The role of interstitial hydrogen in SrCoO 2.5 antiferromagnetic insulator
TThe role of interstitial hydrogen in SrCoO . antiferromagnetic insulator Li Liang,
1, 2, 3
Shuang Qiao,
1, 2
Shunhong Zhang, ∗ Jian Wu,
4, 5, † and Zheng Liu
1, 5, ‡ Institute for Advanced Study, Tsinghua University, Beijing 100084, China State Key Laboratory of Low Dimensional Quantum Physics andDepartment of Physics, Tsinghua University, Beijing 100084, China Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621999, China State Key Laboratory of Low Dimensional Quantum Physics,Department of Physics, Tsinghua University, Beijing 100084, China Collaborative Innovation Center of Quantum Matter, Beijing 100084, China (Dated: January 14, 2020)Hydrogen exhibits qualitatively different charge states depending on the host material, as nicelyexplained by the state-of-the-art impurity-state calculation. Motivated by a recent experiment [Na-ture 546, 124 (2017)], we show that the complex oxide SrCoO . represents an interesting example,in which the interstitial H appears as a deep-level center according to the commonly-used transitionlevel calculation, but no bound electron can be found around the impurity. Via a combinationof charge difference analysis, density of states projection and constraint magnetization calculation,it turns out that the H-doped electron is spontaneously trapped by a nonunique Co ion and isfully spin-polarized by the onsite Hund’s rule coupling. Consequently, the doped system remainsinsulating, whereas the antiferromagnetic exchange is slightly perturbed locally. The brownmillerite SrCoO . is known to be a high-temperature antiferromagnetic (AFM) insulator (T N >
500 K), reducing from the perovskite SrCoO ferromag-netic (FM) metal (T c ∼
250 K) via a long-range orderingof 0.5 oxygen vacancies per formula unit [1–3]. The or-dered oxygen vacancies form hollow channels, in whichinterstitial ions can diffuse with a high mobility [4]. Re-cent ionic liquid gating experiment has demonstrated re-versible insertion and extraction of interstitial hydrogenions into the hollow channels, reaching a new HSrCoO . insulating phase that exhibits magnetic hysteresis below125 K [5]. A schematic summary of these rich elec-tronic and magnetic transitions is shown in FIG. 1, whichpresents SrCoO . as a useful platform for applicationssuch as magnetoelectric devices and solid-state fuel cells.Despite a number of studies on SrCoO . δ (0 ≤ δ ≤ .
5) [1, 6, 7], the physics of hydrogenated SrCoO . re-mains largely unexplored, because this new phase was notaccessed before via traditional growth methods. In con-trast to the oxidation side, where an insulator-to-metaltransition occurs, the insulating gap of SrCoO . appearsintact upon hydrogenation. More peculiarly, accordingto the magnetization and soft X-ray magnetic circulardichroism measurements, HSrCoO . is a weak FM insu-lator [5], which is rather rare in nature.Here, we aim to present a theoretical understanding ofthe role of interstitial hydrogen in SrCoO . . Based onfirst-principles calculations, we show that the insertedhydrogen acts as an electron donor, but the doped elec-tron is not mobile. Instead, it is spontaneously trappedaround a Co site, reducing the local Co valence state from+3 to +2. Due to the multivalent nature of Co ions, thisCo state is stable. The consequences are: (a) no im-purity state is introduced around the band edge; and (b)the AFM order is slightly perturbed locally. These re- FIG. 1. A schematic summary of the tri-state phase tran-sitions of SrCoO . upon oxidation and hydrogenation asdemonstrated in Ref. [5]. sults not only put forth a theoretical basis to understandthe experimental observations on HSrCoO . , but alsoshed new light on the impurity calculation methodologywhen strongly-correlated electrons are involved.First-principles calculations are performed within theframework of density functional theory (DFT) as im-plemented in the Vienna Ab initio
