On Nuclear-Spin Lattice Relaxation Time in a Superconductor Containing Non-Magnetic Transition-Metal Impurities

Abstract

A calculation of the nuclear-spin lattice relaxation time T, in a superconductor containing resonance type impurities is presented. The Anderson model in a superconductor is adopted to describe the impurity in a metal and is solved in the Hartree-Fock approximation. The temperature dependence of T 1, calculated by the use of the non-magnetic solution, is corn­ pared with a recent experiment made on Al-Mn alloys: Measured relaxation times deviate from the law of corresponding states which is thought to be valid for non-magnetic resonance states in the superconducting Anderson model. This comparison leads to the conclusion that there exists apparent spin fluctuation effects in Al-Mn alloys. An experiment on the nuclear-spin lattice relaxation time for superconducting Al-Mn alloys recently appeared.v Anomalous short relaxation time was observed when non-magnetic Mn impurities are present. The observed relaxation behavior indicates that the density of states in the energy gap is modified appreciably by the Mn impurities. This fact cannot be explained on the basis of the law of correspond­ ing states, which is thought to be valid for superconducting non-magnetic alloys such as the 3d-transition metal impurities in aluminum. As is kno\vn, even certain non-magnetic impurities in a superconductor described by the Anderson model drastically change the density of states. 2J.aJ That is, there exist localized excited states in the energy gap. Although the sharp peaks remain and merge into the gap, singularities at the gap edges disappear as the concentration of non-magnetic impurities is increased. Generally speaking, transport coefficients such as the nuclear-spin relaxation time directly reflect low lying excitations, that is, the density of states at low energy. These are a good probe to detect the structure of the localized excited states in the energy gap. In this paper we treat the Anderson model within the Hartree-Fock approxi­ mation. We calculate the temperature dependence of the nuclear-spin lattice re­ laxation time and compare the results with the experiment on Al-Mn. The superconducting ,1\l-JVIn alloy is thought to be in the transition region (the spin fluctuation region) between magnetic and non-magnetic behavior. It is, however, worth while studying the nuclear-spin lattice relaxation time within the