PREDICTION OF SHAPIRO STEPS IN THE DC VOLTAGE ACROSS A MAGNETIC DOMAIN-WALL TRAVERSED BY A DC CURRENT AND EXPOSED TO HIGH-FREQUENCY MAGNETIC-FIELDS

In metallic ferromagnets, a current of electrons traversing a domain wall exerts a torque on the wall spins through the s-d exchange interaction. This torque may induce a precession of the wall spins around the easy axis. In turn, the wall precession at a rate omega-0 generates a dc voltage delta-V across the wall, given by the formula e-delta-V = h-omega-0 similar to the Josephson equation for superconducting junctions. In the present theoretical work, a high-frequency (hf), in-plane, hard-axis magnetic field is also applied. For a certain range of values of the dc current density, the rate of wall precession is synchronous with that of the hf drive field. In other ranges, precession is asynchronous, or there is no precession. As a result, the voltage delta-V has a stepwise dependence on the current density. This is the analog of the well-known Shapiro steps for the superconducting Josephson voltage.