Group-Theoretical Analysis of Second Harmonic Generation at (110) and (111) Surfaces of Antiferromagnets

Extending our previous work we classify the nonlinear magneto-optical response at low index surfaces of fcc antiferromagnets, such as NiO. Antiferromagnetic bilayers are discussed here as models for the termination of bulk antiferromagnets.Comment: 7 pages, 4 figures (figures no. 1 and 3 updated

Femtosecond electron and spin dynamics probed by nonlinear optics

A theoretical calculation is performed for the ultrafast spin dynamics in nickel using an exact diagonalization method. The present theory mainly focuses on a situation where the intrinsic charge and spin dynamics is probed by the nonlinear (magneto-)optical responses on the femtosecond time scale, i.e. optical second harmonic generation (SHG) and the nonlinear magneto-optical Kerr effect (NOLIMOKE). It is found that the ultrafast charge and spin dynamics are observable on the time scale of 10 fs. The charge dynamics proceeds ahead of the spin dynamics, which indicates the existence of a spin memory time. The fast decay results from the loss of coherence in the initial excited state. Both the material specific and experimental parameters affect the dynamics. We find that the increase of exchange interaction mainly accelerates the spin dynamics rather than the charge dynamics. A reduction of the hopping integrals, such as present at interfaces, slows down the spin dynamics significantly. Besides, it is found that a spectrally broad excitation yields the intrinsic speed limit of the charge (SHG) and spin dynamics (NOLIMOKE) while a narrower width prolongs the dynamics. This magnetic interface dynamics then should become accessible to state of art time resolved nonlinear-optical experiments.Comment: 5 pages with 3 figures, to appear in Applied. Phys. B 68, (1999

Nonlinear Magneto-Optics of freestanding Fe monolayers from first principles

The nonlinear magneto-optical Kerr-effect (NOLIMOKE) is determined for freestanding Fe monolayers with several in-plane structures from first principles. Based on the theory of nonlinear magneto-optics by H\"ubner and Bennemann [Phys. Rev. B, {\bf 40}, 5973 (1989)] we calculate the nonlinear susceptibilities of the monolayers using the ab initio FLAPW-method WIEN95 with the additional implementation of spin-orbit coupling and the calculation of the dipole transition matrix elements appropriate for freestanding monolayers. We present results for the spectral dependence of the nonlinear susceptibility tensor elements and the resulting intensities and Kerr angles. Special emphasize is put on the effects of structural changes such as the variation of the lattice constant and different surface orientations. The influence of spin-orbit coupling on the tensor elements for different magnetization directions is presented as well as the azimuthal dependence of the intensities generated by several low index surfaces, showing the pronounced sensitivity of second harmonic generation to lateral structural changes as well as magnetic properties even in the monolayer range

On the Effect of Constraint Enforcement on the Quality of Numerical Solutions in General Relativity

In Brodbeck et al 1999 it has been shown that the linearised time evolution equations of general relativity can be extended to a system whose solutions asymptotically approach solutions of the constraints. In this paper we extend the non-linear equations in similar ways and investigate the effect of various possibilities by numerical means. Although we were not able to make the constraint submanifold an attractor for all solutions of the extended system, we were able to significantly reduce the growth of the numerical violation of the constraints. Contrary to our expectations this improvement did not imply a numerical solution closer to the exact solution, and therefore did not improve the quality of the numerical solution.Comment: 14 pages, 9 figures, accepted for publication in Phys. Rev.

A Scheme to Numerically Evolve Data for the Conformal Einstein Equation

This is the second paper in a series describing a numerical implementation of the conformal Einstein equation. This paper deals with the technical details of the numerical code used to perform numerical time evolutions from a "minimal" set of data. We outline the numerical construction of a complete set of data for our equations from a minimal set of data. The second and the fourth order discretisations, which are used for the construction of the complete data set and for the numerical integration of the time evolution equations, are described and their efficiencies are compared. By using the fourth order scheme we reduce our computer resource requirements --- with respect to memory as well as computation time --- by at least two orders of magnitude as compared to the second order scheme.Comment: 20 pages, 12 figure

Ultrafast Spin Dynamics in Nickel

The spin dynamics in Ni is studied by an exact diagonalization method on the ultrafast time scale. It is shown that the femtosecond relaxation of the magneto-optical response results from exchange interaction and spin-orbit coupling. Each of the two mechanisms affects the relaxation process differently. We find that the intrinsic spin dynamics occurs during about 10 fs while extrinsic effects such as laser-pulse duration and spectral width can slow down the observed dynamics considerably. Thus, our theory indicates that there is still room to accelerate the spin dynamics in experiments.Comment: 4 pages, Latex, 4 postscript figure

The origin of the 90 degree magneto-optical Kerr rotation in CeSb

We calculate the linear magneto-optical Kerr rotation for CeSb in the near-infrared spectral range. Using an exact formula for large Kerr rotation angles and a simplified electronic structure of CeSb we find at \hbar \omega = 0.46 eV a Kerr rotation of 90 degree which then for decreasing \omega jumps to -90 degree as recently observed. We identify the general origin of possible 180 degree polarization rotations as resulting from mainly nonmagnetic optical properties, in particular from the ratio of the dominant interband resonance frequency to the plasma frequency. The dependence of the Kerr rotation on moments and magnetization is discussed.Comment: 6 pages, REVTEX, 5 eps figure

Electronic Theory for the Nonlinear Magneto-Optical Response of Transition-Metals at Surfaces and Interfaces: Dependence of the Kerr-Rotation on Polarization and on the Magnetic Easy Axis

We extend our previous study of the polarization dependence of the nonlinear optical response to the case of magnetic surfaces and buried magnetic interfaces. We calculate for the longitudinal and polar configuration the nonlinear magneto-optical Kerr rotation angle. In particular, we show which tensor elements of the susceptibilities are involved in the enhancement of the Kerr rotation in nonlinear optics for different configurations and we demonstrate by a detailed analysis how the direction of the magnetization and thus the easy axis at surfaces and buried interfaces can be determined from the polarization dependence of the nonlinear magneto-optical response, since the nonlinear Kerr rotation is sensitive to the electromagnetic field components instead of merely the intensities. We also prove from the microscopic treatment of spin-orbit coupling that there is an intrinsic phase difference of 90$^{\circ }$ between tensor elements which are even or odd under magnetization reversal in contrast to linear magneto-optics. Finally, we compare our results with several experiments on Co/Cu films and on Co/Au and Fe/Cr multilayers. We conclude that the nonlinear magneto-optical Kerr-effect determines uniquely the magnetic structure and in particular the magnetic easy axis in films and at multilayer interfaces.Comment: 23 pages Revtex, preprintstyle, 2 uuencoded figure

Substrate effects on surface magetetism of Fe/W(110) from first principles

Surface magnetic properties of the pseudomorphic Fe(110) monolayer on a W(110) substrate are investigated from first principles as a function of the substrate thickness (up to eight layers). Analyzing the magnetocrystalline anisotropy energies, we find stable (with respect to the number of substrate layers) in-plane easy and hard axes of magnetization along the [1[overline 1]0] and [001] directions, respectively, reaching a value in good agreement with experiment for thick substrates. Additionally, the changes to the magnetic spin moments and the density of the Fe d states are analyzed with respect to the number of substrate layers as well as with respect to the direction of magnetization. With respect to the number of W(110) substrate layers beneath the Fe(110) surface, we find that the first four substrate layers have a large influence on the electronic and magnetic properties of the surface. Beyond the fourth layer, the substrate has only marginal influence on the surface properties.Comment: 8 Pages, 3 Figures, 3 Table