Four-magnon Processes Research Articles

Damping of dipole-exchange spin waves in ferromagnetic thin films at elevated temperatures

A non-bosonic technique, based on the drone-fermion perturbation method and a high-density expansion, is employed to study the spin-wave (SW) scattering processes in a ferromagnetic thin film with exchange and dipole–dipole interactions. Specifically, the diagrammatic contributions to the spin–spin Green’s functions are evaluated within a 1/z perturbation expansion, where z is the number of spins interacting with any given spin. The results are used to calculate the SW damping at temperatures below the Curie temperature T C. It is found that, apart from the usual contributions due to three-magnon and four-magnon processes in the film, which are dominant at relatively low temperatures (consistent with boson expansion methods), there is an additional mechanism that becomes important for temperatures above about This is spin disorder damping, previously studied in bulk magnetic materials; it occurs when a spin wave is scattered by the instantaneous disorder produced when a longitudinal spin component undergoes a large thermal fluctuation. Numerical estimates are presented for thin films of Permalloy and EuO.

Nonlinear Parallel-Pumped FMR: Three and Four Magnon Processes

The nonlinear response of a magnetic thin film subject to microwave radiation is quantitatively predicted in the steady state. Three- and four-magnon processes are shown to cause this nonlinearity with a strong dependence on magnetic bias field, microwave frequency, and applied power. Predictions are calculated using large-scale micromagnetic simulations executed on graphics processing units (GPUs) and include thermal fluctuations. A 2-D simulation paradigm is proposed for reducing the resource requirements while being able to capture the qualitative and quantitative behavior of the significant microwave-ferromagnet interactions in the parallel pumping configuration. A mathematical formalism specific to thin films is then developed to explain the aforementioned behavior of such magnetic materials based on their predicted magnon dispersion relation. The simulated predictions for high-power (nonlinear) performance are in close agreement with experiment even though the material parameters are only taken from low-power (linear) data.

Spin-wave Theory for the Magnetic Damping in Microwave Nano-Oscillators

Here we present a calculation for the linewidth of the spin-wave that is generated when a spin valve nanostructure is traversed by a high-density spin-polarized direct current. In this case, the magnetization excitations are considered to be standing spin-wave modes interacting through the four-magnon processes. We obtain an analytic expression for the effective nonlinear dissipation rate of a magnetic spin-torque nano-oscillator, taking into account a nonlinear phenomenological model of magnetic dissipation and the natural nonlinear contributions due to the demagnetizing fields. The calculation is applied for the general case of the external magnetic field applied in an arbitrary direction.

Microscopic theory of dipole-exchange spin waves in ferromagnetic films: Linear and nonlinear processes

The linear and nonlinear processes in ferromagnetic films at low temperatures $(T\ensuremath{\ll}{T}_{c})$ are studied in a microscopic theory. Both the long-range magnetic dipole-dipole and the Heisenberg exchange interactions to nearest and next-nearest neighbors are included. The results obtained for the linearized spin-wave spectrum are compared with previous macroscopic theories. For ultrathin films (or for large wave vectors) the microscopic theory provides important corrections. The nonlinear dynamics of the spin waves are studied through a finite-temperature perturbation theory based on Feynman diagrams. We obtain explicit results for the energy shift and damping (or reciprocal lifetime) of the dipole-exchange spin waves due to all possible three-magnon and four-magnon processes involving combinations of the surface and quantized bulk spin waves at low temperatures. To investigate different dipole interaction strengths (relative to the exchange) numerical results are presented using parameters for Fe, EuO, and ${\mathrm{GdCl}}_{3}.$

Spin-wave interactions in ultrathin ferromagnetic films: the dipole-exchange regime

A perturbation formalism is employed to study nonlinear processes for the interactions between the discrete spin waves in ferromagnetic films, taking account of both dipole–dipole and exchange coupling. By contrast with previous macroscopic theories of spin-wave interactions the dipolar terms are treated within a Hamiltonian method to obtain results applicable to ultrathin films. The roles of three-magnon and four-magnon processes in the spin-wave energy shift and damping are evaluated and numerical applications to EuO are discussed.

