Tuning charge and orbital ordering in DyNiO3 by biaxial strain*

Litong Jiang(姜麗桐) Kuijuan Jin(金奎娟) Wenning Ren(任文寧) and Guozhen Yang(楊國楨)

1Beijing National Laboratory for Condensed Matter Physics,Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China

2School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

3Songshan Lake Materials Laboratory,Dongguan 523808,China

Keywords: charge ordering,orbital ordering,Jahn-Teller distortion,biaxial strain

1. Introduction

The rare-earth nickelates,RNiO3(RNO,Rstrands for La or Ce, Pr,..., Lu of the rare-earth series), have been studied for decades, because of a large variety of the possible physical properties.[1-4]Actually, this material is a type of ABO3perovskites. TheRelement locates on the A site and the Ni locates on the B site. An idealRNO perovskite,which has six equal Ni-O bond lengths in its NiO6octahedra, is inPmˉ3mphase.[4]RNO has a sharp metal-insulator transition, exceptR=La. This transition temperature (TMI) increases as theRcation decreases.[5,6]

The structural changes of DyNiO3(DNO), one in the family ofRNiO3perovskite rare-earth nickelates, leading to the metal-insulator transition (TMI=564 K), have been explored via experiments.[7]This sharp transition is accompanied by a structural phase transition. BelowTMI, namely, in the insulating or semi-conducting regime,DNO favors monoclinic withP21/nspace group. The charge disproportionation breaks the equivalent NiO6octahedra into two nonequivalent ones: a type of NiO6octahedra with longer bonds (NiL) and the other type of octahedra with shorter bonds (NiS), which results from charge ordering.[3,6,8]AboveTMI,DNO becomes orthorhombic withPbnmspace group with orbital ordering states. Experiments show thatTMIis related to the strength of the orthorhombic distortion.[9]

The substrate fixes the in-plane lattice constants of epitaxial growth films with distortions,rotations,octahedral tilts,and lattice symmetry,so that the thin films behave differently from their bulk counterpart.[16,17]The crystal structures of nickelates are capable of being tuned by producing epitaxial films on various substrates, which has been reported in several materials ofRNO family under the in-plane biaxial strain.[2,17-20]Because of the in-plane mismatch, the out-of plane lattice parameter of the film will be stretched or compressed. Consequently,the oxygen octahedra obtain the staggered Jahn-Teller distortion under the tensile strain or the charge disproportion under sufficient compressive strain.[10]ForRNO, epitaxial strain is a widely investigated method to manipulate functional properties.[17-22]Mikheevet al.reported that NdNiO3thin films are capable of being manipulated between the paramagnetic metallic state and the antiferromagnetic insulating state by applying epitaxial strain and changing thickness.[23]So many research works tried strain engineering to obtain charge or orbital ordering of egorbitals for other common nickelates inRNO series.[24-26]Heet al.explored the LuNiO3under biaxial strain in Ref.[24],which revealed that with sufficient applied strain(around 4%)the system undergoes a first-order transition. Zhanget al.suggested that the metal-insulating transition temperature is relevant to symmetry. SinceTMIis suppressed in NdNiO3/YAlO3by tuning the distortion of the epitaxial films.[25]Varignonet al.focused on PrNiO3and NdNiO3in Ref. [26], which reported that the first order phase transition can be tuned by strain. But no study about the strain effect in DNO has been reported yet.In this paper,by carrying out density functional theory(DFT)calculation, we present that a sufficient applied tensile strain forces the system into a non-charge-ordered state. Additionally,the staggered Jahn-Teller distortion can be characterized by this tensile strain. We also show how the in-plane biaxial compressive and tensile strains modify the electronic configuration. This work provides some theoretical results for further experiments about growing DNO thin films for manipulating its electronic structures.

