First-Principles Study of the Thermoelectric Properties of SrRuO3
First-Principles Study of the Thermoelectric Properties of SrRuO3 Naihua Miao,∗,†,‡ Bin Xu,¶,§ Nicholas C. Bristowe,†,k Daniel I. Bilc,†,⊥ Matthieu J. Verstraete,¶ and Philippe Ghosez∗,† Theoretical Materials Physics, Q-MAT, CESAM, Universit´e de Li`ege, B-4000 Sart Tilman, Belgium., School of Materials Science and Engineering, Beijing University of Technology, Chaoyang District, Beijing 100124, China., Physique des Mat´eriaux et Nanostructures, Q-MAT, CESAM, Universit´e de Li`ege, B-4000 Sart Tilman, Belgium., Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA., Department of Materials, Imperial College London, Exhibition Road, London, SW7 2AZ, UK., and Molecular and Biomolecular Physics Department, National Institute for Research and Development of Isotopic and Molecular Technologies, RO-400293 Cluj-Napoca, Romania. E-mail: [email protected]; [email protected]
∗
To whom correspondence should be addressed Theoretical Materials Physics, Q-MAT, CESAM, Universit´e de Li`ege, B-4000 Sart Tilman, Belgium. ‡ School of Materials Science and Engineering, Beijing University of Technology, Chaoyang District, Beijing 100124, China. ¶ Physique des Mat´eriaux et Nanostructures, Q-MAT, CESAM, Universit´e de Li`ege, B-4000 Sart Tilman, Belgium. § Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA. k Department of Materials, Imperial College London, Exhibition Road, London, SW7 2AZ, UK. ⊥ Molecular and Biomolecular Physics Department, National Institute for Research and Development of Isotopic and Molecular Technologies, RO-400293 Cluj-Napoca, Romania. †
1 S1
Electronic Supporting Information Table S1 presents the calculated structural and magnetic properties of SRO within various functionals in comparison with previous experimental and theoretical results, which has been discussed extensively in the main text with mode analysis (Table 1). Our calculated results show reasonable agreement with previous literature. The calculated density of dates of SRO with/without R+ 4 mode in fixed experimental lattice using GGA-PBE is illustrated in Fig. S1. It seems that suppressing the R+ 4 mode greatly enhances the value around DOS of up-spin DOS of SRO (as shown in the dash line of Fig. S1); but it does not obviously influence the Fermi level of the down-spin channel at Fermi level. The magnetic moment is reduced to 1.78 µB /f.u. by removing the R+ 4 rotation.
Polarized Two-Dimensional Electron Gas in SrTiO3 /SrRuO3 Superlattices. Phys. Rev. Lett. 108, 107003. [7] Rondinelli, J. M., Caffrey, N. M., Sanvito, S., and Spaldin, N. A. (2008) Electronic Properties of Bulk and Thin Film SrRuO3 : Search for the Metal-Insulator Transition. Phys. Rev. B 78, 155107. [8] Zayak, A., Huang, X., Neaton, J., and Rabe, K. M. (2006) Structural, Electronic, and Magnetic Properties of SrRuO3 Under Epitaxial Strain. Phys. Rev. B 74, 094104. 15
References [1] Longo, J., Raccah, P., and Goodenough, J. (1968) Magnetic Properties of SrRuO3 and CaRuO3 . J. Appl. Phys. 39, 1327– 1328.
Density of States
10
[2] Kanbayasi, A. (1976) Magnetic Properties of SrRuO3 Single Crystal. J. Phys. Soc. Jpn. 41, 1876–1878. [3] Bushmeleva, S., Pomjakushin, V. Y., Pomjakushina, E., Sheptyakov, D., and Balagurov, A. (2006) Evidence for the Band Ferromagnetism in SrRuO3 from Neutron Diffraction. J. Magn. Magn. Mater. 305, 491–496. [4] Miao, N., Bristowe, N. C., Xu, B., Verstraete, M. J., and Ghosez, P. (2014) First-Principles Study of the Lattice Dynamical Properties of Strontium Ruthenate. J. Phys.: Condens. Matter 26, 035401. [5] Jones, C., Battle, P., Lightfoot, P., and Harrison, W. (1989) The Structure of SrRuO3 by Time-of-Flight Neutron Powder Diffraction. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 45, 365–367. [6] Verissimo-Alves, M., García-Fernández, P., Bilc, D. I., Ghosez, P., and Junquera, J. (2012) Highly Confined Spin-
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0
-5
-10
-6
-4
-2
0
2
4
6
Energy-Ef (eV) Figure S1 The calculated density of states of SrRuO3 for spin-up (red) and spin-down (black) channels with (full line, µ=1.96 µB /f.u.) and without (dash line, µ=1.78 µB /f.u.) R+ 4 mode in fixed experimental lattice.
