Multiple magnetoelectric coupling effect in BaTiO3/Sr2CoMoO6 heterostructures

Due to the demand of controlling magnetism by electric fields for future storage devices, materials with magnetoelectric coupling are of great interests. Based on first-principles calculations, we study the electronic and magnetic properties of a double perovskite Sr2CoMoO6 (SCMO) in a hybrid heterostructure combined with BaTiO3 (BTO) in different polarization states. The calculations show that by introducing ferroelectric state in BTO, SCMO transforms from an antiferromagnetic semiconductor to a half-metal. Specially, altering the polarization direction not only controls the interfacial magnetic moment, but also changes the orbital occupancy of the Co-3d state. This novel multiple magnetoelectric coupling opens possibilities for designing new type of spintronic and microelectronic devices with controllable degree of freedom of interfacial electrons in the heterostructures.

The orbital degree of freedom plays an important role in electronic structure and magnetic ordering and hence has a significant effect on physical properties 26,27 . Usually, the orbital occupancy and shape can be modulated through introducing strain, but it is hardly controllable and inevitably introduces defects to materials. Very recently, Song et al. found in their experiment that the interfacial orbital occupancy can be partially changed under electric field in BaTiO 3 /La 2/3 Sr 1/3 MnO 3 multiferroic heterostructures 28,29 , providing an orbital mediated new ME coupling mechanism. However, theoretical study on this new type of ME coupling is rare, and new materials with better performance are vital for future applications.
In this paper, by means of first-principles calculations, we have studied three types of multiferroic heterostructures composed by ferroelectric material BaTiO 3 (BTO) and antiferromagnetic (AFM) double perovskite Sr 2 CoMoO 6 (SCMO) with different BTO polarization states. SCMO has a conventional double perovskite structure: the alternated CoO 6 and MoO 6 octahedrons with opposite rotations along [001] are arranged as a checkerboard configuration. Its antiferromagnetic order is along [101] direction and the Neel temperature is about 34 K 30, 31 . When introducing electric polarization in the BTO-SCMO heterostructure, SCMO transforms from AFM semiconductor to a ferromagnetic (FM) half metal. Via changing the direction of the dipole moments in BTO, a considerable variation of interfacial magnetization has been achieved, corresponding to a strong ME coupling. Particularly, we find that the orbital occupancy of interfacial Co 2+ ions can also be controlled by the polarization. This new degree of freedom of interfacial electrons together with magnetism, conductivity and spin polarization, are all coupled with the electric polarization, leading to a multiple ME coupling effect. We believe that such coupling opens new perspectives in applications of composite multiferroic heterostructures for magnetic storage, microelectronic and spintronic devices.

Results
As shown in Fig. 1, three types of BTO-SCMO-BTO slab structures have been built along the c-direction with different BTO polarization states: Nonpolar system (NP) ( Fig. 1 (b)); Type 1 polar system (P1) (Fig. 1 (c)) and Type 2 polar system (P2) ( Fig. 1 (d)). More details for the heterostructures building can be found in the supplementary material (SM). We have calculated the total energy of ferromagnetic (FM) and antiferromagnetic (AFM) solutions in bulk SCMO and the configurations in Fig. 1. The energy difference between the two magnetic states ΔE AFM−FM and the magnetic moments of Co and Mo atoms in the ground states are shown in Table 1. ΔE AFM−FM is negative in bulk SCMO, indicating that AFM state is more stable than FM state. The magnetic moment M Co = 2.73 µ B and M Mo = 0.04 µ B for Co and Mo atoms, respectively, agreeing with previous experimental and theoretical studies [30][31][32][33] .
For NP heterostructure in Fig. 1(b), the ΔE AFM−FM and atomic magnetic moments on Co and Mo atoms are almost the same as in bulk SCMO, indicating that the SCMO slab is almost undisturbed and keeps the AFM state even in very thin film (~7.9 Å) and nonpolar BTO shows negligible effect on SCMO's magnetic state. An interesting phenomenon arises when BTO generates ferroelectric instability in the P1 and P2 configurations, in which both of them turn into FM states from the bulk AFM solution. A considerable change in the atomic magnetic moment is observed (See Table 1), resulting in a large magnetoelectric coupling. For P1 configuration, the magnetic moment of Co is slightly decreased (from 2.73 µ B to 2.69 µ B ), while M Mo varied from 0.05 µ B to −0.42 µ B , corresponding to a large change of about 0.47 µ B . On the contrary, in P2, M Co has a big change from 2.73 µ B to 3.10 µ B , while M Mo remains nearly zero as in NP system.
