- Email: [email protected]
The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study
Computational Condensed Matter xxx (2016) 1e5
Contents lists available at ScienceDirect
Computational Condensed Matter journal homepage: http://ees.elsevier.com/cocom/default.asp
The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study G. Tse a, *, D. Yu a, b a b
State Key Laboratory for Mesoscopic Physics, and Electron Microscopy Laboratory, School of Physics, Peking University, Beijing, 100871, PR China Collaborative Innovation Center of Quantum Matter, Beijing, 100871, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 September 2016 Received in revised form 17 September 2016 Accepted 18 September 2016 Available online xxx
We studied the crystal structure of double perovskite Ca2TiMnO6 using ab initio density functional theory (DFT) calculations. We used the atomic positions given by the X-ray diffraction (XRD) data, in order to create a primitive lattice cell structure using visualization software Material Studio. Such sophisticated structure was found in tetragonal perovskite system, with space group with I4/m (#87) and lattice parameter of a ¼ b ¼ c ¼ 5.32 Å. The exchange-correlation potential was treated with the Local Density Approximation (LDA) method. The calculations were performed with spin-polarization. The bandgaps for up-spin, net zero and down-spin were reported to be 1.051 eV, 0.988 eV and 1.806 eV respectively. The magnetic element Mn had an impact in tuning the bandstructure when the spin was induced. In summary, this double perovskite emits light when at the down spin state. The energy bandgap is opened, by 63 meV from net zero spin state to the up-spin state. Also, the PDOS illustration explains the reasons behind the changes in the bandstructure, between the up-spin, down-spin and net-zero spin, due to the shifts in the 3 d5 orbital states. © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Double perovskite DFT Bandstructure PDOS
1. Introduction Perovskite, a rare mineral to be found on earth, with the structure of ABO3. The chemical compound was discovered in the Ural Mountain by Gustav Rose in 1839, named after the Russian L.A Perovski (1792e1856) [1]. The structure [2] consisted of both cations atom A and atom B, where the size of A is larger than B. They were being connected by the oxygen atoms, which is the anions in this case. According to the crystal structure, the position of atoms was found by using the XRD data [3]. The rare-earth elements Asite cations were situated on the corner-side of the lattice. The Bside cations were transition elements in 3 d, 4 d or 5 d states. The limitations of perovskite were studied by the fact of its reaction in relation with sphene [4]. The double perovskite with the structure of A2BB’O6, where the positions of B atoms were split into B and B0 respectively [5]. More than two types of cations on A and B could produce distortion in the lattice and made the lattice rotate. That would change the optical, electrical and elastic properties [6]. That constructed a conventional cell with eight cubes consisting of cation A in its center, B and B0 cations along its edges.
* Corresponding author. E-mail address: [email protected] (G. Tse).
In relating the valence state of the compound to the spin, Nakagawa et al. has studied the 57Fe Mossbauer in regarding the valence state of Mo and Fe. “Interpreted with the high spin of (S ¼ 5/2) Fe3þ. With small reservation toward a small possibility of high spin of (S ¼ 2) Fe2þ. Consequently, Mo was assigned to 5 þ valence state, the spin of which is ½.” [7e9]. Similarly, the Mn was assigned to the 5 þ valence state, the spin which is ½. Kobayashi et al. has also pointed out, the coupling between Fe3þ and Mo5þ (in this case, Ti3þ and Mn5þ) is found to be ferromagnetic and hence there is a magnetic moment effect [7]. On the Fe (Ti) site, there is a decrease of the net spin from 5/2 to 2. This is because there is no local magnetization on the Mo (Mn) site as the Mo5þ ion (Mn5þ) is itinerant, so the electron of such ion is found to be antiferromagnetic coupled. This is explained by Linden et al. [10]. The variation of the structural properties brought the benefits in sensors and devices for clinical technologies. In the literature of Shi et al. the Ca2TiMnO6 was reported to be the colossal dielectric material [11]. Wang et al. performed dielectric properties, investigating the polaronic relaxation in similar materials at low temperature [12]. The magnetic and ferroelectric responses were explored by Burgos et al. [13]. We carried out theoretical simulations with the computational methods provided in exploring material properties. Materials such as A2BB’O6 had properties in such
http://dx.doi.org/10.1016/j.cocom.2016.09.002 2352-2143/© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article in press as: G. Tse, D. Yu, The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study, Computational Condensed Matter (2016), http://dx.doi.org/10.1016/j.cocom.2016.09.002
2
G. Tse, D. Yu / Computational Condensed Matter xxx (2016) 1e5
the electronic bands were tuned by changing the spin-polarization [14]. What has made the material unique in double perovskite according to Kim et al., was the magnetic transition temperature found higher than the superconducting temperature. Such essential material was used in memory device and spintronic applications [15]. This work was in explicit compared with the FP-LAPW pez et al. [17]. work being carried out, using PBE of GGA [16] by Lo 2. Computational methods Ab. initio DFT calculation [18] was performed by using LDA approach, with the exchange-functional method of Ceperly-Alder, Pardew-Zunger CA-PZ [19,20]. A plane-wave energy cutoff of 340 eV and Monkhorst-Pack [21] k-point grid of 3 3 4 were sufficient in making the electron system to converge, using CASTEP (Cambridge-Sequential-Total-Energy-Package) code [22]. In this work, the Ultrasoft Pseudopotential is applied [23]. The ionic cores for Ca, Ti, Mn and O are represented Troullier-Martin scheme [24]. The valence bands were treated with 3d electrons, while the conduction bands were treated with 3p, 4s electrons. For Ca atoms the configurations were 3s2, 4s2 and 3p6. For Ti atoms, the configurations were 3s2, 3p6, 3d2, and 4s2. For Mn atoms, the configurations Fig. 3. This figure illustrates the variation of convergence against optimization steps in bulk, for a) up-spin, b) net zero spin and c) down-spin. According to figure from the down-spin state, there are more optimization steps are need, in showing more difficult to converge, comparing to up-spin and net-zero spin.
