31P Nuclear Spin Dynamics in Metallic Si:P at Very Low Temperature and High Magnetic Fields

Abstract

Phosphorus-doped silicon (Si:P) is one of the most extensively studied condensed matter systems since a variety of physical phenomena accompanies with doping P in Si, such as impurity-band conduction, metal–insulator transition (M–I). Recently, it has attracted new interest for possible applications to quantum computer where P nuclear spins serve qubits and electron spins are completely polarized for isolated spins bound at the donor. This model of silconbased quantum computer requires NMR control of P nuclear spins under extreme conditions of several tesla magnetic field and millikelvin temperature. Spin dynamics of both nuclei and electrons are of great interest in this regard. However, despite a large amount of works devoted to the magnetic properties of Si:P, P-NMR has never been investigated under such experimental conditions. Here we present the P-NMR of metallic Si:P investigated at temperature between 40mK and 4K and a magnetic field of 7 T. We tried P-NMR in insulator Si:P but could not detect it. Our NMR data show several novel features in longitudinal relaxation time T1 and transverse relaxation time T2 associated with very low temperature and high magnetic field. We prepared a powdered sample from single crystalline silicon wafers with phosphorus dopant concentration of n 1⁄4 5:6 10 cm 3 which is above the critical concentration for M–I, nc ’ 3:7 10 cm . The dopant concentration of Si:P was determined by measuring room temperature resistivity with the Mousty scale. The sample was immersed in He–He mixture which was cooled by a dilution fridge. The NMR spectra at 120MHz were obtained by recording the spin-echo height with varying magnetic fields. The T2 was measured by decay of the echo height with varying time delay of the pulse sequence =2 . The T1 was obtained from the magnetization recovery after -pulse with varying waiting time t of the sequence t =2 . The NMR spectra were typical for metallic sample and did not depend on temperature. The linewidth of about 24mT and the Knight shift agree with those reported in the literature for similar dopant concentrations. The linewidth is believed to be determined by inhomogeneous broadening of hyperfine interactions. The longitudinal relaxation showed a substantial change only below 0.6K from the previous data. Nuclear magnetization was recovered in two steps, following double-exponential curves below 0.6K while the recovery followed single-exponential curves above 0.6K. Typical recovery curves are shown in the inset of Fig. 1. Below 0.6K, we obtained T1 separately for the fast and slow components of the relaxation, T1f and T1s. The T1f and T1s are plotted against temperatures in Fig. 1. T1f above 0.2K follows the Korringa’s relation as, T1T 1⁄4 ( is Korringa constant). It shows, however, a gradual deviation from the Korringa’s relation below 0.2K. The long T1s increases with decreasing temperature as T1s / T n with n ’ 1:3. A double-exponential form of recovery curve was observed only when the nuclear Zeeman bath decays through the electron bath to a third bath in series and the heat capacity of Zeeman bath, CN, becomes comparable to that of the electron bath, Ce. The second stage for the slow recovery process appeared in the magnetization recovery at T 1⁄4 0:6K when CN=Ce ’ 0:01 and [1 MðtÞ=M0] was measured in the range between 2 and 0.01. We understand that both the deviation of T1f from the Korringa’s relation and the appearance of long T1s arise from the large nuclear Zeeman heat capacity at high B=T . Because CN goes with ðB=TÞ while Ce with T , the temperature of electrons actually rises during nuclear spin relaxation when the electron system is decoupled to the third bath (He–He mixture bath) by T1s since T1f T1s. Due to heating up the electron temperature Te the nuclear spins relax at faster rate =Te than that expected from =T where Te > T . The T1s was first observed and was the time constant for the Zeeman and conduction electron baths to decay together to the He–He bath. The T1s is needed to cool down the nuclear spins at low temperatures and may be due to the Kapitza resistance between the sample and He–He mixture. Fig. 1. Longitudinal relaxation times T1f (circle) and T1s (square) with temperature. The inset shows the recovery curves. Dotted line represents the Korringa’s relation derived from the data above 1K. Solid line is a guide to the eye.