Gyroscopes are key components of inertial navigation systems, from smartphones to spacecraft. The dominant technology is capacitive MEMS gyroscopes, where nanometer-scale displacement of a proof mass is converted into a capacitance change. However, further miniaturization of such devices is limited by the need for precise control of capacitive gaps, large proof-mass area, and parasitic interconnects. This work stands apart among neighboring studies: in the archive there are works on spintronic accelerometers and gyroscopes, but they either use MTJs as passive magnetic field sensors or require nonstandard fabrication processes. This work proposes using MTJs as active rectifiers of radio-frequency signals (spin-torque diodes), which allows direct conversion of displacement into voltage without intermediate capacitive circuits.
The authors built a coupled magnetomechanical model that combines the equations of motion of a two-degree-of-freedom mechanical resonator with the magnetization dynamics of three magnetic elements: the proof mass and two MTJs operating as spin diodes. The magnetic system parameters were extracted from experimental measurements of real MTJs: a Ta/Ru/CoFeB/MgO/CoFeB stack with an elliptical cross-section of 300×750 nm showed resonance frequencies from 0.6 to 1.6 GHz and a DC voltage sensitivity of about 20 μV/mT. Mechanical parameters (mass 1 μg, resonance frequency 250 kHz, quality factor 157) were estimated based on typical MEMS resonators. The model accounts for dipolar interaction between magnetic elements and the spin-transfer torque from the injected RF current. To verify operation in a dynamic regime, a digital homodyne demodulator with phase-locked loop was implemented.
In steady state, the differential voltage from the two MTJs increases linearly with angular velocity Ωz, giving a sensitivity KΩ = 0.001 μV/(°/s). The estimated angular random walk (ARW) was 1800 °/√h, which corresponds to the rate-grade class (consumer level), but is 4–5 orders of magnitude worse than tactical grade. For comparison, the thermal (Brownian) limit for this resonator gives an ARW of about 0.04 °/√h, meaning that electronic readout noise dominates. In a dynamic scenario (wind gust, 40 kHz modulation), homodyne demodulation recovered the angular velocity with an error of about 0.05% (maximum 0.35% on sharp transients). In the variant with an active spin-torque nano-oscillator (STNO) instead of a passive proof mass, sensitivity increased by a factor of 70 to 0.065 μV/(°/s), and ARW dropped to 25 °/√h, while the drive amplitude decreased to 150 nm, opening the way to a threefold reduction in size.
This work demonstrates that spintronic readout based on spin-torque diodes can replace or complement capacitive readout in MEMS gyroscopes, removing the main scaling limitation: the need for sub-100 nm capacitive gaps. Unlike neighboring works where MTJs are used as passive field sensors or require nonstandard processes, here a standard vibrating gyroscope architecture is used, and MTJs operate as active rectifiers, simplifying CMOS integration and enhancing radiation hardness. The results show that the current unoptimized design is far from tactical grade, but the path to improvement is clear: increasing MTJ sensitivity, field gradient, and resonator quality factor.
The topic could evolve toward optimizing the MTJ magnetic stack to enhance the spin-torque diode effect, reducing the distance between the proof mass and MTJs to increase the field gradient, and using synchronization between STNO and MTJ to amplify the signal. Also promising is the study of noise characteristics, especially low-frequency 1/f noise, and experimental verification on fabricated prototypes. Integration with machine learning for automatic parameter tuning of the multiphysics system is also possible.
The results could influence the development of compact inertial sensors for navigation, robotics, consumer electronics, and aerospace, especially where radiation hardness and small size are critical.
Immediate next steps include fabricating and experimentally characterizing a prototype of the magnetomechanical gyroscope, measuring noise and long-term stability (Allan variance), and optimizing the design to improve sensitivity.
In the field of inertial MEMS sensors, the problem of further miniaturization while maintaining accuracy remains unsolved: capacitive readout requires precise gaps, which limits scaling. This work proposes an alternative path through spintronics, but it does not yet solve the problem of electronic noise, which dominates over the thermal limit. The connection to fundamental spintronics problems: controlling magnetization at the nanoscale and reducing 1/f noise in MTJs.
The spin-torque diode sensitivity in the experiment was about 20 μV/mT, which allows detecting proof-mass displacements of fractions of a nanometer. In the fully spintronic version, the drive amplitude decreases to 150 nm, which is roughly 500 times thinner than a human hair.