Surface Spin-wave Modes Research Articles

Surface spin-wave in monocrystalline, epitaxial layers of manganese ferrite

We observed two surface spin-wave modes in ferromagnetic resonance in monocrystalline, epitaxial layers of manganese ferrite. The layers, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2-3\mu</tex> m thick, were obtained by CVD on monocrystalline MgO substrates. In MEFL, observations were performed at room temperature and a frequency of 26,6 GHz. The critical angles for which the surface modes vanish amount to 48° and 37° respectively, for line I and line II. The magnetic parameters for uniform mode are: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4\piM_{eff}= 280</tex> Gs, H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</inf> = -290 Oe, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g = 2,00</tex> .

Theory of surface spin waves in itinerant ferromagnets

Using the RPA and specular boudary scattering, we show that a ferromagnetic mental with a surface exhibits a surface spin wave mode. It lies above the bulk spin wave spectrum and only appears when one includes the inter-atomic exchange between electrons.

The spin correlation functions of a semi-infinite Heisenberg ferromagnet

Results are derived for the dynamic correlation functions between a pair of spin operators at any two sites within a semi-infinite Heisenberg ferromagnet at low temperatures, T<<Tc. The correlation functions are found to contain terms describing the effects of the bulk spin-wave modes and the surface spin-wave modes, together with appropriate weighting factors. The results are employed to evaluate the spin deviation in the ferromagnet as a function of temperature and distance from the surface.

ESR in quasi 2-d ferromagnets: The coexistence of paramagnetic excitations and magnetostatic spin waves and new interference effects

The quasi 2-dimensional layer structures (C n H 2 n+1 NH 3) 2CuCl 4 with n = 1,2 have been investigated by electron spin resonance. New phenomena arise for samples with well defined natural surfaces: (i) well resolved magnetostatic volume and surface spin wave modes at 4.2 K comparable in quality with spectra of YIG, (ii) a magnetostatic spin wave spectrum which is coincident with the paramagnetic resonance over a wide temperature range, (iii) interference effects between these two types of resonances.

Exchange-dominated surface spin waves in thin yttrium-iron-garent films

The study of exchange-dominated nonpropagating surface spin-wave modes observed in thin single-crystal yttrium-iron-garnet films is reported. The angle and temperature dependences of these modes and creation of the surface pinning condition necessary for their existence by the controlled annealing of the films are discussed. The data are consistent with a modified Puszkarski surface-inhomogeneity model in which the surface-anisotropy field has a tensorial form. At the substrate surface the in-plane component of this field, ${K}_{\ensuremath{\parallel}}^{s}$, is large and negative and the perpendicular component, ${K}_{\ensuremath{\perp}}^{s}$, is large and positive. The degree of localization varies with the annealing history of the sample, and etching experiments confirm a decay length as small as 500 \AA{} when the magnetization lies in the plane of the film. As the magnetization is rotated out of the film plane, a "critical angle" at which the uniform mode is excited is observed, and at the perpendicular orientation the surface mode has been transformed to the first body mode of the film. With decreasing temperature, ${K}_{\ensuremath{\parallel}}^{s}$ is observed to decrease in magnitude and pass through zero between 100 and 200 K. At 4 K, ${K}_{\ensuremath{\parallel}}^{s}$ is large and positive. These data suggest that a psuedodipolar exchange interaction may be occurring between the Fe and Gd atoms at the substrate interface. By annealing at 1200 \ifmmode^\circ\else\textdegree\fi{}C, a similar surface effect is produced at the free surface of the film having ${K}_{\ensuremath{\parallel}}^{f}&lt;0$ and ${K}_{\ensuremath{\perp}}^{f}&gt;0$. However, the temperature dependence of the free-surface anisotropy field indicates that the origin of the interaction has a very different microscopic basis.

A possibility of identifying the surface spin-wave mode from spin-wave resonance linewidth

Spin-wave resonance linewidth is calculated from the Landau-Lifshits equation including dipole interactions. The graph of the linewidthΔH p vs. the square of the SWR peak number is a straight line for spin-wave space modes, whereas for the peak corresponding to surface spin-wave excitationΔH lies beyond it, thus providing a criterion for distinguishing the surface peak from the others.

Possible identification of magnetostatic surface spin wave modes in ferromagnetic resonance on epitaxial yttrium—iron—garnet films

In ferromagnetic resonance experiments of yttrium—iron—garnet films, resonances have been observed whose characteristics are consistent with their interpretation as magnetostatic surface spin wave modes.

The surface spin-wave mode in FMR of bulk metal ferromagnets

The excitation of the surface spin-wave mode in FMR of a bulk metal ferromagnet is theoretically predicted in the case of negative values of the uniaxial surface anisotropy constant.

Surface spin waves in ferromagnetic thin films

Surface spin-wave modes are calculated for (100) surface of simple cubic structure. An isotropic part as well as an anisotropic part are introduced in the spin Hamiltonian. The anisotropic factor is allowed to vary on the first two surface layers. Dispersion curves are derived by a Green function formalism.

On the existence of optical surface spin waves

Abstract Surface spin-wave modes are calculated for (100) surfaces of simple cubic structure. In contradiction to De Wames and Wolfram results, in most cases no optical branch is found in the surface spin-wave spectrum.

