Authors' response

What we called magneto-thermogalvanic voltage (see, for example, ref. 1) is, in the case of granular systems, the experimental determination of the derivative of the resistivity with respect to temperature. It suppresses the large field- and temperature-independent scattering processes. Its advantage is comparable to that of, for example, dI/dV experiments that reveal conductivity features otherwise undetectable by direct measurements of current versus voltage. We wish to clarify a few points about our samples and measurements.

First, the samples of the study under discussion2 were prepared at a cobalt loading of 8%. They have a magnetic field response that, for each given T, might be roughly approximated by a Langevin-based model. However, SQUID magnetometry3 as well as the GMR data in Fig. 4b of our article, show that they were not superparamagnetic (see also ref. 4).

Second, the dR/dT measurements challenge the models of transport more visibly than the GMR data. For example, Fig. 1a shows GMR data for a dilute sample (0.8%) consisting of cobalt clusters of aproximately 40 atoms in a silver matrix, measured at 3 K. Also shown is a fit according to the superparamagnetic model as used by Fullerton and Mangin in their comment, that is, ΔR/R ∝ ((1–L(H, T)2) with L(H, T) the Langevin function. Despite this low concentration, the superparamagnetic description is not adequate4. However, a reasonable fit to the GMR data can be obtained (see ref. 4). In Fig. 1b, the measured derivative of the resistivity (dR/dT) clearly departs from the calculated derivative based on the Langevin fit of Fig. 1a.

Figure 1: Superparamagnetism model challenged by differential resistance measurements.
figure 1

a,b, Measurements of the magnetoresistance ΔR (a) and (dΔR/dT)IDCΔT , where ΔT is the amplitude of the temperature oscillation (60 mK) and IDC the applied current (1 mA) (b) for a sample containing cobalt clusters with <n> = 40 atoms in a silver matrix with 0.8 at.% Co as measured at 3 K. The red curves exhibit a fit according to the super-paramagnetic model (a) and the corresponding temperature derivative (b).

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We should also add that given that the current densities were of the order of <104 A cm−2, we would not expect any effect from other mechanisms, deriving, for example, spin-torque phenomena5,6.

Regarding the comments by Fullerton and Mangin on measurements of the variation of resistance with temperature, we agree that this type of data should help evaluate better models of spin-dependent transport, in particular the extent to which one should include contributions such as spin-transfer torque5,6 interface spin-flip scattering7, spin mixing8 and spin-disorder scattering9,10.