The divergence of the temperature coefficient of resistivity of nickel at the Curie tem^ perature is emphasized. Application of the modified Ornstein-Zernike spin-pair correlation function is shown to yield results which cannot be made consistent with both resistivity and susceptibility results.The decrease in electrical resistance which is observed upon cooling a ferromagnet through the Curie temperature T c was discussed many years ago by Mott 1 and has been reviewed recently. 2 ' 3 The relationship between critical fluctuations and resistivity has received occasional theoretical attention, but the experimental result that the temperature coefficient of resistivity [a(T)=dp/dt, where p is the resistivity] is divergent at T c appears to have been overlooked. We find a(T) to be positive both above and below T Cf and to diverge logarithmically above T c with the strength of the divergence increasing within a few degrees of the transition. This is contrary to the predictions of Kim 4 and of de Gennes and Friedel. 5 These authors find the resistivity to exhibit a cusp at the Curie temperature, so that the temperature coefficient of resistivity changes sign at the transition. Although a logarithmic divergence of the resistivity is predicted, the sign of a(T) above the transition is negative, in disagreement with experiment.The singular behavior of a(T) was apparently first noted by von Bohlen-Halbach and Gerlach, 6 whose results we reproduce in Fig. 1 [a(T)/p is plotted]. No critical discussion of these results seems ever to have been published. Although the data points are sparse, and the Curie temperature differs somewhat from present-day values, the solid curve is well represented some distance above the Curie temperature by an expression of the form -A In I T-T c I + 5. Experiments illustrating the logarithmic divergence both above and below T c have recently been reported by Kraftmakher. 7 Divergent behavior is typical of equilibrium thermodynamic quantities such as specific heat near second-order phase transitions. 8 It now appears that divergences occur in transport quantities as well.In order to characterize the critical behavior near T c , we have directly measured a(T) in five-9's purity Ni, using an ac resistance bridge 9 (usually operated at 33 cps) in which two of the arms contained identical Ni samples 300 350 400 450 500 550 600 650 700 750 TEMPERATURE T{°K)FIG. 1. The temperature coefficient of resistivity of Ni was measured over three decades ago by a student of Gerlach. The results, reproduced here, illustrate qualitative features (the divergence near T c ) relevant to transport theory today.1334
No abstract
Extensive inelastic-neutron-scattering experiments have been carried out on single crystals of He in the bcc and low-density hcp phases. The results of our present and previous measurements have established the over-all characteristics of the scattering function S(g, eu) for a wide range of energy and momentum transfers. The general features of the scattering function can be described as showing well-defmed, sharp, elementary excitations at energy transfers h co~1.0 meV, and single-particle excitations for scattering vectors ]Q( & 3.0 A ' and hco & 5.0 meV. The changes in the structure of the scattering function to accommodate these two different excitations occur in an ill-defined "transition" region, wherein the spectral response of the sharp excitation gradually becomes more distorted and merges with the multiexcitation response at the higher energies. In the low-energy regime, the scattering cross section for sharp excitations observed in the [011] zone for the bcc phase is found to be unusual in that the efFective Debye-&aller factor constructed from the data via the Ambegaokar, Conway, and Baym sum rule displays oscillations. The data for the lowest transverse branch T "however, do not show oscillations. In our previous work, this anomalous cross section appeared to be associated with an energy transfer of~1. 4 meV, and a concomittant distortion in the Gaussian-like spectral response. The present results show that this is not the case. The unexpected behavior of the cross section was observed for sharp, symmetric excitations whose energy distribution has no extraordinary contribution near 1.4 meV. The measurements in the hcp phase show that these anomalous features of the scattering function are similar in both phases. The high-resolution measurements on the sharp excitations at small wave vector were used to construct a self-consistent set of elastic constants. These elastic constants are considerably more accurate than those from previous measurements. They suggest that the dispersion of the T, mode in the [011] direction need not be anomalous, in contrast to recent theoretical results.Finally, at high energy and momentum transfers, single-particle excitations are observed in both phases.Their dispersion relation is isotropic, and is the same in both phases within the accuracy of the measurements. The profiles of these excitations are very similar to those recently observed by Woods and Cowley in the superfluid phase.
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