The nature of the two-peak structure in NiO valence band photoemission
aa r X i v : . [ c ond - m a t . s t r- e l ] A ug The nature of the two-peak structure in NiO valence band photoemission
Byungkyun Kang and Sangkook Choi ∗ Condensed Matter Physics and Materials Science Department,Brookhaven National Laboratory, Upton, NY 11973, USA (Dated: August 16, 2019)In spite of extensive studies on NiO and their accomplishments, the rich physics still raises un-solved physical problems. In particular, the nature of the two-peak structure in the valence bandphotoemission spectra is still controversial. By using ab initio
LQSGW+DMFT, the two-peakstructure is shown to be driven by the concerted effect of antiferromagnetic ordering and intersiteelectron hopping. Magnetic ordering in the Ni- e g orbitals splits majority- and minority-spin Ni- t g levels due to local Hund’s coupling. Strong hybridization between O- p and Ni- e g , a signature ofthe Zhang-Rice bound state formation, boosts oxygen-mediated intersite Ni- e g orbital hopping, re-sulting in the enhancement of majority-spin Ni t g - e g splitting. Interestingly, these two splittingsof distinct physical origins match and give rise to the observed two-peak structure in NiO. Ournew understanding should be useful in designing advanced devices based on the NiO for the holetransport. Introduction.-
A late-transition metal monoxide NiOhas been an archetypical material to explore intricatestrong correlation phenomenona and propose new con-cepts peculiar to strongly-correlated systems. In early1900s, NiO has been suggested, as a Mott-Hubbard in-sulator where its wide band gap originates from strongon-site d-d Coulomb interactions. In late 1900s, Zaanenet al. classfied NiO as a charge-transfer insulator whereits gap originated from the charge transfer between nickeland oxygen [1]. In recent years, its first ionize state isregarded as a Zhang-Rice bound hole state [2, 3].Lately, the potential usage of NiO in advanced photo-voltaic and spintronic devices has revived scientific andtechnological interests in NiO and require a deeper under-standing of its electronic structure. The p-type NiO hasbeen proposed as hole transport layers in perovskite solarcell to improve device stability against oxidation [4, 5].NiO has been used for spintronic applications to benefitfrom its high Neel temperature ( T N =525K) [6–9].In spite of the extensive studies and accomplishments,the rich physics still raise unclear physical problems inNiO. In particular, the nature of the two-peak structurein angle-integrated valence-band photoemission spectraare still unclear. Fig. 1 (a) shows valence band photoe-mission spectra below the Neel temperature [10]. Twopeaks (A and B) are designated as main peaks in valenceband photoemission spectra and also observed in X-raycore-level photoemission [10–17]. It has been known ex-perimentally that non-locality and antiferromagnetic or-dering are essential to give rise to the two-peak structure.In the valence band photoemission on NiO impurity em-bedded in MgO, B peak is strongly suppressed, implyingthe non-local nature of the peak B [18]. In addition, peakA dominates the line shape and peak B is suppressed atthe Neel temperature, inferring its magnetic origin [10].To understand the nature of the two-peak structuretheoretically, various approaches are being pursued. Oneof the approaches is configuration interaction (CI) calcu- lation of cluster models. From the single NiO cluster cal-culation [12, 19], important low-lying many-body stateshave been identified including T high-spin state (a holein the minority-spin Ni- t g orbitals and surrounding O- p orbital), E low-spin state (a hole in the majority-spinNi- e g orbitals and surrounding O- p orbital), and T low-spin state (a hole in the majority-spin Ni- t g orbitals andsurrounding O- p orbital). Motivated by the experimentalimplication, several ideas to take into account non-localand magnetic nature have been suggested and tested byexpanding the size of the cluster. They succeed to re-produce the observed two-peak structure but reached todifferent interpretation on the nature of the two-peakstructure. Taguchi et al. [16] added additional effectiveorbitals, playing the role of playing the role of Zhang-Rice doublet bound state, to the single NiO cluster cal-culation. They concluded that the two-peak structure isattributed to the effective screening orbitals playing therole of Zhang-Rice bound states with e g symmetry. Kuoet al. expanded the size of the cluster to Ni O chainmade of three corner-shared NiO octahedra. They con-cluded that the two-peak structure is due to T high-spinstate and E low-spin state [10].Strong cluster model dependence on the nature of thetwo-peak structure has motivated the calculation of theline-shape of periodic system from first principles . Theadvantage of this approach is that we can avoid issueswith possible boundary effects as wells as the choice ofmodel and its parameters. It provides density of state,which can be interpreted as a photoemission line-shapewithout matrix element. Various ab initio studies havebeen already conducted to investigate electronic struc-ture of NiO [3, 20–32] but it turns out that under-standing the nature of the two-peak structure from firstprinciples is a challenging task. To illustrate, densityfunctional theory doesn’t display peak A and B splittingbelow Neel temperature. Although ab initio quasipar-ticle GW provides two-peak structure below Neel tem- í í í ( ( A H 9 6 S H F W U D O G H Q V L W \ D U E L X Q L W $ % & ( [ S H U L P H Q W D . . L P S X U L W \ í í í ( ( A H 9 6 S H F W U D O G H Q V L W \ D U E L X Q L W $ % & 7 K H R U \ E $ ) 0 7 . 