Itinerant Spin Dynamics in Structures of ... - Jacobs University
Itinerant Spin Dynamics in Structures of ... - Jacobs University Itinerant Spin Dynamics in Structures of ... - Jacobs University
Chapter 6 Critical Discussion and Future Perspective At first we address the topic of diffusive-ballistic crossover which was discussed in Sec.4.5.1: The ansatz which was used to show a reduction of spin relaxation rate appearing due to cubic Dresselhaus SOC, was a discretization of angles when summing over momenta of the Cooperon. Although the constraint for the angles reduces the Cooperon eigenvalues significantly, this ansatz is still based on linear response. One consequence is that contributions appearing at low channel number and steaming from edge to edge skipping orbits, as shown in Ref.[BvH88b], are not included. Such orbits can lead to flux cancellation effects, which e.g. can weaken the magnetic field dependence of WL correction to the conductivity. However, in further work we will show the reduction of spin relaxation rate dependence on the number of transverse channels in the framework of a nonperturbative theory based on the paper by S. Kettemann et al., Ref.[KM02]. In latter work the magnetic phase-shifting rate 1/τ B has been identified with a correlation function of the magnetic vector potential. In turn this correlation function is related to a term in the nonlinear σ-model which appears due to time-reversal symmetry breaking. Thus, in case of an effective magnetic field due to SOC, which brakes spin rotation symmetry, the respective term in the nonlinear σ-model has to be identified to yield a nonperturbative expression for the spin relaxation rate 1/τ s . The last chapter of this work stands out from the rest by the fact that the focus is more on numerical calculations. The code was developed as general as possible by decomposing all matrix operations in connectivity and hopping matrices including magnetic field and 106
Chapter 6: Critical Discussion and Future Perspective 107 different kinds of SOC. Having coded the KPM in a general form, one of the next steps will be the analysis of diluted magnetic semiconductors using the V-J pd model developed by G. Bouzerar et al.[BBZ07]. Already analytical calculations show[WLZ07b] that in contrast to a lattice with only nonmagnetic impurities, the vertex correction corresponding to ladder diagrams, σ L SH does not cancel the one-loop part σ 0 SH which is equal to that derived by Sinova.[SCN + 04] This can be calculated now rigorously for large systems, i.e. also the clustering of Mn 2+ can be included[Bou]. Numerical works like Ref.[LX06] show interesting change of sign of the SHC by changing the exchange interaction or the impurity density and strength. However the work was limited to smaller sizes, L 2 = 20×20, and focused on energies away from the impurity band. Due to the advantaged of the KPM concerning the obsolete cutoff η adjustment, we are able to go beyond calculations which extracted localization lengths using the computation of SHC by application of the time evolution projection method (see e.g. Ref.[MM07]). Last but not least, due to the general structure of the KPM code, also the extension to the evaluation of other quantities like the anomalous Hall effect is possible.
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Chapter 6: Critical Discussion and Future Perspective 107<br />
different k<strong>in</strong>ds <strong>of</strong> SOC. Hav<strong>in</strong>g coded the KPM <strong>in</strong> a general form, one <strong>of</strong> the next steps<br />
will be the analysis <strong>of</strong> diluted magnetic semiconductors us<strong>in</strong>g the V-J pd model developed<br />
by G. Bouzerar et al.[BBZ07]. Already analytical calculations show[WLZ07b] that <strong>in</strong> contrast<br />
to a lattice with only nonmagnetic impurities, the vertex correction correspond<strong>in</strong>g to<br />
ladder diagrams, σ L SH<br />
does not cancel the one-loop part σ 0 SH<br />
which is equal to that derived<br />
by S<strong>in</strong>ova.[SCN + 04] This can be calculated now rigorously for large systems, i.e. also the<br />
cluster<strong>in</strong>g <strong>of</strong> Mn 2+ can be <strong>in</strong>cluded[Bou]. Numerical works like Ref.[LX06] show <strong>in</strong>terest<strong>in</strong>g<br />
change <strong>of</strong> sign <strong>of</strong> the SHC by chang<strong>in</strong>g the exchange <strong>in</strong>teraction or the impurity density<br />
and strength. However the work was limited to smaller sizes, L 2 = 20×20, and focused on<br />
energies away from the impurity band.<br />
Due to the advantaged <strong>of</strong> the KPM concern<strong>in</strong>g the obsolete cut<strong>of</strong>f η adjustment, we are<br />
able to go beyond calculations which extracted localization lengths us<strong>in</strong>g the computation<br />
<strong>of</strong> SHC by application <strong>of</strong> the time evolution projection method (see e.g. Ref.[MM07]).<br />
Last but not least, due to the general structure <strong>of</strong> the KPM code, also the extension to the<br />
evaluation <strong>of</strong> other quantities like the anomalous Hall effect is possible.
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