Modulations of interlayer exchange coupling through ultrathin MgO-based magnetic tunnel junctions: First-principles study

Ultrathin MgO-based magnetic tunnel junction (MTJ) features high electron/heat current density, presenting important applications in spintronics. Here, we report a first-principles study of the interlayer exchange coupling (IEC) through ultrathin MgO-based MTJs. We investigate the effects of different modulations on the IEC, including temperature, different interfacial disorders, and the type and thickness of the ferromagnetic (FM) materials. It is found that the interfacial disorders, such as oxygen vacancies, boron and carbon impurities, can significantly influence the magnitude and sign of the IEC. The presence of interfacial disorders enhances the anti-FM coupling contribution and reduces the FM coupling contribution to the total IEC, and can thus change the total IEC from FM to Anti-FM in the ultrathin MTJ. We also find that FM materials have important effects on IEC: the IEC with CoFe alloy exhibits much weaker dependence on the interfacial disorders and temperature than that with the Fe. Our first-principles results provide a good explanation for the serious inconsistency between previous experimental measurements. Moreover, by studying the junction structure Vacuum/FM1/MgO/FM2 (FM1, FM2=Fe, CoFe), we find that the ultrathin FM1 layers can dramatically enhance the FM IEC and the IEC enhancement significantly depends on the combination of FM1-FM2. We show that the enhanced FM IEC with ultrathin FM1 can be sustained with a considerable amount of surface roughness in FM1 and interfacial disorder.

Figure 1

(a) Sketch of a two-probe device containing a central region sandwiched by two electrodes: the relative angle between the magnetization of the two FM layers (orange colored) is $\theta$, the dotted line at the center separates the system into left and right parts; (a) MTJ with a tunnel barrier sandwiched by two semi-infinite FM electrodes; (b) MTJ with a tunnel barrier sandwiched by FM1 with finite thickness and semi-infinite FM2. The FM materials considered include Fe and ${\mathrm{Co}}_{0.5}{\mathrm{Fe}}_{0.5}$ alloy.

Figure 2

Temperature-dependent IEC through $\mathrm{FM}/\mathrm{MgO}$(3 ML)$/\mathrm{FM}$ MTJs with different interfacial disorders: clean (black-square), 5% OV (red-circle), and 10% OV (blue-triangle). (a) is for Fe-MTJs and (b) is for CoFe-MTJs.

Figure 3

IEC energy $J$ (at 0 K) for $\mathrm{FM}/\mathrm{MgO}$(3 ML)$/\mathrm{FM}$ MTJs with three types of interfacial disorders, including OV, boron and carbon impurities (presented in the first, second, and third columns, respectively). The disorder concentration is indexed by $x$% ($y$%) for the left (right) interface.

Figure 4

$k_{\left|\right|}$-resolved IEC (${\mathrm{erg}/\mathrm{cm}}^2$) for $\mathrm{FM}/\mathrm{MgO}$(3 ML)$/\mathrm{FM}$ MTJs with different interfacial disorders including OV, boron, and carbon impurities. We consider the disorder concentration 5% at both interfaces. (a)–(d) are for Fe-MTJs and (e)–(h) are for CoFe-MTJs.

Figure 5

(a) FM1 thickness dependence of the IEC in perfect Vac/FM1($n$ ML)$/\mathrm{MgO}/\mathrm{FM}2$ MTJs with four combinations of Fe and CoFe alloy as FM1 and FM2 materials. (b) Energy-resolved IEC $Y$ [in Eq. (5)] for Vac/FM1(1 ML)$/\mathrm{MgO}/\mathrm{FM}2$ junction. (c) $k_{\left|\right|}$-resolved IEC (in unit of ${\mathrm{erg}/\mathrm{cm}}^2$) through Vac/FM1(1 ML)$/\mathrm{MgO}/\mathrm{FM}2$ MTJs.

Figure 6

Energy-resolved $\mathrm{\Delta }Y$ IEC difference between MTJs with one layer FM1 and semi-infinite FM1 layers. (Inset) $k_{\left|\right|}$-resolved IEC difference in the 2D BZ.

Figure 7

IEC dependence on the surface roughness in Vac/${\mathrm{Fe}}_{1-x}{\mathrm{Va}}_x$(1 ML)/MgO(3 ML)/FM2 MTJs, black-square line for FM2=Fe and red-circle line for FM2=CoFe.

Figure 8

IEC dependence on the thickness of FM1=Fe for MTJs with different concentrations of interfacial disordered OVs: (a) is for MTJs with FM2=CoFe and (b) is for MTJs with FM2= Fe.