Theory of hysteresis in magnetic ultrathin films
Ultrathin magnetic films provide a unique system in which to understand
hysteresis. The ability to measure virtually all of the structural properties
of these systems means that it should be possible to to correlate the
magnetization reversal with the structural properties in a way that cannot be
done for any other system. In fact, it is possible not just to measure the
structural properties, but also to vary them in a systematic way by varying the
growth conditions. The ability to vary and measure the structure of the films
should provide enough constraints that it is only possible to theoretically
reproduce the correct behavior by using the correct physics.
For films that are one or two monolayers thick and in which the
magnetization lies in plane, the important energies in the problem are the
exchange interaction between magnetizations at neighboring sites, the intrinsic
anisotropy of the surface and the two-fold anisotropy induced by step edges.
This latter source of anisotropy can completely change the reversal process
from what it is in its absence and completely change the coercive field, for
example. The step density and average length can be varied quite systematically
by varying the average thickness of the film, the deposition rate when growing
the films, and the growth temperature. We have used classical simulations of
the reversal process to investigate the effect of the step-induced anisotropy
for various surface configurations.
Vicinal surfaces, surfaces slightly miscut from a high index crystallographic directions, are simplest systems in which non-uniform reversal mechanisms are important. Ideally, these surfaces have a series of parallel steps that are equally spaced. In this case, the behavior depends on two dimensionless parameters, the ratio of the step anisotropy energy to the in-plane domain wall energy, K, and the ratio of the step spacing to the domain wall length, L. This figure shows a "phase diagram" of hysteresis loop structure as a function of these two dimensionless parameters.
Even on perfectly flat substrates, the growth surface is rough, particularly for growth of incomplete layers. Under the right growth conditions, it is possible to grow surfaces with islands having fairly uniform size and shape distributions. For surfaces with four-fold symmetry, these islands tend to be square. We model the behavior of these systems with a periodic array of square islands. The island edges nucleate magnetization reversal as shown above. The figure at the top shows the hysteresis loop for one such system, with three points on the loop highlighted. The spin configurations around one island are shown in the three panels at the bottom of the figure. As the field is reduced from large values, reversal is first nucleated at the step edges with anisotropy perpendicular to the field direction. A lens shaped domain of rotated spins grows around these step edges as shown in the first panel. At a certain field these domains become unstable and "burst" to the configuration shown in the middle panel, which shows most of the spins in the system rotated to a perpendicular direction. These spins continue to rotate as the field is increased in the negative direction until they are become unstable and jump to the configuration shown in the last panel.
The coercive field is the field at which the magnetization passes through zero in the hysteresis loop. In the model considered here, the coercive field depends on the size of the islands, L, compared to their separation, D, and the domain wall width on the flat surface, W. This figure shows the ratio of the coercive field to the coercive field in the absence of steps as a function of these lengths.
Magnetic Reversal on Vicinal Surfaces
Coercivity of Ultrathin Films with In-plane Magnetization
Magnetization Reversal in Ultrathin Films with Monolayer-scale Surface Roughness
Magnetic Reversal of Ultra-Thin Films with Planar Magnetization
Mark D. Stiles
Ross Hyman - DePaul University
Andrew Zangwill - Georgia Institute of Technology
Online: May 1996
Last Updated: February 2008
Website Comments:egpwebmaster@nist.gov