Effect of Bound States on the Excitation Spectrum of a Heisenberg Ferromagnet at Low Temperature

Abstract

A compact expression for the energy shift and inverse lifetime (energy width) of spin waves in a Heisenberg ferromagnet at low temperatures is given. The two-particle bound states are observable via the resonance they cause in the self-energy of spin waves. Disciplines Physics | Quantum Physics This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/309 VOLUME 19, NUMBER 1 PHYSICAL REVIEW LETTERS 5 Jvr.v 1967 Ref. 3.) In closing, we note that the important role played by the recombination phonons stems from the fact that they are generated at a great rate, i.e. , of order I» and that P is relatively large and comparable with ~& '. As a result, the phonons produced by the recombination of the injected quasiparticles will themselves create quasiparticles at a rate comparable with Ip On the other hand, it may be possible to minimize the effects of the phonons by carrying out a pulse experiment. For times small compared with Tg, the number of recombination phonons will be negligible and thus the initial decay rate of a pulse of injected quasiparticles will be determined solely by p Phys. Rev. Letters 18, 1000 (1967). This recombination takes place primarily via phonon emission rather than photon emission. See E. Burstein, D. H. Langenberg, and B. N. Taylor, Phys. Rev. Letters 6, 92 (1961), and also Refs. 6-8. J. R. Schrieffer and D. M. Ginsberg, Phys. Rev. Letters 8, 207 (1962). 6A. Rothwarf and M. Cohen, Phys. Rev. 130, 1401 (1963). 76. Lucas and M. J. Stephen, Phys. Rev. 154, 349 (1967). This was calculated using the Umklapp process rate for Al as done for Pb in Ref. 6. ~It is assumed that the quasiparticles are injected at the gap edge and that the energy of the recombination phonons is 24 where b is the energy gap parameter. C. Kittel, Introduction to Solid State Physics (John iley & Sons, New York, 1957), 2nd ed. , p. 366. ~~Other decay modes such as electron-phonon and phonon-phonon scattering must have a lifetime longer than 8.5 x10 ~ sec since even at room temperature, such lifetimes are longer than this (see Ref. 10, p. 149). ~2It is unlikely that any temperature dependence in would be sufficiently strong to invalidate these conc usions. EFFECT OF BOUND STATES ON THE EXCITATION SPECTRUM OF A HEISENBERG FERROMAGNET AT LOW TEMPERATURE* Richard Silberglittf and A. Brooks Harris Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania (Received 22 May 1967) A compact expression for the energy shift and inverse lifetime (energy width) of spin waves in a Heisenberg ferromagnet at low temperatures is given. The two-particle bound states are observable via the resonance they cause in the self-energy of spin waves. The purpose of this brief note is to report calculations of the transverse component of the generalized wave-vector and frequencydependent susceptibility y+ (k, ~) for the Heisenberg ferromagnet at low temperatures. These calculations show that at short wavelengths the two-particle bound states' influence the single-particle spin-wave excitations in a dominant and nonperturbative way. We use the Dyson-Ma, leev transformation' S = (2S)' '(1-a a/2S)a; S =(2S)~'ma ' ak ' 6a a'2 k xa —'k + X —'k-X —'k +,a,k „(2)