Electric control of magnetism in low dimensional magnets on ferroelectric surfaces Electric control of magnetism in low dimensional magnets on ferroelectric surfaces Dorj Odkhuu, Tumurbaatar Tsevelmaa[.]
Electric control of magnetism in low-dimensional magnets on ferroelectric surfaces Dorj Odkhuu, Tumurbaatar Tsevelmaa, S H Rhim, Soon Cheol Hong, and Deleg Sangaa Citation: AIP Advances 7, 055816 (2017); doi: 10.1063/1.4975131 View online: http://dx.doi.org/10.1063/1.4975131 View Table of Contents: http://aip.scitation.org/toc/adv/7/5 Published by the American Institute of Physics Articles you may be interested in Magnetoelectric tuning of the inverse spin-Hall effect AIP Advances 7, 055911055911 (2017); 10.1063/1.4973845 Structural and antiferromagnetic properties of Sm-doped chrysene AIP Advances 7, 055707055707 (2017); 10.1063/1.4974284 Exchange bias effect in CaMn𝟏-𝒙Re𝒙O3 AIP Advances 7, 055801055801 (2016); 10.1063/1.4972798 Nonadiabatic Berry phase in nanocrystalline magnets AIP Advances 7, 055802055802 (2016); 10.1063/1.4972804 AIP ADVANCES 7, 055816 (2017) Electric control of magnetism in low-dimensional magnets on ferroelectric surfaces Dorj Odkhuu,1,a Tumurbaatar Tsevelmaa,2 S H Rhim,2 Soon Cheol Hong,2,b and Deleg Sangaa3 Department of Physics, Incheon National University, Incheon 22012, South Korea of Physics and Energy Harvest Storage Research Center, University of Ulsan, Ulsan 44610, South Korea Institute of Physics and Technology, Mongolian Academy of Sciences, Ulaanbaatar 210651, Mongolia Department (Presented November 2016; received 23 September 2016; accepted November 2016; published online 26 January 2017) Employing first-principles electronic structure calculations, we have studied the electric field controls of magnetism and magnetic anisotropy energy (MAE) of the Fe adatoms on ferroelectric BaTiO3 and PbTiO3 surfaces Remarkably, those effects exhibit dependence of the level of coverage as well as adsorption site of Fe atoms While the magnitude of MAE is shown tunable by ferroelectric polarization in the full coverage of Fe monolayer, the direction of magnetization undergoes a transition from perpendicular to in-plane for the half or lower coverages This magnetization reorientation is mainly ascribed to the sitedependent Fe d–O p hybridization, as a consequence of the formation of FeTiO2 layer at the surface © 2017 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4975131] I INTRODUCTION Exploration for magnetism in low dimensional systems such as monolayers, atomic chains, and even single atom dates back several decades Since then, magnetism in reduced dimensions has attracted continuous attention because of intriguing physics as well as possibility in practical applications The low dimensional structures exhibit magnetic properties or physics phenomenon which are radically different from those in naturally existing bulk counterparts For instance, magnetic anisotropy, the directional preference of magnetization, is one of such magnetic properties In particular, perpendicular magnetic anisotropy (PMA), offers great opportunities in spintronics.1 Recent developments of spintronics in magnetic memory technology are based on the control of the direction of magnetization or magnetic anisotropy either through the spin transfer torque2 or magnetoelectric effect.3,4 In the latter, an electric field alone can be used to manipulate magnetization without any external magnetic field or the spin polarized current density This phenomenon is expected to overcome the major drawback of the large critical current density required for magnetization switching in spin transfer torque memories To date, several approaches have been proposed to achieve the electric field control of magnetization: single-phase multiferroics,5 ferroelectrics with a magnetic dopant,6 ferromagnet|multiferroic,7,8 and ferromagnet|ferroelectric multilayers.9,10 Nevertheless, the major