Article pubs.acs.org/JPCC
Polar Catastrophe, Orbital Reconstruction, and Emergent Ferromagnetic Exchange Coupling at the SrFeO2(001) Surface Hai-Shuang Lu,† Tian-Yi Cai,† Sheng Ju,*,† and Chang-De Gong*,‡,§ †
Department of Physics and Jiangsu Key Laboratory of Thin Films, Soochow University, Suzhou 215006, P. R. China Center for Statistical and Theoretical Condensed Matter Physics and Department of Physics, Zhejiang Normal University, Jinhua 321004, P. R. China § National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University, Nanjing 210093, P. R. China ‡
S Supporting Information *
ABSTRACT: The FeO2-terminated (001) surface of the stable antiferromagnetic insulating phase of the infinite-layer oxide SrFeO2 is found to undergo a magnetic reconstruction consisting of a spin-flip process at the surface: Each Fe spin at the surface flips to pair with one in the subsurface layer. In spite of the polar catastrophe inherent at the polar surface, the behavior is driven by a reduced intra-atomic 3dz2−4s hybridization and the enhanced Hund’s coupling due to surface symmetry lowering. These results, based on density-functional theory, show a surface-driven ferromagnetic exchange coupling in transition-metal oxides and provide an effective avenue to realize unusual electronic and magnetic properties.
I. INTRODUCTION The surface and interface of transition-metal oxides exhibit a range of correlated phenomena with applications to many fields, including electronics, spintronics, photovoltaics, and photocatalysis.1−8 In particular, when the polar catastrophe develops, a novel electronic state could be realized via the charge-transfer-driven electronic reconstruction. A well-known example, the polar−nonpolar heterointerface of LaAlO3/ SrTiO3,9 exhibits a two-dimensional electron gas of high mobility, electric tunability, and giant persistent photoconductivity. Replacing the nonmagnetic SrTiO3 with the antiferromagnetic (AFM) perovskites SrMnO3 and EuTiO3 will give rise to the fully spin-polarized two-dimensional electron gas and hole, respectively,10,11 opening a new path for exploring spintronics at the heterointerface of transition-metal oxides. Recently an infinite-layer oxide SrFeO2 was synthesized successfully.12 Unlike the conventional ABO3 perovskite structure, with possible (AO)1−, (AO)0, (AO)1+, (BO2)1+, (BO2)0, and (BO2)1− layers, the infinitely layered structure could sustain a highly charged Sr2+ layer and (FeO2)2− layer. Despite intense research interest in the infinite-layer oxide SrFeO2, which attempted to understand its unusual structural, electronic, magnetic, and optical properties,12−25 very little is known about its surface and interface. As shown in Figure 1a, FeO2-terminated (001) surface with alternating (FeO2)2− and Sr2+ stacking along [001] direction exhibits a polar discontinuity. An electronic reconstruction through the transition from Fe2+ (3d6) to Fe3+ (3d5) at the surface could be expected to avoid the polar catastrophe. However, unlike the electron © 2015 American Chemical Society
doping in transition-metal oxides (e.g., n-type LaAlO3/SrTiO3 heterointerface),9 the hole doping developed here could involve the unoccupied oxygen 2p states as an alternative, therefore making knowledge of the electronic state of the SrFeO2(001) surface illusive. In addition, as shown in Figure 1b, the magnetic ordering at the (001) surface would undergo simultaneously a magnetic reconstruction. As demonstrated in Figure 1b, besides the unreconstructed one, either the spin-flip AFM transition or the spin-flip ferromagnetic (FM) transition is possible. In this paper, based on the density-functional theory, we provide a comprehensive first-principles study of the electronic and magnetic properties of the SrFeO2(001) surface. We find unexpectedly rich effects of surface symmetry lowering: a spinflip occurs on the surface Fe ions coupled ferromagnetically with subsurface Fe ions. The underlying physical mechanism is analyzed by comparing with the electronic and magnetic properties of the (001) surface of an isostructural CaCuO2,26,27 where the intrinsic intra-atomic Hund’s coupling is found to play the crucial role.