were 4s2 and 3d5. For O atoms, the configurations were 2s2, 2p4 respectively. These sets of parameters have produced the total energy convergence of 1 106 eV/atom, maximum force of 0.03 eV/Å, maximum stress of 0.05 GPa, and maximum displacement of 0.001 Å. In providing an accurate description on material, the degree of accuracy was testified by comparing CambridgeSequential-Total-Energy-Package CASTEP [22] with SIESTA [25], with the given datasheet [26]. This simulation required a total of eight processors to perform. In configuration, “spin polarized” Fig. 1. This figure shows a) the atomic lattice primitive cell structure of Ca2TiMnO6, built with Material Studio, based on the atoms found using XRD data. In this figure, the atom positions are shared between the cation B (Ti) and cation B0 (Mn).
Fig. 2. This is brillouin zone (BZ) indicating the high symmetry points for tetragonal structure, the path in direction of Z / G / X / P / N / G.
Fig. 4. This figure shows the variation of the final energy calculated against the optimization steps, for a) up-spin, b) net zero spin and c) down-spin. Similar to Fig. 3, according to figure from the down state, there are more optimization steps are need, in showing more difficult (i.e taking more time) to converge, comparing to up-spin and net-zero spin.
Please cite this article in press as: G. Tse, D. Yu, The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study, Computational Condensed Matter (2016), http://dx.doi.org/10.1016/j.cocom.2016.09.002
G. Tse, D. Yu / Computational Condensed Matter xxx (2016) 1e5
option was enabled, to ensure the spin orbit interaction (SOI) is included in the calculation. The “Initial spin” option was set to “þ2” for up-spin, “2” for the down spin and “0” was set for net zero spin. The self-consistent field (SCF) calculation consists of evaluating the electron density n(r), potential V(r) with numerous iterations,
h2 2 V þ Vext ðrÞ þ V ðinÞ ðrÞ ji ðrÞ ¼ ji ðrÞεi ðrÞ 2m
The terms εi(r) and ji(r) represent the Kohn-Sham (KS) energy and orbital respectively. Vext(r) is the local potential A.K.A. the sum of PP atomic cores. The term i is the occupied state. The input potential V(in)(r) (as a function of the input charge density r(in)(r)) is related to exchange-correlation potential Vxc(r) and the input charge density r(in)(r) given by the formula V ðinÞ ðrÞ ¼ Vxc ½rðinÞ ðrÞ. The εi(r) is related to the output charge density r(out)(r) by the P equation rðoutÞ ðrÞ ¼ jJi ðrÞj2 . The εi(r) calculated is the electronic i structure of the solid. 3. Computational analysis Here, we studied the structural, electronic properties of the double perovskite. The space group obtained was one of the twelve possible groups analyzed theoretically for double perovskite [27]. The atomic positions [17] of Calcium (0, 0.5, 0.25), Titanium (0, 0, 0), Manganese (0, 0, 0.5), oxygen (0.0, 0.0, 0.254) and oxygen (0.25, 0.25, 0.0) [27] were given. This was shown in Fig. 1. The total volume of the lattice before the structural optimization was 106.87 Å3. The bandstructure calculation were done after the optimization. There was a success in convergence after certain number of optimization steps varying with up, net zero and down spin. They were found in Figs. 3 and 4. The bulk DFT lattice lengths a ¼ b ¼ c after the relaxation were found to be 5.32 Å. The total energy calculated was found to be 6886.72 eV. The bandstructure for the up, net zero
3
and down spin were indicated in Fig. 5. The k-points in the desired k-paths were given within the zone boundary along the direction of Z / G / X / P / N / G as shown in Fig. 2. These paths were derived from the base-centered tetragonal lattice BZ system. The beta spin represented the high spin state. Such spin-state so defined was the configuration where the spins of all the valence electrons were in parallel, leading to a spin magnitude of zero or greater. Hence, the magnitude at high spin reached to a maximum when a valence sub-shell was half-occupied. The alpha spin represented the low spin state, occurring when the spins of all the valence electrons were arranged in order to minimize the net spin creating a magnitude of zero or one. Hence, the magnitude at low spin reached a minimum when a valence sub-shell was either empty or fully occupied. To calculate the magnitudes of beta and alpha spin, a number of assumptions were made: i) beta and alpha spin magnitudes were calculated, provided that electrons in s and p orbitals did not contribute to the net spin of an atom. ii) When determining the electron configuration of an ion, electrons were removed from the highest energy s and p orbitals first. iii) There were certain exceptions for the first positive ionization to be treated explicitly. Then, second ionizations and beyond were assumed to follow the above rule. iv) When electrons were interchanged to find beta or alpha spin, they were not moved from their initial orbitals. Our data has demonstrated, the up-spin indirect X / G bandgap energy and direct G / G down-spin were found to be 1.051 eV and 1.806 eV respectively. We also included the indirect X / G energy gap with net zero spin was found to be 0.988 eV. All bandgap energies reported were in alpha spin state. The split-off energy D was evaluated by taking the difference between the Light Hole (LH) band and the Split-Off (SO) band. It was measured to be 0.44 eV (down-spin) and 0.49 eV (net zero) respectively. Acpez et al., the bandgap energy is 1.3 eV cording to the literature of Lo for the spin-up, while 1.5 eV for spin-down [17]. The valence bands > 4 eV were mainly dominated by the 3 d5 orbitals from Mn atoms. The top of valence band (VBT) was primarily made up of 2p4
