Potential enhancement in magnetoelectric effect at Mn-rich Co₂MnSi/BaTiO₃ (001) interface

Multiferroic materials have recently attracted significant interest due to their magnetoelectric (ME) properties, which demand the coupling between ferroelectric and ferromagnetic order parameters [1,2]. The interplay between ferroelectricity and magnetism allows the possibility of controlling ferroelectric properties by magnetic fields and of controlling magnetic properties by electric fields, and could exploit new device concepts, such as ferroelectric and multiferroic tunnel junctions [3–6]. There are several mechanisms resulting in ME effects, and recent reviews can be seen in ref. [7]. Apart from the intrinsic magnetoelectric compounds with no time-reversal and no space-inversion symmetries (i.e., single-phase multiferroics), a mechanism of magnetoelectric coupling may occur in composites of ferroelectric and ferromagnetic or ferrimagnetic compounds. Furthermore, the two-phase composite multiferroics may be promising for magnetoelectric devices, because none of the existing single-phase multiferroics combine large and robust electric and magnetic polarizations at room temperature [2]. At ferromagnet/ferroelectric interfaces, the ME effect may originate from purely electronic mechanisms. First-principles calculations on ferromagnet-ferroelectric composite systems, such as Fe/BaTiO₃ [6,8], Co₂MnSi/BaTiO₃ [9] and Fe₃O₄/BaTiO₃ [10], have predicted that charge redistribution at the interface may cause the ferromagnet to become sensitive to the ferroelectric polarization direction and, reciprocally, may induce magnetic moments in the ferroelectric. Recently, composite multiferroics have also been fabricated in some experiments [6,11] by artificially making ferroelectrics and ferromagnets in nanoscale heterostructures. Both of theoretical and experimental results suggest that a change in the interface magnetization could be caused by ferroelectric switching under the influence of applied electric field. The ME effect due to the interface atomic orbital hybridization mechanism (e.g., charge transfer and chemical bonding [12]) is expected to play a role for these composite multiferroic systems, and another electronic mechanism for an interface ME effect may originate from the spin-dependent screening [13]. For the latter, an applied electric field produces an accumulation of spin-polarized electrons or holes at the metal/insulator interface resulting in a change in the interface magnetization. This mechanism is also relevant to ferromagnet/ferroelectric interfaces where screening of the polarization charge alters with ferroelectric polarization orientation producing a change in surface magnetization, as was predicted for the SrRuO₃/BaTiO₃ interface [14]. The experimental indication of the carrier-induced ME coupling was also found for the PbZr_0.2Ti_0.8O₃/La_0.8Sr_0.2MnO₃ junction [15].

In the present paper, using the first-principle calculations, we estimated an enhanced ME effect at Mn-rich Co₂MnSi/BaTiO₃ (001) interface by modifying the interfacial component. All calculations are performed within the framework of density functional theory using the projected augmented-wave (PAW) method and a plane-wave basis set, as implemented within Vienna ab initio simulation package [16]. To treat electron exchange and correlation, we chose the Perdew-Burke-Ernzerhof [17] formulation of the generalized gradient approximation (GGA), which is essential for the correct description of structural and ferroelectric ground states of tetragonal phase BaTiO₃ multilayers [9, 10, 14, 18, 19] as well as of structural and ferromagnetic ground states of Heusler alloy Co₂MnSi [20–22]. The cutoff energy of the plane waves is chosen to be 520 eV, which is large enough to deal with all the elements considered here within the PAW method.

Co₂MnSi and BaTiO₃ (001) layers were stacked in a supercell approach to simulate the [001]-ordered Co₂MnSi/BaTiO₃ interface. To conclude the interface relative stability, the two same interfaces are constructed within a paraelectric (PE) supercell. The in-plane (x and y) lattice parameters of the superlattice, a and b, are chosen to be in accordance with those of bulk Heusler alloy, i.e., (a and b) are ($a_{{\rm{Co}}_{2} {\rm{MnSi}}} /\sqrt{2} ,a_{{\rm{Co}}_{2} {\rm{MnSi}}} /\sqrt{2}$) for the (001) interface, where a_Co2MnSi is set to the optimized value of 5.638 Å (in good agreement with the experimental value of 5.654 Å [23]), while the out-plane (z) lattice parameter of the superlattice, c, is optimized. In order to study the interplay between ferroelectric/magnetic properties and the interface structure, CoCo, MnSi and modified MnMn (replacing Si with Mn in MnSi surface) terminations in Co₂MnSi layers were simulated and only TiO₂ termination was considered for the BaTiO₃ slab. Within a supercell, the BaTiO₃ slab is composed of 17 atomic layers (8.5 unit cells) for all considered cases, and this thickness is large enough to recover the bulk properties [8]. As for the Co₂MnSi slab, it is composed of 9 atomic layers for both MnSi/TiO₂ (MS/TO) and modified MnMn/TiO₂ (MM/TO) interfaces, and of 11 atomic layers for CoCo/TiO₂ (CC/TO) interface. To optimize Co₂MnSi/BaTiO₃ (001) supercells, a 13 × 13 × 1 Monkhorst-Pack grid for k-point sampling is adopted for the Brillouin zone integration, and all atomic coordinates within a supercell are fully relaxed until the forces acting on each atom are smaller than 0.02 eV/Å for both PE and ferroelectric (FE) relaxations. Here, the initial Ti-O relative displacement along z orientation is set to be 0.125 Å at TiO₂ layer for the atomic relaxation in the case of FE state, considering the typical soft-mode distortion of bulk BaTiO₃. The spin-orbit interaction is not included in our calculations since its influences on the interface ME effect is suggested to be small [13,24].

