Landau-Lifshitz Theory Research Articles

Spin wave excitations in amorphous itinerant ferromagnet

The Izuyama, Kim and Kubo theory of spin waves in crystalline itinerant ferromagnets is extended to the amorphous itinerant ferromagnetic materials. The qualitative features of this theory are similar to that of the generalized Landau-Lifshitz theory discussed by Henderson and de Graaf.

Quantitative verification of the Landau-Lifshitz theory of second order phase transitions in alpha manganese

The anomaly in the adiabatic compressibility at the Néel point of alpha manganese, as determined from ultrasonic measurements is quantitatively compared with the expected value derived from the Landau-Lifshitz theory of 2nd order transitions. Agreement is satisfactory.

SaturatedHe4near Its Critical Temperature

Measurements of the refractive index $n$ of saturated ${\mathrm{He}}^{4}$ liquid and vapor have been made at $\ensuremath{\lambda}=5462.27$ \AA{} from 4.2\ifmmode^\circ\else\textdegree\fi{}K nearly to the critical temperature (${T}_{c}=5.1994$\ifmmode^\circ\else\textdegree\fi{}K). Careful determinations of $n$ and $\frac{\mathrm{dn}}{\mathrm{dT}}$ as a function of temperature were made using a metal optical cryostat and a Jamin interferometer modified to produce a chart record of the interference fringes. The measurements extended to within 50 mdeg of ${T}_{c}$ for saturated vapor, and to within 36 mdeg of ${T}_{c}$ for saturated liquid. These results, combined with the Lorenz-Lorentz equation, then give the density $\ensuremath{\rho}$ of both saturated liquid and saturated vapor, and the expansion coefficient ${\ensuremath{\beta}}_{s}$ of the saturated liquid. These $n$, $\ensuremath{\rho}$, and ${\ensuremath{\beta}}_{s}$ measurements are the first ever made above 4.4\ifmmode^\circ\else\textdegree\fi{}K except for two early measurements of density at 4.6 and 4.7\ifmmode^\circ\else\textdegree\fi{}K. The critical density is found to be ${\ensuremath{\rho}}_{c}=(0.06948\ifmmode\pm\else\textpm\fi{}0.00030$ g ${\mathrm{cm}}^{\ensuremath{-}3}$, or the critical molar volume, ${V}_{c}=(57.628\ifmmode\pm\else\textpm\fi{}0.25)$ ${\mathrm{cm}}^{3}$ ${\mathrm{mole}}^{\ensuremath{-}1}$.We have modified and extended the Landau-Lifshitz theory of the properties of a substance "near" the critical point, and then find excellent agreement with our experimental values of the molar volumes of saturated ${\mathrm{He}}^{4}$ within about 110 mdeg of ${T}_{c}$. This agreement is taken as evidence that ${(\frac{{\ensuremath{\partial}}^{3}P}{\ensuremath{\partial}{V}^{3}})}_{T}$ is negative at the critical point---in clear contradiction to theories which suggest that this third derivative is zero at ${T}_{c}$. In terms of the "reduced" parameters ${V}^{\ensuremath{'}}=\frac{V}{{V}_{c}}$ and ${P}^{\ensuremath{'}}=\frac{P}{{P}_{c}}$, we find ${(\frac{{\ensuremath{\partial}}^{3}{P}^{\ensuremath{'}}}{\ensuremath{\partial}{V}^{\ensuremath{'}3}})}_{{T}_{c}}=\ensuremath{-}(10.4\ifmmode\pm\else\textpm\fi{}1.8)$ for ${\mathrm{He}}^{4}$. In addition, we can then calculate saturated vapor and liquid molar volumes, and liquid coefficient of expansion values right up to the critical temperature, assuming the continued validity of the modified Landau-Lifshitz theory.