Microscopic model for current-induced switching of magnetization for half-metallic leads

We study the behavior of the magnetization in a half-metallic ferromagnet/nonmagnetic insulator/ferromagnetic metal/paramagnetic metal tunnel junction. It is calculated self-consistently within the nonequilibrium Keldysh formalism. The magnetic regions are treated as band ferromagnets and are described by the single-band Hubbard model. We developed a nonequilibrium spectral density approach to solve the Hubbard model approximately in the switching magnet. By applying a voltage to the junction it is possible to switch between antiparallel (AP) and parallel (P) alignments of the magnetizations of the two ferromagnets. The transition from AP to P occurs for positive voltages while the inverse transition from P to AP can be induced by negative voltages only. This behavior is in agreement with the Slonczewski model of current-induced switching and appears self-consistently within the model, i.e., without using half-classical methods such as the Landau-Lifshitz-Gilbert equation.

Figure 1

Schematic picture of the magnetic tunnel junction with applied voltage $V$. The conduction bands are shown as rectangles. Occupied states in the metals are hatched and the directions of magnetization in the ferromagnets are symbolized by thick arrows.

Figure 2

(Color online) Numerical results for the magnetization as a function of applied voltage for two different values of the hybridization strength ${ϵ}_{MI}$ between the metals and the insulator. Arrows indicate in which direction the voltage was changed. Parameters: band occupation $n=0.7$; band widths: $W_L=3\text{eV}$, $W_I=1\text{eV}$, $W_R=2\text{eV}$, and $W_P=5\text{eV}$; interaction strengths: $U_R=4\text{eV}$, $U_L=4\text{eV}$; band center of the insulator $T_{0,I}=5\text{eV}$; hybridization strength: ${ϵ}_{RP}=0.05\text{eV}$; temperature: $T=0\text{K}$

Figure 3

(Color online) Quasiparticle density of states for the parameter set of Fig. 2 for $V=0$ and ${ϵ}_{MI}=0.5\text{eV}$. Upper picture for parallel alignment of the magnetizations (point A); lower picture for antiparallel alignment (point E). Spin up is shown along the positive; spin down along the negative axis. Black line is the QDOS of the right ferromagnet treated within the NSDA and red (gray) broken line shows the QDOS of the left ferromagnet in mean field.