Fig. 5. This diagram illustrates the variation of electronic bands with the spin-polarization, for a) up-spin, b) net zero spin and c) down-spin. Alpha (in black), and beta (in red) components are shown. The quantity D is the split-off energy (in purple). This figure clearly shows that the double perovskite material can emit light at the down-spin state (c). The bandgap is opened by 0.063 eV from net-zero state (b) to the up-spin state (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: G. Tse, D. Yu, The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study, Computational Condensed Matter (2016), http://dx.doi.org/10.1016/j.cocom.2016.09.002
4
G. Tse, D. Yu / Computational Condensed Matter xxx (2016) 1e5
Fig. 6. This shows the variation of PDOS and total DOS with spin-polarization, for a) up-spin, b) net zero spin and c) down-spin. In this diagram, it shows the 3 d5 alpha state shifts to the left. The 3 d5 beta state shifts to the right. To conclude, the 3 d5 shifts in the PDOS diagram (see red circle) mainly indicates, such magnetic element is found responsible for the changes in bandstructure. Inducing the down (up or net zero) spin state can turn the double perovskite material to (in)direct bandgap semiconductor. This allows tuning the spinstate on the material, to the emission of light. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
states from O atoms. The conduction bands <4 eV were responsible for the 3 d2 electron orbitals from Ti atoms, 3 d5 from Mn atoms and 2p4 from O atoms. Fig. 6 showed the PDOS calculated for up-spin, net zero spin and down-spin orientations. According the PDOS plot, the peaks at 39.6 eV and 20.9 eV corresponded to s and p orbital states from the Ca atoms. The peaks 56.6 eV, 33.4 eV and 2.71 eV turned out to be s, p and d orbital states from Ti atoms respectively. The peaks with the values of >20 eV were responsible for the O atoms. The peaks near to the fermi level were dominated by the d electron states from the Mn atoms. In Fig. 5, the alpha spin state in up-spin turned out to be the beta spin state in down-spin. Likewise, the beta spin in up-spin state became the alpha spin in down-spin. This was explained in Fig. 6, and it was found that the magnetic element Mn was the only component being responsible for such phenomenon, where i) for down-spin, the 3 d5 alpha-spin states shifted towards right and there was a left shift on the 3 d5 beta-spin states, ii) for the up-spin, there was a left-shift on 3 d5 alpha-spin states, while there was a right-shift on 3 d5 beta-spin states. There were similar trends but not found significantly between the beta-spin and the alpha-spin state on other elements such as Ti and O atoms, when inducing the up-spin or down-spin. Finally, there were no shifts found on Ca atoms even with the inducing spin.
short, our PDOS model has reported and explained the reasons behind the bandstructure configurations between beta and alpha spin states, from the up-spin, net zero spin to the down-spin. The 3 d5 electron orbital from the magnetic element Mn is mainly responsible for the changes in the bandstructure. At the down (up or net-zero) spin state, the double perovskite becomes (in)direct bandgap semiconductor and hence (not) able to emit light. Double perovskite can become a bandgap tunable material, for practical applications such as: changing the up (down) spin to turn the light off (on). This phenomenon enables us to extend the work further, in investigating e.g. the dielectric constants (Re)ε and (Im)ε of this material. Our work was shown to be more comprehensive and had a significant enhancement over the existing DOS model carried out pez et al. Our work will have the potential to investigate other by Lo material properties, in exploring the new era of physics.
Conflict of interests G.T. and D.Y. declared in this work, there were no financial competing interests.
Acknowledgements 4. Conclusion To conclude, the electronic bandstructure calculations identified indirect energy gap of 1.051 eV for up-spin and direct 1.806 eV for the down-spin. The valence bands were mainly dominated with the d states from the Mn atoms and p orbitals from the O atoms. the conduction bands were made up of the d electron orbitals from the transitional metals Ti, Mn and p states from O atoms respectively. In
This work was funded by the National Natural Science Foundation of China grant nos. 11234001 and 91433102, under the recipient of Prof. D. Yu (D.Y). Finally, Dr. Geoffrey Tse (G.T.) would also like to thank Peking University (PKU) for the Postdoctoral Research Fellowship. This work made use of the computing facilities at International Center of Quantum Materials (ICQM), supported by PKU.
