KONG Long-JunLIU Gung-Hu②DAI Gen-HongQIANG Ling（Deprtment of Physics, Tinjin Polytechnic University, Tinjin 300387, Chin）（School of Physics, Peking University, Beijing 100871, Chin）

Structural, Electronic and Optical Properties of the Monoclinic α-CoV2O6①

KONG Long-JuanaLIU Guang-Huaa②DAI Gen-HongaQIANG Lingba（Department of Physics, Tianjin Polytechnic University, Tianjin 300387, China）
b（School of Physics, Peking University, Beijing 100871, China）

First-principles calculations based on density functional theory are performed to investigate the structural， electronic and optical properties of monoclinic α-CoV2O6. Firstly， the geometry structures obtained by geometry optimization are consistent with the experimental values. Then， the energy band structure is studied using both GGA and GGA+U methods. It is found that the on-site Coulomb repulsion of the Co 3d orbital plays a key role in describing the electronic properties of α-CoV2O6， and is necessary to open the energy band gap. According to the partial density of states （PDOS）， significant Co-O and V-O hybridizations are observed in the valence and conduction bands， respectively. Furthermore， the Co-O and V-O bonds are found to have significant covalent characters. Below the absorption threshold ～1.9 eV， no absorption can be detected. However， there exists a strong and wide absorption band in the energy range from 1.9 to 11 eV. Such novel optical properties imply that the α-CoV2O6may have some potential optical applications.

geometry structure, electronic property, optical property;

1 INTRODUCTION

Cobalt-based compounds， especially when combined with reduced structural dimensionality， are a subject of increasing attention from chemistry and condensed-matter physics because of their rich behavior such as H-field induced order-disorder transition［1， 2］， strong anisotropy［2-5］and quantum criticality behavior［6-8］. A typical example among these compounds is the quasi-one-dimensional （1D）spin-chain CoV2O6， which exhibits two allotropic phases: α-CoV2O6with a brannerite-like monoclinic structure［3， 9， 10］and γ-CoV2O6［11］presenting a triclinic structure.

Many previous experimental studies have been performed on the basic magnetic features of α-CoV2O6［12， 13］. Major fascinating magnetic phenomena have been reported including: （i） a 1/3 magnetization plateau in the M（H） curve； （ii） an unusual magnetic anisotropy perpendicular to the chain direction； （iii） a magnetic easy axis oriented along the c-axis； （iv） a large magnetic moment （4.5～4.6Bμper Co atom）. In addition， numerous theoretical investigations have been done to study the intriguing properties of α-CoV2O6. For example，Kim et al.［14］investigated the origin of large orbital magnetic moment and unique magnetic anisotropy in the quasi-1D magnetic cobaltate， α-CoV2O6， byab initio and the microscopic cluster model calculations. They suggested that the anomalous magnetic entropy behavior is attributed to strong uniaxial magnetic anisotropy in the quasi-1D chain system. Furthermore， density functional theory （DFT） calculations including spin-orbital coupling and orbital polarization effects have been carried out for the magnetic order in the α-CoV2O6［15］. It is shown that the effective exchange interactions obtained by the DFT calculations correctly predict the occurrence of an antiferromagnetic ground-state order. Recently，the full potential linearized augmented plane wave method has been used to study the origin of the large orbital magnetic moment［16］. It was found that the large orbital magnetic moment results from the occurrence of a hybridized state.

As mentioned above， the previous interest mainly focused on various magnetic properties of such a quasi-1D cobalt-based compound （CoV2O6）［10， 12-20］. However， in comparison with the extensive studies of magnetic properties of α-CoV2O6， the electronic and optical properties of α-CoV2O6seem to be relatively deficient. Hence， in the present paper， we would like to investigate the structural， electronic and optical properties of α-CoV2O6by the firstprinciple calculations based on DFT. We hope that our studies can be helpful for having a further comprehension and assessing the potential application of α-CoV2O6.