II. COMPUTATIONAL METHOD Our ab initio calculations are based on spin-polarized densityfunctional theory (DFT) and are performed using the accurate full potential projector augmented wave (PAW) method28 as implemented in the Vienna ab Initio Simulation Package Received: May 2, 2015 Revised: June 19, 2015 Published: June 23, 2015 17673
DOI: 10.1021/acs.jpcc.5b04221 J. Phys. Chem. C 2015, 119, 17673−17679
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III. RESULTS AND DISCUSSION As shown in Table 1, the spin-flip AFM is energetically favorable at SrFeO2(001) surface, while the spin-flip FM is the Table 1. Total Energies (meV per surface) of SrFeO2(001) and CaCuO2(001) Surfaces with Different Surface Magnetic Orderings SrFeO2 CaCuO2
unreconstructed
spin-flip AFM
spin-flip FM
138.45 313.04
0 315.36
314.59 0
ground state for CaCuO2(001). Compared with the bulk value of 3.7 μB/Fe, the local magnetic moment of surface Fe ions is increased to 4.2 μB. On the other hand, for CaCuO2, the local magnetic moment at the surface Cu sites is almost unchanged, keeping the bulk value of around 0.6 μB. The magnetic exchange coupling constants of 1 (the intralayer coupling at the surface) and 1⊥ (the interlayer coupling between the surface and subsurface) are further derived within a classical spin Hamiltonian, H = −∑ 1SiSj . Here, S = 2 for bulk SrFeO2 and S = 1/2 for bulk CaCuO2. For the surface, S changes to 5/2 for Fe ions. As revealed in Table 2, compared with the bulk, the
Figure 1. (a) Illustration of the polar catastrophe developed at FeO2terminated SrFeO2(001) surface. (b) Magnetic reconstruction at the SrFeO2(001) surface. From left to right is the unreconstructed, the spin-flip AFM, and the spin-flip FM transitions, respectively.
Table 2. Magnetic Exchange Coupling Constants (meV) for SrFeO2 and CaCuO2a XO2
(VASP).29 The generalized gradient approximation (GGA) in the form proposed by Perdew, Burke, and Ernzerhof (PBE) is used.30 The on-site Coulomb correlation is included within the GGA+U approach with an effective Hubbard U = 6 eV for the 3d orbitals of Fe and Cu.31 A large plane-wave cutoff of 600 eV is used throughout the calculations and the convergence criteria for the energy is 10−6 eV. The PAW potentials are used to describe the electron−ion interaction with 10 valence electrons for Sr (4s24p65s2), 10 for Ca (3s23p64s2), 14 for Fe (3p63d64s2), 17 for Cu (3p63d104s1), and 6 for O (2s22p4). The bulk SrFeO2 and CaCuO2 possess a tetragonal structure with space group P4/mmm. We use a slab model to simulate the surface (bulk frozen), which contains seven principle FeO2 (or CuO2) layers, six Sr (or Cu) layers, and a 15 Å vacuum layer. The in-plane geometry is set as √2a × √2a for various magnetic orderings, and a 10 × 10 × 1 Monkhorst−Pack k-point mesh is used in the Brillouin zone integration. In our calculations, ions are relaxed toward equilibrium positions until the Hellman− Feynman forces are less than 1 meV/Å. For SrFeO2 bulk and CaCuO2 bulk, the G-type AFM ordering is the ground state, which is in good agreement with experiments, as well as previous calculations.12,14,15,18,27 Compared with the ground state of G-type AFM, the A-type AFM, C-type AFM, and FM states are 66.45, 13.50, and 72.86 higher in the total energy (meV/f.u.) for SrFeO2. For CaCuO2, the total energies are 183.68, 2.89, 192.36, and 0.00 (meV/f.u.) for the A-type AFM, C-type AFM, FM, and G-type AFM, respectively. The optimized in-plane lattice constant (a) is 4.0637 and 3.8837 Å for SrFeO2 and CaCuO2, respectively. The out-of-plane lattice constant (c) is 3.4798 and 3.1983 Å for SrFeO2 and CaCuO2, respectively. Experimentally, a = 3.9911 Å and c = 3.4741 Å for SrFeO2.12 For CaCuO2, a = 3.8611 Å and c = 3.1995 Å.26
bulk
a
pristine X2O4
X2O3
type I
type II
−0.98 −96.08
−0.42
−0.10
−4.17
−3.16
−3.99
SrFeO2
1∥
−3.93
−4.91
−3.05
CaCuO2
1⊥ 1∥
−1.24 −186.58
6.92 157.10
1⊥
−11.57
−2.32
X indicates Fe or Cu.
