Magnons and their interactions with phonons and photons

2014 A review is given of the theory of spin waves and of the principal physical effects associated with spin,waves. It is shown that the boundary condition mx = my = 0 at the surface permits the excitation of spin waves by a uniform rf field. These excitations have been observed by Waring and Jarrett and by Seavey and Tannenwald. LE JOURNAL DE PHYSIQUE ET LE RADIUM TOME 20, FÉVRIER 1959, A magnon is a quantized spin wave, just as a photon is a quantized electromagnetie wave and a phonon is a quantized elastic_wave. Magnons exist only in’an idealization, just as"photons and phonons_exist only in the idealization that terms in the ’complete hamiltonian representinglinteractions or collisions,amongthe particles are neglected. Two, phonons do not exist independently in the actual anharmonic potentials in real crystals, nor do two magnons exist entirely independently, but for both particles it can be shown that in the limit of small excitation amplitudes the interaction corrections are small. For magnons this has been shown [1] by Bethe, Hulthén, and Dyson; Bethe calculated explicitly the exact energy eigenvalues for two magnons on a line of atoms, and the interaction terms are found to be very small. The bearirig of the electron gas in metals on the existence of phonons and magnons [2] probably does not upset the wave aspect of the phonon and magnon fields. This is explained by the fact that the plasma frequency is very much greater than the Debye frequency and the exchange frequency ; experimentally, it is known [3] from neutron and x-ray work that elastic waves have a reality in metals up to the top of the frequency spectrum, approximately 1013 cps. Neutron diffraction measurements [4] at Harwell give evidence of the existence of spin waves in iron. It is perhaps more convincing to begin the treatment of magnons from a macroscopic viewpoint, just as the idea of a phonon originated with Debye in the quantization of a macroscopic elastic wave in an essentially homogeneous medium. We assert first that work must be done to distort or twist the local direction of magnetization from one point to another in a ferromagnetic specimen, just as work must be done to set up a mechanical deformation or strain in an elastic medium. The most convincing macroscopic evidence for our assertion comes from the observation of Bloch walls of finite thickness in domain patterns and, further from the observations of Rado [15] and others on exchange"effects in ferromagnetic resonance in metals. Granted that the energy of a non-uniform distribution of magnetization directions is higher than for a uniform distribution, we are led directly by a wellknown argument to the Landau and Lifshitz [6] expression for the exchange energy density in a cubic crystal ; here oc isthe unit vector in the direction of the loèal magnetization. Granted Eq" (1), we are then led by purely macroscopic reasoning to a theory of magnon fields. The classical exchange hamiltonian density equivalent to Eq. (1) in the limit of small amplitudes 1 --1 nB where Ç = Mx, and = My/yfg is the conjugate momentum density [7] ; here y = ge/2mc. The Zeeman lagrangian leading to this result for 7c gives the correct spin resonance_frequency for a uniformly magnetized ferromagnet in a magnetic field. The equations of motion in hamiltonian form are Thus, using Eq. (2), If we look for solutions of the form ei(cùg--k.r) , we find from Eqs. (5) and (6) that Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01959002002-3014500