To understand the nature of the polarization induced magnetism change, we have calculated the electronic structure and provide the densities of states (DOS) of bulk SCMO and heterostructures of BTO-SCMO-BTO in Fig. 2 (a) and Fig. 2 (b)-(d) in their ground states, respectively. BTO is a large gapped (about 3.3 eV) semiconductor, it has little contribution to the electronic states near E F , so we only show the local DOS of atoms in SCMO; the local DOS from Sr atom is not shown in Fig. 2 for the same reason. For bulk SCMO in the AFM state ( Fig. 2(a)), we find that it is a semiconductor with a small gap of about 0.4 eV, the valence band maximum (VBM) is composed of Co-3d and O-2p electron states while the conduction band minimum (CBM) mainly contains Mo-4d and O-2p states. There is no big difference in the DOS between the NP configuration ( Fig. 2 (b)) and bulk SCMO, except that the band gap becomes ~0.1 eV larger in NP system. This is probably due to the quantum confinement in ultrathin films 34 . When polarization is induced in the P1 (Fig. 2(c)) and P2 (Fig. 2(d)), interestingly, both systems show half-metallic character where one spin channel (majority-spin) behaves like an insulator with a finite gap, while the other spin channel (minority-spin) has non-zero DOS at E F . The magnetic moment variation in  Mo and Co atom between different polar states can again be understood by comparing their DOS. As mentioned before, the CBM is mainly composed of Mo 4d electron states and system is semiconducting in NP. However, in P1, the minority spin of Mo CBM state is partially filled just below the E F , while the orbitals with majority spin are still unoccupied. Hence Mo produces a negative moment of −0.42 µ B . While in P2, the Mo CBM state is still unoccupied, therefore results in a nearly zero M Mo like in NP. For both P1 and P2 structures, the majority spin of Co is fully occupied while the minority spin only partially filled below the E F , such difference contributes to a net magnetic moment of about 3 µ B where a small part of minority states gets occupied in P1, giving rise to the decrease in M Co (See Table 1). However, the obvious increase of M Co from P1 to P2 seems to be related to the different configuration of Co minority spin state in P2 system. There is a big difference in Co states between P1 and P2 especially in minority-spin channel. The peak of Co states at −1.7 eV in P1 shifts upward to 0.6 eV in P2. Meanwhile, the sharp peak around 1.5 eV in P1 system disappears in P2. This phenomenon may come from a variation of orbital occupancy in Co minority-spin state, and we will analysis this phenomenon next.
We have calculated the projected density of state (PDOS) of the minority spin Co-3d electrons in NP (Fig. 3  (a)), P1 (Fig. 3 (b)) and P2 (Fig. 3 (c)). As Co ions are located in an octahedral coordination with the oxygen ions, the crystalline field causes an energy split between the t 2g and e g orbitals. For both NP and P1, the d xz and d yz orbitals (the red curves in Fig. 3), which belong to t 2g symmetry, are almost completely filled while the other three minority spin orbitals, d yz , d z 2 and − d x y 2 2 , are almost empty. This corresponds to an electron configuration of 3d 7 (t 2g 5 e g 2 ) that two t 2g electrons occupy the minority spin state. The E F in Fig. 3(b) crosses a small part of the Co CBM state and decreases the M Co , turning this system into half-metallic state. In P2 (Fig. 3c), however, the ordering of d xy and d xz /d yz orbitals is changed. The occupied states compose mostly of d xy orbital, and the d xz /d yz peak is pushed above E F . In this new electron configuration, less than 2 electrons are occupied in Co 3d minority spin state, while the majority-spin states are still fully filled, therefore the M Co is increased in P2.
There are two possible origins for the variation of orbital occupancy in Co 3d electrons from P1 to P2. The first one is due to the CoO 6 octahedral distortion and rotation. As shown in Fig. 4(a) 35 . In the P1 case, the electric dipole moment is pointing to the central SCMO (Fig. 4b), hence there are positive bound charges at the interfaces which attract electrons in d xz /d yz states and reduce the orbital energy. On the contrary, in the P2 case, negative bound charges will raise the energy of d xz /d yz states. The d xy orbital does not get much influence in this mechanism because it is located in the xy plane, away from the bound charges. As a result, the change in the Co-O octahedron structure and different interface bound charges together change the orbital occupation in P2.
