Numerical simulation of giant magnetoresistance in magnetic multilayers and granular films

We perform numerical simulations of conductance and conductivity for magnetic multilayers and magnetic granular films which show giant magnetoresistance (GMR). The system size to which the recursive Green’s function method is applied is sufficiently large to eliminate incidental effects caused by the system boundary reported previously. It is shown that the resistivity change in the magnetic granular films is proportional to the inverse of the grain size.

Figure 1

(Color online) Structures used in the numerical simulations. (a) CIP-GMR system, (b) CPP-GMR system, (c) granular film, and (d) types of grains embedded in (c). The cross section is $40\times 40$ in units of the lattice constant. An asterisk in (d) indicates that the edges of a cluster are truncated.

Figure 2

(a) Densities of states of magnetic and nonmagnetic metals which constitute the magnetic multilayers and granular films. (b) Schematic figures for randomness at the interfaces of magnetic multilayers.

Figure 3

Calculated results of MR ratios for CIP- and CPP-GMR in magnetic multilayers with different number of layers.

Figure 4

Calculated results (◼) of MR ratios for granular films as functions of grain size $r$. Results shown by ◻ are obtained using a different parameter set (see text).

Figure 5

(a) Calculated results of the resistivity with and without a magnetic field as a function of the inverse of the grain size. (b) Calculated and experimental results (Ref. 13, 14) of the resistivity change as a function of the inverse of the grain size. The inset shows replots as a function of the resistivity at $H=0$. The parameter values are $V_{\text{M}\downarrow }=2.0t,V_{\text{NM}}=1.0t$ and $V_{\text{M}\uparrow }=-2.0t$.

Figure 6

Normalized values of MR, $\left[\rho \left(0\right)-\rho \left(H\right)\right]/\rho \left(0\right)$ as a function of ${⟨\text{cos}\theta ⟩}^2$. Closed and open squares are the calculated results for grains with $5\times 5\times 5^{\ast }$ and $8\times 8\times 8$, and circles show experimental values (Ref. 11).