Theory of Injection Locking for Large Magnetization Motion in Spin-Transfer Nano-Oscillators

• Published in: IEEE transactions on magnetics Vol. 45; no. 10; pp. 3441 - 3444
• Main Authors: Serpico, C., Bonin, R., Bertotti, G., D'Aquino, M., Mayergoyz, I.D.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: New York, NY IEEE 01.10.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Cross-disciplinary physics: materials science; rheology; Devices; Dynamic tests; Educational institutions; Equations; Exact sciences and technology; Frequency; Hysteresis; Injection-locked oscillators; Landau-Lifshitz equation; Magnetic field measurement; Magnetic separation; Magnetism; Magnetization; Materials science; Mathematical analysis; Microwave devices; Microwaves; Nanocomposites; Nanoscale devices; Nanostructure; Other topics in materials science; phase-locking; Physics; Saturation magnetization; spin-transfer; Stability; Landau-Lifshitz equation; Magnetization; phase-locking; spin-transfer; Oscillators; Magnetic properties
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2009.2025515

We study magnetization dynamics in spin-transfer devices subject to DC and microwave injected currents. When the frequency of the injected current is sufficiently close to the self-oscillation frequency of the device, phase-locking occurs. This phenomenon is theoretically studied by using Landau-Lifshitz equation with Slonczewski spin-torque term. By exploiting separation of time scales and using averaging technique, we derive equations which are applicable to the study of phase-locking for arbitrary large magnetization motion. The stability diagram in the (detuning, ac current)-plane is determined and it is shown that phase locking is hysteretic at sufficiently large ac currents.