interlayer coupling between the surface and the subsurface Fe ions changes sign and increases significantly in magnitude. The intralayer coupling possesses a similar magnitude and increases a little. On the other hand, the CaCuO2 surface behaves in an opposite way, with the interplane coupling almost diminishing and the intralayer one changing sign. Clearly, for SrFeO2 the magnetic ordering is enhanced, rather than decreased, at the (001) surface, while for CaCuO2, the interplane coupling is weakened significantly, making the nature of the surface much closer to the two-dimensional one of an infinite-layer structure. To understand the magnetic reconstructions revealed above, the electronic density of states of the surface Fe (or Cu) and O are plotted in Figure 2 and are compared with those of the subsurface as well as the center layer. For the center layer of Fe ions, the strong hybridization between 3dz2 and 4s orbitals results in a double occupation of the 3dz2 electronic state.14 However, the 3dz2 orbital gets partially occupied for the subsurface Fe ions, and the electronic state of surface Fe ions changes to a d5 configuration. On the other hand, the surface of CaCuO2 is metallic and the holes reside mainly at oxygen sites. From the exact orbital occupation and the integration of density of states of surface Fe and O and Cu and O, the valence state of surface FeO2 and CuO2 approaches −1, in agreement with the polar catastrophe picture demonstrated in Figure 1a. In Figure 3, we illustrate the evolution of the band diagram at SrFeO2(001) and CaCuO2(001) surfaces. For bulk CaCuO2, 17674
DOI: 10.1021/acs.jpcc.5b04221 J. Phys. Chem. C 2015, 119, 17673−17679
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in an obvious reduction in the Coulomb repulsion and, accordingly, in the corresponding intra-atomic Hund’s coupling J. J, as indicated by the difference between the centers of mass of the spin-up and spin-down bands, is only around 2 eV for the 3dz2 orbital of the center layer. For other orbitals, the intraatomic Hund’s coupling reaches as high as 10 eV. Clearly, both an anisotropic environment for the Fe atom and an effective reduction in the Coulomb repulsion are required for the doubly occupied 3dz2 orbitals, as observed in the bulk (or the center layer of the slab). Considering a charge-transfer insulator, the polar-catastrophe-driven hole doping at the (001) surface will lead to a rigid shift of the Fermi energy, crossing the formally fully occupied O 2p states. For the CaCuO2 surface, the original charge transfer energy gap Δ systematically decreases upon increasing the atomic number or formal valence of the metal element. However, for the surface layer of SrFeO2, instead of the itinerant state, a band gap exists between the occupied O 2p states and the empty down-spin Fe 3dz2 state. Such a p−d band gap looks like the conventional charge-transfer-type band gap. The loss of the inversion symmetry along the c axis leads to an obvious reduction of the hybridization between the Fe 3dz2 and 4s orbitals (see Figure 2). Therefore, the enhanced Hund’s coupling between Fe 3dz2 orbitals lifts the energy level of the minority 3dz2 with a band gap opened at the surface. The role played by the Hund’s coupling can be judged further from the electronic structure of the subsurface layer. As shown in Figure 2, the subsurface of CaCuO2 has a similar band structure as the surface layer, which can be described within the above picture for the hole doping in a charge-transfer insulator. However, for the subsurface of SrFeO2, a small gap appears between Fe 3dz2 sub-bands of down-spin channels, corresponding to the charge fluctuation between two split 3dz2 bands, and can be regarded as a dz2−dz2 gap to distinguish it from the conventional Mott−Hubbard d−d type gap in bulk strongly correlated systems. Indeed, both a reduction of Hund’s coupling J in the Fe 3dz2 orbital (the existence of the inversion symmetry in Fe along c axis