Electric-field-induced modulation of giant perpendicular magnetic anisotropy obtained by insertion of an Ir layer at the Fe/MgO interface: a first-principles study

Voltage-torque magnetoresistive random access memory, ^1–10) in which the magnetocrystalline anisotropy (MA) is controlled by an external electric-field, is attracting increasing interest for the realization of the storage devices with both high-density and low-power consumption. ^11–17) The MA is an important physical property that determines the memory retention of the MRAM, and the retention time increases exponentially with the increase of the MA energy (MAE). On the other hand, the energy required to write an information bit increases as the MAE increases. Therefore, in order to achieve high-density and low-power consumption of the MRAM, it is necessary to develop ferromagnetic thin films that have large MAE and whose MA can be controlled by applying an electric-field. ^18,19)

In the voltage-controlled MA (VCMA) of thin films, it is important to control the spin-orbit coupling (SOC) of the magnetic layer. For the magnetic tunnel junctions (MTJs) with the Fe/MgO(001) interface, the perpendicular MA (PMA) due to the hybridization between Fe d- and O p-orbitals at the interface ^20–22) is an important tool for the success of perpendicular MTJ devices. ¹⁶⁾ However, the strength of the SOC is weak in 3d transition-metals, and the MAE is generally limited to a few mJ m^{− 2} or less even in ultra-thin films. ²³⁾ One of the solutions is to employ elements with large SOC in the magnetic layer at the interface. Recent experiments and first-principles calculations have reported that the insertion of heavy-metal elements at the Fe/MgO interface improves the MAE and the VCMA coefficients. ^7,24,25) On the other hand, the thin films with the large MAE often exhibit in-plane MA (IMA). It is necessary to design the insertion layers that can provide large PMA and large VCMA coefficients.

In this paper, we investigated the effect of the insertion of magnetic layers composed of 3d, 4d, and 5d elements at the Fe/MgO interface on the MAE and its modulation by an external electric-field by using first-principles calculations. The results indicate that the insertion of an Ir layer on the MgO substrate increases the MAE. In particular, we found that the insertion of a Fe/Co/Ir magnetic layer leads to a large PMA. The largest PMA and the largest VCMA coefficient is obtained for the Au/Fe/Co/Ir/MgO system.

The calculations are carried out using the film full-potential linearized augmented plane-wave (FLAPW) method. ^20,26) This method deals with a single slab geometry, which can naturally contain an external electric-field, F. The corresponding electrostatic potential along the surface normal (z-axis) is given by Fz, where z is the position of the z-axis. This term is expanded to the interstitial, the muffin-tin (MT) sphere, and the vacuum regions. ¹³⁾ This electrostatic potential is included self-consistently in the generalized gradient approximation ²⁷⁾ and the scalar relativistic approximation (SRA). LAPW functions with a cutoff of ∣k + G ∣ ≤ 3.9 a.u. and MT sphere radii of 2.30, 2.40, and 2.45 a.u. are used for the 3d, 4d, and 5d elements. The angular momentum wave function, charge density, spin density, and potential were expanded by truncating at l = 8. To determine the MAE, the second variational method ²⁸⁾ for treating the SOC is performed by using the calculated eigenvectors in the SRA. The MAE is determined by the force theorem, ²⁹⁾ which is defined as the energy difference for between the magnetizations oriented along the in-plane (100) and the out-of-plane (001) directions.

The calculated model of the atomic structure is shown in Fig. 1(a), where the magnetic layers are stacked in the order of the first transition-metal layer (TM1), the second transition-metal layer (TM2), and the three Fe layers on MgO(001) substrate. The three Au layers are employed as the cap layer. The TM1 and TM2 are substituted for the 3d elements (Fe, Co), 4d elements (Ru, Rh), and 5d elements (Os, Ir). The in-plane lattice constant is fixed at 2.86 Å, which is the experimental value of the bulk Fe. The F is applied along the out-of-plane direction. The direction of the positive F is from top to bottom, as indicated by the gray arrow. The atomic positions in the out-of-plane direction are fully optimized by the atomic-force FLAPW calculation. ³⁰⁾

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Figure 1(b) shows the calculated MAEs for Au/Fe/TM2/TM1/MgO system. The calculated results show that a model with TM1 = Ir and TM2 = Co has the largest PMA. This MAE is 28.18 mJ m⁻², which is about 70 times larger than that for the pure Fe films. In the case of TM1 = Ir, the PMA is observed when TM2 is group 9 elements. On the other hand, the IMA is observed when TM2 is group 8 elements. The magnitude of the MAE decreases in the order of 3d elements > 4d elements > 5d elements in TM2.

