Prediction of large magnetoelectric coupling in Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ junctions from a first-principles study

Abstract

The magnetoelectric (ME) effects of Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ junctions are investigated using first-principles calculations. Compared with the very weak ME coupling effects for FeN/TiO₂ interfaces in both Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ junctions, the large ME coefficients are achieved at the more stable Fe₂/TiO₂ interface in the Fe₄N/BaTiO₃ junction and the more stable MnFe/TiO₂ and Mn₂/TiO₂ interfaces in the MnFe₃N/BaTiO₃ junction. The magnetoelectric effect originates from the interface bonding mechanism which alters the chemical bonding and the hybridization at the interface when the electric polarization reverses. In addition, from the detailed analysis, we find that the interfacial Fe^II(Mn^II) (the face-centered sites Fe or Mn in Fe₄N and MnFe₃N) atom plays a more important role in the ME coupling than the interfacial Fe^I(Mn^I) (the corner sites Fe or Mn in Fe₄N and MnFe₃N) atom. These results suggest that Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ junctions could be designed as multiferroic materials with large magnetoelectric coupling under their more stable interfaces. And the magnetic Mn-substitution doping at the interfacial Fe^II position in the Fe₄N/BaTiO₃ junction can possibly obtain a relatively large ME coefficient difference compared with doping at the interfacial Fe^I position.

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1. Introduction

The coupling between ferroelectric and ferromagnetic components in the heterostructures has recently been attracting great scientific and technological research interest.^1–7 A strong ME effect^8–11 allows magnetic control of ferroelectric properties and electric control of magnetic properties. There are two types of magnetoelectric coupling.^12–14 An intrinsic ME coupling may be observed in single phase compounds if time reversal and space inversion symmetries are broken. But the magnetoelectric coupling in single phase compounds is usually very weak at room temperature,¹ which restricts their practical applications in multifunctional devices. Therefore, much efforts have focused on extrinsic ME coupling through artificial multiferroic heterostructures, such as ferroelectric (FE)/ferromagnetic (FM) interfaces.^15–17 In addition to the common way to engineer ME coupling through strain,¹⁸ interface bonding and the spin-dependent screening mechanisms are other two important extrinsic coupling mechanisms. In the interface bonding mechanism, the interfacial atomic displacements change when polarization is reversed, which alters the chemical bondings and the orbital hybridizations at the interface, and hence affecting the interface magnetization. It is predicted that this effect plays an important role in the ME effect at many interfaces, such as Fe/BaTiO₃, Co₂MnSi/BaTiO₃, Fe₃O₄/BaTiO₃, Co₂FeAl/BaTiO₃, etc.^5,19–24 In the spin-dependent screening mechanism, the magnetic response is mediated by the accumulation of spin-polarized carriers at the interface between the FM/FE phases, such as, La_1−xSr_xMnO₃/BaTiO₃, SrRuO₃/BaTiO₃, etc.^25–28 Besides, a large ME coupling effect can also be obtained at an asymmetric FM/FE junction.^29–32 Experimentally, the artificial multiferroic heterostructures have been fabricated by the ferroelectrics and ferromagnets.^33,34

Here, we present Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ layered nanostructure as FM/FE junctions showing a remarkable ME effect. For Fe₄N, there are two types of Fe atoms, which occupy the corner (Fe^I) and face-centered (Fe^II) sites, respectively, and a N atom locates at the body-centered position. This substance could be considered an attractive candidate as a spin injection electrode in magnetic tunnel junctions because of its excellent properties, namely: high magnetic moments (9.84 μ_B) per formula unit (f.u.),³⁵ high chemical stability, low coercivity, a high Curie temperature (761 K) and a high spin polarization of almost −100%.^36,37 Meanwhile, BaTiO₃ is a prototypical ferroelectric material. So far, although the magnetic properties of Fe₄N/BaTiO₃ interface has already been studied under first-principles calculations,³⁸ the magnetoelectric coupling in Fe₄N/BaTiO₃ junction has never been studied.