Simulation Pack-age (VASP) [8]. We employ projector augmented wavemethod [9] to treat the core electrons, and the general-ized gradient approximation as parametrized by Perdew,Burke, and Ernzerhof (PBE) [10] for the exchange- a r X i v : . [ c ond - m a t . m t r l - s c i ] M a y correlation functional of the valence electrons. A ki-netic energy cutoff of 500 eV is found to achieve nu-merical convergence. The strong on-site Coulomb re-pulsion of Co-3 d orbitals are treated by the simplifiedDFT+U method [11]. An effective U-J value of 6.5 eVis used for all calculations following Ref. [12]. The initialmagnetic moments of any two neighboring Co ions areset anti-parallel, which reproduces the so-called G-typeAFM configuration as determined by previous neutronscattering measurements [2]. The spin density is thentreated self-consistently in the DFT calculation. Theself-consistent electronic iteration are performed until thetotal energy change is smaller than 10 − eV.The crystal structure of SrCoO . is shown inFIG. 2(a). There are two inequivalent Co sites, one isin a tetrahedral CoO coordination (denoted as Co Tet )and the other is in an octahedral CoO coordination (de-noted as Co Oct ). Accordingly, the O atoms can be classi-fied into three types: O in the tetrahedral plane (O
Tet ),O in the octahedral plane (O
Oct ), and O in the inter-layerspace (O
Int ). Both the lattice and atomic positions arefully relaxed without subjecting to a specific symmetrygroup, until the forces are smaller than 10 − eV/˚A. Theoptimized structure is found to fit best to the Ima2 spacegroup.We note that some ambiguity remains in the experi-mentally refined structure data, primarily implying slightdifferences in the arrangement of the CoO tetrahe-dra [2, 13]. We do not intend to address this controversyhere, considering that it is a minor effect compared to theH-induced distortion of the CoO tetrahedra [FIG. 2(c)].To simulate hydrogen doping, we construct a supercellcontaining 32 Sr, 80 O and 32 Co atoms, and introduceone H within, corresponding to a low H-concentrationcase (marked by the red dot in FIG. 1). The distancebetween two nearest H atoms under the periodic bound-ary condition is larger than 10 ˚A and a single Γ point isused to sample the mini Brillouin zone. The atomic posi-tions in the supercell are relaxed again, while the latticeconstants are fixed to the primitive-cell optimized values.We first determine the most stable H position. Pre-vious study suggests that the ions under liquid gatingare preferably inserted into the hollow channels [5]. Wehave tested several different initial positions, and the low-est total energy is obtained when the H binds with anO Int [FIG. 2(c)]. In comparison, the total energy is 0.19eV higher when the H binds with an O
Oct , and 0.45 eVhigher when the H binds with an O
Tet . Our structuralrelaxation does not find any local energy minimum forthe H to bind with a Co or Sr. The formation of an H-O
Int bond is found to induce distortion of the associatedCoO tetrahedron and weaken the associated O Int -Co
Oct bond.We then calculate the electronic band structures be-fore and after H doping. Figure 2(b) clearly reveals aband gap of the size ∼ . . FIG. 2. Crystal structures of SrCoO . (a) before and (b)after H doping. Red circle marks the lowest-energy positionof the interstitial H locating in the hollow channel. (c) and(d), the corresponding DFT+U band structures. This gap value is larger than the previous DFT+U re-sults, which varied the onsite Coulomb repulsion U from3 to 5 eV [2], yet smaller than the experimental value ∼ Oct and Co
Tet converge to ∼ . µ B , slightlylarger than the previous calculation results obtained witha smaller U [14]. The previous neutron scattering datashowed temperature dependence and a small differenceof the magnetic moment values for Co Oct and Co
