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^†^†thanks: The reported study was funded by the Russian Scientific Foundation according to research project No. 21-12-00179. ¹¹institutetext: I. Piyanzina and R.Mamin ²²institutetext: Zavoisky Physical-Technical Institute, FIC KazanSC of RAS, 420029 Kazan, Russia
Tel.: +79196931320
²²email: [email protected]

Electronic and magnetic properties of the BaTiO₃/LaMnO₃ interface: a DFT study

Irina Piyanzina Rinat Mamin

(Received: date / Accepted: date)

Abstract

By means of ab initio calculations withing 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.

Keywords:

ferroelectric interface magnetoelectric coupling DFT

1 Introduction

The LaAlO₃/SrTiO₃ (LAO/STO) heterostructure has been widely investigated during last 20 years after the two-dimensional gas (2DEG) observation at the interface of that system ohtomo . It was also found the conducting state coexists with magnetic state. The arising magnetic order in the LAO/STO system is a matter of intensive discussion pavlenko ; michaeli . From ab initio calculations it was revealed that the bare heterostructure is non-magnetic, and magnetic ordering was related to defects formation, in particular, to oxygen vacancies at the interface and/or the surface pavlenko ; piyanzina . The arising magnetization is weak and in according to Ref. piyanzina the maximal magnetic moment per Ti atom equals to 0.232 $\mu_{B}$ .

Besides, below 300 mK LAO/STO system passes into the superconducting state reyren . Recently, in one of our previous research by means of ab initio it was demonstrated that the usage of the high-temperature superconductor (PCHTSC), La₂CuO₄ (LCO), as a substrate and ferroelectric oxide BaTiO₃ in the heterostructure as an overlayer may result in conducting state located mostly at the interfacial LCO layer. Lately, a high-temperature quasi-two-dimensional superconducting state has been observed in the Ba_0.8Sr_0.2TiO₃/La₂CuO₄ heterostructure with $T$ _c=30 K pavlov . This $T$ _c is 100 times larger than Tc in LAO/STO reyren .

The experimental observation of conducting state was also realized in the Ba_0.8Sr_0.2TiO₃/ LaMnO₃ system pavlovJETP . 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 weng ; kabanov . Hence, in the LaMnO₃/BaTiO₃ (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.

2 Calculation details

The ab initio calculations were based on density functional theory (DFT) hohenberg1964 ; kohn1965 . Exchange and correlation effects were accounted for by the generalized gradient approximation (GGA) as parametrized by Perdew, Burke, and Ernzerhof (PBE) perdew1996 . The Kohn-Sham equations were solved with projector-augmented-wave (PAW) potentials and wave functions bloechl1994paw as implemented in the Vienna Ab-Initio Simulation Package (VASP) kresse1996a ; kresse1996b ; kresse1999 , which is part of the MedeA^® software of Materials Design medea . 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 monkhorst1976 including $5\times 5\times 1$ ${\bf k}$ -points. A set of calculations was carried out with a +U correction applied to Mn 3d, Ti 3d and La 4f states piyanzina2017 . A simplified Dudarev approach was used dudarev1998 : 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 ${\rm LaMnO_{3}}$ comprising $2\frac{1}{2}$ unit cells with ${\rm LaO}$ termination on both sides and varying number of ${\rm BaTiO_{3}}$ overlayers with ${\rm TiO_{2}}$ termination towards the central slab and ${\rm BaO}$ surface termination also on both sides. In order to avoid interaction of the surfaces and slabs with their periodic images, $\approx$ 20 Å-wide vacuum region was added.

3 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 LaMnO₃, 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 weng . 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 $\mu_{B}$ , respectively. Those values agree well with experimental ones of 1.7 eV and $3.7\pm 0.1$ $\mu_{B}$ , respectively saitoh . 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 sawada and also to the previous ab initio research, for example Ref. ciucivara2008 .

Refer to caption — Figure 1: Density of states spectra for the A-AFM bulk LaMnO₃ along with the corresponding unit cell structure.

Table 1: Calculated lattice constants in Å of bulk LaMnO₃, bulk BaTiO₃ and a rotated by 45^∘ along z-axis BaTiO₃ unit cell in order to merge with the LaMnO₃ unit cell. The last row lists the BaTiO₃/LaMnO₃ supercell lattice constants. Experimental data are presented as well for comparison.

	a	b	c
LMO	5.709	5.675	8.018
Expt. sawada	5.742	5.532	7.669
BTO	3.986	3.986	4.014
Expt. crystal	3.992	3.992	4.036
BTO ( $\times\sqrt{2}$ )	5.637	5.637	4.014
Supercell	5.709	5.675	50

BaTiO₃ is one of the most well known ferroelectric, which has a ferroelectric polarization in a tetragonal system with moderate polarization of 26 $\mu$ C/cm² subarao .

Table 2: Calculated energy (E) per unit cell, c/a ratio, the band gaps (

\varepsilon

), displacement of Ti atoms with respect to the O planes (

\bigtriangleup

) and polarization P in

\mu

C/cm² of the cubic, tetragonal and orthorombic phases of bulk BaTiO₃. Experimental values are given for the tetragonal phase.

Phase	c/a	$\varepsilon$ , eV	$\bigtriangleup$ , Å	P
Cubic	1	2.169	0	0
Tetragonal	1.007	2.249	0.13	31
Expt.	1.010 shirane	3.27 wemple	0.15 shirane	26 subarao
Orthorhombic	1.428	2.259	0.09

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.

3.1 LaMnO₃/BaTiO₃ 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 $a_{BTO}\times\sqrt{2}$ are very close to the $a_{LMO}$ and $b_{LMO}$ 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.

Performed structural optimization resulted in the insignificant shift of Ti atoms out of oxygen planes ( $\Delta$ z_Ti-O). For the heterostructure with two BTO overlayers $\Delta$ z_Ti-O distances within the interfacial layer equal to -0.046 Å and 0.247 Å, within the surface layer shifts are less significant and equal to 0.049 Å and 0.101 Å, 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 piyanzina . 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 pavlovJETP 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 $\mu_{B}$ . Ferromagnetic magnetization should increase with increasing the electron doping.

4 Conclusions

In the present paper by means of DFT+ $U$ calculation the electronic and magnetic properties of bulk LaMnO₃ and BaTiO₃, 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. pavlovJETP 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.

Acknowledgements.

The reported study was funded by the Russian Scientific Foundation according to research project No. 21-12-00179.

Conflict of interest

The authors declare that they have no conflict of interest.

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Electronic and magnetic properties of the BaTiO3/LaMnO3 interface: a DFT study