Eur. Phys. J. B 68, 221-231 (2009)
https://doi.org/10.1140/epjb/e2009-00091-9

Analytical treatment of synchronization of spin-torque oscillators by microwave magnetic fields

¹ Politecnico di Torino - sede di Verrès, via Luigi Barone 8, 11029 Verrès (AO), Italy
² Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy
³ Dipartimento di Ingegneria Elettrica, Università di Napoli “Federico II”, via Claudio 21, 80125 Napoli, Italy
⁴ Electrical and Computer Engineering Department and UMIACS, University of Maryland, College Park, MD, 20742, USA
⁵ Dipartimento per le Tecnologie, Università di Napoli “Parthenope”, via Medina 40, 80133 Napoli, Italy

Corresponding author: ^a bonin.roberto@gmail.com

Received: 15 October 2008
Revised: 27 January 2009
Published online: 14 March 2009

Abstract

An analytical approach is presented for the study of synchronization effects in spin-transfer-driven nanomagnets subjected to radio-frequency magnetic fields. The conditions are derived and discussed under which the current-induced magnetization precession is synchronized by the radio-frequency field. Exact analytical results are obtained for the case when the problem exhibits uniaxial symmetry around the axis perpendicular to the device plane. It is demonstrated that the magnetization dynamics under nonzero current and nonzero rf field is identical in structure to that under zero current. On this basis, analytical predictions are obtained for: the existence of phase-locking between current-induced magnetization precession and rf field oscillations; the frequency pulling effect in proximity of phase locking; the occurrence of hysteresis effects in phase-locking as a function of the spin-polarized current. The proposed approach is valid for arbitrary rf field amplitude and current intensity.