A study of spin‐phonon interactions in ferromagnetic insulators. II. The phonon spectrum and spin‐lattice relaxation bate

Abstract

The formalism of a previous paper is employed to evaluate the renormalised energy and damping of phonon excitations due to spin-phonon interactions in a Heisenberg ferromagnet. The calculations make use of a field theoretical perturbation technique and an expansion in powers of the high density parameter l/z. The results are applicable over a wide range of temperatures below T,. Calculations are also presented for the spin-lattice relaxation rate, which can be closely related to the phonon damping.On applique le formalisme du travail precedent pour calculer la renormalisation de I'6nergie et l'amortissement des phonons dues au couplage spins-phonons dans un ferromagnetique de Heisenberg. On utilise la mhthode de perturbation de la th6orie des champs et un dbveloppement en s6rie en puissances d'un parametre de haute densit6 l/z. Les resultats obtenus sont valables sur un domaine large des temperatures en-dessous de T,. On calcule aussi le temps de relaxation spin-reseau, qui est directement reli6 B l'amortissement des phonons.

Spin-phonon interaction in transition-metal difluoride antiferromagnets: Theory and experiment

“…The low frequency B 1g mode can only decay into acoustic phonon modes and hence its extreme sharpness even at room temperature. For the phonons in antiferromagnets below T N , an additional decay channel is possible into pairs of magnons of equal and opposite wave vector [9,11,12]. However, in NiF 2 a lowfrequency "ferromagnetic" magnetic branch exists, as mentioned earlier.…”

“…In fact, the four Raman-active modes leave the magnetic atoms stationary, while producing displacements in r n that can be written down following [29]. Then a Taylorseries expansion in terms of these displacements yields a leading-order spin-phonon coupling Hamiltonian that is quadratic in the spin operators and linear in the phonon operators (see, e.g., [6][7][8][9][10][11]). The effects of the weaker intra-sublattice exchange [1] on the phonon modes in the rutile antiferromagnets will be neglected here, but it is important to include the magnetic single-ion anisotropy terms in the full Hamiltonian, since these are relatively large for some of the materials studied here.…”

“…The basic mechanism assumed for the spin-phonon coupling in the rutile-structure antiferromagnets arises from a spatial modulation of the dominant exchange parameter due to the relative displacements of the atoms corresponding to the phonon modes, as first proposed by Akhiezer [6]. This effect can lead to a modification of both the phonon and magnon dispersion relations, and has been studied theoretically for ferromagnets [7][8][9] and antiferromagnets [10,11]. In this work an extended version of the approach used in our previous spin-phonon calculations [12,13], and applied primarily to FeF 2 and MnF 2 , will be followed.…”

The Phonon Self-Energy in an Anisotropic Heisenberg Ferromagnet With Single-Ion Anisotropy

“…The diagrammatic theory adopted was that used by Chakraborty and Tucker [I] in a recent study of the magnetic excitations in an anisotropic ferromagnet with spin-phonon interactions. A similar approach has been used by Kamenskii [2], and Jones and Cottam [3], for the isotropic magnet, and by Kamensky [4], for the ferromagnet with anisotropic exchange. However, in those cases the situation was somewhat simpler because of the absence of any single-ion terms in the Hamiltonian.…”

“…In the isotropic limit, when J+ = J0 and D vanishes, it is seen that the optical branch drops out and ~i reduces to the familiar spin-wave energy, ~k = y -bJ (k) of the isotropic magnet. The result of [3] for the phonon self-energy is thenrecovered. To extend the calculation to higher temperatures, other diagrams involving two momentum summations, but still of order 1 / z , have to be included.…”