2 THEORETICAL METHOD AND CALCULATION DETAILS

DFT has become a more and more popular tool for computational material science. In the framework of DFT， the CASTEP code［21］has been successfully employed to calculate the structural， electronic and optical properties based on a plane wave basis set with periodic boundary condition. The electron-electron exchange-correlation effects are treated with the generalized gradient approximations （GGA）［22］implemented in the Perdew-Burke-Ernzerhof （PBE） functionals［23］. In order to reduce the number of plane wave basis vector， the interaction between the ion and valence electrons is described by Vanderbilt ultrasoft pseudopotentials［24］. According to the Monkhorst-Pack scheme［25］， a 6×5×5 Monkhorst-Pack grid in the irreducible Brillouin zone is adopted. All the geometry structures are relaxed by the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm［26-29］，which provides a fast way to find the lowest energy structure and supports cell optimization. A planewave cutoff energy of 765 eV is set in our calculations， which assures a total-energy convergence of 1 × 10-5eV/atom. It is well-known that for the strongly correlated transition-metal systems with localized d orbital （for instance the Co and V in the present case）， the DFT often gives incorrect results. Therefore， for the so-called correlated systems， the DFT+U approach， a mixture of the Hubbard model theory and DFT， is required for studying the electronic properties. The most popular imple-mentation of DFT+U is known as LDA+U， which has been integrated in the CASTEP code［30］. The LDA+U method with a GGA-PBE functional will be applied in our calculations. For simplicity， hereafter， we call it GGA+U method. Considering that the Co of α-CoV2O6is in the divalent state （d7） with partially filled 3d orbital， while V of α-CoV2O6is in the pentavalent （5+） state without any occupied d electrons （d0）［10］， the on-site Coulomb repulsion （Ueff）of the Co atoms may be significant， but that of the V atoms can be neglected. Therefore， Ueff=5eV for the 3d orbital of Co atoms and Ueff=0 eV for other atoms， which were suggested previously by Daniel and Lenertz［16， 17］， are adopted by us. As will be shown， the on-site Coulomb repulsion of Co-3d states is very important for the electronic properties of α-CoV2O6.

3 RESULTS AND ANALYSIS

3. 1 Geometry optimization

The α-CoV2O6was reported to crystallize in a structure described by space group C121 withgeometric parameters a = 9.256， b = 3.508， c = 6.626， and β = 111.5º［9］. The geometrical optimized lattice constants are as follows: a = 10.021， b = 3.393， c = 7.108 Å. We can see that the lattice constant a is slightly lager than that from Ref. ［9］. Such a slight deviation between the theoretical and experimental data may deserve further investigations. In Fig. 1， we illustrate the unit cell crystal structure of α-CoV2O6. One of the most remarkable structural features of α-CoV2O6is that divalent cobalt ions are located in a distorted CoO6octahedron so as to form linear chains. These chains are linked together through VO5square pyramids， which results in a quasi-1D structure. The optimized bond length between Co and its six O ligands has two values of 1.929 and 2.161 Å， which are in agreement with the experimental values［13］. Two different distances of Co-O indicate the distorted CoO6octahedra existing in α-CoV2O6. This distortion is responsible for Co-3d ligand field splittings［14］. The detailed distances of V-O will be provided in the next section.

Fig. 1. Schematic geometry structure of α-CoV2O6

3. 2 Electronic properties

To consider the strong on-site Coulomb correlation effects for Co atoms， the band structures of α-CoV2O6are calculated by both GGA and GGA+U methods （Fig. 2（a） and （b））. As shown in Fig. 2（a），the α-CoV2O6with Ueff=0eV seems to be metallic because no energy gap can be detected. However，the energy gap opens gradually as the on-site coulomb repulsion Ueffincreases. The band structure calculated by the GGA+U method with Ueff=5eV is plotted in Fig. 2（b）. One can find that it is quite different from that predicted by GGA with Ueff=0（see Fig. 2（a））. According to the band structure shown in Fig. 2（b）， a direct band gap ～1.88 eV at symmetry point Z is observed， and it is consistent with the previous theoretical prediction value 1.9 eV［13］. Our numerical results show that the on-site coulomb correlation effects of 3d orbital play an important role in opening the energy band gap of α-CoV2O6.

