Nuclear spin-lattice relaxation rate in disordered paramagnetic diluted magnetic semiconductors

Nuclear spin -lattice relaxation signatures in paramagnetic diluted magnetic semiconductors involving magnetic disorder are examined. By utilizing the dynamical mean -field theory for the Kondo lattice model with disorder potential, in the infinite -dimensional limit, we have derived a set of self -consistent equations to enable the numerical evaluation of the single -particle Green's function and its self -energy. The local dynamical spin susceptibility function and then the nuclear spin -lattice relaxation rate is evaluated in terms of the single -particle Green's function. Our numerical results reveal the spin fluctuations, evidenced by the sharp peak appearing at a low frequency in the spin dynamical susceptibility function, become dominant in the case of large magnetic coupling and high magnetic impurity density with temperatures close to the paramagnetic -ferromagnetic transition. In that situation, the nuclear spin -lattice relaxation divided by temperature obeys the Curie law that attributes the formation of the coherent magnetic bound states or the magnons in the paramagnetic state. Sufficiently large intensity of the magnetic disorder or the thermal fluctuations might deplete all of the bound states and then the system would settle in the normal metallic state expressing the Korringa mechanism or the nematic instability. Our observations thus have underlined the significance of the magnetic coupling and the magnetic disorder in determining the spin -lattice relaxation processes in DMSs and highlighted the advantage of the dynamical mean -field theory in studying the spin dynamics in a doped magnetic system.