Ab initio prediction of giant perpendicular magnetic anisotropy at Fe/ CuIn1-xGaxSe2 interface

Perpendicular magnetic anisotropy (PMA) at the interface between ferro-magnetic and barrier layers is an essential property in magnetic tunnel junctions (MTJs) to realize sufficient thermal stability and low critical current in non-volatile spin transfer torque magnetic random access memories (STT-MRAMs) [1]. The PMA is also advantageous for reducing write error rates in voltage-controlled MRAMs [2].Therefore, it is of importance to find heterostructures which give rise to stronger interfacial PMA. Up to now, strong interfacial PMA has been observed in heterostructures consisting of ferromagnets (FMs) and insulator MgO. Ikeda et al. obtained a large interfacial anisotropy constant $K_{i}$ of $\sim 1.3$ mJ/m² at the interface of CoFeB/ MgO [3]. In a subsequent work, Koo et al. observed higher interfacial PMA with $K_{i} \sim 2.0$ mJ/m² in Fe/MgO [4]. However, no previous studies have reported such strong interfacial PMA on heterostructures with non-MgO barrier layers. Recently, Kasai et al. succeeded in fabricating novel MTJs where semiconductor CuIn0.8 Ga0.2 Se2(CIGS) is sandwiched between ferro- magnetic Heusler alloys [5]. They observed both high magnetoresistance (MR) ratios and low resistance-area products $(RA)$, which are also required for MRAM and hard disk drive (HDD) applications. In particular, when we consider the application of this MTJ to STT-MRAM cells, the possibility of obtaining high interfacial PMA should be investigated; however, no theo- retical and experimental studies have focused on this issue. In this work, we theoretically studied interfacial magnetocrystalline anisotropies in various Fe/semiconductor(001) heterostructures including Fe/CuIn $_{1- {x}}$ Gax Se $_{2}(001)$. As semiconductor barriers, 14 types of semiconductors were considered in the present study (see Fig. 1 for details). We calculated values of $K_{i}$ in these heterostructures by means of first-principles calculations based on densi- ty-functional theory, which is implemented in the Vienna ab initio simulation program (VASP). We first prepared supercells composed of 7 layers of Fe and 17 layers of the semiconductor barrier. Since quite thin Fe electrodes are used in experiments on PMA, we fixed the in-plane lattice constant of each supercell to the experimental lattice constant of the barrier. In all the supercells, we confirmed that Se, S, or As layer is energetically favored as the termination layer of the semiconductor barrier. In addition, all the atomic positions and the distance between ferromagnetic and barrier layers were optimized so that the total energy of the supercell is minimized. The values of $K_{i}$ were calculated using the force theorem as $K_{i} \quad = ( E_{[{100}]}- E_{[{001}]})/ 2 S$, where $E_{[{100}]} ( E_{[{001}]})$ is the sum of the eigenenergies of the supercell for the magne- tization along the [100] ([1]) direction, S is the cross-sectional area of the supercell, and the factor 2 reflects the fact that two interfaces are included in the supercell. From this definition, a positive (negative $) K_{i}$ shows the tendency toward perpendicular (in-plane) magnetic anisotropy. We used $10 \times 10 \times 1\mathrm {k}$ points to calculate total energies of the heterostructures with chalcopyrite semiconductors. We used more k points for other heterostruc- tures owing to their smaller supercell sizes. Figure 1 shows the values of $K_{i}$ obtained for various Fe/semiconductor systems. For comparison, we also show $K_{i}$ for Fe/MgO(001) with a similar barrier thickness. It is found that most of the Fe/semiconductor systems investigated in this study have posi- tive $K_{i}$. Particularly, Fe/CuInSe2 has the largest $K_{i}$ of 2.305 mJ/m², which is about 1.6 times as large as that of Fe/MgO (1.396 mJ$/ \mathrm {m}^{2})$. In Fig. 1, we also show the values of anisotropy of orbital magnetic moment $\otimes M_{orb,i}$ at interfacial Fe atoms. By comparing $K_{i}$ and $\otimes M_{orb,i}$, we see that Bruno's rela- tion $(K_{i}$”$\otimes M_{orb,i})$ holds for almost all the systems considered in this study. This implies that the interfacial PMA in the present systems comes from the structure of the minority-spin local density of states (LDOS) of interfacial Fe atoms [6]. Figure 2 shows the projected $d -$orbital LDOSs of interfacial Fe atoms in Fe/CuInSe2. We find some sharp peaks in the minority-spin LDOSs both just above and just below $E_{F}$, which enable excitations with quite small energies. In addition, these peaks have favorable $d -$orbital components for yielding large PMA [6]. These features are consistent with the largest $K_{i}$ in Fe/CuInSe2. Furthermore, we revealed that the positions of Se atoms at the interface is the key for such favorable $d -$orbital components in the LDOSs [6]. In summary, using ab initio calculations, we predict the largest $K_{i}$ of 2.305 mJ/m² for Fe/CuInSe2, which is about 1.6 times as large as that of Fe/ MgO (1.396 mJ$/ \mathrm {m}^{2})$. Thus, Fe/CuInSe $_{2} /$Fe MTJ may be suitable for application as perpendicular MTJ for high capacity MRAM application with a small cell size. This work was partly supported by Grant-in-Aids for Scientific Research (S) (Grant No. 16H06332) and (B) (Grant No. 16H03852) from the Ministry of Education, Culture, Sports, Science and Technology, Japan, by NIMS MI2I, and also by the ImPACT Program of Council for Science, Technology and Innovation, Japan.