Tet - atT = 10K, the values are 3.12 µ B and 2.88 µ B , respec-tively [2]. These values roughly coincide with a Co S= 2 high-spin state with some hybridization with the Op-orbitals [2].It is surprising to find that after H doping, the band-edge properties barely change [FIG. 2(d)]. In particular,we do not observe any impurity band within the gap oraround the band edge, and the Fermi level remains at thevalence band maximum. The most noticeable effect is asplitting of the spin degeneracy, signaling the breaking ofthe AFM symmetry. A quick check of the spin densityshows that the supercell carries a net magnetic momentof ∼ µ B , close to the contribution of a single electron.A widely-used calculation method [15, 16] to charac-terize the electrical activity of impurities in conventionalsemiconductors or insulators is to purposely change theelectron number in the supercell and restore the chargeneutral condition with a homogeneous charge back-ground. Such a simulation can be regarded as artificiallyliberating some electrons or holes into a free carrier state,leaving a charged impurity state behind [e.g. a H + (H − )impurity state by removing (adding) one electron]. De-pending on the choice of the Fermi level that accomm-dotates the liberated electrons or holes, the energy dif-ference between such a constraint electronic system andthe original fully-relaxed one defines an estimated activa-tion energy for the system becoming conductive, which iscommonly termed as the defect transition level [15, 16].Following this recipe, we find that the H /H + transitionenergy is 0.95 eV below the conduction band minimumand the H /H − transition energy is 0.52 eV above the va-lence band maximum, both sufficiently deep within thegap. Although these values are subject to various uncer-tainties, e.g. band gap errors and long-range interactionsbetween the charged impurities, it appears at the firstsight that the interstitial H can be reasonably classifiedas a deep-level impurity, and thus the preserving of aninsulating state under hydrogenation becomes natural.However, a second thought alerts that a clean bandgap after H-doping is distinct from what a deep-level im-purity typically manifests. For example, interstitial H isknown to be a deep-level impurity in MgO [17]. Accord-ingly, a bound state deep inside the band gap presents,which reflects the fact that the electron is trapped by thehighly localized impurity potential and thus is difficult toget activated into a free carrier. In our case, such an in-gap impurity level is always absent no matter whetherthe impurity is charged or not (c.f. FIG. 4). One mightcontend that the impurity level could lie deep inside thevalence or conduction bands, but the difficulty is to sat-isfy the electron counting. Recall that the interstitial Hintroduces one extra electron. To keep the Fermi levelwithin the gap, the only possibility is that the spin de-generacy of the impurity level is somehow removed, lead-ing to one spin-polarized level inside the valence bandsand the other inside the conduction bands. In this way,the emergence of a net magnetic moment close to 1 Bohrmagneton is clarified as well.Then, how could such a large spin splitting at least ofthe size of the band gap occur? This puzzle is resolvedby noticing that the doped electron is trapped by a Coion instead of the interstitial H. Consequently, the strongHund’s rule coupling of the 3d orbitals polarize the elec-tron spin. In specific, given that the 6 d-electrons ofa Co form a high-spin state, the spin of the trappedelectron is enforced to lie in antiparallel, effectively giv-ing rise to a Co S = 3/2 state. Figure 3(a) plots thecharge difference due to the introduction of an intersti-tial H with the charge state H + , H and H − , respectively.For the H + case, only one proton is introduced and theelectron number does not change. We observe a charge FIG. 3. (a) Charge difference induced by an interstitial Hin different charge states. (b) The electrostatic potential in-duced by the H + ion. The isovalue contour indicates therange, within which the potential has decayed by one orderof magnitude from the maximum value. Also shown is theground-state AFM configuration of the Co ions. The spin ro-tation angle θ of a single Co ion is defined in the inset. (c)Change of total energy ∆ E by rotating different Co sites be-fore and after H doping. The inset shows the ∆ E -cos θ fitting.FIG. 4. Comparison of DOS projected