Calorimetric Study of Yttrium and Rare-Earth Iron Garnets between 0.4 and 4.5°K

We present the results of a calorimetric study on iron-garnet polycrystalline samples of Y, Eu, Tm, Sm, and Yb between 0.4 and 4.2\ifmmode^\circ\else\textdegree\fi{}K in zero magnetic field. Results for another sample of YIG between 0.7 and 4.2\ifmmode^\circ\else\textdegree\fi{}K in magnetic fields up to 13 kOe are also presented. In YIG it is shown that in addition to the lattice vibration and acoustic spin-wave-mode contributions, ${C}_{L}$ and ${C}_{\mathrm{acous}}$, there is a residual specific heat $\mathcal{R}(T)$ that is linear with temperature and somewhat dependent on magnetic field. This new term $\mathcal{R}(T)$ is tentatively attributed to surface effects although its magnitude is much larger than that predicted for surface spin-wave modes in a ferromagnetic sintered sample with the same dispersion constant $D$. The data in YIG are compared with previous work, and it is shown that the analysis of the calorimetric data on this compound is more complex than was thought previously, and in particular that data on ${C}_{v}$ in zero field are not suited for obtaining the value of $D$ from the usual $\frac{{C}_{v}}{{T}^{\frac{3}{2}}}$-versus-${T}^{\frac{3}{2}}$ plot. The same comments apply to EuIG, where a residual term, linear in temperature, was also obtained. From the nuclear specific heat of this compound, we obtain an rms magnetic field at the nucleus ${H}_{N}=597\ifmmode\pm\else\textpm\fi{}5$ kOe, in excellent agreement with results from M\ossbauer experiments. In TmIG, the effect of acoustical spin waves on ${C}_{v}$ could be detected, and (as expected) there was no evidence of population of the optical modes. However, no firm conclusions could be reached about a residue, since it was difficult to estimate ${C}_{\mathrm{acous}}$ theoretically. The nuclear contribution $\frac{{C}_{N}{T}^{2}}{R}=(7.8\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ was found to be in good agrement with that predicted from M\ossbauer data. In SmIG, the first excited electronic level was deduced to be $\frac{E}{{k}_{B}}=(38\ifmmode\pm\else\textpm\fi{}3)\ifmmode^\circ\else\textdegree\fi{}$K, in good agreement with predictions from White's theory. The nuclear specific heat of SmIG was analyzed as corresponding to an rms field at the nucleus ${H}_{N}=(2.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ Oe, while an analysis of M\ossbauer data had given (2.8\ifmmode\pm\else\textpm\fi{}0.15)\ifmmode\times\else\texttimes\fi{}${10}^{6}$ Oe. A broad anomaly in ${C}_{v}$ centered at 2\ifmmode^\circ\else\textdegree\fi{}K remains unexplained, but is possibly due to an unreacted samarium oxide impurity. It is responsible for the uncertainty in $E$ and ${H}_{N}$. In YbIG, a sizable discrepancy remains below 3\ifmmode^\circ\else\textdegree\fi{}K between the theory using the 12 low optical spin-wave modes and the experimental data. Apparently the dispersion curve of the exchange mode is significantly different from that calculated by Tinkham using a simple model. The nuclear specific heat in YbIG, $\frac{{C}_{N}{T}^{2}}{R}=(1.6\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, was in fair agreement with that predicted from the electron-nucleus coupling parameter and the ground-state electronic moment.

Theory of Surface Spin Waves in the Heisenberg Ferromagnet

The eigenvalue matrix for a number of semi-infinite cubic system of spins coupled by nearest neighbors is derived for the Heisenberg ferromagnet. The mathematical formulation used allows solutions for an arbitrary variation in the surface exchange constants. Surface spin-wave modes for the simple cubic structure are calculated for the {100} and {110} surfaces. By allowing the exchange parameters to deviate from the bulk values, the full richness of the surface spin-wave spectra is displayed. Surface spin-wave modes are found to exist above and below the bulk spectrum. The dispersion curves can be truncated, i.e., they exist only over a limited region of ${\mathrm{k}}_{11}$ space, where ${\mathrm{k}}_{11}$ is the two-dimensional propagation vector parallel to the crystal surface. The eigenvectors of the surface spin-wave modes are also discussed.

Surface spin waves in a semi-infinite anisotropic Heisenberg ferromagnet

The surface spin wave modes in an anisotropic Heisenberg ferromagnet are shown to exist for nearest neighbour coupling and to lie below the volume spin wave band.

General Exchange Boundary Condition and Surface Anisotropy Energy of a Ferromagnet

The general exchange boundary condition applicable to a line of spins placed in a static field of arbitrary orientation and whose end spins are subjected to different environments are first formulated. The result is then applied to the problem of spin wave resonance in thin magnetic films. Both the line and absorption spectra are calculated assuming different types of surface anisotropy. By comparing our theoretical results with various experiments, it is concluded that the shape of the energy surface of the surface anisotropy energy are uniaxial with the easy axis of magnetization in the direction of the surface normal and the hard plane of magnetization parallel to the film plane. The possible origin of this anisotropy, including the question of dynamic pinning, is discussed in some detail. Aside from the usual volume spin-wave resonance modes, we found also some surface spin wave modes whose presence may have an important bearing upon the magnetization reversal process in thin Permalloy films. An apparent departure from the ${k}^{2}$ dispersion low for spin waves and its relevance upon the determination of the exchange constant is also discussed.