Determining thin-film magnetoelastic constants

Abstract

A formalism is presented for determining the magnetoelastic (ME) coefficients of tetragonally distorted surfaces and thin films. The equation of motion of the magnetization is determined from free-energy-density expressions containing terms for crystalline and shape anisotropy, ME anisotropy, and applied field. Canonical magnetization curves, described by simple equations of motion and recorded under different strains, are shown to differ by an area equal to the magnetoelastic energy density. Thus, division of this area by the applied strain allows determination of the ME coefficients. A more general method is proposed which allows ME coefficients to be determined from arbitrarily shaped M-H curves taken at different strains by calculating the area between them over a conveniently chosen magnetization range. This reduces error in the ME coefficients by avoiding hysteretic effects at low fields and ambiguity about saturation at high fields. Examples are given that illustrate how the magnetic anisotropy and ME coefficients can be determined in three simple cases from Kerr or M-H loops in ultrathin films subjected to various bending strains.

Engineering domain structures in nanoscale magnetic thin films via strain

“…1(b), the major part of the map consists of tetragonal (a 1 , a 2 , c) domains while the orthorhombic domains (O 12 , O 13 , O 23 ) appear as their intermediate phases. This is determined by the six-fold cubic symmetry of the magnetoelastic energy in isotropic magnets 51 which tends to align the magnetization along the three principle axes. There also exists a very small region occupied by a rhombohedral r domain (M 1 6 ¼ 0, M 2 6 ¼ 0, and M 3 6 ¼ 0) in the map at the intersection of all the other phases.…”

The correlation between mechanical stress and magnetic anisotropy in ultrathin films

“…Strain is a further important parameter that influences the magnetic anisotropy, as indicated in the linear strain-anisotropy relation of the magneto-elastic energy density above in (3.1). In ultrathin films the misfit between film and substrate is often as high as several per cent and strain-dependent corrections to the magneto-elastic coupling coefficient should be considered [100][101][102]. The strain correction in its simplest form B eff 1 = B 1 + D was successfully applied to account for the stress dependence of the magneto-elastic coupling in epitaxial Fe(100)films of 100 nm thickness [9] and will be shown to describe the magneto-elastic coupling in epitaxially strained nm Fe-films in section 7.…”

Strain dependence of the magnetic properties of nm Fe films on W(100)

“…This result proves that the assumption of bulk ME constants for the description of the magnetic film properties is wrong. According to a phenomenological model, 1,2 we ascribe this thickness dependence to the epitaxial film strain, which is induced by the lattice mismatch between the Fe film and the W substrate. To study the effects of epitaxial strain in ultrathin Fe films on both the ME coupling and the in-plane anisotropy, we measured the thickness dependence of the intrinsic film stress F , the magnetoelastic coupling B 1 , and the magnetic in-plane anisotropy K 4 by combining film stress measurements with magnetooptical Kerr-effect ͑MOKE͒ measurements.…”

“…We find that both B 1 and K 4 depend strongly on the Fe film thickness. The thickness dependence of B 1 can be described by considering a second order magneto-elastic coupling constant D ϭ1 GJ/m 3 as a strain dependent correction of B 1 . We tentatively ascribe the deviation of K 4 from its bulk value to the tetragonal lattice distortion caused by an effective tensile in-plane strain of 5.3% in the pseudomorphic region and of 0.2% in thicker films.…”