Study of the nonlinear magneto-optical Kerr rotations at the surfaces and interfaces in transition metal thin films

Based on the symmetric theory, the laws of Fresnel reflection and refraction and electronic theory at surface and buried interface, we have derived the dependence of NOMOKE angles Φk,α(2) on the angle of incidence θ, the polarization angle ϕ, Φ and the photon energy ℏω in the magnetic films of bcc Fe, hcp Co and fcc Ni. The calculated results are given as follows: (i) comparing the values of Φk,α(2) with the linear magneto-optical Kerr angles, we found that the values of Φk,α(2) of three different transition metals have a great increase, especially, as θ→0°,Φk,α(2)→90°; (ii) the values of Φk,p(2) of three different transition metals all have an absolute maximum at about ℏω=1.5 eV and the values of Φk,s(2) decrease with the increase of the photon energy on the whole in the range ℏω=0.64∼3.5 eV, but the curves of Φk,α(2)∼θ and ∼ℏω for three different transition metals are quite different; (iii) the values of Φk,α(2) depend sensitively on the direction of magnetization at surfaces and interfaces of thin magnetic films.