Field- and concentration-tuned scaling of a quantum phase transition in a magnetically doped semiconductor

Scaling analysis was performed on families of DC and AC conductivity curves falling on the metallic and insulating sides of the metal-insulator transition in the amorphous magnetically doped semiconductor, a-GdₓSi_1-x. The transport curves were obtained both as a function of discretely varying both the gadolinium dopant concentration, x, and separately by changing an applied magnetic field, H. Both tuning parameters result in correlation length exponents of ν=1 and dynamical scaling exponents of $z=2$. Temperature-frequency results differ markedly as compared to previous work on the nonmagnetic analog a-NbₓSi_1-x. Our data also indicate a broader than predicted parameter space showing quantum critical behavior, and a phenomenologically determined quantum critical line in the zero temperature x-H plane is presented. The results are explained in terms of a single tunable parameter, namely disorder.