Please cite this article in press as: G. Tse, D. Yu, The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study, Computational Condensed Matter (2016), http://dx.doi.org/10.1016/j.cocom.2016.09.002
G. Tse, D. Yu / Computational Condensed Matter xxx (2016) 1e5
References [1] D. Barthelmy, Mineralogy Database, Webmineral, Online under, 2007, http:// www.webmineral.com. [2] H.R. Wenk, A. Bulakh, Minerals: Their Constitution and Origin, Cambridge University Press, 2004. [3] H.P. Rooksby, Compounds of the structural type of calcium titanate, Nature 155 (3938) (1945) 484. [4] I.V. Veksler, M.P. Teptelev, Conditions for crystallization and concentration of perovskite-type minerals in alkaline magmas, Lithos 26 (1) (1990) 177e189. llez, J. Roa-Rojas, High temperature-induced [5] C.A. Triana, L.T. Corredor, D.L. Te phase transitions in Sr 2 GdRuO 6 complex perovskite, Mater. Res. Bull. 46 (12) (2011) 2478e2483. [6] P.A. Cox, Transition Metal Oxides: an Introduction to Their Electronic Structure and Properties, vol. 27, OUP Oxford, 2010. [7] K.-I. Kobayashi, T. Kimura, H. Sawada, K. Terakura, Y. Tokura, Room-temperature magnetoresistance in an oxide material with an ordered doubleperovskite structure, Nature 395 (1998) 677e680 no. 6703. [8] M. Itoh, I. Ohta, Y. Inaguma, Valency pair and properties of 1: 1 ordered perovskite-type compounds Sr 2 MMoO 6 (M¼Mn, Fe, Co), Mater. Sci. Eng. B 41 (1) (1996) 55e58. [9] B. Garcıa-Landa, C. Ritter, M.R. Ibarra, J. Blasco, P.A. Algarabel, R. Mahendiran, J. Garcıa, Magnetic and magnetotransport properties of the ordered perovskite Sr 2 FeMoO 6, Solid State Commun. 110 (8) (1999) 435e438. n, T. Yamamoto, M. Karppinen, H. Yamauchi, T. Pietari, Evidence for [10] J. Linde valence fluctuation of Fe in Sr2FeMoO6-w double perovskite, Appl. Phys. Lett. 76 (2000) 2925. [11] C.Y. Shi, Y.M. Hao, Z.B. Hu, Microstructure and colossal dielectric behavior of Ca 2 TiMnO 6 ceramics, Scr. Mater. 64 (3) (2011) 272e275. [12] G. Wang, C. Wang, S. Huang, C. Lei, X. Sun, T. Li, J. Mei, Polaronic relaxation in Ca 2 TiMnO 6 at low temperatures, Mater. Res. Bull. 47 (9) (2012) 2692e2695. llez, E. vera [13] R. Ochoa Burgos, D. Martinez, C.A. Parra Vargas, D.A. Landínez Te Lopes, A. Sarmiento Santos, J. Roa-Rojas, Magnetic and ferroelectric response of Ca2TiMnO6 manganite-like perovskite, Rev. Mex. Fısica 57 (2) (2012)
5
44e46. llez, J.A. Rodríguez, J.A. Aguiar, J. Roa-Rojas, Study of half[14] M. Bonilla, D.L. Te metallic behaviour in Sr 2 CoWO 6 perovskite by ab initio DFT calculations, J. Magn. Magn. Mater. 320 (14) (2008) e397ee399. [15] J. Kim, A. Paul, P. Crowell, S.J. Koester, S.S. Sapatnekar, J.P. Wang, C.H. Kim, Spin-based computing: device concepts, current status, and a case study on a high-Performance microprocessor, Proc. IEEE 103 (1) (2015) 106e130. [16] J.P. Perdew, K. Burke, M. Ernzerhof, Perdew, burke, and Ernzerhof reply, Phys. Rev. Lett. 80 (4) (1998) 891. pez, R. Cardona, A.S. Santos, D.L. Te llez, J. Roa-Rojas, Crystallographic [17] J.G. Lo and electronic structure of the Ca 2 TiMnO 6 double perovskite, Phys. B Condens. Mat. 455 (2014) 53e55. [18] F.K. Schulte, A theory of thin metal films: electron density, potentials and work function, Surf. Sci. 55 (2) (1976) 427e444. [19] J.A. Perdew, A. Zunger, Self-interaction to density-functional approximation for many-electon systems, Phys. Rev. B 23 (1981) 5048. [20] D.M. Ceperley, B.J. Alder, Ground state of electron gas by a stochastic method, Phys. Rev. Lett. 45 (1980) 566. [21] H.J. Monkhorst, J.D. Pack, Special points for brillouin-zone integrations, Phys. Rev. B 13 (12) (1976) 5188. [22] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.I. Probert, K. Refson, M.C. Payne, First principles methods using CASTEP, Z. für Kristallogr. 220 (5/6/ 2005) (2005) 567e570. [23] K. Laasonen, R. Car, C. Lee, D. Vanderbilt, Implementation of ultrasoft pseudopotentials in ab initio molecular dynamics, Phys. Rev. B 43 (8) (1991) 6796. [24] N. Troullier, J.L. Martins, Efficient pseudopotentials for plane-wave calculations, Phys. Rev. B 43 (3) (1991) 1993. [25] R.E. Cohen, Fundamental physics of ferroelectrics (AIP Proc.) Cohen RE 1992, Nature 359 (2000) 136. [26] Supplementary Material for Chemical Communications, The Royal Society of Chemistry, 2002. [27] C.J. Howard, B.J. Kennedy, P.M. Woodward, Ordered double perovskitesea group-theoretical analysis, Acta Crystallogr. Sect. B Struct. Sci. 59 (4) (2003) 463e471.