on selective Co sitesin (a) stoichiometric SrCoO . and HSrCoO . ; and (b) theH-doped supercell as shown in FIG. 3. redistribution around the H, the O int bonded to the H,and the Co Tet bonded to the hydroxyl [labeled as Co(a)in FIG. 3(a)], which is attributed to the perturbation ofthe proton potential. The other Co sites [e.g. Co(c) la-beled in FIG. 3(a)] are almost unperturbed. For the H case, the same charge redistribution around the impurityalso presents. In addition, one Co Oct away from the H[labeled as Co(b) in FIG. 3(a)] possesses extra electrondensity, which is attributed to the H-doped electron. Forthe H − case, one more Co [labeled as Co(b’) in FIG. 3(a)]possesses extra electron density.It is intriguing that the extra electrons are bound toneither the H nor the nearest-neighbor Co, but some dis-tant Co ions. Figure 3(b) plots the electrostatic poten-tial difference due to the introduction of an interstitialH + , i.e. the proton potential. It is clear that Co(b) andCo(b’) are beyond the impurity potential range. We donot see any direct connection between the locations ofCo(b), Co(b’) and H. We have observed that the dopedelectron can localize around another Co site when theinitial conditions of the iteration slightly differ. Thus,the doped Co site picked by the self-consistent iterationsmay subtly depend on some finite-size effects of our su-percell. In the thermodynamic limit, we consider thatthis is a spontaneous symmetry breaking process - thedoped electron falls into a local energy minimum ran-domly. From this perspective, interstitial H in SrCoO . is not a deep-level impurity, but rather a good n -typedonor, given that it has effectively donated its electroninto the host lattice. It is the multivalent “goblin” - theoriginal meaning of cobalt in German - that traps thedoped carrier, giving rise to the large activation energy.We can further confirm from the atomic projected den-sity of states (PDOS) that the doped electron is absorbedinto a Co forming a Co , while the other Co ionsare not affected. We first reproduce the PDOS of Co instoichiometric SrCoO . and HSrCoO . [5] as the bench-mark of Co and Co in the brownmillerite environ-ment [FIG. 4(a)]. They exhibit distinct features - espe-cially, the gap size shown in the Co PDOS is muchlarger than in the Co PDOS. An increase of the insu-lating gap in HSrCoO . was indeed observed in experi-ment [5]. In our H-doped supercell, the PDOS of Co(b)and Co(b’) closely resembles Co [FIG. 4(b), right col-umn]. All the other Co atoms, including Co(a), dis-play features similar to Co [FIG. 4(b), left and centralcolumns].The remaining question is whether H doping frus-trates the AFM structure. It is worth mentioning thatdoping an AFM insulator usually spawns various ex-otic electronic phases owing to the competition betweenthe electron kinetic energy and the AFM exchange en-ergy, as long studied in the context of high-temperaturecuprate superconductors. If so, the magnetic order ofH x SrCoO . would become rather complicated, depend-ing on the H concentration. We analyze this problemby manually rotating the spin orientation of Co(a) andCo(b) starting from the ground state AFM configurationin a series of constraint noncollinear magnetization cal-culations [inset of FIG. 3(b)]. For the pristine SrCoO . ,there is no doubt that the total energy change (∆ E )as a function of the rotation angle ( θ ) reflects the over- all exchange strength of the Co Tet and Co
Oct sites withtheir neighbors. Figure 3(c) shows the calculated datapoints. The energy is the lowest at θ = 0, and increasesmonotonously when the configuration deviates from theAFM ground state. A good linear relation between ∆ E and cos θ is found, indicating a primary Heisenberg-typeexchange. We note that the ratio between ∆ E [ Co Tet ]and ∆ E [ Co Oct ] is roughly 2/3, because of the CoO andCoO coordination. Both the previous paper [12] andour own calculation indicate that the Co-O-Co exchangeis very isotropic. We then apply the same calculationto the doped supercell. The data indicates that the lin-ear fitting still