Fig. 1.1 Schematic representation of an epitaxial Ni thin film deposited on a Cu (001) surface. The misfit strain is accommodated by misfit dislocations above a critical Ni thickness.
1. Surface Magnetoelastic Interactions
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Epitaxial thin films can show very large strains due mostly to the lattice mismatch between the film and thee substrate as depicted in Fig. 1.1 below.
Fig. 1.1 Schematic representation of an epitaxial Ni thin film deposited on a Cu (001) surface. The misfit strain is accommodated by misfit dislocations above a critical Ni thickness.
The dependence of misfit strain on
Ni layer thickness has been measured by Bragg diffraction and grazing incidence
diffraction using synchrotron-generated x-rays at Brookhaven National Lab.
It is found that above the critical thickness for misfit dislocation formation,
about 2.7 nm in this system, the residual strain drops off as the -2/3
power of Ni layer thickness. It is often assumed that the residual strain
should vary inversely with the thickness of the deposited layer because
of the theoretically derived form. However, this assumption neglects the
logarithmic term in the theoretical expression. When the log term is evaluated
numerically, the thickness dependence is indeed very close to the -2/3
power dependence measured here. Fig. 1.2 below.
The effective uniaxial anisotropy energy density of thin films, g = Kusin2q, must contain terms to account for magnetostatic, elastic and interface energy densites as well as any uniaxial magnetocrystalline anisotropy that may be present. Fig. 1.3 shows schematically how these terms are conveniently decoupled by plotting Kut versus t. The figure also shows data for the Cu/Ni/Cu system taken by iindependent measurements in two different groups.
Fig. 1.3 Plot of Kut versus t for the Cu/Ni/Cu system by Jungblut et al., Bochi et al. and Ha et al. When Kut is positive, perpendicular magnetization is favored in this uniform magentization, uniaxial approximation.
An internal stress called the magnetoelastic (ME) coupling coefficient, results when the direction of magnetization is rotated in a magnetic material. In a bulk material, this ME stress gives rise to a magneotstrictive strain generally referred to as magnetostriction, l. In a thin film on a substrate, this ME stress causes the film/substrate cantilever to bend as the direction of magnetization is changed with an applied field. The curvature of bending is a direct measure of the ME coupling coefficient, Bag. The inverse effect also exists. When a magnetic material is strained, the strain couples with the ME coefficient to give rise to a strain-induced ME anisotropy. This new anisotropy adds to the magnetocrystalline, shape and other anisotropies that might be present, changing the equilibrium orientation of the magnetization. For example, a 0.1% strain in Ni causes an anisotropy of order 10 kJ/m3, with a preference for magnetization in the direction(s) of contraction.
We have measured the ME coupling coefficients in a number of thin film systems, most recently epitaxial Ni and Ni90Fe10 films sandwiched by Cu (001). Fig. 1.4 shows some of the results for films of different thicknesses and different directions of the applied field. Such measurements indicate that the ME properties of thin films can differ significantly from those of the corresponding bulk material and the difference correlates with the state of strain in the film. This correlation suggests that the deviation from bulk ME behavior in thin films is a second-order effect. The data are well described by a second-order ME analysis.
Fig. 1.4 Magnetoelastic stress versus applied field in various orientations for two different thicknesses of epitaxial Ni and Ni-Fe films.
It is important to understand these ME interactions, including the second-order effects, because they may strongly affect the preferred direction of magnetization in a material. The preferred direction of magnetization controls the magnetic domain structure as well as many technical properties of the material.
Some relevant publications:
"Surface Magnetoelastic Coupling," R.C. O'Handley and S.W. Sun, Phys. Rev. Lett. 66, 2798 (1991).
"Giant Surface Magnetostriction in Polycrystalline Ni and NiFe Films," R.C. O'Handley, O.S. Song, and C.A. Ballentine, Appl. Phys. Lett.. 64, 2593
"Non-Linear Magnetoelastic Anisotropy in Cu/Ni/Cu/Si(001) Films," Kin Ha and R.C. O'Handley, J. Appl. Phys. 85, 5282 (1999).
"X-Ray Study of Strains and Dislocation Density in Epitaxial Cu/Ni/Cu/Si(001) Films," K. Ha, M.A. Ciria, R.C. O'Handley, P.W.Stephens, and S. Pogola,