Please cite this article in press as: G. Tse, D. Yu, The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study, Computational Condensed Matter (2016), http://dx.doi.org/10.1016/j.cocom.2016.09.002
Contents lists available at ScienceDirect
Computational Condensed Matter journal homepage: http://ees.elsevier.com/cocom/default.asp
The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study G. Tse a, *, D. Yu a, b a b
State Key Laboratory for Mesoscopic Physics, and Electron Microscopy Laboratory, School of Physics, Peking University, Beijing, 100871, PR China Collaborative Innovation Center of Quantum Matter, Beijing, 100871, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 September 2016 Received in revised form 17 September 2016 Accepted 18 September 2016 Available online xxx
We studied the crystal structure of double perovskite Ca2TiMnO6 using ab initio density functional theory (DFT) calculations. We used the atomic positions given by the X-ray diffraction (XRD) data, in order to create a primitive lattice cell structure using visualization software Material Studio. Such sophisticated structure was found in tetragonal perovskite system, with space group with I4/m (#87) and lattice parameter of a ¼ b ¼ c ¼ 5.32 Å. The exchange-correlation potential was treated with the Local Density Approximation (LDA) method. The calculations were performed with spin-polarization. The bandgaps for up-spin, net zero and down-spin were reported to be 1.051 eV, 0.988 eV and 1.806 eV respectively. The magnetic element Mn had an impact in tuning the bandstructure when the spin was induced. In summary, this double perovskite emits light when at the down spin state. The energy bandgap is opened, by 63 meV from net zero spin state to the up-spin state. Also, the PDOS illustration explains the reasons behind the changes in the bandstructure, between the up-spin, down-spin and net-zero spin, due to the shifts in the 3 d5 orbital states. © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Double perovskite DFT Bandstructure PDOS
1. Introduction Perovskite, a rare mineral to be found on earth, with the structure of ABO3. The chemical compound was discovered in the Ural Mountain by Gustav Rose in 1839, named after the Russian L.A Perovski (1792e1856) [1]. The structure [2] consisted of both cations atom A and atom B, where the size of A is larger than B. They were being connected by the oxygen atoms, which is the anions in this case. According to the crystal structure, the position of atoms was found by using the XRD data [3]. The rare-earth elements Asite cations were situated on the corner-side of the lattice. The Bside cations were transition elements in 3 d, 4 d or 5 d states. The limitations of perovskite were studied by the fact of its reaction in relation with sphene [4]. The double perovskite with the structure of A2BB’O6, where the positions of B atoms were split into B and B0 respectively [5]. More than two types of cations on A and B could produce distortion in the lattice and made the lattice rotate. That would change the optical, electrical and elastic properties [6]. That constructed a conventional cell with eight cubes consisting of cation A in its center, B and B0 cations along its edges.
* Corresponding author. E-mail address: [email protected] (G. Tse).
In relating the valence state of the compound to the spin, Nakagawa et al. has studied the 57Fe Mossbauer in regarding the valence state of Mo and Fe. “Interpreted with the high spin of (S ¼ 5/2) Fe3þ. With small reservation toward a small possibility of high spin of (S ¼ 2) Fe2þ. Consequently, Mo was assigned to 5 þ valence state, the spin of which is ½.” [7e9]. Similarly, the Mn was assigned to the 5 þ valence state, the spin which is ½. Kobayashi et al. has also pointed out, the coupling between Fe3þ and Mo5þ (in this case, Ti3þ and Mn5þ) is found to be ferromagnetic and hence there is a magnetic moment effect [7]. On the Fe (Ti) site, there is a decrease of the net spin from 5/2 to 2. This is because there is no local magnetization on the Mo (Mn) site as the Mo5þ ion (Mn5þ) is itinerant, so the electron of such ion is found to be antiferromagnetic coupled. This is explained by Linden et al. [10]. The variation of the structural properties brought the benefits in sensors and devices for clinical technologies. In the literature of Shi et al. the Ca2TiMnO6 was reported to be the colossal dielectric material [11]. Wang et al. performed dielectric properties, investigating the polaronic relaxation in similar materials at low temperature [12]. The magnetic and ferroelectric responses were explored by Burgos et al. [13]. We carried out theoretical simulations with the computational methods provided in exploring material properties. Materials such as A2BB’O6 had properties in such
http://dx.doi.org/10.1016/j.cocom.2016.09.002 2352-2143/© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article in press as: G. Tse, D. Yu, The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study, Computational Condensed Matter (2016), http://dx.doi.org/10.1016/j.cocom.2016.09.002
2
G. Tse, D. Yu / Computational Condensed Matter xxx (2016) 1e5
the electronic bands were tuned by changing the spin-polarization [14]. What has made the material unique in double perovskite according to Kim et al., was the magnetic transition temperature found higher than the superconducting temperature. Such essential material was used in memory device and spintronic applications [15]. This work was in explicit compared with the FP-LAPW pez et al. [17]. work being carried out, using PBE of GGA [16] by Lo 2. Computational methods Ab. initio DFT calculation [18] was performed by using LDA approach, with the exchange-functional method of Ceperly-Alder, Pardew-Zunger CA-PZ [19,20]. A plane-wave energy cutoff of 340 eV and Monkhorst-Pack [21] k-point grid of 3 3 4 were sufficient in making the electron system to converge, using CASTEP (Cambridge-Sequential-Total-Energy-Package) code [22]. In this work, the Ultrasoft Pseudopotential is applied [23]. The ionic cores for Ca, Ti, Mn and O are represented Troullier-Martin scheme [24]. The valence bands were treated with 3d electrons, while the conduction bands were treated with 3p, 4s electrons. For Ca atoms the configurations were 3s2, 4s2 and 3p6. For Ti atoms, the configurations were 3s2, 3p6, 3d2, and 4s2. For Mn atoms, the configurations Fig. 3. This figure illustrates the variation of convergence against optimization steps in bulk, for a) up-spin, b) net zero spin and c) down-spin. According to figure from the down-spin state, there are more optimization steps are need, in showing more difficult to converge, comparing to up-spin and net-zero spin.