In addition, Monachesi et al. have calculated the magnetic properties of Mn, Co, and Ni substituted Fe₄N from first-principles theory with a GGA scheme recently. They have reported that Mn-substitution doping at the cubic corner Fe^I position is possibly the only doping process that can further enhance the magnetic moment of Fe₄N, but it is an energetically unfavorable case.³⁵ However, Wu et al. have shown that this structure is the ground state of MnFe₃N using a GGA+U scheme,³⁹ which is consistent with the results from recent Mössbauer and X-ray diffraction studies which showed that Mn mainly occupies the cubic corner position in MnFe₃N,⁴⁰ which is the structure we considered in this study.

In the present paper, we investigate and compare the ME effects in Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ junctions based on density functional theory. Two interfaces of Fe₄N/BaTiO₃ junction (FeN/TiO₂ and Fe₂/TiO₂) and three interfaces of MnFe₃N/BaTiO₃ junction (FeN/TiO₂, MnFe/TiO₂ and Mn₂/TiO₂) are considered. Interfacial separation work reveals that the Fe₂/TiO₂ interface is more stable than the FeN/TiO₂ interface in Fe₄N/BaTiO₃ junction, and the MnFe/TiO₂ and Mn₂/TiO₂ interfaces are more stable than the FeN/TiO₂ interface in MnFe₃N/BaTiO₃ junctions. In addition, for FeN/TiO₂ interfaces in both Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ junctions, the ME coupling effects are very weak. But the large ME coefficients are achieved for the other three interfaces. Comparing with the Fe₂/TiO₂ interface at Fe₄N/BaTiO₃ junction, when the interfacial cubic corner Fe^I atom is replaced by Mn^I atom, a small change of ME coefficient is achieved for MnFe/TiO₂ interface at MnFe₃N/BaTiO₃ junction. But when the interfacial face-centered Fe^II atom is replaced by Mn^II atom, a large ME coefficient difference is achieved for Mn₂/TiO₂ interface at MnFe₃N/BaTiO₃ junction. From the detailed analysis of electronic DOS and the spin density difference, we find it is due to the strong hybridizations between the interfacial Fe^II(Mn^II) and Ti atoms compared with the hybridizations between interfacial Fe^I(Mn^I) and Ti atoms for Fe₂/TiO₂(MnFe/TiO₂, Mn₂/TiO₂) interface.

2. Computational details

All the calculations are performed by using the density functional theory (DFT), as implemented in the Vienna Ab-initio Simulation Package (VASP).^41,42 The Perdew–Burke–Ernzerhof form⁴³ of generalized gradient approximation (GGA) for electron exchange and correlation is adopted. Based on a recent report,³⁹ a GGA+U scheme must be used for Fe₄N and MnFe₃N in order to obtain the correct structures and magnetic states. In this work, the effective Coulomb-exchange interaction U_eff = U − J is used, where U and J are the Coulomb part and the exchange part, respectively. We use U_eff = 2.0 eV for Mn atoms and U_eff = 0.4 eV for Fe atoms.³⁹ The plane wave functions are expanded with the energy cutoff of 500 eV. Atomic relaxations are performed using a 6 × 6 × 1 Monkhorst–Pack k-point mesh⁴⁴ and the atomic positions are converged until the Hellmann–Feynman force on each atom is less than 0.01 eV Å⁻¹. For subsequent electronic structure calculations, the grid is increased to 12 × 12 × 1.

The bulk Fe₄N and MnFe₃N are periodically stacked with BaTiO₃ (001) layers to simulation the [001]-oriented Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ junctions, respectively. The lattice mismatch between Fe₄N and BaTiO₃ is about 4.9% and the value between MnFe₃N and BaTiO₃ is about 3.6%. Here, we assume the epitaxial growth of the [001]-oriented Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ ultrathin bilayers are both on SrTiO₃ substrate, considering the small lattice mismatches and the recent experiments.^45,46 The in-plane lattice parameters of supercells are fixed to be that of the bulk SrTiO₃ (3.905 Å), while the out of plane lattice parameter is relaxed. For the BaTiO₃ slab, only TiO₂ termination is considered, because it is believed to be more stable than the BaO termination with magnetic materials.^5,47 Here, the initial Ti–O relative displacement along z orientation at each TiO₂ layer is artificially set to be 0.125 Å. In order to study the ME coupling's dependence on interface configuration, the FeN and Fe₂ terminations in the Fe₄N slab are simulated for Fe₄N/BaTiO₃ junction, meanwhile, the FeN, FeMn and its modified Mn₂ (replacing Fe with Mn) terminations in the MnFe₃N slab are simulated for MnFe₃N/BaTiO₃ junction. The symmetric structure allows us to discuss the effect of polarization reversal at left (right) interface by comparing properties of the two interfaces.