same as the center layer) and the effective hole doping (the extended distribution of the doped hole from the surface layer) are required for this particular dz2− dz2 gap opening. Here, it should be noted that the magnitude of the dz2−dz2 band gap is related neither to the Hubbard Coulomb energy U nor to the charge-transfer energy Δ in a direct way. The band gap opens as a consequence of the competition between the Hund’s coupling and the carriers’ kinetic energy. Now we are able to explain the magnetic reconstruction from the orbital states. For the SrFeO2 surface with an electronic configuration of (dz2)1(dxz/dyz)2(dxy)1(dx2−y2) 1, the intraplane interaction is still dominated by the dx2−y2 orbitals of two adjacent Fe ions through O pσ, which favor the AFM order of Fe ions as the center layer. For the magnetic interaction between the surface and subsurface layers, the direct exchange interactions between the singly occupied degenerate dxz/dyz orbitals still favor AFM coupling for the bulk SrFeO2 (see Figure 3b). However, strong FM coupling via the virtual hopping process between Fe doubly occupied (3dz2)2 states of the subsurface layer and singly occupied (3dz2)1 states of the surface one develops (see Figure 3c). Therefore, it is the enhanced Hund’s coupling Jdz2 at the surface layer that drives a FM coupling between the surface and subsurface layers. For the CaCuO2 surface, the FM intralayer coupling is mediated by the
Figure 2. Orbital resolved density of states of the (001) surfaces of SrFeO2 (left) and CaCuO2 (right). From top to bottom is the surface, the subsurface, and the center layer. The shaded area is for the oxygen at the corresponding layer. The Fermi level is at energy zero, as indicated with a dotted line.
Figure 3. (a) Illustration of the electronic band diagram of CaCuO2 and SrFeO2 surfaces. Pink and blue colors represent O 2p and Cu/Fe 3d states, respectively. Fe dz2 state in SrFeO2 is highlighted with red. The Hubbard Coulomb repulsion energy (U), the charge-transfer energy (Δ), and the Hund’s exchange energy (J) are indicated. (b) AFM coupling in the case of half-occupied degenerate dyz/dzx orbitals. (c) FM coupling between the doubly and singly occupied dz2 orbitals.
the band gap opens between the occupied O 2p states and the empty Cu 3dx2−y2 states, showing a typical charge-transfer-type electronic state. In contrast, a Mott−Hubbard band gap is revealed for bulk SrFeO2, where the Fe 3dz2 minority state locates right below the gap and other 3d orbitals of the same spin-channel locate above it. Due to the tetragonal point symmetry at the Fe site, the 3dz2 orbital is fully symmetric and hybridizes with the formally empty Fe 4s state. Such a mixing is very different for the majority and minority spins, which results 17675
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The Journal of Physical Chemistry C itinerant holes, which arise mainly from O 2px(y) states and slightly from Cu 3dx2−y2 states. The interlayer interaction remains AFM due to the weak hybridization between these orbitals. It should be pointed that Sr-terminated SrFeO2(001) possesses the G-type AFM ordering, and orbital occupation of surface Fe ions does not change from the bulk. The outmost Sr layer becomes metallic, effectively screening the polar field developed by alternatively stacked Sr2+−(FeO2)2−−Sr2+− (FeO2)2−... along the c axis. Up to now, we have focused on pristine surfaces. The polar catastrophe developed at the polar oxide surface could also be removed by atomic reconstructions. To incorporate such situations, nonstoichiometric surfaces are considered further. As shown in Figure 4, four kinds of atomic configurations are
Figure 5. Orbital-resolved density of states of nonstoichiometric Fe2O3 and Cu2O3 surfaces. From top to bottom is the surface, the subsurface, and the center layer. The shaded area is for the oxygen at the corresponding layer. The Fermi level is at energy zero, as indicated with a dotted line.
