Magneto-optics of multilayers with arbitrary magnetization directions

Abstract

Equations are derived for determining magneto-optic coefficients in multilayer systems with arbitrary directions of their magnetizations. The equations are cast in a matrix form that is suitable for numerical simulations. This establishes a framework for calculating the Kerr and Faraday effects for a multilayer system in much the same way as has been applied previously to the bulk. Numeri-0 cal Kerr results are presented for the following systems: bulk Fe, an overlayer of 50 A of Fe on Au, and for an Fe/Au superlattice for different directions of the magnetization and different angles of incidence.

Separation of ultrafast spin currents and spin-flip scattering in Co/Cu(001) driven by femtosecond laser excitation employing the complex magneto-optical Kerr effect

“…We used the matrix formalism by Zak et al [41] with dz = 0.2 nm and refractive indices n Cu and n Co . The static MO constant q Co which enters the determination of ζ was determined experimentally to q Co = 0.017−i·0.020 by fitting the thickness dependent MO contrast and the ratio ǫ/θ for d = 2 − 20 nm (not shown).…”

Antiferromagnetic dipolar ordering in[Co2MnGe∕V]Nmultilayers

“…Lee et al have given a theoretical formulation of x-ray resonant magnetic scattering [175,176] from rough surfaces and interfaces within the distorted-wave Born approximation. A matrix based formalism for magneto-optics with arbitrary magnetization direction has been developed by Zak et al [177,178,179]. It offers the possibility to calculate the specular reflectivity without any restrictions to the geometry, i.e.…”

“…[178] needs the knowledge of the energy dependence of the refractive index n = 1 − (δ c + δ m ) + i(β c + β m ) with the charge contributions δ c and β c and the magnetic contributions δ m and β m (Fig. 7.9).…”

Theory of a magnetic microscope with nanometer resolution

“…We also note that in this limit, φ ′ and φ ′ + π yields exactly the same ρ CP . Thus, if we introduce the quantity 13) we find that in the dipole limit, without a Kerr effect, ∆ρ CP = 0. This is an important observation since we will see that when the sample is magnetic this symmetry is lost.…”

“…This expression can be derived by the methods developed by Zak et al 13 There is also a contribution from the off-diagonal elements in the dielectric tensor to the s-to-s reflection coefficient. However, this contribution is exceedingly small since it depends on the square of ǫ 1 (ω) and we neglect it in the following.…”