We assume the O atoms occupy atop sites on the M (M = Fe, Mn) atoms, which is considered to be the most stable structure in many previous first-principles studies^5,22,47 and experimental findings,^48,49 as shown in Fig. 1. And the ferroelectric polarization of BaTiO₃ is pointing rightward. The FeN/TiO₂ interface in MnFe₃N/BaTiO₃ junction is similar to Fig. 1a and not shown. Within the Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ supercells, the Fe₄N and MnFe₃N slabs are composed of 9 atomic layers, and the BaTiO₃ slab is composed of 13 atomic layers in our calculations. The most stable pattern among the different interfaces is determined by calculating the work of separation, which is defined as⁴⁷

W_sep = (E_FM + E_BaTiO3 − E_FM/BaTiO3)/2A

where E_FM/BaTiO3 is the total energy of the relaxed Fe₄N/BaTiO₃(MnFe₃N/BaTiO₃) junction, E_FM and E_BaTiO3 are the energies of the same supercell containing either the Fe₄N(MnFe₃N) or BaTiO₃ slabs, respectively. A represents the surface area of the interface. The factor 2 accounts for the two interfaces present in the supercell.

Fig. 1 The atomic structures of Fe₄N/BaTiO₃/Fe₄N junction with (a) FeN/TiO₂ and (b) Fe₂/TiO₂ interfaces and MnFe₃N/BaTiO₃/MnFe₃N junction with (c) MnFe/TiO₂ and (d) Mn₂/TiO₂ interfaces. The FE polarization is pointing rightward.

3. Results and discussion

3.1 The Fe₄N/BaTiO₃ junction

First, we examine the equilibrium geometry and the energetic stability of the Fe₄N/BaTiO₃ junction. The values of the interfacial separation work W_sep and the bond lengths for the left and right interfaces of FeN/TiO₂ and Fe₂/TiO₂ interfaces are presented in Table S1 (see ESI†). They both have a positive interfacial separation work, suggesting the formation of these interfaces is an exothermic process and thermodynamically stable. The calculated interfacial separation works are 2.075 and 3.263 J m⁻² for the FeN/TiO₂ and Fe₂/TiO₂ interfaces, respectively. It suggests that the Fe₂/TiO₂ interface is more stable. The large interfacial separation work is from the strong Fe^I–O, Fe^II–O and Fe^II–Ti ionic bonds with short bond lengths at both left and right interfaces for Fe₂/TiO₂ interface (see Table S1†).

Then, we focus on the ferroelectric properties of the Fe₄N/BaTiO₃ junction. The displacements of Ti atoms related to the O atoms within each BaTiO₃ layers are plotted in Fig. 2a. For both the Fe₂/TiO₂ and FeN/TiO₂ interfaces, the relative Ti–O displacements are all positive, although there is a significant difference between these two cases. In other words, every Ti atom is displaced in the same direction related to the O atom and there are overall net polarizations along the z orientation in the BaTiO₃ slabs for the two interfaces. In the FeN/TiO₂ interface, the relative Ti–O displacements at the central region of BaTiO₃ barrier are close to a constant 2.4 Å but decrease near the interface. This result is due to the effect of the depolarizing field.⁵⁰ The polarization, generated in the ferroelectric thin film by a polar pattern of atomic displacements, leads to surface charges of opposite sign at the interfaces with the electrodes. Then these charges are partially screened by the electrons in the metal, resulting in sizeable depolarizing. The depolarizing field reduces the amplitude of the spontaneous polarization and suppresses the ferroelectricity near the interface. However, in the Fe₂/TiO₂ interface, a larger Ti–O displacement over 0.255 Å is found at left interfacial TiO₂ layer and a smaller Ti–O displacement over 0.08 Å is found at the right one. Thus one of the Fe₂/TiO₂ interfaces enhances the overall polarization while the other one weakens it. The Ti–O displacements at the left interface layers are larger than the central region, which is because of the weaker Fe–TiO₂ interaction in the left interface. It is the typical characteristic of metal-oxide interfacial ferroelectricity.⁵¹ In ref. 51, the interface-specific effects of purely electronic screening and of interatomic force constants are both considered to assess the overall performance of the capacitor.