2. Method

Our DFT calculations were conducted by generalgradient approximation (GGA) with the Perdew-Burke-Ernzerhof revised for solids (PBEsol)[27]and projector augmented wave(PAW)method[28]as implemented in the Viennaab initiosimulation package (VASP).[29]For the relaxation part, the 6×6×2 centeredk-point meshes were used. For magnetism, we considered four 20-atom-structure antiferromagnetic configurations: A-type antiferromagnetic(A-AFM),C-type antiferromagnetic(C-AFM),G-type antiferromagnetic(G-AFM),and ferromagnetic(FM)ones. Here,a HubbardUcorrection[30]withUNi=2 eV (J=0 eV) was added to improve the description of the electronic structure of Ni(transition metal). Previous works showed that a smallUwas used normally for describing nickelates accurately.[31,32]Some articles reported thatU(Ni)=0-6 eV does not impact the crystal geometry very much.[21,26,33]Some articles showed different values ofUhave negligible effects on the crystal structure,but open the band gap with largerU.[30]Here,we also used otherUvalues (i.e., 1 eV, 3 eV, 4 eV, 5 eV, and 6 eV). The PAW potentials were Ni (3p63d84s2), Dy (6s26p), and O (2s22p4).The energy cutoff was 540 eV.The bond lengths and octehedra volumes were read via VESTA.[34]

3. Results

Fig.1. The structure of the ground state of DNO in P21/n space group.NiO6 octahedra are illustrated by gray cubes. The navy, gray, and red spheres represent Dy,Ni,and O atoms,respectively.

Table 1. Calculated optimized and experimental lattice parameters of DNO.

Fig.2. Total energy versus lattice mismatch. The purple line represents Pbnm phase;the pink line represents P21/n phase.

The energy of DNO with applied compressive or tensile biaxial strain is plotted in Fig.2. A first-order phase transition fromP21/ntoPbnmoccurs driven by the tensile strain, obviously. Since the energy of theP21/nphase is lower than that of thePbnmphase when the tensile strain is less than 4.7%, which also means the charge ordering is more stable.The transition occurs in theabplane around 4.7%mismatch,corresponding toasub=3.95 ?A.In contrast,the orbital ordering (Pbnm) phase is energetically favorable, if the mismatch under tensile strain is larger than 4.7%.

Fig.3. The schemes of(a)breathing modes. (b)Type-d Jahn-Teller distortion and(c)type-a Jahn-Teller distortion.

Figure 3 demonstrates the diagrams of octahedra distions in breathing mode and Jahn-Teller distortions. In the breathing mode,as depicted in Fig.3(a),the NiLand NiSare adjacent alternatively. A large difference between the NiLand NiSoctahedra implies a strong breathing mode. For the Jahn-Teller distortions, there are two types, which play important roles under biaxial strains. The one, which forces the shrink ofzdirection of the octahedra,is named by type-a Jahn-Teller distortion in Fig.3(c). The other one,which distorts the in-plane bonds of the octahedron, is termed as type-d Jahn-Teller distortion (see Fig. 3(b)). The Nixis defined as its Ni-O bonds inxdirection longer than that inydirection in an octahedron.Meanwhile, in the adjacent octahedron Niy, the Ni-O bonds alongxdirection are shorter than that alongydirection.

Before exploring the distortions in DNO under biaxial strain, it is to be mentioned that, thePbnmcrystal structure is very close to its bulk crystal structure and is far away from theP21/nbulk crystal structure after relaxation. Moreover,the symmetry ofPbnmcrystal structure is lower than that ofP21/n. Therefore, it is reasonable to use thePbnmto denote the state without charge disproportionation, and use theP21/nto denote the state with charge disproportionation. We use symmetrical vibration modes to illustrate the lattice distortions and phase transition in DNO under biaxial strain. The breathing mode can be characterized byQ1mode,as shown in Fig. 4(a). The strength of theQ1mode is defined as Eq. (1).TheQ1values can represent the shrink or expansion of the NiO6octahedra.The difference betweenQ1values of adjacent octahedra(NiSand NiL)is shown in Fig.3(a). The larger difference leads to a strong breathing mode. The Jahn-Teller distortions can be specified byQ2andQ3modes(see Figs.4(b)and 4(c)). The strengths ofQ2andQ3modes are defined as Eqs.(2)and(3),respectively.[35,36]The largerQ2andQ3that we obtain in the system, the stronger the type-d and type-a Jahn-Teller distortion occur.

whereLL,LM, andLSrepresent the long, medium, and short(zdirection)Ni-O bonds,respectively.