Next, we analyzed in detail the MAEs for the Co-system (TM1 = Ir, TM2 = Co), which has a large PMA, and the Fe-system (TM1 = Ir, TM2 = Fe), which has a large IMA. Figure 2 shows the calculated results of the MAE and the spin magnetic moment of the Ir atom in the TM1 layer. The atomic positions were adopted from the results of atomic relaxation in the Au/Fe/TM2/TM1/MgO system. First, we found that a single Ir layer on the MgO substrate has a large positive MAE. In this case, the spin magnetic moment of the Ir atom is calculated as 1.26 μ_B , indicating that Ir is spin-polarized. Here, for Ir/MgO, we confirmed the stability of the ferromagnetic ordering of the magnetic moment of Ir atoms. The calculated results predict that the ferromagnetic ordering of neighboring pairs is 154.6 mJ m⁻² more stable than the anti-ferromagnetic ordering. When Ir/MgO is stacked with a magnetic layer (Co or Fe), the MAEs are drastically reduced. In contrast, there is a difference in the magnitude of the decrease in MAEs for Co/Ir/MgO and Fe/Ir/MgO, i.e. the decrease is smaller in the Co-system than in the Fe-system. In the Co-system the MAE increases to a large positive value when the Fe layers are stacked, while the negative MAE is retained in the Fe-system. From these results, we can see that the coupling of Fe–Co–Ir–MgO is a key factor for a large PMA. Focusing on the spin magnetic moment of the Ir atom, the change in the MAE and the spin magnetic moment show similar behavior when the magnetic layers are stacked one after another. This result predicts that there is a direct relationship between the magnitude of the MAE and the spin magnetic moment of the Ir atom.

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Figure 3 shows the calculated density of states (DOS) of Ir d-orbitals for Ir/MgO, Co-, and Fe-systems. Compared to the DOS for Ir/MgO with a large PMA, the DOS for Co-system is more similar to that for Fe-system. In the case of the Ir/MgO and Co-system, the majority-spin is almost fully occupied, whereas for the Fe-system there is a peak of majority-spin at the Fermi energy (E_F). This is because the Co atom has one more valence electron than the Fe atom, which shifts the peak of majority-spin to the valence band in the Co-system. Here, we calculated the MAEs acting between each spin (majority–majority, majority–minority, and minority–minority spin) in the Co- and Fe-systems. In both systems, the MAE between the minority–minority spin is 3.8 mJ m⁻², indicating a small PMA. On the other hand, the MAE between majority–minority spin is 41.3 mJ m⁻² (a large PMA) in the Co-system, which is about 3.3 times larger than that in the Fe-system, and the MAE between majority–majority spin is −45.4 mJ m⁻² (a large IMA) in the Fe-system, which is about 3.3 times larger than that in the Co-system. This result indicates that the appearance of majority spin peak at E_F in the Fe-system mainly contributes of the IMA.

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Finally, we calculated the MAEs and the spin magnetic moments of the Ir atom for the Co- and Fe-systems when an external electric-field of F is varied from −8 to 8 V nm⁻¹. Figure 4 shows the calculated results of the modulation in the MAE and the spin magnetic moment of the Ir atom with respect to the application of the F. The zero on the vertical axis is the reference value of the MAEs (spin magnetic moments) at F = 0 V nm⁻¹. The VCMA coefficients for the Co- and Fe-systems are −189.71 and −118.57 fJ Vm⁻¹, and that for the Co-system is about 7.1 times larger than that for the pure Fe films. The calculated results indicate that there are a positive correlation between the modulation in MAE and spin magnetic moment of Ir atom by applying the F. In addition, the VCMA coefficients are calculated for the model of TM2 = group 8 elements (the Au/Fe/Rh/Ir/MgO and Au/Fe/Ir/Ir/MgO systems) with a PMA, and these coefficients are −103.17 and −111.54 fJ Vm⁻¹. These results indicate that the Au/Fe/Co/Ir/MgO system has the largest PMA and the largest VCMA coefficient. We turn our attention to the modulation in the spin magnetic moment of the Ir atom when the F is applied. The magnitude of this change is 5.2, 0.73, and 2.1 × 10⁻² μ_B for the TM2 = Co, Rh, and Ir in TM1 = Ir, respectively. The change in the modulation MAE due to the application of the F corresponds to the magnitude in the induced spin magnetic moment of the Ir atom.

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In summary, we study the effect of the insertion of magnetic layers composed of 3d, 4d, and 5d elements at the Fe/MgO interface on MAE and its modulation by an external electric-field. The largest PMA and the largest VCMA coefficient obtained by the insertion of a Fe/Co/Ir magnetic layer are 28.18 mJ m⁻² and −189.71 fJ Vm⁻¹, which are larger than those for the pure Fe films by a factor of 70 and 7.1, respectively. It is also found that the modulation of the MAE by applying an electric-field has a positive correlation with the magnitude of the induced spin magnetic moment of the Ir atom. The results evidently suggest that the Fe/Co/Ir magnetic layer is promising for realizing high-density and low-power MRAMs.