The polarization induced half-metallic property may be responsible for the magnetism transition between the AFM and FM states. When SCMO turns into the half-metallic state due to the polarization from BTO, hopping interactions between the localized electrons and the conduction electrons cause a large spin splitting of the effective Mo d band 36,37 , resulting in a strong FM coupling between Co 2+ ions via the induced spin-polarized mobile  electrons. It has been proposed that the oxygen-deficient SCMO has a strong FM state (T C = 350 K to 370 K) with a dramatic increase of conductivity 32 . This is also clear evidence that conducting electrons may induce FM magnetic coupling between Co 2+ ions via the double-exchange mechanism in SCMO. Unfortunately, as the Neel temperature of SCMO is only about 34 K, it is therefore difficult to achieve the AFM−FM transition at room temperature. However, it is possible that double perovskites that have higher Neel temperature can be found through rational material design, and our approach provides a possible way to realize controllable AFM−FM transition though magnetoelectric coupling.
We have also tested a structure with thicker SCMO layers (1.5 u.c. SCMO + SrO) in P2 type of BTO polarization. We find that M Co equals to 3.06 µ B near the interface; while for the Co atom in the center of SCMO, M Co is reduced to 2.96 µ B , indicating that the moment near the interface is mostly affected. Furthermore, we perform a calculation of a new BTO-SCMO polar state where both BTO polarizations point to the same direction (see Fig. S5 in Supplementary material). The magnetic response near the interface resembles the characters in P1 and P2 depending on whether the BTO polarization pointing to or away from SCMO (more details can be found in Supplementary material). By switching electric fields between SCMO and BTO, one can change the polarization state between P1, P2 and this new polar state and thereby control the system magnetization. The resulting surface ME coefficient α s can be estimated by formula 38 μ 0 ΔM = α s E, where ΔM is the range of magnetization change, E is the strength of applied electric field and μ 0 is the vacuum permeability. Taking ΔM = 0.84 μ B /a 2 (a is the lattice constant of SCMO) and assuming the coercive field of BTO E c = 100 kV/cm, we obtain a ME coefficient α s ≈ 3.1 × 10 −10 Gcm 2 /V which is comparable to that in Fe/PbTiO 3 system as reported by Lee et al. 39 .
In summary, we have demonstrated multiple magnetoelectric effects in the BTO/SCMO/BTO heterostructures based on first-principles calculations. It is shown that the polarization state in BTO can be used to tailor the magnetic ground state, interfacial magnetic moments and conductivity of SCMO. More importantly, switching polarization direction changes the orbital occupancy of the Co-3d states drastically, which is originated from the distortion of the CoO 6 octahedron in addition to the bound charges at the interface. Our results not only provide a novel ME system with tunable multiple magnetoelectric effects, but also present a broad opportunity to realize applications of orbital degree of freedom in spintronic and microelectronic devices.

Methods
We have performed first-principles calculations of the electronic structures for three different BaTiO 3 /Sr 2 CoMoO 6 [001] multilayer heterostructures (Fig. 1) using the Vienna Ab initio Simulation Package (VASP) 40,41 with the projector augmented wave (PAW) method generated pseudopotentials 42,43 . For all types of multilayers, a vacuum layer of 15 Å were used with a BaO surface termination as shown in Fig. 1. BTO layers close to the vacuum are fixed to their bulk positions and are more than 1 nm away from the BTO-SCMO interface. We have tested that the effects from such artificial surface states are negligible. The in-plane lattice constants are fixed to the experimental value of the bulk SCMO (5.565 Å) 30 which is slightly smaller than 2 times of BaTiO 3 's lattice (3.991 Å in experiment) 44 , the induced compressive strain in BTO can therefore suppress the in-plane ferroelectricity instability 45 . Several optimizing processes have been made to eliminate possible artificial strains along c-direction. Details about the BTO-SCMO interface construction are shown in the supplementary material (SM). The convergence criterion was set to 10 −5 eV for the self-consistent electronic minimization and 0.03 eV/Å for forces during the ionic relaxations. Since Co has 3d valence electrons, the on-site Coulomb interaction has been taken into account by using the LSDA+U approach 46 . We have used U = 5.0 eV and J = 0.89 eV for Co atom because they well reproduced the AFM semiconductor state in SCMO 33 . After careful convergence tests, we have chosen a cutoff energy of 530 eV for the plane wave basis and a k-mesh grid of 13 × 13 × 1 for Brillouin zone sampling. The tetrahedron method was used for the Brillouin zone integration. More calculation details can be found in the supplementary material (SM).