Asymmetric Metal-Insulator Transition in Disordered Ferromagnetic Films

We present experimental data and a theoretical interpretation of the conductance near the metal-insulator transition in thin ferromagnetic Gd films of thickness $b\approx 2–10\mathrm{nm}$. A large phase relaxation rate caused by scattering of quasiparticles off spin-wave excitations renders the dephasing length $L_{\varphi }\lesssim b$ in the range of sheet resistances considered, so that the effective dimension is $d=3$. The conductivity data at different stages of disorder obey a fractional power-law temperature dependence and collapse onto two scaling curves for the metallic and insulating regimes, indicating an asymmetric metal-insulator transition with two distinctly different critical exponents; the best fit is obtained for a dynamical exponent $z\approx 2.5$ and a correlation (localization) length critical exponent ${\nu }_{-}\approx 1.4$ (${\nu }_{+}\approx 0.8$) on the metallic (insulating) side.

Figure 1

Normalized conductivity as a function of temperature in a log-log plot for all samples in the range $15<R_0<31\mathrm{k}\Omega$. Fitting of Eq. (3) to one sample (red line) is shown with fitting parameters displayed in the inset.

Figure 2

$W$ as a function of $T$, showing the existence of a critical separatrix ($A=0$) with $R_0=22.67\mathrm{k}\Omega$, separating the metallic ($A>0$) and the insulating ($A<0$) samples.

Figure 3

Collapse of the data for different values of $R_0$ according to the scaling relation given by Eq. (2) for ${\nu }_{-}=1.38$ on the metallic side (top panel) and ${\nu }_{+}=0.77$ on the insulating side (bottom panel). Here $T_0=5\mathrm{K}$ is a reference temperature. The insets of each panel show the dependence of ${\chi }^2$ on ${\nu }_{-}$ and ${\nu }_{+}$ for the values of $p=1/z$ listed in the legends. The best-fit values occur at $p=0.390(5)$ with well-defined minima at ${\nu }_{-}=1.38(11)$ and ${\nu }_{+}=0.77(11)$.