Magnetoelastic coefficients at tetragonal surfaces (abstract)

Abstract

Surfaces and thin films are generally highly strained relative to their bulk structures. The magnetoelastic (ME) coefficients coupling these strains to magnetic properties must be considered in lower symmetry than the bulk values. We outline a method of analyzing the ME problem at a surface in tetragonal symmetry (assuming the bulk is cubic). Five ME coefficients are required. Two methods have been developed to extract these surface ME coefficients from the M-H behavior of films subjected to different strains. One method fits the M-H behavior with that predicted by an equation of motion derived from a free energy which includes ME, magnetostatic, crystal field, and Zeeman terms. This method is useful in certain simple cases where canonical linear M-H behavior is observed. In more complicated cases, it can be shown that the ME coefficients are related to the area A(ΔH,Δe) between two anhysteretic M-H curves at two different strain levels and between arbitrary field limits (see Fig.). The choice of field limits allows the M-H results near the origin, H≤Hc, and near saturation H≥HK to be omitted from the analysis. The validity of the method is illustrated with measurements on thin cobalt, nickel, and permalloy films.