Magnetization reversal and current hysteresis under spin-injection conditions
E. M. Epshtein1,
R. J. Elliott2, and P. E. Zilberman1
1Institute of Radio Engineering and Electronics
of the Russian Academy of Sciences, Fryazino Moscow District 141190
Russia.
2University of Oxford, Department of Physics,
Theoretical Physics, Oxford, UK
Spin-injection effect on magnetic state and transport properties of a magnetic
junction is investigated. A three-layered magnetic junction is considered that
consists of (i) a single-domain hard magnetic layer 1 with fixed orientation
of the magnetic moment, (ii) a single-domain soft magnetic layer 2, and (iii)
a thin dielectric layer in between with ballistic (specifically, tunnel)
current transport through the latter. Spin-polarized electron injection from
the layer 1 by an electric field applied to the junction creates a range of
nonequilibrium spin polarization in the layer 2, the range width being of the
order of the electron spin relaxation length. The energy of the s-d exchange
interaction of injected free electrons and localized magnetic moments in that
range is minimal in the case of parallel spin orientation. So, the exchange
interaction tends to turn the localized magnetic moments in parallel to their
orientation in the layer 1. The resulting orientation of the layer 2
magnetization is determined by minimum condition for the magnetic energy of
the layer. The magnetic energy consists of the s-d exchange energy, the
magnetic anisotropy energy and the Zeeman energy in the external magnetic
field. The s-d exchange energy as a function of the angle between the injected
electron spin direction and the layer 2 magnetization vector contains terms of
zero, first and second powers in cosine of the angle. It means that the s-d
exchange is reduced effectively to a renormalization of the magnetic field and
the anisotropy constant. The renormalized values depend on the applied
voltage. If the layer 2 magnetic moment is aligned initially antiparallel to
the layer 1 magnetic moment by an external magnetic field then antiparallel to
parallel switching is possible at some threshold voltage. It leads to stepwise
decrease in the junction resistance and corresponding increase in the current
through the junction. At reverse change of the applied voltage the inverse
switching occurs at another (lower) voltage so that the current – voltage
characteristic of the junction contains a hysteresis loop. Such behavior was
observed in experiments repeatedly.