Anomalous Spin-Lattice Relaxation in Dilute RhFe at Positive and Negative Nanokelvin Spin Temperatures

Abstract

We have investigated at ultralow temperatures the spin-lattice relaxation in rhodium samples with about 10p.p.m. of iron impurities. A strong decrease in the Korringa constant K, dependent on the sign of the nuclear spin temperature T, was observed below 1 mT. Our data on the spin-lattice relaxation time T ~, , measured at the electronic temperature T, = 120 pK, fit the equation l / z ll/(xo/T,) = l/r;"P(B, T), where the impurity term @(B, T ) has a contribution proportional to the inverse nuclear spin temperature in small fields.

Nuclear spin relaxation at ultralow temperatures

“…12 We assume that the nuclear spin system is in internal thermal equilibrium at temperature T, different from the temperature of the reservoir T e . In the experiments, 7 performed in magnetic fields less than 400 T, T e was about 100 K, whereas T was on the order of Ϯ1 nK. We denote the inverse of temperature (1/k B T) as ␤ and ␤ e for the system and reservoir, respectively.…”

“…͑27͒ varies proportionally to (␤ Ϫ␤ C ), which shows critical slowing down of the relaxation time. To obtain semiquantitative understanding of the experimental results 7 we next proceed with estimations based on Monte Carlo simulation and on high-temperature expansion.…”

“…As the high-temperature expansion is valid for ␤J NN , ␤g H 0 Ӷ1, it is difficult to compare directly with the experiments done at H 0 ϭ40 T and Tϳ1 nK (ϭ20.8 Hz•h) since this field corresponds to ␥H 0 /2 ϭ53.6 Hz in Rh (␥/2 ϭ1.34 MHz/T). 7 The calculated results for E ex and E z at 20 T are presented in Fig. 1͑b͒.…”

“…This behavior of ͗I z ͘ is consistent with the experimental result. 7 For a detailed comparison with the experimental results, the calculation should be done at the experimental value H 0 ϭ40 T. However, such an attempt displayed unphysical behavior in the time dependence of ␤(t) in the third-order approximation. It is therefore necessary to go to higher order in the high-temperature expansion, or to use more accurate results for E ex (␤) and E z (␤).…”

“…6 Furthermore, Hakonen et al found that, at the extreme temperatures, the nuclear spin relaxation is about two times slower at TϽ0 than at TϾ0. 7 When the temperature of spins decreases and becomes comparable with the internal field seen by the nuclei, the assumption of high temperature adopted in the conventional theories cannot be applied anymore. At these temperatures, a deviation from the Korringa law is expected to occur.…”