To further elucidate the detailed composition and the nature of energy band structure， the DOS of α-CoV2O6and PDOS of Co， V， and O elements are calculated by the GGA+U approach. Fig. 3（a）displays the total DOS， and the PDOS of Co， V， and O elements are provided in Fig. 3（b）， （c） and （d）. Two distinctive energy bands below the Fermi energy level can be observed. According to PDOS，we find that lower bands from -18 to -16 eV are mainly contributed by the O 2s states （Fig. 3（a） and （c）. But， the upper valence band from about -7 to 0 eV is dominated by Co 3d and O 2p characters （Fig. 3（b） and （c）.It indicates that a distinctive hybridization between Co 3d and O 2p states occurs， and therefore strong covalent bonds form between Co and O atoms. Above the Fermi level， the lowest conduction band from 1.88 to 5 eV is found to be mainly contributed by O 2p and V 3d states （Fig. 3（b） and （c））， which means strong covalent bonds form between the V and O. By analyzing the DOS and PDOS of α-CoV2O6， we conclude that the Co-O interactions are dominant at the top of valence bands and V-O interactions contribute considerably at the bottom of the conduction bands.

Fig. 2. Band structure obtained by GGA (a) and GGA+U with U = 5 ev (b). The Fermi level is indicated by a horizontal dashed line

Fig. 3. Density of states (DOS) and partial density of states (PDOS) calculated by GGA+U with U = 5 eV. The dashed line denotes the Fermi level

To get a better understanding of the chemical bonding characters， we calculate Mulliken bond （overlap） populations of α-CoV2O6. The Mulliken overlap populations are provided in Table 1. According to the definition， a positive Mulliken overlap population corresponds to the bonding characters but negative value denotes antibonding characters. Generally， a large positive population means a high degree of covalency of the bond. Furthermore， if the value of Mulliken bond population is close to zero， ionic interaction increases between two atoms forming the bond［31］. As shown in Table 1， the V-O and Co-O bonds all have positive and nonzero overlap populations， which are mainly ascribed to the strong hybridization between the 3d and 2p states. It verifies the conclusion obtained by the above DOS analysis. And， all the positive overlap populations imply that all these bonds have obvious covalent characters. We also find that the values of the overlap populations exhibit distinctive relation to the bond lengths. The bond with shorter bond length usually has larger overlap population， which is verified by our calculations （Table 1）. For example， the V-O（3） and Co-O（1） have relatively longer distances （2.177 and 2.161 Å） but small overlap populations （0.17 and 0.29）. These phenomena can be naturally understood by the fact that the interaction between two atoms will decrease with increasing the distance.

Table 1. Mulliken Bond Populations and Corresponding Bond Lengths

3. 3 Optical properties

Besides the electronic properties discussed above，the optical properties of such a semiconductor are also an interesting topic. The optical properties of α-CoV2O6are described by the frequency-dependent dielectric functionε（ω ）= ε1（ω）+i ε2（ω）， which is mainly contributed from the electronic structures. The imaginary part of the dielectric constant （）ωε2is calculated from the momentum matrix elements between the occupied and unoccupied electronic states， and is defined as［32］

where ω is the light frequency， e is the electronic charge， andandare the conduction bands and valence band wave functions at k， respectively. The real part （）ωε1can be evaluated by （）ωε2using the Kramer-Kronig relations［33］

The calculated frequency-dependent complex dielectric function of α-CoV2O6is plotted in Fig. 4. The peaks of the imaginary part of dielectric function are related to the optical absorption peaks. We find that there exists an energy threshold at ～1.9 eV， below which there are not any optical absorption. Such an optical threshold at 1.9 eV recognized by the imaginary part2εis consistent with the energy gap obtained above. However， as the optical energy becomes larger than the threshold value 1.9 eV， a very wide and strong absorption band from 1.9 to 11 eV can be observed. It indicates that the light within such an energy range will be strongly absorbed by the α-CoV2O6. In such an absorption band， several relative stronger optical absorption peaks at 3.3， 3.9， 4.5， 5.6， 6.1， 6.5， 6.9，and 7.7， 8.9 and 9.6 eV and so on can also be recognized. Furthermore， in the vicinity of 20 eV，there exist two weak absorption peaks. The absorption spectrum is also calculated by us. All the positions of absorption peaks determined by the dielectric function can also be obtained directly by the absorption spectrum shown in Fig. 5. However，two absorption peaks in the vicinity of 20 eV （Fig. 5）can be seen more clearly than that determined by the imaginary part of the dielectric function （Fig. 4）.

