J. Zak

Universal approach to magneto-optics☆

Magneto-optics is described in a unique framework. Reflection and transmission of a general multilayer system is expressed by means of medium boundary and propagation matrices which are universal and apply to any configuration of films and media. The results for the magneto-optic coefficients are cast in the form of sets of four linear, inhomogeneous equations. It is shown that in the thin-film limit, the Kerr effect obeys an additivity law for a system consisting of any number of magnetic films. Computer simulations were performed on different film-configurations, including an overlayer, a sandwich and a superlattice.

The Kq-Representation in the Dynamics of Electrons in Solids

Publisher Summary In the Bloch theory of conduction electrons in solids, the concept of quasimomentum k is of great importance, because it is a conserved quantity and, in addition, it carries the significant information about the momentum of the electron. One should expect k to be a suitable coordinate in describing the motion of an electron in a periodic structure. It can, however, be seen that k does not carry complete quantum-mechanical information about the motion. From the point of view of elementary quantum mechanics, it is possible along with k to specify also to some extent the coordinate of the electron. This is so because k carries only partial information about the linear momentum p of the electron and when k is given, p is defined only up to an additive constant, 2πħ/a, where a is the lattice constant. It can easily be seen in this chapter that along with k quantum mechanics allows also to specify the quasicoordinate q of the electron that gives the position x up to the additive constant a. The coordinate q carries the most relevant information about the location of the electron in a periodic structure. The periodic potential of a crystal varies only inside a unit cell and is therefore a function of the quasicoordinate q only. From the point of view of the periodic structure it is completely irrelevant in which of the unit cells the electron is located. This chapter demonstrates the usefulness of the coordinates k and q in the following examples: The impurity problem in semiconductors, the dynamics in a constant electric field, and the effective Hamiltonian for a Bloch electron in a magnetic field.

Fundamental magneto‐optics

The reflection‐transmission problem is considered for light from a boundary between two magnetic media with arbitrary direction of the magnetization within each medium. Explicit formulas are derived for the magneto‐optic coefficients.

Kerr effect from Pt/Co superlattices and the role of the magneto-optic activity of Pt

The magneto‐optic response of Pt/Co superlattices is simulated to gain insight into the recent experimental findings of favorable information‐storage characteristics. Major trends are reproduced qualitatively, and the calculations indicate that the Pt contributes significantly to the short‐wavelength polar Kerr signal (at 4 eV). The influences of the wavelength, angle of incidence, component thicknesses, overcoat, and substrate on the rotation, ellipticity, and reflectivity are evaluated.

Instability of the continuous spectrum: The N‐band Stark ladder

It is shwn that the energy spectrum of the Bloch electron in an external field is continuous. Furthermore, it is shown that all approximations which take into account interband coupling whithin groups of finite number of bands (the N‐band approximation) lead to a pure‐point spectrum of intertwining Wannier‐stark ladders. This instability of the continuous spectrum under the N‐band approximation is related to a theorem due to Weyl and von Neumann. Approximation methods for dealing with interband coupling within a group of finite number of bands are given.

Quantised Hall conductance in a perfect crystal

Using magnetic translation symmetry, the Hall conductance of an isolated magnetic band in units of e2/h is shown to satisfy the Diophantine equation p sigma +qm=1, where p and q are relatively prime integers giving the number of flux quanta per unit cell area, phi =p/q, and m is an integer. This equation holds for a general periodic Schrodinger Hamiltonian with an arbitrary magnetic field and is a direct consequence of the q-fold degeneracy of magnetic bands. Extension to general real phi gives the equation phi sigma H- rho =integer with sigma H the Hall conductance and rho the number of electrons per unit cell, from which sigma H is uniquely determined once rho , phi and the gap structure are given.

Role of the substrate in enhancing the magneto‐optic response of ultrathin films: Fe on Au

Simulations are presented for the magneto‐optic rotation and ellipticity as a function of Fe thickness in the 0–400 A range for the system Fe on Au (100). The results, which are based on tabulated bulk optical constants, agree with recent experiments and explicitly demonstrate the role of the Au underlayer in enhancing the signal from the ferromagnetic overlayer.

Method to Obtain the Character Tables of Nonsymmorphic Space Groups

A method is developed to obtain the character tables of nonsymmorphic space groups. The method is based on the possibility of obtaining all the irreducible representations of a group, if one knows all the irreducible representations of its invariant subgroup of index 2 or 3. It turns out that all the space groups have an invariant subgroup of index 2 or 3.

Additivity of the Kerr effect in thin-film magnetic systems☆

Abstract A universal approach is developed for calculating magneto-optic coefficients in multimedia systems. Three configurations are described: (i) a two-media, one-boundary system, (ii) a film sandwiched between two media and (iii) a multilayer system, such as a superlattice or even a randomly stacked sequence. It is proven that in the thin-film limit, the Kerr effect for a multilayer system obeys an additivity law: it is equal to the algebraic sum of the Kerr signals of the individual magnetic films in the system. The prediction is verified experimentally and in numerical calculations on an Fe/Cu/Fe 3-layer stack grown on a Pd-substrate.

Analysis of Kerr rotation from Cu/Co, Pd/Co, and Pt/Co superlattices

Numerical simulations of the Kerr signals from Cu/Co, Pd/Co, and Pt/Co superlattices show, in general, a scaling of the signal with the amount of Co in the superlattice. Experimentally, however, the signal from Pt/Co superlattices at ∼4 eV is larger than that from bulk Co, despite the lesser total amount of Co. This is due to the magnetization induced in the Pt by the Co. Comparison of the Pd/Co and Pt/Co results with experiment indicates that the magnetization induced in the Pt by the Co plays a more important role in the magneto‐optic activity than does the induced magnetization of Pd.