were 4s2 and 3d5. For O atoms, the configurations were 2s2, 2p4 respectively. These sets of parameters have produced the total energy convergence of 1 106 eV/atom, maximum force of 0.03 eV/Å, maximum stress of 0.05 GPa, and maximum displacement of 0.001 Å. In providing an accurate description on material, the degree of accuracy was testified by comparing CambridgeSequential-Total-Energy-Package CASTEP [22] with SIESTA [25], with the given datasheet [26]. This simulation required a total of eight processors to perform. In configuration, “spin polarized” Fig. 1. This figure shows a) the atomic lattice primitive cell structure of Ca2TiMnO6, built with Material Studio, based on the atoms found using XRD data. In this figure, the atom positions are shared between the cation B (Ti) and cation B0 (Mn).
Fig. 2. This is brillouin zone (BZ) indicating the high symmetry points for tetragonal structure, the path in direction of Z / G / X / P / N / G.
Fig. 4. This figure shows the variation of the final energy calculated against the optimization steps, for a) up-spin, b) net zero spin and c) down-spin. Similar to Fig. 3, according to figure from the down state, there are more optimization steps are need, in showing more difficult (i.e taking more time) to converge, comparing to up-spin and net-zero spin.
Please cite this article in press as: G. Tse, D. Yu, The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study, Computational Condensed Matter (2016), http://dx.doi.org/10.1016/j.cocom.2016.09.002
G. Tse, D. Yu / Computational Condensed Matter xxx (2016) 1e5
option was enabled, to ensure the spin orbit interaction (SOI) is included in the calculation. The “Initial spin” option was set to “þ2” for up-spin, “2” for the down spin and “0” was set for net zero spin. The self-consistent field (SCF) calculation consists of evaluating the electron density n(r), potential V(r) with numerous iterations,
h2 2 V þ Vext ðrÞ þ V ðinÞ ðrÞ ji ðrÞ ¼ ji ðrÞεi ðrÞ 2m
The terms εi(r) and ji(r) represent the Kohn-Sham (KS) energy and orbital respectively. Vext(r) is the local potential A.K.A. the sum of PP atomic cores. The term i is the occupied state. The input potential V(in)(r) (as a function of the input charge density r(in)(r)) is related to exchange-correlation potential Vxc(r) and the input charge density r(in)(r) given by the formula V ðinÞ ðrÞ ¼ Vxc ½rðinÞ ðrÞ. The εi(r) is related to the output charge density r(out)(r) by the P equation rðoutÞ ðrÞ ¼ jJi ðrÞj2 . The εi(r) calculated is the electronic i structure of the solid. 3. Computational analysis Here, we studied the structural, electronic properties of the double perovskite. The space group obtained was one of the twelve possible groups analyzed theoretically for double perovskite [27]. The atomic positions [17] of Calcium (0, 0.5, 0.25), Titanium (0, 0, 0), Manganese (0, 0, 0.5), oxygen (0.0, 0.0, 0.254) and oxygen (0.25, 0.25, 0.0) [27] were given. This was shown in Fig. 1. The total volume of the lattice before the structural optimization was 106.87 Å3. The bandstructure calculation were done after the optimization. There was a success in convergence after certain number of optimization steps varying with up, net zero and down spin. They were found in Figs. 3 and 4. The bulk DFT lattice lengths a ¼ b ¼ c after the relaxation were found to be 5.32 Å. The total energy calculated was found to be 6886.72 eV. The bandstructure for the up, net zero
3
and down spin were indicated in Fig. 5. The k-points in the desired k-paths were given within the zone boundary along the direction of Z / G / X / P / N / G as shown in Fig. 2. These paths were derived from the base-centered tetragonal lattice BZ system. The beta spin represented the high spin state. Such spin-state so defined was the configuration where the spins of all the valence electrons were in parallel, leading to a spin magnitude of zero or greater. Hence, the magnitude at high spin reached to a maximum when a valence sub-shell was half-occupied. The alpha spin represented the low spin state, occurring when the spins of all the valence electrons were arranged in order to minimize the net spin creating a magnitude of zero or one. Hence, the magnitude at low spin reached a minimum when a valence sub-shell was either empty or fully occupied. To calculate the magnitudes of beta and alpha spin, a number of assumptions were made: i) beta and alpha spin magnitudes were calculated, provided that electrons in s and p orbitals did not contribute to the net spin of an atom. ii) When determining the electron configuration of an ion, electrons were removed from the highest energy s and p orbitals first. iii) There were certain exceptions for the first positive ionization to be treated explicitly. Then, second ionizations and beyond were assumed to follow the above rule. iv) When electrons were interchanged to find beta or alpha spin, they were not moved from their initial orbitals. Our data has demonstrated, the up-spin indirect X / G bandgap energy and direct G / G down-spin were found to be 1.051 eV and 1.806 eV respectively. We also included the indirect X / G energy gap with net zero spin was found to be 0.988 eV. All bandgap energies reported were in alpha spin state. The split-off energy D was evaluated by taking the difference between the Light Hole (LH) band and the Split-Off (SO) band. It was measured to be 0.44 eV (down-spin) and 0.49 eV (net zero) respectively. Acpez et al., the bandgap energy is 1.3 eV cording to the literature of Lo for the spin-up, while 1.5 eV for spin-down [17]. The valence bands > 4 eV were mainly dominated by the 3 d5 orbitals from Mn atoms. The top of valence band (VBT) was primarily made up of 2p4
