Dephasing by Extremely Dilute Magnetic Impurities Revealed by Aharonov-Bohm Oscillations

We have probed the magnetic field dependence of the electron phase coherence time ${\tau }_{\phi }$ by measuring the Aharonov-Bohm conductance oscillations of mesoscopic Cu rings. Whereas ${\tau }_{\phi }$ determined from the low-field magnetoresistance saturates below 1 K, the amplitude of Aharonov-Bohm $h/e$ oscillations increases strongly on a magnetic field scale proportional to the temperature. This provides strong evidence that a likely explanation for the frequently observed saturation of ${\tau }_{\phi }$ at low temperature in weakly disordered metallic thin films is the presence of extremely dilute magnetic impurities.

Figure 1

Phase coherence time ${\tau }_{\phi }(B\approx 0)$ vs temperature determined by fitting the low field magnetoresistance of long wires to weak localization theory. The uncertainties are indicated by error bars at the lowest temperature where they are usually the largest. The samples are made of silver Ag1 ($+$) (data taken from 6) and copper Cu1 ($▴$), Cu2 ($⧫$), Cu3 ($▾$), and Cu4 ($\blacksquare$). ${\tau }_{\phi }(B\approx 0)$ increases continuously with decreasing temperatures in the silver sample, whereas in all Cu samples ${\tau }_{\phi }(B\approx 0)$ shows a saturation at low temperatures. Inset: symbols represent the relative variation of the resistance of sample Cu4 in a small magnetic field $B=50\mathrm{m}\mathrm{T},$ plotted as a function of $1/\sqrt{T}$. The continuous line is a fit using the functional form $A/\sqrt{T}$ predicted by the theory of electron-electron interaction in diffusive metallic wires [17]. The best fit is obtained with $A=7.6\times {10}^{-4}{\mathrm{K}}^{1/2}$ in close agreement with the theoretical prediction $7.2\times {10}^{-4}{\mathrm{K}}^{1/2}$.

Figure 2

Photograph of the Aharonov-Bohm ring in sample Cu4. We obtain the resistance by a four-lead measurement. The bottom left voltage lead is a very long wire used to extract ${\tau }_{\phi }(B\approx 0)$ from the low field magnetoresistance.

Figure 3

Measured conductance of the ring in sample Cu4, in units of $e^2/h$, as a function of magnetic field at a temperature $T=100\mathrm{m}\mathrm{K}$. The narrow Aharonov-Bohm oscillations ($\Delta B\simeq 2.5\mathrm{m}\mathrm{T}$) are superimposed on the larger and much broader universal conductance fluctuations. Left inset: blowup of the data near zero field. The AB oscillations are hardly visible. Right inset: blowup of the data at large magnetic field. The AB oscillations are much larger.

Figure 4

Symbols: mean amplitude of the AB $h/e$ oscillations ($\Delta G_{h/e}$) in units of $e^2/h$ in sample Cu4 at $T=40$ ($▵$) and 100 mK ($\blacksquare$), plotted as a function of the reduced magnetic field $2{\mu }_{B}B/k_{B}T.$ Lines: fits to the two data sets using Eqs. (1, 2, 3) with $C$ and $g$ as fit parameters (see text).