Calorimetric Study of Yttrium and Rare-Earth Iron Garnets between 0.4 and 4.5°K

Abstract

We present the results of a calorimetric study on iron-garnet polycrystalline samples of Y, Eu, Tm, Sm, and Yb between 0.4 and 4.2°K in zero magnetic field. Results for another sample of YIG between 0.7 and 4.2°K in magnetic fields up to 13 kOe are also presented. In YIG it is shown that in addition to the lattice vibration and acoustic spin-wave-mode contributions, $C_L$ and $C_{\mathrm{acous}}$, there is a residual specific heat $\mathcal{R}\mathrm{}\left(T\right)\mathrm{}$ that is linear with temperature and somewhat dependent on magnetic field. This new term $\mathcal{R}\mathrm{}\left(T\right)\mathrm{}$ is tentatively attributed to surface effects although its magnitude is much larger than that predicted for surface spin-wave modes in a ferromagnetic sintered sample with the same dispersion constant $D$. The data in YIG are compared with previous work, and it is shown that the analysis of the calorimetric data on this compound is more complex than was thought previously, and in particular that data on $C_v$ in zero field are not suited for obtaining the value of $D$ from the usual $\frac{C_v}{T^{\frac{3}{2}}}$-versus-$T^{\frac{3}{2}}$ plot. The same comments apply to EuIG, where a residual term, linear in temperature, was also obtained. From the nuclear specific heat of this compound, we obtain an rms magnetic field at the nucleus $H_N=597\mathrm{}\pm 5$ kOe, in excellent agreement with results from Mössbauer experiments. In TmIG, the effect of acoustical spin waves on $C_v$ could be detected, and (as expected) there was no evidence of population of the optical modes. However, no firm conclusions could be reached about a residue, since it was difficult to estimate $C_{\mathrm{acous}}$ theoretically. The nuclear contribution $\frac{C_N{T}^2}{R}=(7.8\mathrm{}\pm 0.4)\times {10}^{-4\mathrm{}}$ was found to be in good agrement with that predicted from Mössbauer data. In SmIG, the first excited electronic level was deduced to be $\frac{E}{k_B}=(38\mathrm{}\pm 3)°$K, in good agreement with predictions from White's theory. The nuclear specific heat of SmIG was analyzed as corresponding to an rms field at the nucleus $H_N=(2.2\mathrm{}\pm 0.2)\times {10}^6$ Oe, while an analysis of Mössbauer data had given (2.8±0.15)×${10}^6$ Oe. A broad anomaly in $C_v$ centered at 2°K remains unexplained, but is possibly due to an unreacted samarium oxide impurity. It is responsible for the uncertainty in $E$ and $H_N$. In YbIG, a sizable discrepancy remains below 3°K between the theory using the 12 low optical spin-wave modes and the experimental data. Apparently the dispersion curve of the exchange mode is significantly different from that calculated by Tinkham using a simple model. The nuclear specific heat in YbIG, $\frac{C_N{T}^2}{R}=(1.6\mathrm{}\pm 0.2)\times {10}^{-3\mathrm{}}$, was in fair agreement with that predicted from the electron-nucleus coupling parameter and the ground-state electronic moment.