Long-Range Polarization in High Susceptibility Metals

Abstract

Recent electron paramagnetic resonance (EPR) experiments on metals and alloys of high paramagnetic susceptibility (Pd and NigLa) 1 " 3 have shown an anomalous long range of the spin polarization around magnetic impurities. Wolff 4 has suggested that the exchange interaction between valence electrons in metals will increase the range of the polarization in space. By connecting the enhancement of the polarization in momentum space with the observed uniform susceptibility of the studied metal, we have found that exchange interactions can bring predicted and observed data into agreement.The susceptibility function of a system is defined by its linear response to an external magnetic field. If the system is homogeneous,where (M(q,f)), x(q,0 are the spatial Fourier transforms of (M(r,£)),x( r >0, respectively. For an electron gas, x is given by where andV is the volume of the system, 10) is the ground state of the isolated system, and T is the time ordering operator. EPR measurements of magnetic impurities in metals allow one to get some insight into the shape of this function.In a series of recent experiments, the shift and the broadening of the EPR lines of 2% Gd (im-purity A) in a matrix formed by 96% of high-susceptibility metals and 2 % of additional magnetic impurities (B) have been studied. 1 The magnetic moment of rare earth impurities was found to be practically equal to their ionic moment, contrary to transition elements, which show giant moments in solid solution in Pd alloys. 5 The deformation of the EPR line of Gd in the matrix is very sensitive to the shape of the susceptibility function. This can be best understood by thinking first of only one ion of Gd in the host metal: Each magnetic inpurity B will polarize the valence electrons of the host metal and will therefore shift the g value of the Gd ion. The magnitude of this shift will depend on the value of the susceptibility function of the host metal at the Gd site. Since the magnetic impurities are distributed at random, the statistical average over all Gd ions will give both a displacement and a deformation of the resonance line.The shift of a resonance line is defined bywhere H 0 is the center of the nonperturbed line and 1(H) the perturbed intensity line; and the mean square deviation byOne can express 5 and B in terms of x(?) = J X(r, t)dt\ s = c B n Q a yh(x>Pr 9 B = c B n 0 a 2 ±f X 2 (r)d 3 r,where eg is the concentration of magnetic impurities in the matrix, n 0 the number of lattice sites per cc, and a is a constant depending on the characteristics of the system. The value of the ratio of the shift squared to the mean square 736

Effect of Spin-Orbit Scattering on the Magnetic and Superconducting Properties of Nearly Ferromagnetic Metals: Application to Granular Pt

“…The first effect of U ef f is to shift the curve to larger r increasing the spin correlation range σ, an effect discussed by Giovannini, Peter, and Schrieffer [17]. Further increasing U ef f pushes the curve above the axis for small r. IncreasingJ ′ ef f has a similar effect.…”

“…Here we plot the dimensionless susceptibilityχ(r) which is defined by χ(r) = 2µ 2 B N (0)(Ω/a 3 )χ(r) , where Ω is the atomic volume (a 3 /4 for the fcc lattice). The first effect of U ef f is to shift the curve to larger r increasing the spin correlation range σ, an effect discussed by Giovannini, Peter, and Schrieffer [17]. Further increasing U ef f pushes the curve above the axis for small r. IncreasingJ ′ ef f has a similar effect.…”

Relevance of knight shift measurements to the electronic density of states

“…For Fe in Pd the latter is known to cover many lattice sites. This is due to a large 1/2kF value (which affects the main peak as well a.s the Friedel oscillations) and)o the substantial conduction-electron conduction-electron enhancement of)(p [152][153][154].…”

Electron Spin Polarization due to a Magnetic Impurity

“…The experimental results, 12 -14 however, seem to indicate an amplitude several times that of RKY. This discrepancy is not understood, but it is felt that effects such as electron-electron interactions, 15 corrections to the point contact form of interaction, 16 use of Bloch waves rather than plane waves, 17 etc., will contribute to it. It is evident that these effects will considerably dominate the spin-flip effect discussed here, and will prohibit its detection until they are better understood.…”