1S2
Table S1 The calculated lattice parameters a, b, c in Å, reduced atomic positions, lattice volume (Å3 ) as well as the magnetic moment µ (µB /f.u.) of ground state SrRuO3 in comparison with available experimental and other theoretical data.The experimental data (Expt.) for the magnetic moments are taken from Ref. 1–3.
a b c Sr x Sr y Sr z Ru x Ru y Ru z O(1) x O(1) y O(1) z O(2) x O(2) y O(2) z V (Å3 ) µ
VASP LSDA 5.491 5.447 7.731 -0.00413 0.02529 0.25 0.5 0 0 0.06292 0.49577 0.25 0.72001 0.28021 0.03255 231.23 0.76
VASP PBE 5.512 5.458 7.754 -0.0042 0.02923 0.25 0.5 0 0 0.06537 0.49676 0.25 0.71574 0.28468 0.03378 233.28 1.94
VASP PBEsol 5.442 5.367 7.626 -0.00424 0.02928 0.25 0.5 0 0 0.06616 0.49925 0.25 0.71601 0.28465 0.03406 222.74 1.38
ABINIT 4 WC-GGA 5.555 5.539 7.837 -0.0048 0.0301 0.25 0.5 0 0 0.063 0.4932 0.25 0.7156 0.2843 0.0326 241.13 1.98
ABINIT 4 LSDA 5.500 5.487 7.754 -0.0053 0.0303 0.25 0.5 0 0 0.0642 0.4924 0.25 0.7163 0.2835 0.0334 234.01 1.7
S3
2
Expt. 5 5.567 5.530 7.845 -0.0027 0.0157 0.25 0.5 0 0 0.0532 0.4966 0.25 0.7248 0.2764 0.0278 241.52 1.1-1.6
CRYSTAL 6 B1-WC 5.570 5.528 7.839 -0.0036 0.0276 0.25 0.5 0 0 0.0612 0.4943 0.25 0.717 0.2837 0.0313 241.35 2
SIESTA 6 LSDA+U 5.525 5.488 7.776 -0.0041 0.0274 0.25 0.5 0 0 0.0639 0.4953 0.25 0.7837 0.2162 0.033 235.77 2
VASP 7 LSDA 5.492 5.489 7.756 -0.005 0.0304 0.25 0.5 0 0 0.0650 0.4942 0.25 0.7158 0.2834 0.034 233.82 0.79
VASP 8 LSDA 5.503 5.483 7.755 -0.005 0.0296 0.25 0.5 0 0 0.0647 0.4941 0.25 0.7165 0.2834 0.0336 233.97 0.98
∗
To whom correspondence should be addressed Theoretical Materials Physics, Q-MAT, CESAM, Universit´e de Li`ege, B-4000 Sart Tilman, Belgium. ‡ School of Materials Science and Engineering, Beijing University of Technology, Chaoyang District, Beijing 100124, China. ¶ Physique des Mat´eriaux et Nanostructures, Q-MAT, CESAM, Universit´e de Li`ege, B-4000 Sart Tilman, Belgium. § Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA. k Department of Materials, Imperial College London, Exhibition Road, London, SW7 2AZ, UK. ⊥ Molecular and Biomolecular Physics Department, National Institute for Research and Development of Isotopic and Molecular Technologies, RO-400293 Cluj-Napoca, Romania. †
1 S1
Electronic Supporting Information Table S1 presents the calculated structural and magnetic properties of SRO within various functionals in comparison with previous experimental and theoretical results, which has been discussed extensively in the main text with mode analysis (Table 1). Our calculated results show reasonable agreement with previous literature. The calculated density of dates of SRO with/without R+ 4 mode in fixed experimental lattice using GGA-PBE is illustrated in Fig. S1. It seems that suppressing the R+ 4 mode greatly enhances the value around DOS of up-spin DOS of SRO (as shown in the dash line of Fig. S1); but it does not obviously influence the Fermi level of the down-spin channel at Fermi level. The magnetic moment is reduced to 1.78 µB /f.u. by removing the R+ 4 rotation.