Fig. 2 The displacements of Ti atoms related to the O atoms within each BaTiO₃ layers in (a) Fe₄N/BaTiO₃ junction with FeN/TiO₂ and Fe₂/TiO₂ interfaces, and (b) MnFe₃N/BaTiO₃ junction with FeN/TiO₂, MnFe/TiO₂ and Mn₂/TiO₂ interfaces. The positive value denotes the ferroelectricity displacement of Ti atoms pointing to the right, which is the same as that in Fig. 1.

Next, the magnetic moments of the interfacial atoms for the Fe₄N/BaTiO₃ junction are listed in Table S2 (see ESI†). Ferroelectric displacements break the symmetry between the left and right terminations, which causes the magnetic moments of the interfacial atoms to deviate from their values in the paraelectric state. (i) In the FeN/TiO₂ interface, the magnetic moments of the interfacial Fe atoms are slightly enhanced compared with that in bulk, as reported in the Fe/BaTiO₃ and Fe₃O₄/BaTiO₃ heterostructures.^23,25 The Fe^III magnetic moment in secondary interface layer is smaller than that in bulk due to the enhanced hybridization with the nearest N, which is discussed in ref. 38. Because of the large distance between the Fe^II and Ti atoms (see Table S1†), the induced magnetic moments of Ti can be ignored. Considering the large magnetic moment change in the secondary interface layer, the magnetic moments of both the first interface and secondary interface layers are included to compute the interfacial magnetic moment difference. The total magnetic moment for the left interface is 10.703 μ_B and the value is 10.768 μ_B for the right interface. Therefore, the total magnetic moment difference is only 0.065 μ_B. (ii) In the Fe₂/TiO₂ interface, the magnetic moments in the secondary interface layer are changed very small, and the values are very close to those at the middle layer. For the first interface layer, the magnetic moment difference is Δμ_Fe = 0.406 μ_B for Fe atoms and Δμ_Ti = 0.382 μ_B for Ti atoms, leading to a large total interfacial magnetic moment difference Δμ = 0.834 μ_B per unit cell. It is different from the case of Fe/BaTiO₃ junction, in which the difference of magnetic moments between the two interfaces is mainly from the Δμ_Ti.⁵

According to previous works, the intensity of ME coupling can be characterized by the surface ME coefficient α_s, which is calculated by the following expression^5,25

α_s = μ₀ΔM/E

where ΔM is the difference of total magnetic moments between the left and right interfaces per unit cell. In the present paper, the atomic magnetic moments at the first and secondary interface layers are both considered. E is the coercive field of the BaTiO₃, and it is assumed to be E = E_C = 100 kV cm⁻¹. We obtain the surface ME coefficient α_s = 0.4 × 10⁻¹⁰ G cm² V⁻¹ for the FeN/TiO₂ interface and α_s = 5.5 × 10⁻¹⁰ G cm² V⁻¹ for the Fe₂/TiO₂ interface. It is obvious that the magnitude of α_s at the Fe₂/TiO₂ interface is much larger than that at the FeN/TiO₂ interface, and it is also larger than those at the Fe/BaTiO₃ (2.2 × 10⁻¹⁰ G cm² V⁻¹)⁵ and Fe₃O₄/BaTiO₃ (2.1 × 10⁻¹⁰ G cm² V⁻¹)²¹ interfaces. Thus, the magnetoelectric properties are studied only for Fe₂/TiO₂ interface in the following discussion.

