Theory of Diluted Ferromagnetic III-V compound semiconductor materials of Spintronics

Spintronics = Spin + Electronics The most interesting material is Diluted Ferromagnetic semiconductor III-V based with Mn impurity i.e. (In,Mn)As, (Ga,Mn)As

III-V DMSs : S = 5/2 (Mn 2+) hole concs. ~ 10% impurities concs. (compensated doping) hole spins couple with Mn AF (p-d coupling)

Compensated doping

Carrier mediated ferromagetism Dilute electrons Local moments RKKY indirect interaction

Kondo Lattice model With Zeeman energies

Arbitrary S local moment Green’s function Equation of motion The time derivative of local spin greens function

Where Then Through RPA mean field

Including spin flip Greens function of conducting electrons equal to Through the Fourier transformation Local spin Greens function spin flip Greens function

Combined together

Self-energy Dyson’s general formula of magnetization where

RPA first order approx. for electrons take the dilute limit by conversing the kinetic energy to free electrons like The summation becomes

Spinwave Spectrum where

for By L’Hospital rule

Imaginary part of self energy will cause the spin waves spread The delta function made a constraint the existing region for the imaginary part

Considering the zero temperature situation the existing region for the imaginary part

From Dyson’s general formula of magnetization Magnetization profile is comparable for Monte Carlo result for Ising interaction(Osamu Sakai, Physica E 10,148(2001)

To evaluate the temperature dependence of static susceptibility, Where and are expectation values of local spin with magnetic field turned on and off

Conclusions: Kondo lattice model utilizes the equation of motion method with RPA approximation in dilute limitation to obtain a local spin greens function of self consistent solution can well describe the magnetic properties of diluted ferromagnetic semiconductors

From examining the imaginary part of self energy reveals that the spin excitations are well established in this model The temperature dependence of magnetization is qualitatively consistent with Monte Carlo result the significant peak of susceptibility appearing before Tc agrees with experimental result