drawbacks still include a complete magnetization switching or potentially large sensitivity of magnetic anisotropy to the electric field Meanwhile, the physics origin of the electrically controlled magnetic anisotropy in the aforementioned magnetoelectric systems needs to be clarified In particular, it is quite indispensable to a Electronic mail: odkhuu@inu.ac.kr Electronic mail: schong@ulsan.ac.kr b 2158-3226/2017/7(5)/055816/7 7, 055816-1 © Author(s) 2017 055816-2 Odkhuu et al AIP Advances 7, 055816 (2017) identify the detailed atomic and electronic structures, and magnetism of a ferromagnet on ferroelectric surfaces In this study, ab initio electronic structure calculations reveal magnetoelectric effect in subto-full coverage of Fe monolayer (ML) on ferroelectric BaTiO3 and PbTiO3 films We show that, as a common phenomenon in ferromagnet|ferroelectric, the spin orientation depends on the level of coverage of Fe atoms: PMA for the full coverage of Fe ML but in-plane magnetization at a lower level of coverage of Fe The adsorption site of the Fe atoms on TiO2 surface layer also turns out crucial for magnetization reorientation, which we attribute to site-dependent Fe-d and O-p hybridization Furthermore, the sensitivity of magnetic anisotropy to the ferroelectric polarization depends on the choice of ferroelectric surface: positive for Fe|BaTiO3 , whereas negative for Fe|PbTiO3 II METHODOLOGY Density functional theory (DFT) calculations were performed using Vienna ab initio simulation package (VASP)11 using the projector augmented wave (PAW) basis sets.12 The exchange-correlation interactions were described by generalized gradient approximation formulated by Perdew, Burke, and Ernzerhof (PBE).13 We modelled a slab supercell consisted of the half and full coverages of Fe ML on five unit cell (u.c.) layers of BaTiO3 (001) and PbTiO3 (001) A vacuum region of about 15 Å was added between repeated slabs in the z-axis The experimental lattice constants of the bulk BaTiO3 (4.00 Å)14 and PbTiO3 (3.904 Å)15 were used for the lateral xy-plane of √ Fe|BaTiO3 (001) √ and Fe|PbTiO3 (001) slabs, respectively For the full coverage of Fe ML, a ( × 2) lattice of body centered cubic (bcc) Fe was adapted to the (1 × 1) lattice of BaTiO3 (PbTiO3 ) with negligible lattice mismatch (about 2.5 %) Ionic positions of Fe atoms and u.c layers of BaTiO3 (PbTiO3 ) next to the interface were fully relaxed while the bottommost u.c layers were kept fixed in their bulk polarizations to retain ferroelectricity Here the P↓ (P↑ ) represents the polarization in z < (z > 0) direction, i.e., the relative displacement of Ti ions with respect to the O-plane away from (pointing toward) the Fe atoms, as depicted in Figs 1(a) and 1(b) Spin-orbit coupling (SOC) is included using the second-variation method employing the scalar-relativistic eigenfunctions of the valence states.16 The magnetic anisotropy energy (MAE) per unit interfacial area, A, is determined from MAE = (E[100] – E[001])/A, where the E[100] and E[001] are the total energies with magnetization along the [100] and [001] directions, respectively An energy cutoff of 500 eV and a 31 × 31 × k-point mesh were substantial to get reliable MAE III RESULTS AND DISCUSSION Regarding low coverage adsorption of Fe atoms on BaTiO3 and PbTiO3 , we first consider only the half coverage of Fe ML as a simple case, which corresponds to the single Fe atom on (1×1) lattice of BaTiO3 (PbTiO3 ) In view of the extended in-plane cells, the magnetic adatoms are distributed evenly with the same distances from each other across the surface As shown in Fig 1(c), the three distinct principal adsorption sites on the TiO2 surface layer have been taken into account, which is energetically more favorable than the BaO (PbO) surface termination:9 hollow (denoted as H site), top-of-O (O site), and top-of-Ti (T site) Relative energies (∆E) of these adsorption sites with respect