Fig. 4. Calculated imaginary and real parts of the dielectric function

Fig. 5. Absorption spectrum of monoclinic α-CoV2O6

4 SUMMARY

In the present paper， theoretical investigations on the structural， electronic， and optical properties of α-CoV2O6have been performed by using the firstprinciple calculations based on DFT. The optimized structural parameters and lattice constants are consistent with experimental data. Furthermore， we have presented a study on analyzing the band structure， DOS， PDOS and Mulliken bond populations. Our results showed that once the on-site correlation of the Co 3d orbital is taken into account，a band gap （1.88 eV） will be obtained. It has also been confirmed that the Co-O and V-O have obvious covalent characters. Moreover， the complex dielectric function and absorption spectrum werecalculated and discussed. We find that there exists an absorption threshold ～1.9 eV， below which no absorption can be observed. However， a strong and wide absorption band is detected in the energy range from 1.9 to 11 eV. Such novel optical properties imply that the α-CoV2O6may have some potential optical applications.

REFERENCES

（1） Kimura， S.； Yashiro， H.； Okunishi， K.； Hagiwara， M.； He， Z.； Kindo， K.； Taniyama， T.； Itoh， M. Field-induced order-disorder transition in antiferromagnetic BaCo2V2O8driven by a softening of spinon excitation. Phys. Rev. Lett. 2007， 99， 087602， 1-4.

（2） He， Z.； Taniyama， T.； KyÔmen， T.； Itoh， M. Field-induced order-disorder transition in the quasi-one-dimensional anisotropic antiferromagnet BaCo2V2O8. Phys. Rev. B 2005， 72， 172403， 1-4.

（3） He， Z.； Yamaura， J. I.； Ueda， Y.； Cheng， W. CoV2O6single crystals grown in a closed crucible: unusual magnetic behaviors with large anisotropy and 1/3 magnetization plateau. J. Am. Chem. Soc. 2009， 131， 7554-7555.

（4） Kobayashi， S.； Mitsuda， S. M.； Ishikawa， M. K.； Kohn， K. Three-dimensional magnetic ordering in the quasi-one-dimensional Ising magnet CoNb2O6with partially released geometrical frustration. Phys. Rev. B 1999， 60， 3331-3345.

（5） Wu， H.； Haverkort， M. W.； Hu， Z.； Khomskii， D. I.； Tjeng， L. H. Nature of magnetism in Ca3Co2O6. Phys. Rev. Lett. 2005， 95， 186401， 1-4.

（6） Coldea， R.； Tennant， D. A.； Wheeler， E. M.； Wawrzynska， E.； Prabhakaran， D.； Telling， M.； Habicht， K.； Smeibidl， P.； Kiefer， K. Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry. Science 2010， 327， 177-180.

（7） Lee， S.； Kaul， R. K.； Balents， L. Interplay of quantum criticality and geometric frustration in columbite. Nat. Phys. 2010， 6， 702-706.

（8） Sachdev， S.； Keimer， B. Quantum criticality. Phys. Today 2011， 64， 29-35.

（9） Jasper-Tönnies， B.； Muller-Buschbaum， H. K. Synthese und Strukturuntersuchung von CoV2O6. Anorg. Allg. Chem. 1984， 508， 7-11.

（10） Singh， K.； Maignan， A.； Pelloquin， D.； Perez， O.； Simon， C. Magnetodielectric coupling and magnetization plateaus in α-CoV2O6crystals. J. Mater. Chem 2012， 22， 6436-6440.

（11） Müller-Buschbaum， H.； Kobel， M. Zur Kristallchemie von Oxovanadaten: ©-CoV2O6und MnV2O6. J. Alloys Comp. 1991， 176， 39-46.

（12） Nandi， M.； Khan， N.； Bhoi， D.； Midya， A.； Mandal， P. Field-induced spin-structural transition and giant magnetostriction in Ising chain α-CoV2O6. J. Phys. Chem. C 2014， 118， 1668-1673.

（13） Lenertz， M.； Alaria， J.； Stoeffler， D.； Colis， S.； Dinia， A. Magnetic properties of low-dimensional α and β-CoV2O6. J. Phys. Chem. C 2011， 115，17190-17196.