Given the difference of atom relative positions at each Co₂MnSi/BaTiO₃ (001) interface, we firstly optimized the interface atom relative positions for each interface in the case of PE state. Different from the results of Yamauchi et al. [9], it is found that the favorable position is always the interface X (X = Mn, Co) atoms are located on the top of oxygen for all considered cases. According to these results, we assume the atomic configuration of the Co₂MnSi/BaTiO₃ (001) interfaces as shown in fig. 1. In order to determine the relative stability of CC/TO, MS/TO and modified MM/TO interfaces, the phase diagram of interfaces was calculated by comparing corresponding PE interface energies as a function of atomic chemical potentials within the framework of ab initio atomistic thermodynamics [25]. The interface energy per unit of the interface area, γ, is defined as [21]

$$\begin{equation} \gamma = \frac{1}{{2A}}\left[ {G - \sum\limits_i {N_i \mu _i } } \right], \end{equation} \tag{ 1 }$$

where G is the Gibbs free energy of a Co₂MnSi/BaTiO₃ superlattice, N_i and μ_i are the number of atoms in a superlattice and chemical potential of the i-th element. It is worth mentioning that the vibrational and pV contributions to the Gibbs free energy is small [26], so this allows us to replace the Gibbs free energies for solids with the total energies obtained in the electronic structure computations. Since the dependencies of the chemical potentials of solids on the temperature and pressure are relatively weak [26], we neglected these effects in the present consideration. In order to obtain the phase diagram, we compare PE interface energies of CC/TO, MS/TO and modified MM/TO interfaces in a reasonable range of chemical potentials to find the interface with the minimal interface energy for any given chemical potentials. The detailed calculation for the phase diagram can be found in the article of Bottin et al. [27]. It is concluded from the phase diagram that, within the accessible region (bound by blue solid lines in fig. 2), the chosen three interfaces could be stabilized under the moderate condition. Under Mn-rich and Co-rich conditions, for instance, the MM/TO interface may be achieved, this is corresponding to the case of the Co₂MnSi (001) surfaces where the MnMn free surface is suggested to be stable [20]. In addition, the predicted phase under Mn-rich and Mn-deficient conditions is comparable with the recent experimental results of the nonstoichiometric Co₂MnSi film [28].

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Next, we further focus our attention to the FE properties of Co₂MnSi/BaTiO₃ (001) superlattices. In this paper, the FE polarization orientation is set to point to the right (z orientation illustrated in fig. 1). The calculated energy difference, ΔE_PE-FE , between the PE and FE states shows that the FE state is strongly stable for both CC/TO (ΔE_PE-FE ≈ 0.13 eV) and MM/TO (ΔE_PE-FE ≈ 0.04 eV) interfaces, while the PE state is more stable than the FE state for MS/TO interface (ΔE_PE-FE ≈ −0.08 eV). Thus, in the following the FE properties are inspected only for CC/TO and MM/TO (001) interfaces, unless otherwise specified. For the relaxed Co₂MnSi/BaTiO₃ (001) supercells with FE state, fig. 3 shows relative displacements between M (M = Ti, Ba) and O atoms in BaTiO₃ slab which is the typical soft-mode distortion that gives rise to the FE polarization. Although the polar displacement exists remarkably different between CC/TO and MM/TO interfaces, there is an overall net polarization along z orientation in tetragonal phase BaTiO₃ film for both cases, which is consistent with the recent experimental result [6,29].

