Electrical transport in disorderd magnetic multilayers Josef Kudrnovsk'y a, V'aclav Drchal

k
X tr f 1 ( k
kk
B
k
பைடு நூலகம்
; E ) G1;N (kk ; z+ )
where Nk is the number of kk -points in the surface Brillouin zone (SBZ), z = EF i with EF being the Fermi energy, and tr denotes the trace over angular momenta L. The quantities B1 ; BN characterize the left and right leads, respectively, and are evalueated in terms of the so-called surface Green functions of isolated semi-in nite leads 3]. Finally, G1;N ; GN;1 are corresponding blocks of the Green function of the sample between its terminal layers (layers 1 and N ). The magnetoresistance ratio is then de ned as " # " # GM R = (RAF + RAF )=(RF + RF ) ? 1 " # " # = (CF + CF )=(CAF + CAF ) ? 1 ; where RM = 1=CM is the resistance per interface atom. The above formalism will be illustrated for the model of combined disorder in the spacer (Cu85 Ni15 substitutional alloy) and in magnetic slabs (Co85 Ni15 substitutional alloy). We have used selfconsistent potentials determined for a given alloy composition in the framework of the local spin-density approximation and the so-called coherent potential approximation 3]. We have thus neglected all possible uctuations of the potentials of A and B atoms due to a variation of their local environment within a supercell for a given random con guration. This is a very good approximation for metallic systems. We have used 7 7 random supercells with 49 sites occupied randomly by A- and B-atoms corresponding roughly to a A85 B15 random substitutional alloy, namely 41 A atoms and 8 B atoms. Typically an average over 3 { 5 con gurations was used and the results for partial currents CF=AF agreed within 1{3% among di erent con gurations. The kk integration extends over 196 points in the full fcc(001) supercell SBZ (corresponding to 10000 points in the SBZ of the underlying lattice), and = 10?7 Ry.
BN (kk ; E ) GN;1 (kk ; z? ) ;
g
Conductances / atom (in units e2/h)
The results are presented in Fig. 1. We observe a monotonic decrease of the GMR ratio as a function of the spacer thickness. Disorder lowers the large value of the GMR for ideal (ballistic) sample and also suppreses the quantum-size oscillations present for the ideal spin-valve. The origin of this decrease can be traced down from plots of partial conductances. In an ideal sample, the F"-conductance is high due to very weak intrinsic scattering of electrons at interfaces because of great similarity between the Cu- and the Co"-bands. On the contrary, the large di erence between the Cu- and Co#-bands can be viewed as an e ective potential barrier at the interface for #electrons which, in turn, gives rise to much smaller F#- and AF-conductances. It should be noted that in Cu-rich alloys the states at the Fermi energy are in uenced only weakly by impurities. Therefore, the F#- and AF-conductances are only slightly smaller than those of an ideal trilayer. The e ect of alloying, however, dominates the F"-conductance (where intrinsic scattering is negligibly small) resulting at its signi cant decrease with increasing number of disordered layers. Its nearly linear decrease with the spacer thickness is characteristic for the 'ohmic' regime of the current. The e ect of disorder in magnetic layers is different. Due to the similarity of the Co"- and the Ni"-bands at the Fermi energy the F"-conductance is nearly the same as for the ideal trilayer. Since the Co#-bands are higher in energy as compared to the Ni#-bands, alloying of Co with Ni decreases e ectively the potential barrier height at the interface resulting thus in a larger transmission coe cient (conductance) as compared to the ideal trilayer. Consequently, the AF-conductance of the alloyed magnetic layers is larger than for an ideal trilayer. The same e ect, but weaker, applies for the F#-conductance indicating dominating intrinsic scattering at interfaces for this channel. The AF- and F#-conductances as a function of the spacer thickness behave 'ballistically', namely they are nearly independent on the spacer thickness as they are essentially not in uenced by the spacer disorder as discussed above. The decrease of the GMR ratio is thus due to the scattering of F"electrons on impurities in the spacer. Its absolute value is further reduced by an increase of the AFconductance due to the decrease of e ective potential barrier for Co#-electrons due to alloying of Co-layers with Ni-atoms.