to the H site are shown in Table I, where the H site is the most stable for both P↓ and P↑ We also tabulate the equilibrium displacement of Ti, denoted as d Ti–O , and Fe atom, denoted as d Fe–O , at the interface with respect to the O-plane in Table I The positive (negative) value of d Ti–O represents upward (downward) shift of Ti atom toward (away from) the Fe overlayer with respect to the O-plane Substantial enhancement of the d Ti–O over the center layer or bulk value of 0.185 Å (0.47 Å) for BaTiO3 (PbTiO3 ) is a generic for all adsorption sites when P↓ On the other hand, the depolarization effect is rather strong for P↑ In particular, it turns out that the presence of Fe in Fe|BaTiO3 gives rise to the negative d Ti–O (–0.39 Å) for the ground phase of H site In contrast to the large separation of Fe atoms on the atop of O (d Fe–O =1.85 Å for P↓ and 1.89 Å for P↑ ) and Ti (d Fe–O =2.34 Å for P↓ and 2.73 Å for P↑ ), it is noticeable that the Fe atoms tend to penetrate into the substrate layers and find the preferable positions almost in the same plane of the surface O atoms for both polarization states 055816-3 Odkhuu et al AIP Advances 7, 055816 (2017) FIG Side-view atomic structures of the Fe|BaTiO3 or Fe|PbTiO3 for (a) P↓ and (b) P↑ The atomic species are denoted in spheres with different colors: The larger brown, green, gray, and smaller red spheres are the Fe, Ba or Pb, Ti, and O atoms, respectively Top views of different adsorption sites for the (c) half- and (d) full-coverage of the Fe adatoms on the TiO2 surface layer of the H site, forming the FeTiO2 layer at the surface Similar trend is also found for the Fe|PbTiO3 case The calculated magnetic moments and MAE values of the H, O, and T sites for Fe|BaTiO3 and Fe|PbTiO3 are shown in Table I for P↓ and P↑ For the most stable H site of Fe|BaTiO3 (Fe|PbTiO3 ) when P↓ , the interface Ti atoms have a noticeable induced moment of −0.54 µB (−0.39 µB ), antiparallel to the Fe moment 2.79 µB (2.82 µB ) Both the interface Ti and Fe moments further increase in magnitude as P↓ →P↑ , which can be ascribed to the charge transfer and strong hybridization in the spin-down state between the Fe and Ti d-orbitals.9,17 Similarly, the MAE alters significantly when the polarization reverses with net changes, ∆MAE = MAE(P↑ ) − MAE(P↓ ), of 0.05, 1.14, and 0.48 erg/cm2 for the H, O, and T sites in Fe|BaTiO3 , respectively Those for Fe|PbTiO3 are –1.05, 0.82, and –2.28 erg/cm2 , respectively This phenomenon occurs quite often in magnetoelectric systems.18,19 Notably, for both P↓ and P↑ the two most stable adsorption sites of the Fe atoms exhibit distinct trends in MAE: negative in sign for the H and positive for the O site, as shown in Table I Furthermore, it is interesting that the spin direction of Fe atoms can be reoriented under the polarization reversal if one can place it on the top of Ti atoms in BaTiO3 The different adsorption sites of the Fe adatoms evolve in different energy landscapes around the Fermi level, which consequently modulates MAE In Figs 2(a)–2(d), we show the Fe d- and O p-orbital projected density of states (PDOS) at the interface of Fe|BaTiO3 for the H and O sites for P↑ The electronic features of the Fe d states near the Fermi level are altered significantly from the H to the O site, especially in the spin-down state; 1) A large d z2 peak at around –1 eV below the Fermi level shifts upward and becomes a rather dispersive 2) The unoccupied d xy band shifts downward across the Fermi level and develops a stronger peak just below the Fermi level 055816-4 Odkhuu et al AIP Advances 7, 055816 (2017) TABLE I Relative energy ∆E (eV/cell) with respect to the H site, interlayer displacement of Ti (d Ti-O ) and Fe atoms (d Fe-O ) relative to the O-plane (Å), and magnetic moments of the surface Ti (MTi ) and Fe adatoms (MFe ) (µB ) for the H, O, and T sites of the 1/2ML Fe | BaTiO3 and Fe|PbTiO3 for P↓ and P↑ Fe|BaTiO3 H O T Fe|PbTiO3 H O T ∆E(P↓ ) ∆E(P↑ ) d Ti-O (P↓ ) d Ti-O (P↑ ) d Fe-O (P↓ ) d Fe-O (P↑ ) MTi (P↓ ) MTi (P↑ ) MFe (P↓ ) MFe (P↑ ) MAE (P↓ ) MAE (P↑ ) 0.00 1.58 2.98 0.00 0.99 1.91 –0.57 –0.38 –0.27 –0.39 0.03 0.02 0.02 1.85 2.34 0.45 1.89 2.73 –0.54 –0.07 –0.06 –0.61 –0.58 –0.13 2.79 3.31 3.45 3.10 3.00 3.44 –1.35 0.62 –0.20 –1.30 1.76 0.28 0.00 2.86 4.40 0.00 0.11 0.45 –0.66 –0.63 –0.73 0.22 0.19 0.36 –0.02 1.77 1.56 0.94 1.97 2.65 –0.39 0.02 –0.06 –0.85 –0.60 –0.44 2.82 3.35 3.26 3.07 3.09 3.04 –1.26 1.22 –0.50 –2.31 2.04 –2.78 From the comparison of the Fe and O PDOS, the common feature of peak structures reveals strong orbital hybridization between the Fe d xy and O px ,y states for the H and Fe d z –O pz for the O site.20 To get more insights on the sign change of MAE, we plot the k-resolved MAE, MAE(k), over two-dimensional Brillouin zone (BZ) in Figs 3(a) and 3(b) for the H and O sites, respectively The dominant contribution that yields the negative for the H and positive MAE for the O site is mainly at the M point and along the BZ line between the Γ and X points The corresponding spin-down band structures projected onto the Fe d orbitals are also shown in Figs 3(c) and 3(d), respectively, where the size of the symbols is proportional to their weights Here, we follow the recipe of the second-order perturbation theory by Wang et al., where MAE is determined by the SOC between FIG PDOS of the (a) and (b) Fe adatom and (c) and (d) O atom of the Fe |BaTiO3 for the H and O sites with P↑ In (a) and (b), the d xy , d xz , d z2 , d yz , and dx2 −y2 orbital states of the Fe adatom are shown in black, orange, red, green, and blue, respectively In (c) and (d), the px , pz , and py orbital states of the O atom are shown in black, red, and blue, respectively The Fermi level is set to zero energy 055816-5 Odkhuu et al AIP Advances 7, 055816 (2017) FIG (a) and (b) MAE(k) (in unit of meV) and (c) and (d) the spin-down band structure of the Fe adatom of the Fe |BaTiO3 for the H and O sites with P↑ , respectively In (c) and (d), the d xy , d xz , d z2 , d yz , and dx2 −y2 orbital states of the Fe adatom are shown in black, orange, red, green, and blue, respectively Size of symbols is proportional to their weights and the Fermi level is set to zero energy occupied and unoccupied bands;21 MAE↓↓ = ξ P o,u [ |hΨo↓ |Lz |Ψu↓ i| Eu↓ − Eo↓ − |hΨo↓ |Lx |Ψu↓ i| ], Eu↓ − Eo↓ where Ψo↓ (Ψu↓ ) and Eo↓ (Eu↓ ) represent the eigenstates and eigenvalues of occupied (unoccupied) states for the spin-down state (↓), respectively The other spin-channel decomposition terms of MAE, which involve the spin-up state, ↑↓ and ↑↑, are neglected, owing to the completely filled majority bands (Figs 2(a) and 2(b)) analogs to the 3d-to-5d transition metals explored in the previous full-potential calculations.22,23 The positive and negative contributions to MAE are characterized by L z and L x operators, respectively As seen in Fig 3(c), the SOC states between the occupied d z2 (d xy ) and unoccupied d yz bands at M point can lead to the negative MAE(k) therein These negative contributions by hz2 |Lx |yzi and hxy|Lx |yzi are not applicable to the O site because of the almost filled d yz and empty d z2 bands at M, as discussed in Figs 2(a) and 2(b) Instead, the positive MAE(k) must be developed at M through hyz|Lz |xzi and hxy|Lz |x − y2 i (Fig 3(d)) The latter also gives the main contribution to the PMA of the O site at ΓX, which has the largest contribution to the PMA, by a factor of 2, compared to the other matrix elements.21 We next investigate the effect of the full coverage of the Fe adatoms on magnetism and MAE in Fe|BaTiO3 and Fe|PbTiO3 For the full coverage of Fe ML, where there are two Fe atoms on (1 × 1) unit cell lattice of BaTiO3 (PbTiO3 ), only two possible adsorption sites of Fe atoms exist; namely O and H-and-T [Fig 1(d)] In consistent with the previous studies,9,18,19 the total energy