The density of states (DOS) projected on d orbitals of Fe^I, Fe^II, and Ti atoms at the Fe₂/TiO₂ interface are plotted in Fig. 3. Due to the small change in the magnetic moments of the secondary interfacial atoms, we have only considered the first interface layer. It is clear that the Fe^I and Fe^II states are different, but the hybridizations with Ti atoms are similar. At the right interface, a remarkable hybridization between the Fe^I, Fe^II and Ti atoms is observed in the minority spin channel (highlighted by arrows). It induces a large occupation of Ti minority spin states, and causes a large negative magnetic moment on Ti atom (−0.45 μ_B). However, at the left interface, only a very weak hybridization is observed between Fe^I, Fe^II and Ti atoms in the minority spin channel near Fermi energy E_F, which induces a small magnetic moment on Ti atom (−0.068 μ_B). It is because the Fe–Ti distance at the left interface is much longer than that at the right interface (see Table S1†). Because of the weak hybridization between Fe 3d and O 2p states (not shown), the induced magnetic moments of the interfacial O atoms are relatively small.

Fig. 3 Orbital-resolved DOS for the left (solid lines) and right (dashed lines) interfacial atoms in the Fe₄N/BaTiO₃ junction with the Fe₂/TiO₂ interface. And the shaded areas correspond to the DOS of atoms in the bulk. Majority- and minority-spin DOS are plotted in the upper and lower panels. The Fermi energy is set to zero.

In order to further study the mechanism of magnetoelectric coupling and compare the effects of different positions of Fe atoms on the magnetoelectric coupling, the spin density difference on the (100) and (010) planes are shown in Fig. 4. The spin density difference is calculated by subtracting the spin density of freestanding Fe₄N and BaTiO₃ slabs from the total spin density in the Fe₄N/BaTiO₃ junction. (i) For both (100) and (010) planes, it is evident that the spin charge distributions of Ti atoms at right interface have the same shape of d_xz(d_yz) orbital as that of the Fe/BaTiO₃ junction.⁵ In Fe₄N/BaTiO₃ junction, the spin charge transfer from interfacial electrodes Fe atoms to Ti atoms via O atoms occupy the d orbital of Ti atoms. It is clear that the transfers at the right interface are much more than those at the left interface, so the spin charges gained by the right interfacial Ti atoms are far greater than the left interfacial Ti atoms. As a result, the larger magnetic moment of right interfacial Ti atom is induced with respect to that at left interface for the Fe₂/TiO₂ interface (Δμ_Ti = 0.382 μ_B). The symmetry of the magnetic properties is broken due to the structural asymmetry, which is because of the appearance of ferroelectricity in symmetry Fe₄N/BaTiO₃ junction. (ii) Comparing the spin density difference on (100) plane with (010) plane, it is found that the spin charge transfers between Fe^II and Ti atoms are more than those between Fe^I and Ti atoms for both the left and right interfaces. It gives rise to relatively strong hybridizations between interfacial Fe^II and Ti atoms with respect to the hybridizations between interfacial Fe^I and Ti atoms. It is because the Fe^II–Ti bond length is relatively smaller (2.867 Å for left interface; 2.628 Å for right interface) than the Fe^I–Ti bond length (2.987 Å for left interface; 2.745 Å for right interface). Therefore, the interfacial Fe^II atom is suggested to play a more important role in the ME coupling than the interfacial Fe^I atom.

Fig. 4 The spin density difference (in e Å⁻³) at the left and right interfaces for the Fe₂/TiO₂ termination in Fe₄N/BaTiO₃ tunnel junctions on (a) and (b) the (100) plane and (c) and (d) the (010) plane.

3.2 The MnFe₃N/BaTiO₃ junction

The values of the interfacial separation work W_sep of MnFe₃N/BaTiO₃ junction in J m⁻² are listed in Table S1† for the FeN/TiO₂, MnFe/TiO₂ and Mn₂/TiO₂ interfaces. They all have a positive interfacial separation work. The stability order is found to be FeN/TiO₂ < Mn₂/TiO₂ < MnFe/TiO₂, and the energetically favorable case is MnFe/TiO₂ interface. The large separation work W_sep 4.162 eV is from the strong Fe–O and Mn–O bonds (see Table S1†).

The ferroelectric properties of the MnFe₃N/BaTiO₃ junction are shown in Fig. 2b. There are overall net polarizations along the z orientation in the BaTiO₃ slab for these three interfaces, although the relative Ti–O displacement is negative at the right interface for the Mn₂/TiO₂ interface. Comparing Fig. 2b with 2a, it is apparent that the ferroelectric properties of the BaTiO₃ multilayer for the FeN/TiO₂ interface in MnFe₃N/BaTiO₃ and Fe₄N/BaTiO₃ junctions are very similar. And the same is true between the Mn₂/TiO₂ interface in MnFe₃N/BaTiO₃ junction and the Fe₂/TiO₂ interface in Fe₄N/BaTiO₃ junction.