（14） Kim， B.； Kim， B. H.； Kim， K.； Choi， H. C.； Park， S. Y.； Jeong， Y. H.； Min， B. I. Unusual magnetic properties induced by local structure in a quasi-one-dimensional Ising chain system: α-CoV2O6. Phys. Rev. B 2012， 85， 220407（R）， 1-5.

（15） Saúl， A.； Vodenicarevic， D.； Radtke， G. Theoretical study of the magnetic order in α-CoV2O6. Phys. Rev. B 2013， 87， 024403， 1-5.

（16） Stoeffler， D. First principle study of the origin of the large orbital magnetic moment in α-CoV2O6. Thin Solid Films 2014， 563， 24-27.

（17） Lenertz， M.； Alaria， J.； Stoeffler， D.； Colis， S.； Dinia， A.； Mentré， O.； André， G.； Porcher， F.； Suard， E. Magnetic structure of ground and field-induced ordered states of low-dimensional α-CoV2O6: experiment and theory. Phys. Rev. B 2012， 86， 214428， 1-8.

（18） Belaïche， M.； Bakhache， M.； Drillon， M.； Derrory， A.； Vilminot， S. Magnetic properties of MV2O6compounds （M = Cu， Co， Ni）. Physica B 2001，305， 270-273.

（19） Markkula， M.； Arevalo-Lopez， A. M.； Attfield， J. P. Neutron diffraction study of monoclinic brannerite-type CoV2O6. J. Solid State Chem. 2012， 192，390-393.

（20） Markkula， M.； Arevalo-Lopez， A. M.； Attfield， J. P. Field-induced spin orders in monoclinic CoV2O6. Phys. Rev. B 2012， 86， 134401， 1-4.

（21） Segall， M. D.； Lindan， P. L. D.； Probert， M. J.； Pickard， C.； Hasnip， P. J.； Clark， S. J.； Payne， M. C. First-principles simulation: ideas， illustrations and the CASTEP code. J. Phys. Condens. Matter. 2002， 14， 2717-2744.

（22） Perdew， J. P.； Chevary， J. A.； Vosko， S. H.； Jackson， K. A.； Pederson， M. R.； Singh， D. J.； Fiolhais， C. Atoms， molecules， solids， and surfaces: applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 1992， 46， 6671-6687.

（23） Perdew， J. P.； Burke， K.； Ernzerhof， M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996， 77， 3865-3868.

（24） Vanderbilt， D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 1990， 41， 7892-7895.

（25） Monkhorst， H. J.； Pack， J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 1976， 13， 5188-5192.

（26） Broyden， C. G. The convergence of a class of double rank minimization algorithms—Part 2: The new algorithm. J. Inst. Math. Appl. 1970， 6，222-231.

（27） Fletcher， R. A new approach to variable metric algorithms. Comput. J. 1970， 13， 317-322.

（28） Goldfarb， D. A family of variable metric methods derived by variational means. Math Comput. 1970， 24， 23-26.

（29） Shanno， D. F. Conditioning of quasi-Newton methods for function minimization. Math Comput. 1970， 24， 647-656.

（30） Cococcioni， M.； de Gironcoli， S. Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Phys. Rev. B 2005， 71， 035105， 1-16.

（31） Segall， M. D.； Shah， R.； Pickard， C. J.； Payne， M. C. Population analysis of plane-wave electronic structure calculations of bulk materials. Phys. Rev. B 1996， 54， 16317， 1-4.

（32） Saha， S.； Sinha， T. P.； Mookerjee， A. Electronic structure， chemical bonding， and optical properties of paraelectric BaTiO3. Phys. Rev. B 2000， 62，8828-8834.

（33） Yu ， P. Y.； Cardona， M. Fundamentals of Semiconductors. Springer Verlag， Berlin 1996.

Received 20 November 2014； accepted 4 March 2015

① This work was supported by the Chinese National Science Foundation （No. 11347008）

② Corresponding author. Liu Guang-Hua， born in 1976， Ph. D in physics. E-mail: liuguanghua@tjpu.edu.cn

10.14102/j.cnki.0254-5861.2011-0580