Ordinal Excitation of Three-Magnon and Four-Magnon Processes of Magnetostatic Surface Waves in YIG Films

Ordinal excitations of three-magnon decay, modulation instability and four-magnon decay processes of magnetostatic surface waves propagating in a pure yttrium iron garnet film are investigated in accordance with the relationship between the magnetostatic wave frequency and the internal magnetic field. Onset of the modulation instability is realized as a result of modification of magnetostatic surface wave dispersion characteristics by a metallic ground plane.

The magnon-magnon interactions in easy-plane antiferromagnets

In the framework of the spin-operator diagram technique, the processes of relaxation of lower branch magnons in a two-sublattice easy-plane antiferromagnet are investigated. The procedure of the spin Hamiltonian diagonalization allowing to obtain compact expressions for magnon interaction amplitudes is proposed. The relaxation frequencies due to three- and four-magnon processes, processes of elastic scattering and interbranch transformation by thermal and concentrational magnetization fluctuations as well as the three-magnon confluence processes with rescattering of thermal magnons by fluctuations are calculated. The results obtained are consistent with the experimental data on parametric excitation of spin waves in the low-temperature antiferromagnets MnCO3 and CsMnF3.

Nuclear-spin-relaxation mechanisms of nuclear-ordered bcc solid 3He in the low-field phase.

cw-NMR experiments have been performed on nuclear-ordered bcc solid $^{3}\mathrm{He}$ in the low-field phase. We measured the cw-NMR spectrum and its linewidth as a function of external magnetic fields and temperatures for single-crystal samples having various crystal orientations relative to the external field. From the data on the external magnetic field dependence of the linewidth, we found clear evidence of the field region where the three-magnon process is forbidden. We compared our experimental data with the recent theoretical calculation by Ohmi and Tsubota on the lifetime of a uniform spin precession via the three- and four-magnon processes. The agreement is satisfactory. We estimated the size and distribution of the magnetic domains by using an NMR imaging technique. The size of a magnetic domain was found to be comparable to that of a whole crystal. We found some evidence that a crystal in the ordered phase was distorted (on order of ${10}^{\mathrm{\ensuremath{-}}3}$) uniaxially due to magnetostriction. In some crystal samples, we observed a peculiar field dependence of the antiferromagnetic resonance frequency ${\mathrm{\ensuremath{\Omega}}}_{0}$.

Spin relaxation in U2D23He

The spin relaxation in the U2D2 phase of solid 3 He is investigated theoretically. Following the procedure similar to the spin-wave theory of the electronic anti-ferromagnetic resonance, the multimagnon Hamiltonian is derived with the use of the Holstein-Primakoff method. We calculate the spin-relaxation rate due to three- and four-magnon processes that dominate at low temperatures and compare it with the linewidth of cw-NMR measured by Sasaki et al.

Far-Infrared Optical Absorption of Manganese Fluoride

Optical absorption in MnF2 in the region from 50 to 350 cm−1 was studied. A search was made in particular for multiple-magnon processes previously reported in the literature. While, for example, four-magnon processes can be obtained theoretically from an expansion of the Heisenberg spin Hamiltonion, we found no temperature dependent absorption in the region studied other than the well-known two-magnon peak at 100 cm−1. All the observed peaks above 100 cm−1 could be attributed to phonons.

Ferromagnetic Relaxation. II. The Role of Four-Magnon Processes in Relaxing the Magnetization in Ferromagnetic Insulators

The role of four-magnon processes in relaxing the uniform precession, in relaxing magnons of nonzero wave vector in parallel pumping experiments, and in establishing thermal equilibrium is considered. It is shown that the effect of the exchange-induced four-magnon process should be observable in parallel pumping experiments, but it is found that the four-magnon processes arising from dipole, cubic anisotropy, and exchange coupling are not very effective in relaxing the uniform precession. Both three- and four-magnon processes are important in the later stages of the relaxation scheme by which thermal equilibrium is established.