Polarized Two-Dimensional Electron Gas in SrTiO3 /SrRuO3 Superlattices. Phys. Rev. Lett. 108, 107003. [7] Rondinelli, J. M., Caffrey, N. M., Sanvito, S., and Spaldin, N. A. (2008) Electronic Properties of Bulk and Thin Film SrRuO3 : Search for the Metal-Insulator Transition. Phys. Rev. B 78, 155107. [8] Zayak, A., Huang, X., Neaton, J., and Rabe, K. M. (2006) Structural, Electronic, and Magnetic Properties of SrRuO3 Under Epitaxial Strain. Phys. Rev. B 74, 094104. 15
References [1] Longo, J., Raccah, P., and Goodenough, J. (1968) Magnetic Properties of SrRuO3 and CaRuO3 . J. Appl. Phys. 39, 1327– 1328.
Density of States
10
[2] Kanbayasi, A. (1976) Magnetic Properties of SrRuO3 Single Crystal. J. Phys. Soc. Jpn. 41, 1876–1878. [3] Bushmeleva, S., Pomjakushin, V. Y., Pomjakushina, E., Sheptyakov, D., and Balagurov, A. (2006) Evidence for the Band Ferromagnetism in SrRuO3 from Neutron Diffraction. J. Magn. Magn. Mater. 305, 491–496. [4] Miao, N., Bristowe, N. C., Xu, B., Verstraete, M. J., and Ghosez, P. (2014) First-Principles Study of the Lattice Dynamical Properties of Strontium Ruthenate. J. Phys.: Condens. Matter 26, 035401. [5] Jones, C., Battle, P., Lightfoot, P., and Harrison, W. (1989) The Structure of SrRuO3 by Time-of-Flight Neutron Powder Diffraction. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 45, 365–367. [6] Verissimo-Alves, M., García-Fernández, P., Bilc, D. I., Ghosez, P., and Junquera, J. (2012) Highly Confined Spin-
5
0
-5
-10
-6
-4
-2
0
2
4
6
Energy-Ef (eV) Figure S1 The calculated density of states of SrRuO3 for spin-up (red) and spin-down (black) channels with (full line, µ=1.96 µB /f.u.) and without (dash line, µ=1.78 µB /f.u.) R+ 4 mode in fixed experimental lattice.
1S2
Table S1 The calculated lattice parameters a, b, c in Å, reduced atomic positions, lattice volume (Å3 ) as well as the magnetic moment µ (µB /f.u.) of ground state SrRuO3 in comparison with available experimental and other theoretical data.The experimental data (Expt.) for the magnetic moments are taken from Ref. 1–3.
a b c Sr x Sr y Sr z Ru x Ru y Ru z O(1) x O(1) y O(1) z O(2) x O(2) y O(2) z V (Å3 ) µ
VASP LSDA 5.491 5.447 7.731 -0.00413 0.02529 0.25 0.5 0 0 0.06292 0.49577 0.25 0.72001 0.28021 0.03255 231.23 0.76
VASP PBE 5.512 5.458 7.754 -0.0042 0.02923 0.25 0.5 0 0 0.06537 0.49676 0.25 0.71574 0.28468 0.03378 233.28 1.94
VASP PBEsol 5.442 5.367 7.626 -0.00424 0.02928 0.25 0.5 0 0 0.06616 0.49925 0.25 0.71601 0.28465 0.03406 222.74 1.38
ABINIT 4 WC-GGA 5.555 5.539 7.837 -0.0048 0.0301 0.25 0.5 0 0 0.063 0.4932 0.25 0.7156 0.2843 0.0326 241.13 1.98
ABINIT 4 LSDA 5.500 5.487 7.754 -0.0053 0.0303 0.25 0.5 0 0 0.0642 0.4924 0.25 0.7163 0.2835 0.0334 234.01 1.7
S3
2
Expt. 5 5.567 5.530 7.845 -0.0027 0.0157 0.25 0.5 0 0 0.0532 0.4966 0.25 0.7248 0.2764 0.0278 241.52 1.1-1.6
CRYSTAL 6 B1-WC 5.570 5.528 7.839 -0.0036 0.0276 0.25 0.5 0 0 0.0612 0.4943 0.25 0.717 0.2837 0.0313 241.35 2
SIESTA 6 LSDA+U 5.525 5.488 7.776 -0.0041 0.0274 0.25 0.5 0 0 0.0639 0.4953 0.25 0.7837 0.2162 0.033 235.77 2
VASP 7 LSDA 5.492 5.489 7.756 -0.005 0.0304 0.25 0.5 0 0 0.0650 0.4942 0.25 0.7158 0.2834 0.034 233.82 0.79
VASP 8 LSDA 5.503 5.483 7.755 -0.005 0.0296 0.25 0.5 0 0 0.0647 0.4941 0.25 0.7165 0.2834 0.0336 233.97 0.98
