Magnetron-Sputtered MEMS Bi-Planar Coils for Chip-Scale SERF Magnetometry and Ultra-Low-Field NMR Relaxometry

Miniaturizing magnetic-field compensation for atomic spin sensors is challenging with conventional 3D wire-wound coils. We report the MEMS design, fabrication and system-level validation of bi-planar coils for a chip-scale spin-exchange relaxation-free (SERF) atomic magnetometer. Confining conductors to two parallel planes preserves full three-axis field control and makes the field accuracy lithography-limited. For an 8 mm × 8 mm footprint with 7.5 mm plane separation, finite-element analysis predicts coil constants of 81.3nT/mA (in-plane) and 438.6nT/mA (normal), with 0.2% and 0.02% non-uniformity over a 2 × 2 × 2 mm³ target volume. Coils were patterned with 40 μm traces and integrated into a 12 × 15 × 43 mm packaged head. Two independent calibrations were performed: reference-coil substitution (giving 68.2 and 396.0 nT/mA; 16.1% and 9.7% below simulation) and in-situ ¹²⁹Xe free-precession calibration in a ϕ3 × 3 mm cell (yielding 74.3 and 433.6 nT/mA; within 8.6% and 1.1% of simulation). The in-situ approach removes the reference scale factor and directly samples the interrogated volume, validating the numerical model. With 1 kHz modulation, the integrated noise floor reached 38fT/Hz^1/2 and enabled ULF-NMR at 100 nT, resolving water-proton precession and linear CuSO₄ relaxometry down to 50 μM.