Yonko T. Millev

Demagnetization factors for elliptic cylinders

The magnetometric (volume averaged) demagnetization factors for cylinders with elliptical cross section are computed using a Fourier-space approach and compared with similar results obtained with a different treatment. The demagnetization factors are given as a series expansion in the eccentricity � of the elliptical cross section, where the terms up to order � 10 are given explicitly as a function of the cylinder aspect ratio. Other simplified expressions, valid in restricted regimes, are also given. Two different series expansions, obtained previously and valid in particular combinations of shape parameters, are recalled and compared with the new results. After the computation of the magnetostatic and exchange-energy terms associated with a vortex closure-domain state in the elliptic cylinder, the single-domain limit, or the critical size below which the structure can support quasi-uniform magnetization, is derived and discussed.

The reorientation transition in Co/Au(111)

The spin reorientation transition in as-grown wedge-shaped Co/Au(111) films has been analyzed. Two critical thicknesses have been detected just like in the annealed case. Here, these are shifted to smaller values. The behavior of the system can be explained on the basis of the thickness-driven trajectory in the anisotropy space of the system. Both the first and second anisotropy constants have been determined: K1s=0.66 mJ/m2, K2s=−0.12 mJ/m2. They are both smaller by modulus than their counterparts from the annealed case. The results provide quantitative evidence for the increase of surface anisotropy after annealing.

Demagnetization factors of the general ellipsoid: An alternative to the Maxwell approach

A transparent, exhaustive, and self-contained method for the calculation of the demagnetization tensor of the uniformly magnetized ellipsoid is presented. The method is an alternative to the established Maxwell derivation and is based on a Fourier-space approach to the micromagnetics of magnetized bodies. The key to the success of the procedure lies in the convenient treatment of shape effects through the Fourier representation. The scaled form of the demagnetization factors which depends on two dimensionless aspect ratios is argued to be their natural integral representation. Amongst other advantages, it allows for the immediate implementation of symmetry arguments such that only one of the principal factors needs to be computed. The oblate and prolate ellipsoids of revolution are examined from the same general point of view. The demagnetization factors for these distinct types of spheroid are seen to be related by analytic continuation of well-known Gaussian hypergeometric functions.

Magnetostatics of the uniformly polarized torus

We provide an exhaustive description of the magnetostatics of the uniformly polarized torus and its derivative self-intersecting (spindle) shapes. In the process, two complementary approaches have been implemented, position-space analysis of the Laplace equation with inhomogeneous boundary conditions and a Fourier-space analysis, starting from the determination of the shape amplitude of this topologically non-trivial body. The stray field and the demagnetization tensor have been determined as rapidly converging series of toroidal functions. The single independent demagnetization-tensor eigenvalue has been determined as a function of the unique aspect ratio α of the torus. Throughout the range of values of the ratio, corresponding to a multiply connected torus proper, the axial demagnetization factor Nz remains close to one half. There is no breach of smoothness of Nz(α) at the topological crossover to a simply connected tight torus (α=1). However, Nz is a non-monotonic function of the aspect ratio, such that substantially different pairs of corresponding tori would still have the same demagnetization factor. This property does not occur in a simply connected body of the same continuous axial symmetry. Several self-suggesting practical applications are outlined, deriving from the acquired quantitative insight.

Dipolar magnetic anisotropy energy of laterally confined ultrathin ferromagnets: multiplicative separation of discrete and continuum contributions

Very recent exact summation has indicated that the lateral confinement of ultrathin ferromagnetic islands brings about significant deviations from the usually assumed laterally infinite sample so far as the dipolar magnetic anisotropy is concerned. Here, it is demonstrated that the phenomenological rescaling of the structural detail leads to a fundamental micromagnetic (continuum theory) quantity, namely, the demagnetizing energy for the assumed shape of the mesoscopic island. The derivation of a compact analytical formula for the demagnetization factor of any right circular cylinder has been instrumental for this insight. The effects of discrete geometry (lattice and substrate orientation), thickness, and overall shape of the ultrathin structure are thus distilled into a form which exhibits a great deal of universality.

Critical dynamics of zero-temperature structural phase transitions

The critical dynamics of a class of displacive second-order phase transitions is studied in the limit Tc to 0 (Tc being the critical temperature). Both the renormalisation-group recursion relations method and direct calculation are used for the derivation of the critical exponents up to order epsilon 2 ( epsilon =3-d). The static exponents remain, in some sense, universal, whereas the dynamic exponent has no epsilon corrections.

On the analytic inversion of functions, solution of transcendental equations and infinite self-mappings

The solution of seemingly simple transcendental equations is in effect equivalent to the general problem of analytical inversion of functions. Within a powerful and systematic method, based on the solution of an associated Riemann–Hilbert boundary value problem, beautiful explicit results for various inverse functions of physical importance have been found which inevitably take on the guise of integral representations of these functions. In an attempt to reduce one such solution to a standard-function expression which would then be easy to evaluate, we recognize an infinite ladder self-mapping solution. This new perspective, born out of complicated complex analysis, is straightforwardly and uniquely related to the systematic generation of fast converging expansions within the corresponding regions of single-valuedness of the inverse function.

Bose - Einstein integrals and domain morphology in ultrathin ferromagnetic films with perpendicular magnetization

We demonstrate how the stripe-domain configuration which is the most stable one in thin ferromagnetic films with perpendicular magnetization can be easily analysed in terms of Bose - Einstein integrals. Exact values for the equilibrium thickness of stripes as well as for the minimal free energy of the domain configuration in ultrathin samples are derived from little-known asymptotic expansions of the Bose - Einstein integrals. It is found that, due to an incidental cancellation, the lowest-order results for the stripe structure are exact also to the next order in the small parameter (the ratio of thickness to domain width). The minimization equation for the determination of the equilibrium quantities of interest is cast in a form that makes it applicable analytically to films which are not necessarily ultrathin and that allows one to control quantitatively the approximations made. The analytic solution, valid to a high order in the small ratio, is also given.

Random field effects in classical and quantum critical phenomena

The effect of quenched random fields on classical and quantum critical behaviour is studied by means of the ϵ-analysis for a number of systems. The investigation is performed in terms of a generalized random-field correlation function. The interplay of short-range correlations as well as of a parameter-dependent variety of long-range correlations with thermal and quantum fluctuations is revealed.

How peculiar can the temperature variation of magnetic anisotropy be: limitations by a general theorem

The variation of anisotropy constants is studied within the three-constant approximation to the anisotropy free energy. The anisotropy-flow concept for tracing the evolution of the system in the anisotropy space of the system is introduced. Unexpected features of the variation of anisotropy are uncovered for realistic values of the intrinsic parameters as, for example, two zero points for the first anisotropy constants and, correspondingly, two successive reorientation transitions between phases with different easy axes of magnetization. The question of the ultimate possible peculiarity of variation of anisotropy and magnetostriction is addressed by formulating and proving a far-reaching theorem by virtue of which the superposition of p different functions with certain widely met properties may not have more than p-1 zeroes or internal extrema.