Fig. 4. (a)-(c) The Q1, Q2, and Q3 modes. The arrows illustrate the displacements generated by the displacement of the oxygen atoms with respect to the regular octahedron.

Fig.5. (a)-(c)Calculated Q1,Q2,and Q3 given by Eqs.(1),(2),and(3)versus lattice mismatch of NiL,NiS,Nix,and Niy.

Figure 5 demonstrates the changing trend ofQ1,Q2,andQ3under the impact of the lattice mismatch. In Fig.5(a),the increase inQ1means the expansion of the NiO6octahedra becomes larger with the increasing tensile strain. The difference between the values ofQ1for NiLand NiSin the charge ordering phase is larger than zero. This can be understood that the purple cubes are larger than the crayon ones, as shown in Fig. 3(a). As mentioned above, it means the breathing mode does exist. However,when the mismatch is larger than 4.7%,the breathing mode vanishes in the orbital ordering phase,because of the zero difference between the values ofQ1for Nixand Niy. In Fig. 5(b),Q2of Nixis near zero under the compressive strain. With the increasing tensile strain,Q2rises promptly. This helps us to explain the emergency of type-d Jahn-Teller distortion in thePbnmphase. In Fig.5(c),Q3for both states shrinks,when the lattice mismatch gets larger.This can be accepted that the lattice constantcis compressed when the film grows on a substrate with large lattice. So, it concludes that the tensile strain strengthens the type-a Jahn-Teller distortion efficiently.

Then, we focus on the electronic structure of DNO. The O 2p bands hybridize with the egorbitals of NiS, because the stronger Coulomb repulsion is induced by the shorter distance between the Ni and O. For the charge ordering phase,the splitting energy of eg/t2gin NiSis larger than that of NiL,resulting in the energy difference of egin the two neighboring Ni ions and a charge ordering. So, Ni-O octahedron being expanded can localize the NiLegstates, which further results in a relatively larger magnetic moment. The NiLobtains 1.2μB, according to our calculations. These results are in agreement with that the charge ordering is more likely to be 2×3d8L→3d8+3d8L2.[11,13,14,32]In the orbital ordering state, one of the egstates is occupied alternately. A longer bond of Ni-O is less capable of attracting charge than a shorter one, which is formed by the hybridization between O 2p and Ni 3d. This is consistent with the result that the real charge value is more than 7 by our calculations. For the Nixin orbital ordering, the tensile strain strengthens the JT distortion,leading to a splitting of eglevels, which enhances the orbital ordering.

We then represent the orbital-resolved electronic density of states(DOS)of NiS,NiL,and Nix(see Fig.6).The different DOS between NiSand NiLsites also interprets their different electronic states. The calculated orbital-resolved density of states of NiSand NiLinP21/nphase is presented in Fig. 6,

where five d orbitals are divided by Jahn-Teller distortion into distinct orbitals egand t2g,respectively. These results indicate that egand t2gorbitals of the Ni atoms split into a high and a low energy regions. In Fig. 6(a), the major spins of the NiLorbitals are mostly occupied. In Fig. 6(c), the minor spins of the egorbitals are basically unoccupied. In contrast, NiSegorbitals(major spin)are occupied partly, with the t2gorbitals are fully occupied,as shown in Figs.6(b)and 6(d). From the DOS configuration, it is shown that the DOS splitting in the 3d shell of NiLis more strong than that of NiS.

