We report on the observation of quantized surface spin waves in periodic arrays of magnetic Ni81Fe19 wires by means of Brillouin light scattering spectroscopy. At small wavevectors (q_1 = 0 - 0.9*100000 cm^-1 ) several discrete, dispersionless modes with a frequency splitting of up to 0.9 GHz were observed for the wavevector oriented perpendicular to the wires. From the frequencies of the modes and the wavevector interval, where each mode is observed, the modes are identified as dipole-exchange surface spin wave modes of the film with quantized wavevector values determined by the boundary conditions at the lateral edges of the wires. With increasing wavevector the separation of the modes becomes smaller, and the frequencies of the discrete modes converge to the dispersion of the dipole-exchange surface mode of a continuous film.
The level splitting formulae much discussed in the study of spin tunneling in macroscopic ferromagnetic particles and previously derived only by complicated pseudoparticle methods for the ground state, are derived from those of eigenvalues of periodic equations and extended to excited states.
The reduced O(3)-oe model with an O(3) ! O(2) symmetry breaking potential is considered with an additional Skyrmionic term, i. e. a totally antisymmetric quartic term in the field derivatives. This Skyrme term does not affect the classical static equations of motion which, however, allow an unstable sphaleron solution. Quantum fluctuations around the static classical solution are considered for the determination of the rate of thermally induced transitions between topologically distinct vacua mediated by the sphaleron. The main technical effect of the Skyrme term is to produce an extra measure factor in one of the fluctuation path integrals which is therefore evaluated using a measure-modified Fourier-Matsubara decomposition (this being one of the few cases permitting this explicit calculation). The resulting transition rate is valid in a temperature region different from that of the original Skyrme-less model, and the crossover from transitions dominated by thermal fluctuations to those dominated by tunneling at the lower limit of this range depends on the strength of the Skyrme coupling.
A formula suitable for a quantitative evaluation of the tunneling effect in a ferromagnetic particle is derived with the help of the instanton method. The tunneling between n-th degenerate states of neighboring wells is dominated by a periodic pseudoparticle configuration. The low-lying level-splitting previously obtained with the LSZ method in field theory in which the tunneling is viewed as the transition of n bosons induced by the usual(vacuum) instanton is recovered.The observation made with our new result is that the tunneling effect increases at excited states. The results should be useful in analyzing results of experimental tests of macroscopic quantum coherence in ferromagnetic particles.
The tunneling splitting of the energy levels of a ferromagnetic particle in the presence of an applied magnetic field - previously derived only for the ground state with the path integral method - is obtained in a simple way from Schr"odinger theory. The origin of the factors entering the result is clearly understood, in particular the effect of the asymmetry of the barriers of the potential. The method should appeal particularly to experimentalists searching for evidence of macroscopic spin tunneling.
An unusual interlayer coupling, recently discovered in layered magnetic systems, is analysed from the experimental and theoretical points of view. This coupling favours the 90 orientation of the magnetization of the adjacent magnetic films. It can be phenomenologically described by a term in the energy expression, which is biquadratic with respect to the magnetizations of the two films. The main experimental findings, as well as the theoretical models, explaining the phenomenon are discussed.
The room-temperature wall energy sw 54.0310 23 J/m 2 of an exchange-coupled Tb 19.6 Fe 74.7 Co 5.7 /Dy 28.5 Fe 43.2 Co 28.3 double layer stack can be reduced by introducing a soft magnetic intermediate layer in between both layers exhibiting a significantly smaller anisotropy compared to Tb FeCo and Dy FeCo. sw will decrease linearly with increasing intermediate layer thickness, d IL , until the wall is completely located within the intermediate layer for d IL > d w , where d w denotes the wall thickness. Thus, d w can be obtained from the plot sw versus d IL .We determined sw and d w on Gd FeCo intermediate layers with different anisotropy behavior ~perpendicular and in-plane easy axis! and compared the results with data obtained from Brillouin light-scattering measurements, where exchange stiffness, A, and uniaxial anisotropy, K u , could be determined. With the knowledge of A and K u , wall energy and thickness were calculated and showed an excellent agreement with the magnetic measurements. A ten times smaller perpendicular anisotropy of Gd 28.1 Fe 71.9 in comparison to Tb FeCo and Dy FeCo resulted in a much smaller sw 51.1310 23 J/m 2 and d w 524 nm at 300 K. A Gd 34.1 Fe 61.4 Co 4.5 with in-plane anisotropy at room temperature showed a further reduced sw 50.3310 23 J/m 2 and d w 517 nm. The smaller wall energy was a result of a different wall structure compared to perpendicular layers.
The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite dimensional superspaces, and construct superanalogs of the classical function spaces with a reproducing kernel - including the Bargmann-Fock representation - and of the Wiener-Segal representation. The latter representation requires the investigation of Wick ordering on Z 2 -graded algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck semigroup on the Fock space.