Perpendicular anisotropy detected by transversely biased initial susceptibility via the magneto-optic Kerr effect in FexSi1-x thin films and FexSi1-x/Si multilayers: Theory and experiment

We studied experimentally and theoretically the perpendicular anisotropy and the stripe-domain structure in both FexSi1-x thin films and FexSi1-x/Si multilayers, the latter being in the low-modulation-length regime (0.4 nm<lambda<7 nm). The experimental study was made by means of the transversely biased initial susceptibility chi(t beta) via the magneto-optic Kerr effect. The samples under study were prepared by de triode sputtering at T-S = 300 K. It is found that the appearance of stripe domains is more pronounced for decreasing lambda as x remains constant and may be caused by both the increase in effective magnetic thickness and the reduction in effective magnetization as lambda decreases. For multilayers with lambda = 0.4 nm, the observed field dependence of chi(t beta)(-1) is similiar to that found in homogeneons thin films when weak stripe-domain structures arise as a consequence of the existence of perpendicular anisotropy K-N. We propose a quasistatic one-dimensional model to explain the behavior of chi(t beta)(-1) when stripe domains are present, and we analyze the critical occurrence of stripe domains. We calculated the so-called pseudo-uniaxial anisotropy field H-Ks, associated with the stripes, in two extreme cases: exchange-driven susceptibility or magnetic free poles (nonzero divergence in the bulk). The latter case agrees better with experiment. We found that perpendicular anisotropy is nor exclusive of a well-defined multilayer structure; i.e., K-N arises even when there are no interfaces in the volume. By setting the experimental saturation field H-S (obtained by hysteresis loops) into our model, we obtain both the perpendicular anisotropy constant K-N=10(4)-10(5) J/m(3) and the critical thickness t(c) for the occurrence of a stripe-domain structure. Some possible sources of perpendicular anisotropy are discussed, for example, the associated isotropic compressive stress sigma, whose contribution is found to be \K-N\(magnetoel)approximate to 1.5-4.5 x 10(4) J/m(3).