Fig.4: The resistance of a pure disordered Mg film is plotted versus 1/B, the inverse magnetic field, in a semi-log plot (upper curve). This is equivalent with plotting the integrated coherent electron echo as a function of time (upper scale). When the curve becomes flat the echo disappears. The second curve shows the corresponding results after the Mg is covered with a fraction of a monolayer of Au. The Au nuclei rotate the electron spins and cause a destructive interference, equivalent to a negative coherent echo.

What we see in Fig.4 is really the coherent echo of the conduction electrons on a pico-second time scale. We can dramatically alter this echo by manipulating the spin of the electrons. This is done for the lower curve of Fig.4. Here we covered the Mg film with a fraction of a monolayer of Au /11/. The Au nuclei have a large electrical charge of Ze. If a conduction electron passes close by a Au nucleus its spin is slightly rotated (the effect is called spin-orbit scattering). The spin rotated partial electron waves yields a destructive interference in the back-scattering (corresponding to a negative echo, see ref. /3/). Therefore the resistance in the Au/Mg film decreases for large times, i.e. small fields. In the maximum of the plateau the electron spin are rotated by an angle of /2.

If we evaporate on top of the Mg magnetic atoms, for example Fe atoms, then the echo disappears at a much shorter time or larger magnetic fields respectively. This way one can directly identify the dephasing time of magnetic impurities.

Although our plot of the resistance versus log(1/B) is most instructive one generally plots as a function of the magnetic field B (R|0| is the film resistance per square). Then one uses the theory by Hikami et al. /9/ to fit the magnetoresistance curves. This fit yields the dephasing time with an accuracy of a few percent (and the spin-orbit scattering time ).

In Fig.5 we have plotted the magnetoresistance curve of a pure Au film, quench condensed onto a quartz plate at helium temperature. Here the echo is negative because the Au nuclei rotate the electron spins after a very short time, shorter than 0.03 ps, our lower limit in the time scale. The second curve shows the magnetoresistance of the same Au film after it is covered with 1/100 atomic layer of Mo. (This means that only every 100th surface position is filled with a Mo atom.) This small Mo coverage broadens the magnetoresistance by a factor of 25. The (negative) coherent echo lasts in the pure Au at 4.5K up to about 25 ps. In the Au/Mo film the echo is already destroyed after 1 ps. Nothing besides a magnetic scattering can have such a devastating effect on the echo. Therefore the investigation of the magnetoresistance is an extremely sensitive method to detect magnetic moments.

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