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Ferroelectric displacements break the symmetry between I_L and I_R, causing magnetic moments of the interface metal atoms at the two interfaces to deviate from their values in the PE state. Table 1 lists the magnetic moments of the interface atoms for two interfaces with FE state. As a result of the ferroelectricity in the BaTiO₃, the magnetizations at the two interfaces occur significantly different, which reflect the magnetic change at one interface when the polarization in BaTiO₃ reverses. Compared with CC/TO, Fe/BaTiO₃ [6,8] and Fe₃O₄/BaTiO₃ [10] interfaces, there is more net change in magnetic moments at the MM/TO interface if the electric polarization reverses. Interestingly, a notable antiparallel alignment of the Ti magnetic moments, by reversing the FE polarization of BaTiO₃, can be achieved at the MM/TO interface. The net spin density shown in fig. 4 can clearly reveal the change in order of the Ti magnetic moments at I_L and I_R. Additionally, the ferroelectricity-induced change in the magnetic moments of Mn atoms located at the MM/TO interface, to some degree, can be detected from the overlap of spin charge between interface layer and first MnSi sublayer (see fig. 4).

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According to other studies [6,14], we can estimate the magnitude of the interface ME coefficient α_s (a figure of merit for the ME coupling), which is defined as

$$\begin{equation} \mu _0 \Delta M = \alpha _s E, \end{equation} \tag{ 2 }$$

where E is the strength of the applied electric field. Assuming that the applied electric field is given by the coercive fields of BaTiO₃ films (i.e., E_c ∼ 100 KV/cm), we estimate the interface ME coefficient α_s to be 8.7 × 10⁻¹⁰ and 2.1 × 10⁻¹⁰ Gcm²/V for MM/TO and CC/TO interfaces, respectively. For comparison the ME coefficients at Fe/BaTiO₃ [6,8] and Fe₃O₄/BaTiO₃ [10] (001) interfaces are found to be ∼3.0 × 10⁻¹⁰ Gcm² /V and ∼2.6 × 10⁻¹⁰ Gcm² /V, respectively, using the same applied electric field. The results suggest that the Co₂MnSi/BaTiO₃ (001) multilayers with modified MM/TO interface may have an advantage in the area of electrically controlled magnetism, compared with previous Fe/BaTiO₃ and Fe₃O₄/BaTiO₃ (001) multilayers. Actually, such strong ME effect at the MM/TO (001) interface is related to the specific "interface effect" which results in the different magnetic interaction at two polarized MM/TO interfaces. Detailedly, electronic hybridization mechanism is dominant at I_R while spin-dependent electrostatic effect is dominant at I_L. They can be gained further insight by analyzing spin-resolved densities of states (DOS).

Figure 5 shows the spin-resolved DOS of interface Ti and Mn atoms for the MM/TO and CC/TO interfaces with the FE state. The detailed analysis for DOS of the MM/TO interface reveals that, below and close to the Fermi energy, appreciable hybridization in the minority spin channel is observed between the Mn and Ti atoms at I_R, resulting in the negative magnetic moment of the Ti atom. This is consistent with the results of Fe/BaTiO₃ (001) multilayers [6,8]. Contrarily, such result is not obtained between the Mn and Ti atoms at I_L, and the measurable positive magnetic moment of the Ti atom, in this condition, may mainly originate from the Mn strong spin-dependent electrostatic effect. As for the CC/TO interface, somewhat weaker hybridization in the minority spin channel can also be concluded between the Co and Ti atoms at I_R, which gives rise to a small magnetic moment of about −0.12μ_B for the Ti atom.

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Finally, we point out that the predicted phenomenon is qualitatively different from the "standard" ME effect. The latter is the volume effect and for which the magnetization is a linear function of the applied electric field. In our case, the ME effect is confined to the interfaces and represents a change of the interface magnetization at the coercive field of the ferroelectric. The effect described in this work is mainly due to the interaction between the interface Ti (less than half-occupied d bands) and Mn (half-occupied d bands) or Co (more than half-occupied d bands) atoms. This has a universal significance for understanding most ferromagnetic/BaTiO₃ composites where the ME effect is expected to be largely related to the interplay between interface layers. We, therefore, hope that the theoretical predictions will stimulate experimental studies of such multilayers to search for the ME properties driven by the interface effect (e.g., electrically controlled magnetism).

This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 61078057, 50702046 and 51172183) and the Northwestern Polytechnical University (NWPU) Foundation for Fundamental Research (Grant No. NPU-FFR-JC200821 and JC201048). Particularly, we would like to thank the Science computational grid (ScGrid) of Supercomputing Center of the Chinese Academy of Sciences (SCCAS) for computational facilities.