The magnetic moments of the interfacial atoms for the FeN/TiO₂, MnFe/TiO₂ and Mn₂/TiO₂ interfaces are listed in Table S3 (see ESI†). For the FeN/TiO₂ interface, there is a large magnetic moment change in the secondary interface layer. But the total magnetic moment difference of the first and secondary interfacial layers is only 0.041 μ_B per unit cell, and the corresponding surface ME coefficient is very small (0.3 × 10⁻¹⁰ G cm² V⁻¹). The case is similar to the FeN/TiO₂ interface in Fe₄N/BaTiO₃ junction. For the MnFe/TiO₂ and Mn₂/TiO₂ interfaces, the change values of magnetic moment in the secondary interface layer can be neglected. Taking into account that Δμ = 0.892 μ_B for the MnFe/TiO₂ interface and Δμ = 0.65 μ_B for the Mn₂/TiO₂ interface, the corresponding surface ME coefficient is α_s = 5.9 × 10⁻¹⁰ G cm² V⁻¹ for the MnFe/TiO₂ interface and α_s = 4.3 × 10⁻¹⁰ G cm² V⁻¹ for the Mn₂/TiO₂ interface. They are both larger than those at the Fe/BaTiO₃ (ref. 5) and Fe₃O₄/BaTiO₃ (ref. 21) interfaces. Due to the small magnetoelectric coupling for FeN/TiO₂ interface, only the MnFe/TiO₂ and Mn₂/TiO₂ interfaces are considered in the following discussion.

The DOS of Mn^I 3d, Fe^II 3d, and Ti 3d orbitals at the MnFe/TiO₂ interface and Mn^I, Mn^II and Ti 3d orbitals at the Mn₂/TiO₂ interface are shown in Fig. 5. (i) For the MnFe/TiO₂ interface, at the right interface, a remarkable hybridization in the minority spin channel below the Fermi level is presented between the Fe^II 3d and Ti 3d states, as highlighted by the arrows in Fig. 5a. And the hybridization between the Mn^I 3d and Ti 3d states is also observed through the enlarged figure. At the left interface, only a very weak hybridization is observed between Mn^I, Fe^II and Ti atoms in the minority spin channel near the Fermi level. (ii) For the Mn₂/TiO₂ interface (see Fig. 5b), at the right interface, the hybridization between the Mn^I, Mn^II and Ti atoms is shown in the minority spin channel (the enlarged figure is similar to Fig. 5a and not shown). Although the hybrid peaks of Mn^I and Mn^II are very weak, they also induce a large antiparallel magnetic moment of −0.447 μ_B on the right interfacial Ti atom. It may be attributed to the peaks moving further toward the Fermi level compared with that in the MnFe/TiO₂ interface. At the left interface, no hybridization occurs between the Mn^I, Mn^II and Ti atoms. Thus, there is almost no induced magnetic moment on the left interfacial Ti atom. The changes of Mn^I and Mn^II states between the left and right interfaces are both very small. Especially the Mn^II state, the change is much smaller than that of the Fe^II states in Fig. 5a, which lead to a relatively small difference of the magnetic moment for Mn^II atom (see Table S3†). Therefore, the ME coupling in Mn₂/TiO₂ interface is weaker than that in the MnFe/TiO₂ interface.

Fig. 5 Orbital-resolved DOS for the left (solid lines) and right (dashed lines) interfacial atoms in the MnFe₃N/BaTiO₃ junction with the (a) MnFe/TiO₂ and (b) Mn₂/TiO₂ interfaces. And the shaded areas correspond to the DOS of atoms in the bulk. Majority- and minority-spin DOS are plotted in the upper and lower panels. The Fermi energy is set to zero. The illustration in figure (a) is the partial enlargement of DOS of Mn^I 3d orbitals.

