Elastic Constants of Single-Crystal Rare-Earth Bismuth Iron Garnet Films

Abstract

Complete sets of elastic constants of rare-earth bismuth iron garnet (111) films containing Pb were determined by resonantultrasound spectroscopy. Resonant-ultrasound spectroscopy can be used to determine all independent elastic constants from one specimen by measuring the resonance frequencies of free vibrations. For accurate measurement of the resonance frequencies, we used a tripod transducer, and the vibration modes of each resonance frequency were identified by laser-Doppler interferometry. Rare-earth bismuth-iron garnet belongs to the space group Ia 3 3d, and shows cubic symmetry. However, it was nearly elastically isotropic; 2C 44 =ðC 11 À C 12 Þ ¼ 0:99. Their elastic constants were almost independent of the Pb content; C 11 ¼ 242:9 AE 4:4 GPa, C 12 ¼ 99:1 AE 2:0 GPa, and C 44 ¼ 71:1 AE 0:8 GPa. The observed isotropic elasticity corresponds to that of the other garnet group crystals.

Magnetic Properties and Growth‐Induced Anisotropy in Yttrium Thulium Iron Garnet Thin Films

“…[ 11 ] A significant difference in c 44 values for PLD‐grown garnets appears unlikely, because a study on LPE‐grown Bi:YIG showed c 44 very close to bulk. [ 42 ] One possibility is the existence of growth‐induced anisotropy from cation ordering on the iron sublattice. Previous work on iron‐deficient YIG has shown that vacancies preferentially form on the octahedral sublattice during PLD growth, giving rise to an additional growth induced anisotropy.…”

Substrate‐Dependent Anisotropy and Damping in Epitaxial Bismuth Yttrium Iron Garnet Thin Films

“…[ 40–43 ] The complex transmission parameter S 21 was measured at a fixed frequency while the external perpendicular magnetic field was swept, [ 40 ] as shown in Figure a,b. The resonance field for the films was fitted to the Kittel equation for perpendicular geometry to extract the effective magnetization M eff and the Landé g‐factor, [ 44 ] as shown in Figure 5c for one film as an example. Here: $$$$\begin{equation}{H}_{{\mathrm{res}}} = \frac{{2\pi {\mathrm{f}}}}{{\left| \gamma \right|{\mu }_o}} + {M}_{{\mathrm{eff}}}\end{equation}$$$$where H res is the resonance field, f is the excitation frequency, and γ is the gyromagnetic ratio ( gµ B )/ h , where µ B is the Bohr magneton and ħ is the reduced Planck constant.…”

“…To extract the damping of the BiYIG thin films, their dynamic magnetic properties were studied with broadband perpendicular FMR spectroscopy based on the vector network analyzer (VNA) technique in the 10-40 GHz range. [40][41][42][43] The complex transmission parameter S 21 was measured at a fixed frequency while the external perpendicular magnetic field was swept, [40] as shown in The resonance field for the films was fitted to the Kittel equation for perpendicular geometry to extract the effective magnetization M eff and the Landé g-factor, [44] as shown in Figure 5c for one film as an example. Here:…”

“…Figure5a,b. The resonance field for the films was fitted to the Kittel equation for perpendicular geometry to extract the effective magnetization M eff and the Landé g-factor,[44] as shown in Figure5cfor one film as an example. Here:…”

Introduction of measurement techniques in ultrasonic electronics: Basic principles and recent trends

“…Therefore, the research related to ultrasonic nonlinearity has been valuable. 82 Ultrasonic properties of materials, phonon physics, acousto-optics Properties of materials viscosity [20][21][22][23][24][25][26][27] elasticity [28][29][30][31][32][33][34][35][36][37][38] Wave propagation [39][40][41][42][43] Waveguides 44) Piezoelectric materials [45][46][47][48][49][50][51][52][53][54] Quantum acoustics 55) Acousto-optics 30,31,34,39,40,[56][57][58][59][60][61][62][63]…”