Synthesis and Magnetostrictive Properties of High-Pr Content  ${\rm Sm}_{1-x}{\rm Pr}_{x}{\rm Fe}_{1.9}$ Cubic Laves Alloys
Polycrystalline Sm<sub>1-</sub><i>x</i>Pr<i>x</i>Fe<sub>1.9</sub> (0.4 ≤ <i>x</i> ≤ 1.0) magnetostrictive alloys were synthesized by arc-melting and subsequent high-pressure annealing. Measurements of x-ray diffraction, magnetization, and magnetostriction were performed on the alloys. Due to the effects of high-pressure, the alloys are stabilized in cubic Laves phase with MgCu<sub>2</sub>-type structure. The Curie temperature of the cubic Laves phase decreases linearly with the increase of <i>x</i>, which can be associated with the decreasing strength of 3<i>d</i>-4<i>f</i> coupling. With increasing <i>x</i> , the anisotropy of the alloys first decreases to a minimum at <i>x</i> = 0.6 and then increases. The magnetostriction of Sm<sub>1-</sub><i>x</i>Pr<i>x</i>Fe<sub>1.9</sub> changes signs from negative into a positive at <i>x</i> = 0.6 . The saturation magnetostriction increases with increasing <i>x</i>, while the sample with <i>x</i> = 0.9 shows a peak at low magnetic fields.
Magnetostriction and magnetic anisotropy of (Sm,Ce)Fe2 compounds
The structural, magnetic and magnetostrictive properties of Sm(1-x)Ce(x)Fe(2) (0 <= x <= 1) Laves compounds have been investigated. The magnetostriction coefficient lambda(111) and the anisotropy of the Sm(1-x)Ce(x)Fe(2) compounds decrease with increasing Ce content. The decreasing of anisotropy results in an enhancement of the anisotropic magnetostriction at low magnetic fields for the compounds with a small amount of Ce substituted for Sm. (C) 2009 Elsevier B.V. All rights reserved.
The Invariance of the Vacuum is the Invariance of the World
The following theorem is demonstrated: If the vacuum is invariant under the group generated by the space integral of the time component of a local vector current, then the Hamiltonian is invariant also. A similar theorem holds for the group generated by the space integral of a space component of a local axial-vector current.