Magnetoelastic Coupling Constants of Terbium and Europium Iron Garnets

Abstract

The purpose of this paper is twofold: (1) to present data on the magnetoelastic constants of rare-earth iron garnets, a subject which for various reasons has been little studied thus far, and (2) to describe a new method for obtaining these constants which is applicable to many ferromagnetic insulators and does not require the use of strain gauges. The new method was developed from a study of the coupling introduced between long wavelength acoustic modes and long wavelength spin-wave modes by ions in which the orbital moment is not quenched, such as rare-earth ions, Co2+, and Fe2+. The effect of the coupling caused by such ions is observed as a magnetic field dependence of the resonant frequency of an acoustic resonator made from the given material, even above dc saturation. The acoustic Q above dc saturation is also field-dependent. A theory has been obtained which explains the observed field dependences of both v(H) and Q(H) as well as other important features of the magnetoacoustic interaction. It will appear elsewhere.1 One of the results of this theory is a relation between the cubic magnetoelastic constants, B1 and B2, and the acoustic resonant frequency v of a thin disk vibrating in a thickness shear mode. For a (110) disk with the external field H0 in the plane along [100] and the rf driving field perpendicular to the disk, we obtain ν=ν∞(1−B222c44MHeff),where Heff=H0+Hanis+4πM, and c44 is the usual shear elastic modulus, which may be obtained directly from v∞ and the thickness of the disk. Equation (1) applies to the mode with displacement along [100]. B1 is obtained similarly, only now H0 is along [110] in the plane, and the shear displacement is along [110]. Here we have ν=ν∞(1−B122c44MHeff). All data thus far have given excellent fits to these equations as Heff is varied, making it easy to obtain the unknown constants. It should be noted that Eqs. (1) and (2) are high-temperature approximations and at low temperatures will not in general be as simple. For TbIG and EuIG at room temperature we find the following (all in ergs cm−3): For TbIG, |B1|≤3.5×106, |B2|=30×106; and for EuIG, |B1|=45×106 and |B2|≤4.2×106. The signs must still be determined from strain gauge measurements. The observed reversal of the magnetoelastic anisotropy (ratio of B1 to B2) is being investigated, as well as the temperature dependences of B1 and B2.