Fig. 6 shows the spin density difference for the MnFe/TiO₂ and Mn₂/TiO₂ interfaces on the (100) plane. For both interfaces, the spin charge transfers between the Fe^II(Mn^II) and Ti atoms at the right interface are much more than the case of the left interface and it induces a larger magnetic moment of Ti atom at the right interface. In addition, we have compared the spin density difference on the (100) plane to the (010) plane (the case is similar to the Fe₂/TiO₂ interface in the Fe₄N/BaTiO₃ junction, so we have not shown). It finds a relatively strong hybridization between interfacial Fe^II(Mn^II) and Ti atoms compared with the hybridization between interfacial Mn^I and Ti atoms for MnFe/TiO₂(Mn₂/TiO₂) interface, which is because the Fe^II–Ti(Mn^II–Ti) bond length is comparably smaller than that between Mn^I and Ti atoms (see Table S1†). It illustrates the interfacial Fe^II(Mn^II) atom has a more important effect on the ME coupling than the interfacial Mn^I atom, which is similar to the case of the Fe₂/TiO₂ interface in the Fe₄N/BaTiO₃ junction. Therefore, comparing the Fe₂/TiO₂ interface in the Fe₄N/BaTiO₃ junction, when the interfacial Fe^I atom is replaced by Mn^I atom, a small change of ME coefficient is achieved at the MnFe/TiO₂ interface in MnFe₃N/BaTiO₃ junction (Δα_s = 0.4 × 10⁻¹⁰ G cm² V⁻¹). But when the interfacial Fe^II atom is replaced by Mn^II atom, a relatively large ME coefficient difference is achieved at Mn₂/TiO₂ interface (Δα_s = 1.2 × 10⁻¹⁰ G cm² V⁻¹). The similar results are expected for the MFe₃N/BaTiO₃ junctions, in which the MFe₃N is the Fe₄N class of materials while the cubic corner Fe atom is replaced by the other magnetic atom M in the Fe₄N.

Fig. 6 The spin density difference (in e Å⁻³) at the left and right interfaces for (a) and (b) the MnFe/TiO₂ and (c) and (d) Mn₂/TiO₂ terminations in MnFe₃N/BaTiO₃ tunnel junctions on the (100) plane.

4. Conclusions

To summarize, the ME effects in Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ junctions have been studied using first-principles calculations based on DFT. Our results show that the ME coupling effects are very weak for FeN/TiO₂ interfaces in both Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ junctions. But the large ME coefficients are achieved at the more stable Fe₂/TiO₂ interface in Fe₄N/BaTiO₃ junction and the more stable MnFe/TiO₂ and Mn₂/TiO₂ interfaces in MnFe₃N/BaTiO₃ junction. The ME effect is mainly determined by the interfacial electronic hybridization between unoccupied transition metal and Ti d states. For the Fe₂/TiO₂ interface in Fe₄N/BaTiO₃ junction and the MnFe/TiO₂ and Mn₂/TiO₂ interfaces in MnFe₃N/BaTiO₃ junction, the interfacial Fe^II(Mn^II) atom is predicted to play a more important role in the ME coupling than the interfacial Fe^I(Mn^I) atom. Therefore, when the interfacial Fe^I atom is replaced by Mn^I atom for Fe₂/TiO₂ interface in Fe₄N/BaTiO₃ junction, a small change of ME coefficient is achieved at the MnFe/TiO₂ interface in MnFe₃N/BaTiO₃ junction. But when the interfacial Fe^II atom is replaced by Mn^II atom, a relatively large ME coefficient difference is achieved at Mn₂/TiO₂ interface. These findings show that the ME coupling effect in Fe₄N/BaTiO₃ and MnFe₃N/BaTiO₃ junctions could be modulated by the selection of the interfacial termination. In addition, the magnetic Mn-substitution doping at the interfacial Fe^II position in Fe₄N/BaTiO₃ junction can possibly obtain a relatively large ME coefficient difference compared with doping at the interfacial Fe^I position. We hope that it is worthwhile to study the ME coupling effects between the Fe₄N class of materials MFe₃N and FE materials experimentally.

Acknowledgements

The work was supported by the National Natural Science Foundation of China No. 11274130 and 11474113.

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Footnote

† Electronic supplementary information (ESI) available: see DOI: 10.1039/c6ra00044d

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