Nonlinear Two‐Magnon‐One‐Phonon Confluence Process in BVC Garnet

Abstract

For cubic monocrystalline Bi 0,5Ca2.5Feg., 5V1.25012 garnets Manzel and Linzen (1) have found the existence of two peaks of the imaginary part of the microwave susceptibility f( h, H, w1 ) for subsidiary ferrimagnetic resonance by parallel pumping with linear polarized microwaves of an amplitude h > h in orientation of applied dc field H parallel to [I00 J at room temperature. h denotes thethreshold value for parametric excitation of magnons, and w1 is the fixed pump frequency.In this letter we will give some results which show that a possible explanation of these two peaks at characterized dc fields called H the linear anisotropic interaction (2, 3) between parametrically excited magnons and lattice phonons with longitudinal (1) and transversal (t) polarization, respectively. In respectof this conception we have calculated the contribution of xu for an isolated 2-magnon-1-phonon confluence process where two parametrically excited and energetically degenerate acoustical magnons with wave vectors a,, a2, frequencies w( 5 ) = w( 'b2) = wl/2, and polar angles e% = 0% = ~/ 2 with respect to [ 1001 as polar axis confluence due to linear magnetoelastic interaction into a nonthermal or thermal acoustical phonon with wave vector g, frequency w (q, a), and polarization s = 1, t . This dynamical relaxation process is nonlinear because both the number and the damping of magnons depend on the microwave power, and conservation of energy fio(al) + Ru, (a,) = %hw (q, 8) and of momentum %g1 + hS2 = hq are demanded. Applying the technique of nonequilibriumGreen's functions (4) we obtain for the nonlinear steady-state response at H C

Quantum Statistical Theory of Parametric Spin‐Wave Excitations in Magnetoelastic Ferromagnets under Parallel Pumping: II. Calculation of Macroscopic Observables

“…18 to 21 were carried out by Haubenreisser [93,110,1111 using the same algebraic approximation scheme that will not be further outlined here. A remarkable difference with respect to the 3m process consists in that the interesting static field region is divided into a first sub-region …”

“…23 denionstrates the agreement between calculated and measured peak positions for a weak anisotropic Ca2,5Bio.5Fe3,75V1,25012 garnet sphere [93, 110, 1111. The elastic anisotropy factor eA = 2c,/(cI1 -cI2) = c~[O01]/c~ [110] of the Ca-Bi-V-Fe garnet deviates only by l2q4, from the value eA = 1 of elastical isotropy.…”

“…There appear, due to the small elastic anisotropy splitting, two peaks in the experimental &H)-curve a t H z m l p h , and H z m l p h t associated with longitudinal and degenerated transverse polarized acoustical phonon modes, respectively [93,110,111,1151. A corresponding variation of the magnon population was observed by using the method of optical Faraday rotation [149] which also confirms the contributions of the 2mlph-process to -& as predicted by the presented theory.…”