calculations reveal that the O site is more favorable than the H-and-T site regardless of polarization for both Fe|BaTiO3 and Fe|PbTiO3 This is in contrast to the H site for the cases of half and low coverages of Fe ML, which is due to the significant energy cost arisen from the unfavorable T site (Table I) However, the d Ti–O and d Fe–O , and the interface Fe and Ti moments tend to retain almost the same features of the O site in 1/2ML Fe|BaTiO3 and Fe|PbTiO3 (Table I) Figures 4(a) and 4(b) show the calculated MAE and its sensitivity (η) to the polarization for Fe|BaTiO3 and Fe|PbTiO3 , respectively, where η = ∆MAE/∆P and ∆P = P↑ − P↓ As for 1/2ML 055816-6 Odkhuu et al AIP Advances 7, 055816 (2017) FIG (a) MAE for P↓ (blue) and P↑ (orange), and (b) η of the 1ML Fe |BaTiO3 and Fe |PbTiO3 Fe|BaTiO3 (Fe|PbTiO3 ), the PMA is still preserved in the 1ML coverage for the O site with MAE = 1.39 (1.91) erg/cm2 for P↓ and 1.72 (1.04) erg/cm2 for P↑ The computed results are more or less comparable with those reported in previous calculations.18,19 Note that the MAE of Fe|BaTiO3 increases from P↓ to P↑ whereas it decreases for Fe|PbTiO3 , resulting in the distinct η in sign (Fig 4(b)) Importantly, these results suggest that the magnetization direction of the Fe adatoms on BaTiO3 and PbTiO3 surfaces can be switched and undergoes a transition from PMA to in-plane orientation by modifying the coverage of Fe atoms Such different behaviours of MAE for different adsorption sites of Fe atoms are the results of the changes in spin-orbit coupled d states near the Fermi level due to the hybridization effects between the Fe-d and O-p orbitals, as addressed previously The further increase in thickness of the Fe films was not considered in the present study, which we believe would not modify at least the sign of MAE because the anisotropic phenomenon is mainly due to the interface effect IV CONCLUSION Based on first-principles electronic structure calculations, we identify the tremendous effects of the coverage and adsorption site of ferromagnetic atoms on magnetic anisotropy and its electric field dependence in ferromagnet|ferroelectric heterostructures More specifically, we show that, as a common phenomenon in ferromagnet|ferroelectric, the spin orientation depends on the coverage of the Fe adatoms; PMA for the full coverage of Fe ML but in-plane magnetization at the half or lower coverages The preferable adsorption site of the Fe atoms on TiO2 surface layer is determinant for magnetization reorientation, in which the underlying mechanism is the coordinate dependent hybridization between the Fe-d and O-p orbitals The present prediction provides an interesting alternative worthy of further experimental investigation in the area of dimensionally controllable magnetoelectric phenomenon ACKNOWLEDGMENTS This work was supported by Incheon National University Research Grant in 20151412 A D Kent and Spaldin, Nat Mater 9, 699 (2010) C Slonczewski, J Magn Magn Mater 159, L1 (1996) W Eerenstein, N D Mathur, and J F Scott, Nat Mater 442, 759 (2006) J F Scott, Nat Mater 6, 256 (2007) T Zhao et al., Nat Mater 5, 823 (2006) D D Dung et al., Mater Lett 156, 159 (2015) J T Heron et al., Phys Rev Lett 107, 217202 (2011) Y.-H Chu et al., Nat Mater 7, 478 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(2017) Electric control of magnetism in low- dimensional magnets on ferroelectric surfaces Dorj Odkhuu,1,a Tumurbaatar Tsevelmaa,2 S H Rhim,2 Soon Cheol Hong,2,b and Deleg Sangaa3 Department of Physics,... opportunities in spintronics.1 Recent developments of spintronics in magnetic memory technology are based on the control of the direction of magnetization or magnetic anisotropy either through the spin... electronic structures, and magnetism of a ferromagnet on ferroelectric surfaces In this study, ab initio electronic structure calculations reveal magnetoelectric effect in subto-full coverage of