Anomalous magnetoresistance in nanocrystalline gadolinium at low temperatures

The results of a detailed investigation of electrical resistivity,.(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, rho(r) (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 rho r (0), which gets progressively suppressed as the applied magnetic field (H) increases in strength. At low temperatures (T less than or similar to 40 K) and fields (H = 0 and H = 5 kOe), rho H (T) varies as T-3/2 with a change in slope at T (+) similar or equal to 16.5K. As the field increases beyond 5 kOe, the T-3/2 variation of rho H (T) at low temperatures (T less than or similar to 40 K) changes over to the T-2 variation and a slight change in the slope d.H /dT(2) at T+(H) disappears at H >= 20 kOe. The electron-electron scattering (Fermi liquid) contribution to the T-2 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 T-min similar or equal to T+, which increases with H as H-2/3. MR at T-min also increases in magnitude with H and attains a value as large as similar to 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 T-min similar or equal to 100 K. Unusually large MR results from an anomalous softening of magnon modes at T similar or equal to T-min approximate to 20 K. In the light of our previous magnetization and specific heat results, we show that all the above observations, including the H-2/3 dependence of T-min (with T-min(H) identified as the Bose-Einstein condensation (BEC) transition temperature, T-BEC(H)), are the manifestations of the BEC of magnons at temperatures T <= T-BEC. Contrasted with crystalline Gd, which behaves as a three-dimensional (3D) pure uniaxial dipolar ferromagnet in the asymptotic critical region, (rho H=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.