Li Yuab,
Guoying Gaoa,
Guangqian Dinga,
Yongfa Duanb,
Yang Liub,
Yan Heb and
Kailun Yao*a
aSchool of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China. E-mail: klyao@mail.hust.edu.cn; Fax: +86 27 87556264; Tel: +86 27 87558523
bDepartment of Basics, Air Force Early Warning Academy, Wuhan 430019, China
First published on 3rd March 2016
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 FeII(MnII) (the face-centered sites Fe or Mn in Fe4N and MnFe3N) atom plays a more important role in the ME coupling than the interfacial FeI(MnI) (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 FeII position in the Fe4N/BaTiO3 junction can possibly obtain a relatively large ME coefficient difference compared with doping at the interfacial FeI position.
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 (FeI) and face-centered (FeII) 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 μB) 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 FeI 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 FeI atom is replaced by MnI atom, a small change of ME coefficient is achieved for MnFe/TiO2 interface at MnFe3N/BaTiO3 junction. But when the interfacial face-centered FeII atom is replaced by MnII 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 FeII(MnII) and Ti atoms compared with the hybridizations between interfacial FeI(MnI) and Ti atoms for Fe2/TiO2(MnFe/TiO2, Mn2/TiO2) interface.
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 studies5,22,47 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
Wsep = (EFM + EBaTiO3 − EFM/BaTiO3)/2A |
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.
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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 FeIII 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 FeII 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 μB and the value is 10.768 μB for the right interface. Therefore, the total magnetic moment difference is only 0.065 μB. (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 ΔμFe = 0.406 μB for Fe atoms and ΔμTi = 0.382 μB for Ti atoms, leading to a large total interfacial magnetic moment difference Δμ = 0.834 μB 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 ΔμTi.5
According to previous works, the intensity of ME coupling can be characterized by the surface ME coefficient αs, which is calculated by the following expression5,25
αs = μ0ΔM/E |
The density of states (DOS) projected on d orbitals of FeI, FeII, 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 FeI and FeII states are different, but the hybridizations with Ti atoms are similar. At the right interface, a remarkable hybridization between the FeI, FeII 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 μB). However, at the left interface, only a very weak hybridization is observed between FeI, FeII and Ti atoms in the minority spin channel near Fermi energy EF, which induces a small magnetic moment on Ti atom (−0.068 μB). 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.
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 dxz(dyz) 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 (ΔμTi = 0.382 μB). 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 FeII and Ti atoms are more than those between FeI and Ti atoms for both the left and right interfaces. It gives rise to relatively strong hybridizations between interfacial FeII and Ti atoms with respect to the hybridizations between interfacial FeI and Ti atoms. It is because the FeII–Ti bond length is relatively smaller (2.867 Å for left interface; 2.628 Å for right interface) than the FeI–Ti bond length (2.987 Å for left interface; 2.745 Å for right interface). Therefore, the interfacial FeII atom is suggested to play a more important role in the ME coupling than the interfacial FeI atom.
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 μB 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 μB for the MnFe/TiO2 interface and Δμ = 0.65 μB for the Mn2/TiO2 interface, the corresponding surface ME coefficient is αs = 5.9 × 10−10 G cm2 V−1 for the MnFe/TiO2 interface and αs = 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 MnI 3d, FeII 3d, and Ti 3d orbitals at the MnFe/TiO2 interface and MnI, MnII 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 FeII 3d and Ti 3d states, as highlighted by the arrows in Fig. 5a. And the hybridization between the MnI 3d and Ti 3d states is also observed through the enlarged figure. At the left interface, only a very weak hybridization is observed between MnI, FeII 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 MnI, MnII 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 MnI and MnII are very weak, they also induce a large antiparallel magnetic moment of −0.447 μB 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 MnI, MnII and Ti atoms. Thus, there is almost no induced magnetic moment on the left interfacial Ti atom. The changes of MnI and MnII states between the left and right interfaces are both very small. Especially the MnII state, the change is much smaller than that of the FeII states in Fig. 5a, which lead to a relatively small difference of the magnetic moment for MnII atom (see Table S3†). Therefore, the ME coupling in Mn2/TiO2 interface is weaker than that in the MnFe/TiO2 interface.
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 FeII(MnII) 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 FeII(MnII) and Ti atoms compared with the hybridization between interfacial MnI and Ti atoms for MnFe/TiO2(Mn2/TiO2) interface, which is because the FeII–Ti(MnII–Ti) bond length is comparably smaller than that between MnI and Ti atoms (see Table S1†). It illustrates the interfacial FeII(MnII) atom has a more important effect on the ME coupling than the interfacial MnI 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 FeI atom is replaced by MnI atom, a small change of ME coefficient is achieved at the MnFe/TiO2 interface in MnFe3N/BaTiO3 junction (Δαs = 0.4 × 10−10 G cm2 V−1). But when the interfacial FeII atom is replaced by MnII atom, a relatively large ME coefficient difference is achieved at Mn2/TiO2 interface (Δαs = 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.
Footnote |
† Electronic supplementary information (ESI) available: see DOI: 10.1039/c6ra00044d |
This journal is © The Royal Society of Chemistry 2016 |