3 0 7 . FIG. 1. (a) Valence band photoemission experiments of NiOtaken at 300 K (black solid line), NiO taken at Neel tempera-ture (525 K, red dotted line), and NiO impurity in MgO (bluedashed line). The experimental spectra have been obtainedfrom Fig. 5 and 6 in Ref. [10]. The zero of energy are setto peak A energy. (b) Total density of states of antiferro-magnetic (AFM) phase (black solid line) as well as param-agnetic (PM) phase (red dotted line) of NiO within ab initio
LQSGW+DMFT. The simulation temperatures are 300 and600K for AFM and PM phases, respectively. The zero of en-ergy is set at the peak A energy. The first (main), second, andthird peaks from the Fermi level are denoted by A, B, and Crespectively on both of experimental and calculated spectra. perature, but it is hard to explain the observed temper-ature dependence of the two-peak structure since NiOis a metal above Neel temperature in the framework.Recently, self-interaction corrected LDA+DMFT repro-duced two-peak structure in the paramagnetic phase andpeak B is attributed to O- p orbitals [32], although bothpeaks (A and B) are known to originate from Ni- d or-bitals experimentally [15, 18].To understand the nature of the two-peak structure, weneed a parameter-free framework suited for both param-agnetic (PM) and antiferromagnetically (AFM) orderedphases. One of the promising frameworks is ab initio LQSGW+DMFT. In this parameter-free approach, non-local electron correlation is treated within ab initio lin-earized quasiparticle self-consistent GW and strong localcorrelation is within dynamical mean-field theory. In thisstudy, by using ab initio
LQSGW+DMFT framework, wecalculated the electronic structure of both paramagneticand antiferromagnetically ordered phases of NiO and in-vestigated the nature of the two-peak structure.
Methods.-
All calculations are conducted usingCOMSUITE package [33], where both ab ini- tio
LQSGW+DMFT and charge self-consistentLDA+DMFT are implemented. COMSUITE is builton FlapwMBPT for the GW/LDA calculations [34–36].Experimental lattice constant 4.17 ˚A [37] is adoptedfor the construction of two-site NiO unitcell in Rhom-bohedral R¯3m space-group for both of AFM and PMsimulations. For the AFM simulations, we constructedantiferromagnetic ordering of AFM II which is proposedas the ground state ordering for NiO [38]. The radii( R MT ) of basis of muffin-tin (MT) used in FlapwMBPTare set 2.12 bohr radius for nickel (Ni) and 1.77 bohrradius for oxygen (O). Wave functions are expanded inthe MT spheres by spherical harmonics with l up to 6for Ni and 6 for O and in the interstitial (IS) regionby plane waves with the energy cutoff determined by R MT,N i × K max = 6.7. Sampling the Brillouin zoneis conducted using 5 × × R MT,N i × K max = 10.0. For polarizability and self-energy calculations,all unoccupied states are taken into account. Spin-orbitcoupling was not included.For ab initio LQSGW+DMFT calculation, five Ni- d orbitals are chosen as correlated orbitals and Wannierfunctions for Ni- s , Ni- p Ni- d , and O- p orbitals are con-structed in a frozen energy window of -10 eV < E - E f < eV . For the charge self-consistent LDA+DMFT, fiveNi- d orbitals are considered as correlated orbitals. Todefine five Ni- d orbitals, Wannier functions for Ni- s , Ni- p Ni- d , and O- p orbitals are constructed in a frozen en-ergy window of -10 eV < E - E f < eV at every chargeself-consistency loop. F = 10 . eV , F = 7 . eV and F = 4 . eV are chosen from EDMFTF database [39]to construct Coulomb interaction tensor associated Ni- d orbitals, corresponding to U = 10 . eV and J = 0 . eV .For the double-counting energy, nominal double-countingscheme [40, 41] is used with d orbital occupancy of 8.0.We tested main calculation with larger lattice constant4.19 ˚ A and different basis set. We did not observe appre-ciable changes in our main result of origin of two-peakstructure. Results.-
In Fig. 1 (b), the total density of statesof NiO in both AFM and PM phases are compared toexperimental valence band photoemission spectra. Thesimulation temperatures are 300K for AFM and 600Kfor PM phases, respectively. Above Neel temperature,we couldn’t observe the two-peak structure. Below Neeltemperature, ab initio
LQSGW+DMFT predicts cleartwo-peak structure. This behavior is consistent with ex-perimental observation of the enhancement of the peakB upon cooling, which is suppressed at the Neel temper-ature.To identify orbital characters of these peaks, we calcu-lated the orbital-resolved density of states for both PMand AFM phases within ab initio
LQSGW+DMFT, as P D M R U L W \ V S L Qd $ ) 0 7 . $ % &