Figure 4. Illustration of atomic configurations of SrFeO2(001) [CaCuO2)(001)] surfaces. From left to right is the pristine (a) Fe2O4 (Cu2O4) and the nonstoichiometric surfaces of (b) Fe2O3 (Cu2O3), (c) FeO2 (CuO2) type I, (d) FeO2 (CuO2) type II, and (e) O.
distinguished in the √2a × √2a surface geometry. For these cases, the valence state of each ion is unchanged from the bulk value, i.e., O2− and Fe2+ or Cu2+. Therefore, agreeing with the scenario depicted in Figure 1a, the polar catastrophe is naturally removed via the formation of (FeO1.5)−1 and (CuO1.5)−1, (Fe0.5O)−1 and (Cu0.5O)−1, and (O0.5)−1 surface layers. Firstprinciples calculations reveal that the magnetic ordering does not change at these nonstoichiometric surfaces. However, as shown in Table 2, certain variations of magnetic exchange coupling constants are found, due to the reduced coordinates of Fe−O bonds or Cu−O bonds at these nonstoichiometric surfaces. Compared with the bulk, all the surfaces are insulating with a reduced band gap. The exchange splitting of 3d orbitals of surface Fe2+ does not change strongly from those of the bulk, showing different strengths of Hund’s coupling between Fe2+ and Fe3+.32,33 The detailed electronic structures of Fe2O3 and Cu2O3 surfaces are shown in Figure 5. For FeO2 and CuO2 surfaces, type II is more energetically favorable than type I for both SrFeO2 and CaCuO2. In addition, compared with the electronic states of type I (see Figure 6), the arrangement of surface oxygens along the O−Cu−O line (see Figure 7) will lead to an obvious change of electronic state of CaCuO2 from the charge-transfer type to the Mott−Hubbard type, with an asymmetry between valence maximum (dxy) and conduction minimum (dyz). For SrFeO2, the effective reduction of 3d−4s hybridization is evident when the surfaces gradually lose D4 symmetry. To show the surface phase stability, we start from the grand potential Ωλ, which is a measure of the excess energy of a symmetric system exposing a termination of a given composition λ to a reservoir. Here, based on density-functional theory, we focus on the zero temperature properties, where the internal energy is calculated and compared among different surface magnetic orderings. Within the mean field framework,
Figure 6. Orbital-resolved density of states of nonstoichiometric FeO2 and CuO2 (type I). From top to bottom is the surface, the subsurface, and the center layer. The shaded area is for the oxygen at the corresponding layer. The Fermi level is at energy zero, as indicated with a dotted line.
the entropy arising from three different surface magnetic orderings at finite temperatures was determined; e.g., at room temperature it is around 28.44 meV, much smaller than the total energy differences (around 140 meV for SrFeO2 and 310 meV for CaCuO2) between the ground state and the other two 17676
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E O2 1 ⎡ λ SrFeO2 ⎢Eslab − NFeE bulk − molecule (NO − 2NFe) 2S ⎢⎣ 2 ⎤ Sr (NSr − NFe)⎥ − E bulk ⎥⎦
(4)
The ranges of the two independent parameters ΔμO and ΔμSr can be determined using the following set of conditions. In order to avoid the elements precipitating into Sr bulk, Fe bulk, and oxygen gas, the upper bounds are set by ΔμSr, ΔμFe, and ΔμO ≤ 0. The lower bounds are obtained using ΔμSr + 2ΔμO > 2 2 −ESrFeO , where the formation energy −ESrFeO is defined as − f f SrFeO2 SrFeO2 O2 Fe Sr Ef = Ebulk − Ebulk − Ebulk − Emolecule. With the above considerations, the exact equations for SrFeO2 surfaces are
Figure 7. Orbital-resolved density of states of nonstoichiometric FeO2 and CuO2 (type II). From top to bottom is the surface, the subsurface, and the center layer. The shaded area is for the oxygens at the corresponding layer. The Fermi level is at energy zero, as indicated with a dotted line.
1 λ [Eslab − NFeμFe − NSrμSr − NOμO)] 2S
Ω FeO2 = 0.068691
(7)
ΩO = −0.097439 − 0.030278(ΔμO + ΔμSr )
(8)
(9)
ΩCu 2O3 = 0.284169 + 0.033150(ΔμO + ΔμCa )
(10)
ΩCuO2 = 0.0633
(11)
ΩO = −0.117548 − 0.033150(ΔμO + ΔμCa )
(12)
Figure 8. Phase stability diagram of (a) SrFeO2(001) and (b) CaCuO2(001) surfaces.