Fig.6. The local and projected density of states of(a)-(d)the NiL and NiS in P21/n structure(charge ordering state)under compressive strain(mismatch=?1%);(e),(f)Nix in Pbnm structure(orbital ordering state)under tensile strain(mismatch=4%). The red(blue)color denotes the major spin(minor spin)states.

The electrons and bonds behaviors in DNO can be characterized by the contour maps of charge densities in (001)and (110) slices, as shown in Fig. 7. In the orbital ordering state,it is proved that the Nixand Niyoctahedra are bond centered instead of charge centered (see Fig. 7(a)). Because the longer bonds between the Nixand O 2p are only in thexdirection. Furthermore, the rotation symmetry between neighboring octahedra is consistent with the egalternate occupations.In Fig.7(b),the disproportional bonds arrangement alongxdirection and equivalent arrangement alongzdirection are consistent with the in-plane Jahn-Teller distortion. For the charge ordering state,the NiSions have obvious NiS-O 2p hybridization which is consistent with the electronic configuration of NiSwith 3d8+3d8L2in both(110)and(001)slices,as shown in Figs. 7(c) and 7(d). Figures 6(e), 6(f), 7(a), and 7(b) are helpful to explain the electronic arrangement for the orbital ordering phase. Here, three almost empty egorbitals (blue)are above the Fermi level with only one occupied spin egorbital (red) left. It implies that the hybridization between Nixand O 2p states obtains a significant occupation.

Fig.7. The contour maps of the electron density: (a),(b)Nix in Pbnm structure (OO state) in (001) and (110) slices; (c), (d) NiS and NiL in P21/n structure (charge ordering state) in (001) and (110) slices. The red green blue (RGB) color scale range bar is given. The RGB scale represents electron density from low(green)to high(yellow).

The band gap has been calculated to explore its change with biaxial strain in Fig.8. The band gap shrinks gradually at the beginning with the tensile strain in charge ordering phase.But in the orbital ordering phase, it becomes larger with the tensile strain.Because the top of the valence band is composed of NiLbonds;the bottom of the conduction band is composed of NiSegbands. The egenergy shift induces the band gap,which is connected with the strength of the bond disproportionation. It is capable of shifting NiLegorbitals downward and the NiSegorbitals upward. So that the breathing mode opens the gap, which can explain that change in band gap is larger with the enhanced charge ordering phase. The splitting of the egorbital induces the generation of the band gap,where the band gap of the orbital ordering structure increases with the tensile strain. In the orbital ordering,the egorbitals(major spin) are mostly unoccupied. So, the gap is enlarged by the type-d Jahn-Teller distortion. Additionally, the tensile strain in the orbital ordering phase is capable of enlarging both typed and type-a Jahn-Teller distortions and then opens the band gap,which is in agreement with Fig.8.

Fig. 8. Band gap of DNO versus lattice mismatch. The purple line represents Pbnm phase and the pink line represents P21/n phase.

4. Conclusion and perspectives

The density functional theory has been used to analyze the effects of biaxial strain on the electronic configuration of the transition between charge ordering state and orbital ordering state in DNO.Our calculations have shown that with large enough tensile strain, the charge ordering vanishes. But the orbital ordering emerges at the lattice mismatchη=4.7%.This transition proves that the emergence of type-d Jahn-Teller mode is encouraged by tensile strain. The breathing mode is encouraged by compressive strain. In the charge ordering state, the breathing mode induces the difference between the neighboring NiO6octahedra and splitting of eg/t2g,which leads to a charge transfer between NiSand NiL. The NiSis with the configuration of 3d8L2, because of the strong hybridization with O 2p. The NiLhas a higher occupation of 3d8, since its lower egenergy level. By applying biaxial strain fromη=?1%toη=6%,the band gap becomes narrow gradually at first but becomes wide slightly in the orbital ordering state. In the same situation, type-d Jahn-Teller distortion is enhanced in orbital ordering state,but the breathing mode is shrunk in charge ordering state. Finally,we hope that these results can inspire the relative experimental research on manipulating the electronic structure in DyNiO3.