverse-cube scaling, consistent with a dipolar-like response field generated by eddy currents in the metal disks.