(2)
It is revealed that the range of accessible values for the surface grand potential depends on the maximum and minimum values of μSr and μO chemical potentials. The possible variations in μ reflect the experimental growth O2 conditions. Under the O-rich condition μO = Emolecule /2 and Sr for the Sr-rich condition μSr = Ebulk. Defining ΔμO = μO − 2 EOmolecule /2 and ΔμSr = μSr −ESr bulk, we obtain Ωλ = Φλ −
(6)
With the above conditions, as shown in Figure 8, the pristine SrFeO2(001) surface is available under a wide range of synthesis conditions, making the spin-flip magnetic reconstruction experimentally accessible.
(1)
1 λ SrFeO2 [Eslab − NFeE bulk − μO(NO − 2NFe) 2S − μSr (NSr − NFe)]
Ω Fe2O3 = 0.254937 + 0.030278(ΔμO + ΔμSr )
ΩCu 2O4 = 0.256652 + 0.033150ΔμCa
Here, S denotes the surface area, and Eλslab is the total energy of λ termination, with λ being either Fe2O4, Fe2O3, FeO2, or O. The quantities μFe, μSr, and μO are the chemical potentials of the Fe, Sr, and O atomic species, respectively, and NFe, NSr, NO are the number of Fe, Sr, and O atoms in the slab. The chemical potential of the bulk SrFeO2 system (μSrFeO2) can be written as the sum of chemical potentials of individual species in the crystal bulk; i.e., μSrFeO2 = μSr + μFe + 2 μO. When the surface is in equilibrium with the bulk, we have μSrFeO2 = 2 ESrFeO and bulk Ωλ =
(5)
For CaCuO2 surfaces, the equations are
surface magnetic orderings. Taking SrFeO2(001) surface as an example, the surface grand potential is defined as follows: Ωλ =
Ω Fe2O4 = 0.207622 + 0.030278ΔμSr
Finally, it should be pointed out that the surface and interface of oxides have provided many novel systems with unusual magnetic properties and have attracted intense interest from researchers in condensed matter physics, materials science, and surface chemistry. Compared with the nonpolar oxide surface,34,35 isopolar heterointerface,36,37 and metal−insulator heterointerface,38−42 the intrinsic tendency of charge transfer associated with polar discontinuity at the surface and interface could provide an effective degree of freedom in tuning the magnetic properties. Polar discontinuity in the conventional perovskite ABO3 system, e.g., +1/0 type as observed for (LaO)+/(TiO2)0 at the n-type LaAlO3/SrTiO3 interface, usually
1 [ΔμO(NO − 2NFe) + ΔμSr (NSr − NFe)] 2S (3)
with 17677
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leads to a noninteger carrier (0.5 electrons or holes) transferred across the interface and consequently the metallic state. The strong polarity of the −2/0 type, which is unique to the infinitely layered structure, could lead to an integer number of the transferred electron and insulating phase, as revealed at the SrFeO2(001) surface.
IV. CONCLUSIONS In conclusion, a ferromagnetic exchange coupling has been revealed at the SrFeO2(001) surface from first-principle density-functional calculations. Although the polar catastrophe developed at (FeO2)2− could guarantee the charge transfer and electronic reconstruction, the exact orbital occupation and magnetic ordering at the surface are determined by the intrinsic Hund’s coupling of the transition metal. Our findings not only provide new insights into the electronic state in transition-metal oxides but also broaden the current interest in the heterointerface of transition-metal oxides from itinerant systems to insulating ones with multiple functionalities.
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ASSOCIATED CONTENT
S Supporting Information *
Total energies of Sr-terminated SrFeO2(001) surface with different surface magnetic orderings (Table I) and partial density of states of Sr-terminated SrFeO2(001) surface (Figure 1). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.jpcc.5b04221.
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AUTHOR INFORMATION
Corresponding Authors
*S.J. e-mail:
[email protected]. *C.-D.G. e-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Basic Research Program of China (973 Program 2013CB934400 and 2014CB920900), the National Natural Science Foundation of China under Grants No. 11104193 and No. 11374220, Qin Lan Project of Jiangsu province, and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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