Polarization-controlled spin reorientation transition and resistive switching in ferromagnetic-ferroelectric nanostructures and tunnel junctions

A spin reorientation transition (SRT) induced in a ferromagnetic nanolayer by the polarization switching in an adjoining ferroelectric film or bulk crystal is described theoretically. It is shown that such a polarization-controlled SRT can be realized in a narrow range of the nanolayer thicknesses only. Our calculations allowing for the polarization-dependent interfacial magnetic anisotropy predict that this “thickness window” is located between two threshold thicknesses, at which a size-induced SRT takes place in the ferromagnetic nanolayer at two different directions of the ferroelectric polarization. Importantly, the polarization-controlled SRT manifests itself in the resistance switching occurring in multiferroic tunnel junctions (MFTJs), where an ultrathin ferroelectric barrier is embedded between a ferromagnetic electrode with controllable magnetization and an electrode with a fixed magnetization. Using ${\mathrm{Fe}/\mathrm{BaTiO}}_3/\mathrm{Fe}$ junctions as a representative example, we demonstrate that such MFTJs can be employed as electric-write nanoscale memory cells with reliable nondestructive readout and high thermal stability of information storage.

Figure 1

Schematic representation of a ferromagnet-ferroelectric-metal trilayer. The application of sufficient dc voltage to the interlayer renders it possible to switch the ferroelectric polarization P between the up and down directions. This polarization reversal may induce the reorientation of the magnetization M from the perpendicular-to-plane orientation (panel a) to an in-plane one (panel b).

Figure 2

Dependence of the energy density Δ$F$ = $F$ − $F_0$ on the magnetization orientation in a Fe nanolayer with the threshold thickness corresponding to a size-driven SRT. The presented three-dimensional plot corresponds to the following set of parameters: nanolayer thickness $t_f$ = 1.0185 nm, interfacial anisotropy parameter $K_s=-1.59\text{mJ}{\text{m}}^{-2}$, demagnetizing factors $N_{11}$ = 0.02, $N_{22}$ = 0.04, $N_{33}$ = 0.94, and lattice strains $u_1$ = $u_2$ = −1.5%.

Figure 3

Voltage-induced switching of ferroelectric and ferromagnetic order parameters in a multiferroic tunnel junction with the perpendicular-to-plane orientation of the fixed magnetization ${\mathbf{M}}_{\mathrm{fixed}}$. (a) initial stable state with the magnetization M of the free layer perpendicular to the ferroelectric barrier having an in-plane spontaneous polarization P; (b) polarization rotation in a downward electric field E and the resulting reorientation of the free layer magnetization; (c) second stable state forming after completion of the voltage pulse, where the free layer keeps an inclined magnetization direction, whereas the barrier polarization returns to in-plane orientation; (d) polarization rotation in an upward electric field, which induces the switching of the free layer magnetization back to the perpendicular-to-plane orientation.

Figure 4

Variations of the free energy density Δ$F$ of a Fe nanolayer subjected to the perpendicular-to-plane effective interaction field $H_3^{\mathrm{int}}$ = 4 × 10${}^4$ A ${\mathrm{m}}^{-1}$ with the angle θ between the magnetization and the $x_3$ axis at ϕ = 0. The parameter $K_s$ of the interfacial magnetic anisotropy is set equal to $K_{s0}=-1.29\text{mJ}{\text{m}}^{-2}$ (a), $K_{s\downarrow }=-1.08\text{mJ}{\text{m}}^{-2}$ (b), and $K_{s\uparrow }=-1.59\text{mJ}{\text{m}}^{-2}$ (c). The square-shaped nanolayer with an area of 1260 ${\mathrm{nm}}^2$ has a thickness of $t_f$ = 0.823 nm.

Figure 5

Voltage-induced switching of two order parameters in a multiferroic tunnel junction with an in-plane magnetized fixed layer. (a) initial stable state with the antiparallel electrode magnetizations and an in-plane polarized ferroelectric barrier; (b) polarization rotation in an upward electric field and the resulting reorientation of the free layer magnetization; (c) second stable state forming after completion of the voltage pulse, where the free layer keeps a tilted magnetization, whereas the barrier polarization returns to in-plane orientation; (d) polarization rotation in a downward electric field, which induces the switching of the free layer magnetization back to the initial in-plane orientation.

Figure 6

Energy density Δ$F$ of a Fe nanolayer subjected to the in-plane effective interaction field $H_1^{\mathrm{int}}$ = 1.5 × 10${}^4$ A ${\mathrm{m}}^{-1}$ plotted as a function of the magnetization orientation angle θ at ϕ = 0. The parameter $K_s$ of the interfacial magnetic anisotropy is set equal to $K_{s0}=-1.29\text{mJ}{\text{m}}^{-2}$ (a), $K_{s\uparrow }=-1.59\text{mJ}{\text{m}}^{-2}$ (b), and $K_{s\downarrow }=-1.08\text{mJ}{\text{m}}^{-2}$ (c). The rectangular-shaped nanolayer with a length of 250 nm along the $x_1$ axis and a width of 200 nm has a thickness of $t_f$ = 0.713 nm.