Origin of the magneto—thermogalvanic voltage in cluster-assembled metallic nanostructures

To the Editor

In their September 2006 article in Nature Materials, Serrano-Guisan et al. describe magneto-transport and thermoelectric measurements of magnetic nanoparticles in a metallic matrix¹ that exhibit giant magneto-resistance^2,3 (GMR). In such systems the resistance is lowest in large magnetic fields when the magnetic particles are aligned. As the applied field is reduced, the magnetization directions of the particles become random due to local variations in the anisotropy, interactions and thermal fluctuations, resulting in increases in the resistance^2,3. For small, low-anisotropy particles, the dominant process for randomizing is thermal activation known as superparamagnetism.

The GMR results of Serrano-Guisan et al. are consistent with previous measurements of granular systems. Interestingly, when the authors measure the magnetic thermogalvanic voltage (MTGV) — the voltage change to an oscillating temperature — they observed a giant magnetic response of 500%, nearly two orders of magnitude greater than the normalized GMR response. The authors argue that the MTGV response measures a spin-dependent transport mechanism counter to most descriptions of GMR^1,4. This conclusion was based, in part, on the experimental observations that the sign, magnitude, field dependence and temperature dependence of the MTGV signal are qualitatively different from the corresponding GMR response. In this correspondence we argue that these observations can be understood from the known physics of GMR and superparamagnetism.

The resistivity of granular magnetic systems is well described by:

where ρ₀ is the residual resistivity and the second term depends on the global magnetization (M) scaled by a magnetic scattering coefficient² (ρ_M). For a non-interacting collection of superaparmagnetic particles M is often estimated by the Langevin function

where X = μH/k_BT, μ is the total moment of the magnetic particles, H is the applied field and k_B the Boltzmann constant. Equations (1) and (2) provide a simple description of resistivity changes to variations of both H and T variations (ρ versus X, in Fig. 1a) and T (Δρ versus X, Fig. 1b). As can be seen from Fig. 1a, the GMR response (that is, ρ versus H) is negative and asymptotically decreases towards saturation as observed experimentally. In contrast, Δρ (Fig. 1b), which would be detected in an MTGV measurement is zero at H = 0, positive for small fields, reaches a maximum at X = ±3 and then decreases for higher fields.

Figure 1: The calculated magneto-thermal transport response assuming a collection of independent superparamagnetic particles of moment m in a metallic matrix.

a, GMR response (ρ versus X = mH/k_BT)) calculated from equations (1) and (2) for −10 < X < 10 assuming ρ₀ = 0. b, Difference between ρ calculated at 15 K and 14 K for common H values (corresponding to the experimental conditions).

The curve in Fig. 1b reproduces many of the features of the experimental MTGV data in ref. 1. For the sample with 15 atoms per cluster, X should be in the range ±1.1 (assuming 2μ_B per Co atom, T = 14 K and maximum field of 0.8 T). For this range of X, both ρ and Δρ are monotonic with increasing H and with opposite signs, whereas for larger magnetic particles one expects the non-monotonic response of Fig. 1b as seen experimentally. For the smallest particles the reported GMR at H = 0.8 T is ∼0.8 ohms, which corresponds to 6.4 mV (ref. 1). The corresponding MTGV response is about 6 μV. From Fig. 1, the calculated Δρ response is about 2% of the GMR signal, which would correspond to roughly a 130-μV MTGV response. Although much larger than the measured MTGV signals, it suggests that such signals are certainly possible from the combination of thermal activation and GMR. Finally, the MTGV data in ref. 1 was normalized to the H = 0 value to determine the 500% response. Within this model the calculated magnetic response of Δρ is zero at H = 0. The measured MTGV response at H = 0 would then result from the temperature dependence of ρ₀, which at 14 K is quite small. The normalized MGTV can then, in principle, be arbitrarily high, limited only by the temperature dependence of the residual resistivity. For higher temperatures the MTGV signal arising from the temperature dependence of ρ₀ would overwhelm the magnetic signals as seen experimentally.

In conclusion, the experimental results of Serrano-Guisan et al. show interesting thermal-magnetic responses of granular systems. We believe many of the observed results can be understood from a combination of GMR and superparamagnetism (or more generally a temperature-dependent response of the magnetic order) and may not require a new description of magneto-transport. This model reproduces all the qualitative features of the reported data. Quantitative differences are expected and reflect the simplicity of the Langevin description that doesn't include particle distributions, anisotropy or interactions. However we believe that this type of measurement, which probes the magnetic response to thermal excitations, is a unique tool for studying the important role of thermal energies in nanomagnetic systems.