Anomalous magnetoresistance in nanocrystalline gadolinium at low temperatures

Abstract

The results of a detailed investigation of electrical resistivity, ρ(T) and transverse magnetoresistance (MR) in nanocrystalline Gd samples with an average grain size d = 12 nm and 18 nm reveal the following. Besides a major contribution to the residual resistivity, ρr(0), arising from the scattering of conduction electrons from grain surfaces/interfaces/boundaries (which increases drastically as the average grain size decreases, as expected), coherent electron–magnon scattering makes a small contribution to ρr(0), which gets progressively suppressed as the applied magnetic field (H) increases in strength. At low temperatures (T ≲ 40 K) and fields (H = 0 and H = 5 kOe), ρH(T) varies as T3/2 with a change in slope at T+ ≃ 16.5 K. As the field increases beyond 5 kOe, the T3/2 variation of ρH(T) at low temperatures (T ≲ 40 K) changes over to the T2 variation and a slight change in the slope dρH/dT2 at T+(H) disappears at H ⩾ 20 kOe. The electron–electron scattering (Fermi liquid) contribution to the T2 term, if present, is completely swamped by the coherent electron–magnon scattering contribution. As a function of temperature, (negative) MR goes through a dip at a temperature Tmin ≃ T+, which increases with H as H2/3. MR at Tmin also increases in magnitude with H and attains a value as large as ∼15% (17%) for d = 12 nm (18 nm) at H = 90 kOe. This value is roughly five times greater than that reported earlier for crystalline Gd at Tmin ≃ 100 K. Unusually large MR results from an anomalous softening of magnon modes at T ≃ Tmin ≈ 20 K. In the light of our previous magnetization and specific heat results, we show that all the above observations, including the H2/3 dependence of Tmin (with Tmin(H) identified as the Bose–Einstein condensation (BEC) transition temperature, TBEC(H)), are the manifestations of the BEC of magnons at temperatures T ⩽ TBEC. Contrasted with crystalline Gd, which behaves as a three-dimensional (3D) pure uniaxial dipolar ferromagnet in the asymptotic critical region, ρH=0(T) of nanocrystalline Gd, in the critical region near the ferromagnetic-paramagnetic phase transition, is better described by the model proposed for a 3D random uniaxial dipolar ferromagnet.