Transport Properties at Critical Points: The Resistivity of Nickel

Abstract

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

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“…Thus, ∆ρ will not only include the scattering from the 4f moments, but will also include scattering associated with the interaction between the 4f moments and itinerant electrons. is more conspicuous and must come from a different conduction electron scattering process (simple models of ρ(T ) due to magnetic scattering cannot explain this anomaly [35,36]). …”

Spin correlations and colossal magnetoresistance inHgCr2Se4

“…Sharp peaks in dρ xx, 0 /dT at T = T C have also been observed in ferromagnetic metals. 34,35 The critical behavior in case of metallic conductivity was explained long ago by Fisher and Langer, 36 who pointed out that short-range spin fluctuations are responsible for the singular behavior in dρ xx, 0 /dT at T = T C . The Fisher-Langer model, however, cannot be used to describe the peak in dρ xx, 0 /dT observed in this work, since ρ xx in n-HgCr 2 Se 4 is on the order of 10…”

“…33,34,52 The Curie temperature T C can be determined by simply finding out which curve passes through the origin of the Arrott plot. According to Eq.…”

Monte Carlo study of the spin transport in magnetic materials

“…They have suggested that the magnetic resistivity is proportional to the spin-spin correlation, therefore it should behave as the magnetic susceptibility with a divergence at T c due to "long-range" fluctuations of the magnetization. Other authors [18][19][20] subsequently suggested that the shape of the resistivity results mainly from "short-range" correlation at T ≥ T c . Fisher and Langer [19] have shown in particular that the form of the resistivity cusp depends on the correlation range.…”