works, with only quantitative change ofthe ∆ E -cos θ slope. The overall AFM coupling betweenCo(a) and its neighbors slightly increases, possibly dueto the distortion of the bonding geometry. The overallAFM coupling between Co(b) and its neighbors is re-duced more remarkably, to a value close to Co Tet . If weformulate the magnetic energy as ∆ E = h MF · S Co ( b ) , inwhich h MF is the molecular field acted on Co(b), the re-duction of the Co(b) magnetic moment from 3d S = 2 to3d S = 3/2 accounts for a large fraction of the change,whereas h MF , i.e. the surounding magnetic order andthe AFM exchange strength, is only slightly weakened.In conclusion, we show that interstitial H in the AFMinsulator SrCoO . is an electron donor, but the kineticenergy of the doped electron is quenched by the mul-tivalent Co ion. In this view, the robust insulating gapobserved in the H − δ SrCoO . sample can be understood.Also, as long as δ (cid:54) = 0 or 1, the difference between theCo + and Co + magnetic moment will give rise to someFM signals. Nevertheless, we should point out that thepresent calculation cannot provide a quantitative expla-nation on the ∼
125 K magnetic transition experimentallyobserved in H − δ SrCoO . [5], which is only 1/5 of theNeel temperature of SrCoO . . It remains an open ques-tion whether additional complexities emerge when theH concentration increases, i.e. the correlation betweenthe doped electrons becomes important. Leaving asidethe intermediate doping region that is difficult for first-principles simulation, some insight could be obtained byapplying our approach to the H-rich limit, studying therole of a single H vacancy in HSrCoO . . To carry outthis calculation, further experimental input about the re-fined atomic and magnetic structures of HSrCoO . isdemanded. ACKNOWLEDGEMENTS
We would like to thank J.-W. Mei, Z.-Y. Weng, M.Coey, J.Y. Zhu and P. Yu for helpful discussion. Thiswork is supported by Tsinghua University Initiative Sci-entific Research Program and NSFC under Grant No.11774196. L.L. acknowledges support from NSFC (GrantNo. 11505162). S.Z. is supported by the NationalPostdoctoral Program for Innovative Talents of China(BX201600091) and the Funding from China Postdoc-toral Science Foundation (2017M610858). ∗ [email protected] † [email protected] ‡ [email protected][1] R. Le Toquin, W. Paulus, A. Cousson, C. Prestipino,and C. Lamberti, J. Am. Chem. Soc. , 13161 (2006).[2] A. Mu˜noz, C. de la Calle, J. A. Alonso, P. M. Botta,V. Pardo, D. Baldomir, and J. Rivas, Phys. Rev. B ,054404 (2008).[3] W. S. Choi, H. Jeen, J. H. Lee, S. S. A. Seo, V. R. Cooper,K. M. Rabe, and H. N. Lee, Phys. Rev. Lett. , 097401(2013).[4] C. Mitra, T. Meyer, H. N. Lee, and F. A. Reboredo, J.Chem. Phys. , 084710 (2014).[5] N. Lu, P. Zhang, Q. Zhang, R. Qiao, Q. He, H.-B. Li,Y. Wang, J. Guo, D. Zhang, Z. Duan, Z. Li, M. Wang,S. Yang, M. Yan, E. Arenholz, S. Zhou, W. Yang, L. Gu,C.-W. Nan, J. Wu, Y. Tokura, and P. Yu, Nature ,124 (2017).[6] H. Jeen, W. S. Choi, M. D. Biegalski, C. M. Folkman,I. C. Tung, D. D. Fong, J. W. Freeland, D. Shin, H. Ohta, M. F. Chisholm, and H. N. Lee, Nat. Mater. , 1057(2013).[7] H. Jeen, W. S. Choi, J. W. Freeland, H. Ohta, C. U.Jung, and H. N. Lee, Adv. Mater. , 3651 (2013).[8] G. Kresse and J. Furthm¨uller, Phys. Rev. B , 11169(1996).[9] P. E. Bl¨ochl, Phys. Rev. B , 17953 (1994).[10] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.Lett. , 3865 (1996).[11] S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J.Humphreys, and A. P. Sutton, Phys. Rev. B , 1505(1998).[12] M. Chandrima, S. F. Randy, O. Satoshi, L. Ho Nyung,and A. R. Fernando, J. Phys. Condens. Matter ,036004 (2014).[13] A. Glamazda, K.-Y. Choi, P. Lemmens, W. S. Choi,H. Jeen, T. L. Meyer, and H. N. Lee, J. Appl. Phys. , 085313 (2015).[14] J. H. Lee, W. S. Choi, H. Jeen, H.-J. Lee, J. H. Seo,J. Nam, M. S. Yeom, and H. N. Lee, Sci. Rep. , 16066(2017).[15] S. B. Zhang, S.-H. Wei, and A. Zunger, Phys. Rev. B , 075205 (2001).[16] C. G. Van de Walle, and J. Neugebauer, Nature ,626 (2003).[17] C. Kılıc and A. Zunger, Appl. Phys. Lett.81