Theory for the reduction of products of spin operators

In this study we show that the sum of the powers of arbitrary products of quantum spin operators such as $(S^+)^l(S^-)^m(S^z)^n$ can be reduced by one unit, if this sum is equal to 2S+1, S being the spin quantum number. We emphasize that by a repeated application of this procedure \em all \em arbitrary spin operator products with a sum of powers larger than 2S can be replaced by a combination of spin operators with a maximum sum of powers not larger than 2S. This transformation is exact. All spin operators must belong to the same lattice site. By use of this procedure the consideration of single-ion anisotropies and the investigation of the magnetic reorientation within a Green's function theory are facilitated. Furthermore, it may be useful for the study of time dependent magnetic properties within the ultrashort (fsec) time domain.Comment: 11 pages, 1 table, uses rotatin

Schwinger boson theory of anisotropic ferromagnetic ultrathin films

Ferromagnetic thin films with magnetic single-ion anisotropies are studied within the framework of Schwinger bosonization of a quantum Heisenberg model. Two alternative bosonizations are discussed. We show that qualitatively correct results are obtained even at the mean-field level of the theory, similar to Schwinger boson results for other magnetic systems. In particular, the Mermin-Wagner theorem is satisfied: a spontaneous magnetization at finite temperatures is not found if the ground state of the anisotropic system exhibits a continuous degeneracy. We calculate the magnetization and effective anisotropies as functions of exchange interaction, magnetic anisotropies, external magnetic field, and temperature for arbitrary values of the spin quantum number. Magnetic reorientation transitions and effective anisotropies are discussed. The results obtained by Schwinger boson mean-field theory are compared with the many-body Green's function technique.Comment: 14 pages, including 7 EPS figures, minor changes, final version as publishe

In-plane dipole coupling anisotropy of a square ferromagnetic Heisenberg monolayer

In this study we calculate the dipole-coupling-induced quartic in-plane anisotropy of a square ferromagnetic Heisenberg monolayer. This anisotropy increases with an increasing temperature, reaching its maximum value close to the Curie temperature of the system. At T=0 the system is isotropic, besides a small remaining anisotropy due to the zero-point motion of quantum mechanical spins. The reason for the dipole-coupling-induced anisotropy is the disturbance of the square spin lattice due to thermal fluctuations ('order-by-disorder' effect). For usual ferromagnets its strength is small as compared to other anisotropic contributions, and decreases by application of an external magnetic field. The results are obtained from a Heisenberg Hamiltonian by application of a mean field approach for a spin cluster, as well as from a many-body Green's function theory within the Tyablikov-decoupling (RPA).Comment: 6 pages, 2 figures, accepted for publication in RP

Model study for the nonequlibrium magnetic domain structure during the growth of nanostructured ultrathin films

The nonequilibrium magnetic domain structure of growing ultrathin ferromagnetic films with a realistic atomic structure is studied as a function of coverage and temperature. We apply a kinetic Monte Carlo method to a micromagnetic model describing the transition from superparamagnetic islands at low coverages to a closed ferromagnetic film. The magnetic relaxation and the island growth happen simultaneously. Near the percolation threshold a metastable magnetic domain structure is obtained with an average domain area ranging between the area of individual magnetic islands and the area of the large domains observed for thicker ferromagnetic films. We conclude that this micro-domain structure is controlled and stabilized by the nonuniform atomic nanostructure of the ultrathin film, causing a random interaction between magnetic islands with varying sizes and shapes. The average domain area and domain roughness are determined. A maximum of the domain area and a minimum of the domain roughness are obtained as a function of the temperature.Comment: 19 pages, 4 Postscript figures; to be published in J. Magn. Magn. Mater., accepted (2001); completely revised manuscrip

Ferromagnetism and Temperature-Driven Reorientation Transition in Thin Itinerant-Electron Films

The temperature-driven reorientation transition which, up to now, has been studied by use of Heisenberg-type models only, is investigated within an itinerant-electron model. We consider the Hubbard model for a thin fcc(100) film together with the dipole interaction and a layer-dependent anisotropy field. The isotropic part of the model is treated by use of a generalization of the spectral-density approach to the film geometry. The magnetic properties of the film are investigated as a function of temperature and film thickness and are analyzed in detail with help of the spin- and layer-dependent quasiparticle density of states. By calculating the temperature dependence of the second-order anisotropy constants we find that both types of reorientation transitions, from out-of-plane to in-plane (``Fe-type'') and from in-plane to out-of-plane (``Ni-type'') magnetization are possible within our model. In the latter case the inclusion of a positive volume anisotropy is vital. The reorientation transition is mediated by a strong reduction of the surface magnetization with respect to the inner layers as a function of temperature and is found to depend significantly on the total band occupation.Comment: 10 pages, 8 figures included (eps), Phys Rev B in pres

Anisotropic susceptibility of ferromagnetic ultrathin Co films on vicinal Cu

We measure the magnetic susceptibility of ultrathin Co films with an in-plane uniaxial magnetic anisotropy grown on a vicinal Cu substrate. Above the Curie temperature the influence of the magnetic anisotropy can be investigated by means of the parallel and transverse susceptibilities along the easy and hard axes. By comparison with a theoretical analysis of the susceptibilities we determine the isotropic exchange interaction and the magnetic anisotropy. These calculations are performed in the framework of a Heisenberg model by means of a many-body Green's function method, since collective magnetic excitations are very important in two-dimensional magnets.Comment: 7 pages, 3 figure

Some basic aspects of quantum phase transitions

Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of quenched disorder on the quantum phase transitions is also discussed. The review is performed within the framework of the thermodynamic scaling theory and by the most general methods of statistical physics for the treatment of phase transitions: general length-scale arguments, exact solutions, mean field approximation, Hubbard-Stratonovich transformation, Feynman path integral approach, and renormalization group in the field theoretical variant. Some new ideas and results are presented. Outstanding theoretical problems are mentioned.Comment: 81 pages, Latex2e, 8 figures, Phys. Rep.(2003) in pres

Higher-order and next-nearest-neighbor Néel anisotropies

The problem of higher-order Néel anisotropies is solved by exploiting the addition theorem for spherical functions. A key advantage of the present approach is the orthonormal character of the expansion of the magnetic energy that simplifies the formalism and makes possible the treatment of nonideal morphologies as well. Explicit expressions for second-, fourth-, and sixth-order anisotropies are obtained for ideal bulk of fcc and bcc symmetry as well as for (001), (110), and (111) surfaces with nearest-neighbor (NN) Néel interactions. The systematic examination of the pair model involves partition by species of inequivalent sites, interaction spheres, and orders in the multipole expansion. It enables us to treat also next-nearest-neighbor (NNN) pair interactions to the same high orders as the NN ones. The analysis sheds light onto the peculiar cases of bcc(100) and bcc(111) surfaces where one finds no symmetry breaking (no second-order contributions) with NN interactions only. With the extension to NNN’s, it is demonstrated that bcc(111) surfaces exhibit a particularly high symmetry and acquire no second-order anisotropy contributions from NNN interactions, whereas the latter induce a second-order symmetry breaking in the bcc(100) case