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Register a new userUnveiling temperature dependence mechanisms of perpendicular magnetic anisotropy at Fe/MgO interfaces
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The perpendicular magnetic anisotropy (PMA) at magnetic transition metal/oxide interfaces is a key element in building out-of-plane magnetized magnetic tunnel junctions for spin-transfer-torque magnetic random access memory (STT-MRAM). Size downscaling renders magnetic properties more sensitive to thermal effects. Thus, understanding temperature dependence of magnetic anisotropy becomes crucial. In this work, we theoretically address the correlation between temperature dependence of PMA and magnetization in typical Fe/MgO-based structures. In particular, the possible mechanisms behind experimentally reported deviations from the Callen and Callen scaling power law are analyzed. First-principles calculations reveal small high-order anisotropy terms ruling out an intrinsic microscopic mechanism underlying those deviations. Neglecting higher-order anisotropy terms in the atomisitic spin Hamiltonian, two possible extrinsic macroscopic mechanisms are unveiled: influence of the dead layer, always present in storage layer of STT-MRAM cells, and spatial inhomogeneities of interfacial magnetic anisotropy. We show that presence of a dead layer simultaneously with scaling the anisotropy constant by the total magnetization of the sample rather than that of the interface itself lead to low scaling powers. In the second mechanism, increasing the percentage of inhomogeneity in the interfacial PMA is revealed to decrease the scaling power. Apart from those different mechanisms, the layer-resolved temperature-dependence of PMA is shown to ideally follow the Callen and Callen scaling power law for each individual Fe layer. These results allow coherently explaining the difference in scaling powers relating anisotropy and magnetization thermal variations reported in earlier experiments. This is crucial for the understanding of the thermal stability of the storage layer magnetization in STT-MRAM applications.
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A characteristic dependence of voltage control of perpendicular magnetic anisotropy (VCMA) on oxygen migration at Fe/MgO interfaces was revealed by performing systematic {it ab initio} study of the energetics of the oxygen path around the interface. We find that the surface anisotropy energy exhibits a Boltzmann sigmoidal behavior as a function of the migrated O-atoms concentration. The obtained variation of the VCMA efficiency factor $beta$ reveals a saturation limit beyond a critical concentration of migrated O, about $54%$, at which the anisotropy switches from perpendicular to in plane. Furthermore, depending on the range of variation of the applied voltage, two regimes associated with reversible or irreversible ions displacement are predicted to occur, yielding different VCMA response. According to our findings, one can distinguish from the order of magnitude of $beta$ the VCMA driving mechanism: an effect of several tens of fJ/(V.m) is likely associated to charge-mediated effect combined with slight reversible oxygen displacements whereas an effect of the order of thousands of fJ/(V.m) is more likely associated with irreversible oxygen ionic migration.
Using first-principles calculations, we investigated the impact of chromium (Cr) and vanadium (V) impurities on the magnetic anisotropy and spin polarization in Fe/MgO magnetic tunnel junctions. It is demonstrated using layer resolved anisotropy calculation technique, that while the impurity near the interface has a drastic effect in decreasing the perpendicular magnetic anisotropy (PMA), its position within the bulk allows maintaining high surface PMA. Moreover, the effective magnetic anisotropy has a strong tendency to go from in-plane to out-of-plane character as a function of Cr and V concentration favoring out-of-plane magnetization direction for ~1.5 nm thick Fe layers at impurity concentrations above 20 %. At the same time, spin polarization is not affected and even enhanced in most situations favoring an increase of tunnel magnetoresistance (TMR) values.
Using first-principles calculations, we elucidate microscopic mechanisms of perpendicular magnetic anisotropy (PMA)in Fe/MgO magnetic tunnel junctions through evaluation of orbital and layer resolved contributions into the total anisotropy value. It is demonstrated that the origin of the large PMA values is far beyond simply considering the hybridization between Fe-3d$ and O-2p orbitals at the interface between the metal and the insulator. On-site projected analysis show that the anisotropy energy is not localized at the interface but it rather propagates into the bulk showing an attenuating oscillatory behavior which depends on orbital character of contributing states and interfacial conditions. Furthermore, it is found in most situations that states with $d_{yz(xz)}$ and $d_{z^2}$ character tend always to maintain the PMA while those with $d_{xy}$ and $d_{x^2-y^2}$ character tend to favor the in-plane anisotropy. It is also found that while MgO thickness has no influence on PMA, the calculated perpendicular magnetic anisotropy oscillates as a function of Fe thickness with a period of 2ML and reaches a maximum value of 3.6 mJ/m$^2$.
The electric field effect on magnetic anisotropy was studied in an ultrathin Fe(001) monocrystalline layer sandwiched between Cr buffer and MgO tunnel barrier layers, mainly through post-annealing temperature and measurement temperature dependences. A large coefficient of the electric field effect of more than 200 fJ/Vm was observed in the negative range of electric field, as well as an areal energy density of perpendicular magnetic anisotropy (PMA) of around 600 uJ/m2. More interestingly, nonlinear behavior, giving rise to a local minimum around +100 mV/nm, was observed in the electric field dependence of magnetic anisotropy, being independent of the post-annealing and measurement temperatures. The insensitivity to both the interface conditions and the temperature of the system suggests that the nonlinear behavior is attributed to an intrinsic origin such as an inherent electronic structure in the Fe/MgO interface. The present study can contribute to the progress in theoretical studies, such as ab initio calculations, on the mechanism of the electric field effect on PMA.
Magnetic tunnel junctions with perpendicular anisotropy form the basis of the spin-transfer torque magnetic random-access memory (STT-MRAM), which is non-volatile, fast, dense, and has quasi-infinite write endurance and low power consumption. Based on density functional theory (DFT) calculations, we propose an alternative design of magnetic tunnel junctions comprising Fe(n)Co(m)Fe(n)/MgO storage layers with greatly enhanced perpendicular magnetic anisotropy (PMA) up to several mJ/m2, leveraging the interfacial perpendicular anisotropy of Fe/MgO along with a stress-induced bulk PMA discovered within bcc Co. This giant enhancement dominates the demagnetizing energy when increasing the film thickness. The tunneling magnetoresistance (TMR) estimated from the Julliere model is comparable with that of the pure Fe/MgO case. We discuss the advantages and pitfalls of a real-life fabrication of the structure and propose the Fe(3ML)Co(4ML)Fe(3ML) as a storage layer for MgO-based STT-MRAM cells. The large PMA in strained bcc Co is explained in the framework of Brunos model by the MgO-imposed strain and consequent changes in the energies of dyz and dz2 minority-spin bands.
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