Ewald Technique Research Articles

Spin-wave calculations for ferromagnetic GdCl3

The magnon spectrum of GdCl3, a two-sublattice ferromagnet in which the dipolar interactions are comparable with the two dominant exchange interactions, is investigated analytically and numerically. The spin-wave energies are found by deriving a generalization of the Holstein-Primakoff result, valid for a system of two equivalent sublattices with arbitrary symmetric interactions between all pairs of spins. The dipole-dipole interactions are treated exactly, by using the Ewald technique to evaluate certain k-dependent lattice sums and their derivatives at k = 0. In the long-wavelength region a formula is obtained for the quadratic approximation to the spectrum, which shows a complicated angular dependence, and this is used to calculate the form of the exponential magnetization curve at very low temperatures. The full dispersion relations are then obtained numerically, without renormalization, using the two possible sets of values for the exchange constants J1 and J2 derived from high-temperature experiments. For set A (J1 = 0.073 °K, J2 = 0.007 °K) the curves for different values of θk cross one another, and the `optical' mode energies are unusually low; for the more likely set B (J1 = -0.025 °K, J2 = 0.040 °K) the spinwave band becomes wider as k increases, and its lower edge is almost flat for an appreciable range of wave numbers. By integrating numerically over the Brillouin zone the zero-point spin defect is shown to be small, and the magnetization and specific heat are found as functions of temperature.

Oxidation of Phenylpyruvates to Aromatic Aldehydes and Oxalate

Ewald and Hubener1 have recently described a new method for the determination of tyrosine-α-ketoglutarate transaminase activity. In their procedure, the p-hydroxyphenylpyruvate generated in the transamination reaction was converted on standing in alkali to an unknown ‘chromogen’ absorbing maximally at 331 mµ with ɛ334 mµ = 16,200. The Ewald and Hubener technique represents another report of the oxidative cleavage of phenylpyruvates to aromatic aldehydes and oxalate according to equation (1) and depends on the strong absorption of the phenolate ion of P-hydroxybenzaldehyde.