Electronic and magnetic properties of the BaTiO$_{3}$/LaMnO$_{3}$ interface: a DFT study

By means of ab initio calculations within the density functional theory (DFT) electronic and magnetic properties of BaTiO3/LaMnO3 interface were investigated. An impact of ferroelectric overlayer thickness onto the interface properties was analysed through the spin-polarized density of states.

and ferroelectric oxide BaTiO 3 in the heterostructure as an overlayer may result in conducting state located mostly at the interfacial LCO layer. Lately, a hightemperature quasi-two-dimensional superconducting state has been observed in the Ba 0.8 Sr 0.2 TiO 3 /La 2 CuO 4 heterostructure with T c =30 K [6]. This T c is 100 times larger than Tc in LAO/STO [5].
The experimental observation of conducting state was also realized in the Ba 0.8 Sr 0.2 TiO 3 / LaMnO 3 system [7]. Such a heterostructute is composed of a ferromagnet which can serve as a source of magnetic state and a antiferroelectric which can be used as a tool for electron doping [8,9]. Hence, in the LaMnO 3 /BaTiO 3 (LMO/BTO) heterointerface it is expected to have the interfacial magnetism along with conducting state. It presented paper we investigate the possibilities of the spin-polarized 2DEG appearing in the LMO/BTO heterostructure. The essential issue is to understand the impact of the ferroelectric BTO slab thickness on the interface electronic and magnetic states. In order to do so we investigate the BTO/LMO heterostructure with varying number of BTO overlayers and analyse the density of state spectrum.

Calculation details
The ab initio calculations were based on density functional theory (DFT) [10,11]. Exchange and correlation effects were accounted for by the generalized gradient approximation (GGA) as parametrized by Perdew, Burke, and Ernzerhof (PBE) [12]. The Kohn-Sham equations were solved with projector-augmented-wave (PAW) potentials and wave functions [13] as implemented in the Vienna Ab-Initio Simulation Package (VASP) [14,15,16], which is part of the MedeA ® software of Materials arXiv:2206.01935v1 [cond-mat.mtrl-sci] 4 Jun 2022 Design [17]. Specifically, we used a plane-wave cutoff of 400 eV. The force tolerance was 0.05 eV/Å and the energy tolerance for the self-consistency loop was 10 −5 eV. The Brillouin zones were sampled using Monkhorst-Pack grids [18] including 5 × 5 × 1 k-points. A set of calculations was carried out with a +U correction applied to Mn 3d, Ti 3d and La 4f states [19]. A simplified Dudarev approach was used [20]: the U values of 4 eV for Mn, 2 eV for Ti and 8 eV for La states were applied.
The heterostructures were modelled by a central region of LaMnO 3 comprising 2 1 2 unit cells with LaO termination on both sides and varying number of BaTiO 3 overlayers with TiO 2 termination towards the central slab and BaO surface termination also on both sides. In order to avoid interaction of the surfaces and slabs with their periodic images, ≈20Å-wide vacuum region was added.

Bulk components
First, the parent materials of the heterointerface have been checked separately in the bulk geometry in order to ensure the reproducibility of the results obtained by the method and computational parameters used in the present research.
Starting from the experimental structure of bulk LaMnO 3 , the lattice constants and atomic positions were fully relaxed. To realize the spin-dependent switching effect, which was mentioned in the introduction, it was suggested to replace FM material by AFM [8]. The spin-polarized density of states (DOS) plot for the A-AFM LMO in the bulk configuration in presented in Fig. 1. The bulk LMO is a semiconductor, with an O 2p dominated valence band, with Mn 3d contribution. The calculated band gap and magnetic moment of the Mn atom equal 1.349 eV and 3.832 µ B , respectively. Those values agree well with experimental ones of 1.7 eV and 3.7±0.1 µ B , respectively [21]. Based on this comparison we concluded that the chosen value of the U parameter can yield relatively correctly both the energy gap and the magnetization. Besides, the calculated cell parameters, shown in Table 1, were found to be close to experimental values [22] and also to the previous ab initio research, for example Ref. [23].
BaTiO 3 is one of the most well known ferroelectric, which has a ferroelectric polarization in a tetragonal system with moderate polarization of 26 µC/cm 2 [25]. Calculated energies per unit cells, band gaps, oxygen displacements and polarization for the cubic, tetragonal and orthorhombic phases are presented in Table 2.
All calculated values agree well with experimental data. The experimental band gap is higher than the computed one, but the difference is reasonable for the DFT.  For the purpose of the present work we are interested in the phases with spontaneous polarization, hence, we will focus on the tetragonal BTO structure. The calculated lattice parameters along with experimental ones are listed in Table 1. The calculated density of state spectra for the bulk BTO is given in Fig. 2.

