Ferromagnetic resonance

At very high frequencies, domain walls are unable to follow the field and the only remaining magnetisation mechanism is spin rotation within domains. This mechanism eventually also shows a dispersion, which always takes the form of a resonance. Spins are subjected to the anisotropy field, representing spin-lattice coupling as an external field is applied (out of the spins easy direction), spins experience a torque. However, the response of spins is not instantaneous spins precess around the field direction for a certain time (the relaxation time, r) before adopting the new orientation. Fig. 4.62. The frequency of this precession is given by the Larmor frequency  

The linewidth of resonance peaks (width measured at half the height of resonance peak), AH, depends on a variety of factors. Anisotropy field effects can be expressed in terms of a damping constant leading to a contribution to AH. If the dc field is not strong enough to saturate the 

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The dielectric permittivity as a function of frequency may show resonance behavior in the case of gas molecules as studied in microwave spectroscopy (25) or more likely relaxation phenomena in soUds associated with the dissipative processes of polarization of molecules, be they nonpolar, dipolar, etc. There are exceptional circumstances of ferromagnetic resonance, electron magnetic resonance, or nmr. In most microwave treatments, the power dissipation or absorption process is described phenomenologically by equation 5, whatever the detailed molecular processes. 

M. Che, M. Richard, and D. OUvier ferromagnetic resonance study of dispersed nickel particles prepared by reduction of nickel ion-exchanged X-zeolites by hydrogen molecules or hydrogen atom beams, J. Chem. Soc. Faraday Trans. 176,1526-1534 (1980). 

The strain modulated ferromagnetic resonance (SMFMR) method.Ill... 

Various experimental methods have been developed for investigating the magnetoelastic properties of thin films and nanoscale magnetic systems. In the following subsections, we discuss the most important ones (i) the magnetoelastic cantilever, (ii) strain induced anisotropy, (iii) magnetostriction in spin valves, (iv) strain modulated ferromagnetic resonance, (v) secondary-electron spin-polarisation, and (vi) strain-induced anisotropy due to the spontaneous strains. 

Mukhin et al. (2000) found that increasing Sr doping in Lai- Sr MnOs does suppress the (quasi-)ferromagnetic resonance frequency, whereas the (quasi-)AF resonance frequency is only slightly decreased (20%). This behaviour corresponds to a canted magnetic structure and its evolution with increasing x. 

Wajnberg, E. El-Jaick, L.J. Linhares, M.P. Esquivel, D.M. Ferromagnetic resonance of horse spleen ferritin core blocking and surface ordering temperatures. J. Magn. Reson. 2001, 153(1), 69-74. 

Note that Eqs. (4.127)-(4.130) describe only the longitudinal (with respect to the easy axis) relaxation of the magnetic moment. We remark that under condition 0) L, that is, far from the ferromagnetic resonance range, the transversal components of hi = p(e) are of minor importance. 

G. V. Skrotskii andL. V. Kurbatov, in Ferromagnetic Resonance, S. V. Vonsovsii, ed., Pergamon Press, Oxford, 1966. 

We have measured the frequency-field dependence of the ESR signal between 30 MHz and 245 GHz. At high fields (Fig. 20) this relation is nearly linear at T=5 K, i.e., well below the ferromagnetic transition temperature [105]. This may be at first glance surprising, as in the magnetically ordered phase one would expect a nonlinear resonance field-resonance frequency relation. The answer to that came only later on from low-field ferromagnetic resonance data discussed in the next section. 

Vonsovskii SV (1996) Ferromagnetic resonance. Pergamon, Oxford Arcon D, Blinc R, Omerzu A (1997) Mol Phys Rep 18/19 89... 

Atomic processes are very fast, so that intrinsic properties obey equilibrium statistics. An intermediate regime is characterized by typical magnetostatic and anisotropy energies per atom, about 0.1 meV, which correspond to times of order t0 0.1 ns. Examples are ferromagnetic resonance and related precession and damping phenomena. When energy barriers are involved, thermal excitations lead to a relatively slow relaxation governed by the Boltzmann-Arrhenius law [99, 133-137]... 

Ignoring the damping term in Eq. (17), the resonance is described by dM/dt = KMxHeff). For homogeneously magnetized ellipsoids of revolution, the effective field is equal to the applied field H = H ez plus the anisotropy field Ha, and the resonance problem is solved by the diagonalization of a 2x2 matrix. This uniform or ferromagnetic resonance (FMR) yields resonance frequencies determined by [17]... 

S. V. Vonsovskii, Ferromagnetic Resonance , Pergamon Press, Oxford 1966. 

The obtained spectra can be explained in the limits of the phenomenological resonance equations for highly anisotropic ferromagnets [14]. Such features are characteristic for imiaxial anisotropy, which rises from the deviation of nanoparticles shape from spherical. The resonance frequency (o of spherical nanoparticles according to the theory of ferromagnetic resonance is determined by the following equation ... 

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