Ferromagnetic Resonance in Thin Films. I. Theory of Normal-Mode Frequencies
TL;DR: In this article, a theory for the frequencies of the general ferromagnetic normal modes of a sample of arbitrary shape and size with both exchange and demagnetization energies included.
Abstract: A theory is developed for the frequencies of the general ferromagnetic normal modes of a sample of arbitrary shape and size with both exchange and demagnetization energies included. The frequencies of the modes of rectangular and circular films are calculated by casting the linearized equation of motion of the magnetization into the form of an eigenvalue equation, which is solved by a variational method. The results explain the experiments of Dillon, Besser, Sparks et al., Freedman and Brundle, and Voltmer in detail qualitatively and typically to within \ensuremath{\sim}5-10% quantitatively for the mode spacings, with possible exceptions for the first few low-order modes in some samples, for which several contributions to the line spacings are difficult to estimate accurately. Pinning the surface spins has little effect on the frequencies and intensities of magnetostatic modes (with negligible exchange energy). The theory has implications concerning the main-resonance position in finite films, and together with experiments, further verifies Portis's modespacing theory. A simple physical explanation of the results is given, and the relation of the results for for finite films to those for infinite films is given.
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TL;DR: In this article, a theory for dispersion characteristics of spin waves in ferromagnetic films taking into account both the dipole-dipole and the exchange interactions is developed.
Abstract: A theory is developed for dispersion characteristics of spin waves in ferromagnetic films taking into account both the dipole-dipole and the exchange interactions. An arbitrary orientation of the internal bias magnetic field is assumed. The general case of mixing exchange boundary conditions (surface spin pinning conditions) is considered. The simple analytical dispersion equations are obtained using the classical perturbation theory. The modification of the spin wave spectrum due to surface anisotropy (or pinning conditions) is discussed.
824 citations
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TL;DR: By using a technique of microwave pumping it is possible to excite additional magnons and to create a gas of quasi-equilibrium magnons with a non-zero chemical potential, and a Bose condensate of magnons is formed.
Abstract: Bose–Einstein condensation (BEC), a form of matter first postulated in 1924, has famously been demonstrated in dilute atomic gases at ultra-low temperatures. Much effort is now being devoted to exploring solid-state systems in which BEC can occur. In theory semiconductor microcavities, where photons are confined and coupled to electronic excitations leading to the creation of polaritons, could allow BEC at standard cryogenic temperatures. Kasprzak et al. now present experiments in which polaritons are excited in such a microcavity. Above a critical polariton density, spontaneous onset of a macroscopic quantum phase occurs, indicating a solid-state BEC. BEC should also be possible at higher temperatures if coupling of light with solid excitations is sufficiently strong. Demokritov et al. have achieved just that, BEC at room temperature in a gas of magnons, which are a type of magnetic excitation. Bose–Einstein condensation, the formation of a collective quantum state of identical particles, called bosons, is observed at room temperature in a gas of magnons, which are a type of magnetic excitation. Bose–Einstein condensation1,2 is one of the most fascinating phenomena predicted by quantum mechanics. It involves the formation of a collective quantum state composed of identical particles with integer angular momentum (bosons), if the particle density exceeds a critical value. To achieve Bose–Einstein condensation, one can either decrease the temperature or increase the density of bosons. It has been predicted3,4 that a quasi-equilibrium system of bosons could undergo Bose–Einstein condensation even at relatively high temperatures, if the flow rate of energy pumped into the system exceeds a critical value. Here we report the observation of Bose–Einstein condensation in a gas of magnons at room temperature. Magnons are the quanta of magnetic excitations in a magnetically ordered ensemble of magnetic moments. In thermal equilibrium, they can be described by Bose–Einstein statistics with zero chemical potential and a temperature-dependent density. In the experiments presented here, we show that by using a technique of microwave pumping it is possible to excite additional magnons and to create a gas of quasi-equilibrium magnons with a non-zero chemical potential. With increasing pumping intensity, the chemical potential reaches the energy of the lowest magnon state, and a Bose condensate of magnons is formed.
758 citations
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TL;DR: In this article, the authors review the current status of a frontier in dynamic spintronics and contemporary magnetism, in which much progress has been made in the past decade, based on the creation of a variety of micro and nanostructured devices that enable electrical detection of magnetization dynamics.
134 citations
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TL;DR: In this paper, the authors present a theory for the dynamics of the magnon gas driven by a microwave field far out of equilibrium that provides rigorous support for the formation of quasiequilibrium Bose-Einstein condensation (BEC) of magnons in a YIG film magnetized in the plane.
Abstract: Strong experimental evidences of the formation of quasiequilibrium Bose-Einstein condensation (BEC) of magnons at room temperature in a film of yttrium iron garnet (YIG) excited by microwave radiation have been recently reported. Here we present a theory for the dynamics of the magnon gas driven by a microwave field far out of equilibrium that provides rigorous support for the formation of a BEC of magnons in a YIG film magnetized in the plane. We show that if the microwave driving power exceeds a threshold value the nonlinear magnetic interactions create cooperative mechanisms for the onset of a phase transition leading to the spontaneous generation of quantum coherence and magnetic dynamic order in a macroscopic scale. The theoretical results agree with the experimental data for the intensity and the decay rate of the Brillouin light scattering from the BEC as a function of power and for the microwave emission from the uniform mode generated by the confluence of BEC magnon pairs.
103 citations
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TL;DR: In this paper, the authors report ferromagnetic resonance experiments on Ga1−xMnxAs thin films. For the dc magnetic field perpendicular to the sample plane, they observe up to eight distinct resonances, which they attribute to spin wave modes.
Abstract: We report ferromagnetic resonance experiments on Ga1−xMnxAs thin films. For the dc magnetic field perpendicular to the sample plane, we observe up to eight distinct resonances, which we attribute to spin wave modes. To account for the spacing of the resonances, we infer a linear gradient in the magnetic properties, which is ascribed to a linear variation of the uniaxial magnetic anisotropy with film thickness. Values of D=(1±0.4)×10−9 Oe cm2 for the spin stiffness and JMnMn≈1 meV for the exchange integral between Mn spins are obtained.
82 citations