D-electron Spin Research Articles

Enhanced Susceptibilities and NMR Relaxation Rates in Co-Rh Alloys

Dilute alloys of Co in Rh show a weakly temperature-dependent susceptibility increase Δχ (Co) ∼20×10−4 emu/mole of Co solute as compared with χ∼1×10−4 emu/mole for pure Rh. This effect is thought to be associated with Coulomb enhancement of the d-electron spin susceptibility in the neighborhood of the Co impurity. By plotting the 9Co NMR shift vs Δχ (Co) one finds an effective core-polarization hyperfine field considerably smaller than that of Co metal. Spin-echo double-resonance studies of these alloys show that the nearest-neighbor 103Rh nuclei to the Co impurity undergo a negative NMR shift of ∼0.56% relative to the bulk 103Rh nuclei. The origin of this shift is not clearly understood. In particular, attributing such a shift to d-spin polarization is not consistent with the short-range polarization effects expected. Measurements of T1 and T2 show strongly enhanced hyperfine field fluctuations at the 59Co nucleus, presumably due to local Coulomb interactions. We find T1T = 39.5 msec°K and T2T = 3.0 msec°K for temperatures ranging from 1.2° to 20.4°K. The discrepancy between T1 and T2 (spin lattice) is apparently a consequence of strong first-order quadrupolar broadening of the 59Co Zeeman levels for | m | >12.

The contribution of s- d exchange scattering to the electrical resistivity of magnetic metals

We discuss the contribution of s- d exchange scattering to the electrical resistivity of magnetic metals. We consider the processes in which a spin flip of the s-electron occurs. The s-electron relaxation time is expressed in terms of the transverse spin correlation function of the d-electron spins. We point out that if the frequency spectrum of the spin density fluctuations in the d-electrons cuts off at a frequency low compared to kT, then a temperature independent relaxation time similar to that discussed previously by de Gennes and Friedel is obtained. If a localized model of the d-electrons is employed, then this situation will occur at temperatures large compared to the Curie temperature T c . If one describes the d-electrons by the one band, short-range interaction model, then at temperature large compared to T c , the s-electron relaxation rate is proportional to T 2. If ϵ d is the Fermi energy of the d-electrons, then this relaxation rate is smaller than the de Gennes-Friedel temperature independent rate by a factor of roughly ( kT/ϵ d ) 2. The expression for the relaxation rate at temperatures low compared to T c is exhibited. In this region, the relaxation rate is proportional to T 2.

The temperature dependence of the nuclear magnetic resonance of vanadium

Measurements have been made of the line width, intensity and shift of the 51V magnetic resonance from vanadium metal over the range 25-330 °K. The absence of any detectable anomalies in these properties shows that the transition at around 250 °K cannot be associated with the occurrence of antiferromagnetism unless the fluctuation frequency of the internal magnetic fields exceeds 2 × 1012 c/s. From consideration of nuclear electric quadrupole interactions, it is estimated that any deviation from cubic crystal symmetry at or below the transition point is less than 2 parts in 103. The Knight shift increases from 0.571% at 25 °K to 0.580% at 330 °K with an accuracy to ±0.001%. From a comparison of the temperature dependence of Knight shift and magnetic susceptibility, the hyperfine field at a vanadium nucleus due to one d-electron spin was estimated to be -112 ± 17 kilogauss.

A Theory of Metallic Ferro- and Antiferromagnetism on Zener's Model

The importance to the mechanism of ferromagnetism of exchange interaction between conduction electrons and unfilled inner shell electrons (called s-d interaction) has been pointed out by Zener. Especially for rare earth metals, this interaction seems to be the only mechanism which can cause ferro- and antiferromagnetism. However Zener's works are unsatisfactory because his model is phenomenological and moreover does not involve antiferromagnetism and spin wave mode. Our paper considers this s-d interaction on a more rigorous basis. By a certain approximation, there appear long range exchange type interactions between d-electron spins and, in certain conditions both ferro- and antiferromagnetism appear. The excitations of spin wave modes are the same as those in the ordinary modes of the short range exchange force, viz, the energy of the spin wave excitations is proportional to q2 for ferromagnetism and q for antiferromagnetism in the region of small wave vector q. The T3/2 law for the temperature dependence of the magnetization of ferromagnetism is applicable up to very high temperatures, and this result is in good agreement with the results of experiments on metallic ferromagnetism.