Itinerant Spin Dynamics in Structures of ... - Jacobs University

Chapter 2: Spin Dynamics: Overview and Analysis of 2D Systems 23
the conduction electrons resulting in a vanishing of the magnetic scattering rate. Thus,
the spin scattering from magnetic impurities has a maximum at a temperature of the order
of the Kondo temperature T K ∼ E F exp(−1/νJ)[MACR06, MHEZ71, ZBvDA04]. In
semiconductors T K is exponentially small due to the small effective mass m e (see Appendix
A) and the resulting small DOS ν. Therefore, the magnetic moments remain free at the
experimentally achievable temperatures. At large concentration of magnetic impurities, the
RKKY-exchange interaction between the magnetic impurities quenches however the spin
quantum dynamics, so that S(S +1) is replaced by its classical value S 2 . In Mn-p-doped
GaAs, the exchange interaction between the Mn dopants and the holes can result in compensation
of the hole spins and therefore a suppression of the Bir-Aronov-Pikus (BAP) spin
relaxation[ADK + 08].
2.4.7 Nuclear Spins
Nuclear spins interact by the hyperfine interaction with conduction electrons. The
hyperfine interaction between nuclear spins Î and the conduction electron spin, ŝ, results in
a local Zeeman field given by [OW53]
ˆB N (r) = − 8π 3
g 0 µ B
∑
γ n Îδ(r−R n ), (2.37)
γ g
whereγ n isthegyromagneticratioofthenuclearspin. Thespatialandtemporalfluctuations
ofthishyperfineinteraction fieldresultinspinrelaxationproportionaltoitsvariance, similar
to the spin relaxation by magnetic impurities.
n
2.4.8 Magnetic Field Dependence of Spin Relaxation
The magnetic field changes the electron momentum due to the Lorentz force,
resulting in a continuous change of the spin-orbit field, which similar to the momentum
scattering results in motional narrowing and thereby a reduction of DP spin relaxation:
[Ivc73, PT84, BB04],
1
τ s
∼
τ
1+ωcτ 2 2. (2.38)
Another source of a magnetic field dependence is the precession around the external magnetic
field. In bulk semiconductors and for magnetic fields perpendicularto a quantum well,
the orbital mechanism is dominating, however. This magnetic field dependence can be used
to identify the spin relaxation mechanism, since the EYS does have only a weak magnetic