LaMnO 3 /BaTiO 3 heterostructure
In order to merge BTO with LMO so that the polarization is parallel to the easy axis of antiferromagnet, the BTO unit cell has to be rotated by 45 • along z -axis. As listed in Table 1 a BT O × √ 2 are very close to the a LM O and b LM O cell parameters. The resulted supercell with two BTO overlayers is presented in Fig. 3 a, where the right half of the unit cell is presented without full vacuum region. The structure was fully optimized. The fully optimized half-right structure of LMO/2BTO heterointerface. The supercell is displayed without the vacuum region, which was 20Å. Arrows indicate magnetic moments directions in the LMO slab. b) Corresponding atom-resolved density of states for the heterostructure with two BTO overlayer and c) with three BTO overlayers. Performed structural optimization resulted in the insignificant shift of Ti atoms out of oxygen planes (∆ z T i−O ). For the heterostructure with two BTO overlayers ∆ z T i−O distances within the interfacial layer equal to -0.046Å and 0.247Å, within the surface layer shifts are less significant and equal to 0.049Å and 0.101Å, respectively. Except for the one, all the movements of Ti are towards the surface, which leads to the total polarization predominantly towards the surface. Such a structural reconstruction leads to the electronic rearrangement as reflected in the DOS spectra shown in Fig. 4 a -d for varying number of BTO layers. With increasing the number of BTO overlayers the band gap decreases from 0.47 eV for heterostructure with one BTO overlayer to 0.113 eV with four. Such a decay of the band gap with the number of overlayers differs from LAO/STO linear dependence as shown in Fig. 5. Indeed, the band gap decrease with increase of LAO overlayers in LAO/STO associated with increase of the field directed towards the surface. As soon as this field overcomes the field arising due do the structural relaxation, the LAO/STO system becomes conductor. That happens above 4 LAO overlayers in according to our previous ab initio research [4]. In contract, in the LMO/BTO heterostructure without polar overlayers the field towards the surface originates from the ferroelectric polarization. Since the slope in Fig. 5 for LMO/BTO in smaller it is obvious that the ferroelectric field is weaker and conductivity occurs with more overlayers. Note, that in experiments [7] the thickness of the ferroelectric film was about 350 nm, and based on the asymptotics of our calculations it is expected that the band gap vanishes completely at such a thickness. Finally, the LMO/BTO system possesses relatively high total magnetization due to the odd number of MnO layers with magnetic moment per Mn equal to 3.8 µ B . Ferromagnetic magnetization should increase with increasing the electron doping.

Conclusions
In the present paper by means of DFT+U calculation the electronic and magnetic properties of bulk LaMnO 3 and BaTiO 3 , as well as LMO/BTO heterostructure have been demonstrated. Within the chosen approach and computational parameters the bulk components of the heterostructure were confirmed to be insulators. In the heterostructure geometry the decrease of the band gap with increasing the number of BTO overlayers was demonstrated. It was found that the curve tends to zero, but the system remains semiconductor up to six BTO overlayers. It means that the conducting state arises with more ferroelectric overlayers, that is consistent with experiment from Ref. [7] where the thickness of ferroelectric film was much higher. It was shown that the LMO/BTO systen possesses relatively high total magnetization, which is expected to increase with increasing the electron doping.