Fig. 5. This diagram illustrates the variation of electronic bands with the spin-polarization, for a) up-spin, b) net zero spin and c) down-spin. Alpha (in black), and beta (in red) components are shown. The quantity D is the split-off energy (in purple). This figure clearly shows that the double perovskite material can emit light at the down-spin state (c). The bandgap is opened by 0.063 eV from net-zero state (b) to the up-spin state (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: G. Tse, D. Yu, The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study, Computational Condensed Matter (2016), http://dx.doi.org/10.1016/j.cocom.2016.09.002
4
G. Tse, D. Yu / Computational Condensed Matter xxx (2016) 1e5
Fig. 6. This shows the variation of PDOS and total DOS with spin-polarization, for a) up-spin, b) net zero spin and c) down-spin. In this diagram, it shows the 3 d5 alpha state shifts to the left. The 3 d5 beta state shifts to the right. To conclude, the 3 d5 shifts in the PDOS diagram (see red circle) mainly indicates, such magnetic element is found responsible for the changes in bandstructure. Inducing the down (up or net zero) spin state can turn the double perovskite material to (in)direct bandgap semiconductor. This allows tuning the spinstate on the material, to the emission of light. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
states from O atoms. The conduction bands <4 eV were responsible for the 3 d2 electron orbitals from Ti atoms, 3 d5 from Mn atoms and 2p4 from O atoms. Fig. 6 showed the PDOS calculated for up-spin, net zero spin and down-spin orientations. According the PDOS plot, the peaks at 39.6 eV and 20.9 eV corresponded to s and p orbital states from the Ca atoms. The peaks 56.6 eV, 33.4 eV and 2.71 eV turned out to be s, p and d orbital states from Ti atoms respectively. The peaks with the values of >20 eV were responsible for the O atoms. The peaks near to the fermi level were dominated by the d electron states from the Mn atoms. In Fig. 5, the alpha spin state in up-spin turned out to be the beta spin state in down-spin. Likewise, the beta spin in up-spin state became the alpha spin in down-spin. This was explained in Fig. 6, and it was found that the magnetic element Mn was the only component being responsible for such phenomenon, where i) for down-spin, the 3 d5 alpha-spin states shifted towards right and there was a left shift on the 3 d5 beta-spin states, ii) for the up-spin, there was a left-shift on 3 d5 alpha-spin states, while there was a right-shift on 3 d5 beta-spin states. There were similar trends but not found significantly between the beta-spin and the alpha-spin state on other elements such as Ti and O atoms, when inducing the up-spin or down-spin. Finally, there were no shifts found on Ca atoms even with the inducing spin.
short, our PDOS model has reported and explained the reasons behind the bandstructure configurations between beta and alpha spin states, from the up-spin, net zero spin to the down-spin. The 3 d5 electron orbital from the magnetic element Mn is mainly responsible for the changes in the bandstructure. At the down (up or net-zero) spin state, the double perovskite becomes (in)direct bandgap semiconductor and hence (not) able to emit light. Double perovskite can become a bandgap tunable material, for practical applications such as: changing the up (down) spin to turn the light off (on). This phenomenon enables us to extend the work further, in investigating e.g. the dielectric constants (Re)ε and (Im)ε of this material. Our work was shown to be more comprehensive and had a significant enhancement over the existing DOS model carried out pez et al. Our work will have the potential to investigate other by Lo material properties, in exploring the new era of physics.
Conflict of interests G.T. and D.Y. declared in this work, there were no financial competing interests.
Acknowledgements 4. Conclusion To conclude, the electronic bandstructure calculations identified indirect energy gap of 1.051 eV for up-spin and direct 1.806 eV for the down-spin. The valence bands were mainly dominated with the d states from the Mn atoms and p orbitals from the O atoms. the conduction bands were made up of the d electron orbitals from the transitional metals Ti, Mn and p states from O atoms respectively. In
This work was funded by the National Natural Science Foundation of China grant nos. 11234001 and 91433102, under the recipient of Prof. D. Yu (D.Y). Finally, Dr. Geoffrey Tse (G.T.) would also like to thank Peking University (PKU) for the Postdoctoral Research Fellowship. This work made use of the computing facilities at International Center of Quantum Materials (ICQM), supported by PKU.
