Elastic and nonlinear acoustic properties of the terbium iron garnet Tb3Fe5O12 in relation to those of other garnets.

Abstract

The elastic behavior as a function of temperature, pressure, and magnetic field of the ferrimagnetic rare-earth garnet ${\mathrm{Tb}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$, in which all the cation sites are occupied by magnetic ions, has been examined experimentally using the ultrasonic pulse overlap technique. The effects on the ultrasonic wave velocities of a magnetic field applied in a fourfold direction have been measured; that for the [001] polarized shear wave propagated in the [110] direction (and thus for the shear modulus ${\mathit{C}}_{44}$) is found to be much larger than for the other ultrasonic modes. Elastic constant determinations made on both sides of the N\'eel temperature ${\mathit{T}}_{\mathit{N}}$ (550\ifmmode\pm\else\textpm\fi{}10) K indicate that the magnetic contributions to the elastic stiffnesses are small, being only \ensuremath{\Delta}${\mathit{C}}_{11}$/${\mathit{C}}_{11}$\ensuremath{\sim}1.0%, \ensuremath{\Delta}${\mathit{C}}_{44}$/${\mathit{C}}_{44}$\ensuremath{\sim}1.3%, \ensuremath{\Delta}${\mathit{C}}_{\mathit{L}}$/${\mathit{C}}_{\mathit{L}}$ [where ${\mathit{C}}_{\mathit{L}}$=(${\mathit{C}}_{11}$+${\mathit{C}}_{12}$+2${\mathit{C}}_{44}$)/2] \ensuremath{\sim}1.0%.The hydrostatic pressure derivatives of the components of the elastic stiffness tensor constants have been measured at room temperature as (\ensuremath{\partial}${\mathit{C}}_{11}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$=7.96, (\ensuremath{\partial}${\mathit{C}}_{44}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$=1.1, (\ensuremath{\partial}C'/\ensuremath{\partial}P${)}_{\mathit{P}=0}$=1.55 [where C'=(${\mathit{C}}_{11}$-${\mathit{C}}_{12}$)/2] and that of the bulk modulus (\ensuremath{\partial}${\mathit{B}}^{\mathit{S}}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$=5.8. These hydrostatic pressure derivative results have been used to determine the vibrational anharmonicity of the long-wavelength acoustic phonons in terms of the acoustic mode Gr\uneisen parameters. The mean acoustic mode Gr\uneisen parameter ${\ensuremath{\gamma}}^{\mathrm{el}}$ (=1.36) for ${\mathrm{Tb}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$ is substantially greater, probably due to a magnetic contribution, than those of the other previously investigated garnets ${\mathrm{Y}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$ (${\ensuremath{\gamma}}^{\mathrm{el}}$=0.727) and ${\mathrm{Y}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$ (${\ensuremath{\gamma}}^{\mathrm{el}}$=0.885). To provide a basis for comparison of the elastic behavior of terbium iron garnet with those of other garnets, the elastic stiffness tensor components, their hydrostatic pressure derivatives and associated lattice dynamical properties, including the thermodynamic ${\ensuremath{\gamma}}^{\mathrm{th}}$ and mean long-wavelength acoustic ${\ensuremath{\gamma}}^{\mathrm{el}}$ Gr\uneisen parameters and their hydrostatic pressure derivatives, have been calculated for a substantial number of garnet crystals on the basis of the atomistic Born model of solids in which a potential model represents the interionic interactions in the crystal.