Please cite this article in press as: G. Tse, D. Yu, The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study, Computational Condensed Matter (2016), http://dx.doi.org/10.1016/j.cocom.2016.09.002
G. Tse, D. Yu / Computational Condensed Matter xxx (2016) 1e5
References [1] D. Barthelmy, Mineralogy Database, Webmineral, Online under, 2007, http:// www.webmineral.com. [2] H.R. Wenk, A. Bulakh, Minerals: Their Constitution and Origin, Cambridge University Press, 2004. [3] H.P. Rooksby, Compounds of the structural type of calcium titanate, Nature 155 (3938) (1945) 484. [4] I.V. Veksler, M.P. Teptelev, Conditions for crystallization and concentration of perovskite-type minerals in alkaline magmas, Lithos 26 (1) (1990) 177e189. llez, J. Roa-Rojas, High temperature-induced [5] C.A. Triana, L.T. Corredor, D.L. Te phase transitions in Sr 2 GdRuO 6 complex perovskite, Mater. Res. Bull. 46 (12) (2011) 2478e2483. [6] P.A. Cox, Transition Metal Oxides: an Introduction to Their Electronic Structure and Properties, vol. 27, OUP Oxford, 2010. [7] K.-I. Kobayashi, T. Kimura, H. Sawada, K. Terakura, Y. Tokura, Room-temperature magnetoresistance in an oxide material with an ordered doubleperovskite structure, Nature 395 (1998) 677e680 no. 6703. [8] M. Itoh, I. Ohta, Y. Inaguma, Valency pair and properties of 1: 1 ordered perovskite-type compounds Sr 2 MMoO 6 (M¼Mn, Fe, Co), Mater. Sci. Eng. B 41 (1) (1996) 55e58. [9] B. Garcıa-Landa, C. Ritter, M.R. Ibarra, J. Blasco, P.A. Algarabel, R. Mahendiran, J. Garcıa, Magnetic and magnetotransport properties of the ordered perovskite Sr 2 FeMoO 6, Solid State Commun. 110 (8) (1999) 435e438. n, T. Yamamoto, M. Karppinen, H. Yamauchi, T. Pietari, Evidence for [10] J. Linde valence fluctuation of Fe in Sr2FeMoO6-w double perovskite, Appl. Phys. Lett. 76 (2000) 2925. [11] C.Y. Shi, Y.M. Hao, Z.B. Hu, Microstructure and colossal dielectric behavior of Ca 2 TiMnO 6 ceramics, Scr. Mater. 64 (3) (2011) 272e275. [12] G. Wang, C. Wang, S. Huang, C. Lei, X. Sun, T. Li, J. Mei, Polaronic relaxation in Ca 2 TiMnO 6 at low temperatures, Mater. Res. Bull. 47 (9) (2012) 2692e2695. llez, E. vera [13] R. Ochoa Burgos, D. Martinez, C.A. Parra Vargas, D.A. Landínez Te Lopes, A. Sarmiento Santos, J. Roa-Rojas, Magnetic and ferroelectric response of Ca2TiMnO6 manganite-like perovskite, Rev. Mex. Fısica 57 (2) (2012)
5
44e46. llez, J.A. Rodríguez, J.A. Aguiar, J. Roa-Rojas, Study of half[14] M. Bonilla, D.L. Te metallic behaviour in Sr 2 CoWO 6 perovskite by ab initio DFT calculations, J. Magn. Magn. Mater. 320 (14) (2008) e397ee399. [15] J. Kim, A. Paul, P. Crowell, S.J. Koester, S.S. Sapatnekar, J.P. Wang, C.H. Kim, Spin-based computing: device concepts, current status, and a case study on a high-Performance microprocessor, Proc. IEEE 103 (1) (2015) 106e130. [16] J.P. Perdew, K. Burke, M. Ernzerhof, Perdew, burke, and Ernzerhof reply, Phys. Rev. Lett. 80 (4) (1998) 891. pez, R. Cardona, A.S. Santos, D.L. Te llez, J. Roa-Rojas, Crystallographic [17] J.G. Lo and electronic structure of the Ca 2 TiMnO 6 double perovskite, Phys. B Condens. Mat. 455 (2014) 53e55. [18] F.K. Schulte, A theory of thin metal films: electron density, potentials and work function, Surf. Sci. 55 (2) (1976) 427e444. [19] J.A. Perdew, A. Zunger, Self-interaction to density-functional approximation for many-electon systems, Phys. Rev. B 23 (1981) 5048. [20] D.M. Ceperley, B.J. Alder, Ground state of electron gas by a stochastic method, Phys. Rev. Lett. 45 (1980) 566. [21] H.J. Monkhorst, J.D. Pack, Special points for brillouin-zone integrations, Phys. Rev. B 13 (12) (1976) 5188. [22] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.I. Probert, K. Refson, M.C. Payne, First principles methods using CASTEP, Z. für Kristallogr. 220 (5/6/ 2005) (2005) 567e570. [23] K. Laasonen, R. Car, C. Lee, D. Vanderbilt, Implementation of ultrasoft pseudopotentials in ab initio molecular dynamics, Phys. Rev. B 43 (8) (1991) 6796. [24] N. Troullier, J.L. Martins, Efficient pseudopotentials for plane-wave calculations, Phys. Rev. B 43 (3) (1991) 1993. [25] R.E. Cohen, Fundamental physics of ferroelectrics (AIP Proc.) Cohen RE 1992, Nature 359 (2000) 136. [26] Supplementary Material for Chemical Communications, The Royal Society of Chemistry, 2002. [27] C.J. Howard, B.J. Kennedy, P.M. Woodward, Ordered double perovskitesea group-theoretical analysis, Acta Crystallogr. Sect. B Struct. Sci. 59 (4) (2003) 463e471.
Please cite this article in press as: G. Tse, D. Yu, The electronic and structural properties in Ca2TiMnO6 double perovskite: The first principle study, Computational Condensed Matter (2016), http://dx.doi.org/10.1016/j.cocom.2016.09.002