Ab initio calculation of thermoelectric properties in 3d ferromagnets based on spin-dependent electron-phonon coupling

density functional theory; electron-phonon coupling; ferromagnets; transport phenomena; Ab initio calculations; Boltzmann; Density-functional-theory; Electron phonon couplings; Ferromagnets; First principles; Thermoelectric properties; Transport phenomenon; Transport theory; Variational approaches; Physics and Astronomy (all); General Physics and Astronomy

Abstract :

[en] Crossed magneto-thermo-electric coefficients are central to novel sensors and spin(calori)tronic devices. Within the framework of Boltzmann’s transport theory, we calculate the resistivity and Seebeck coefficients of the most common 3d ferromagnetic metals: Fe, Co, and Ni. We use a fully first-principles variational approach, explicitly taking electron-phonon scattering into account. The electronic band structures, phonon dispersion curves, phonon linewidths, and transport spectral functions are reported, comparing with experimental data. Successive levels of approximation are discussed: constant relaxation time approximation, scattering for a non-magnetic configuration, then spin polarized calculations with and without spin-orbit coupling (enabling spin-flips). Spin polarization and explicit electron-phonon coupling are found to be necessary to reach a correct qualitative picture: the effect of spin flipping is substantial for resistivity and very delicate for the Seebeck coefficient. The spin-dependent Seebeck effect is also predicted.

Research Center/Unit :

CESAM - Complex and Entangled Systems from Atoms to Materials - ULiège

Disciplines :

Physics

Author, co-author :

Ma, Xue ; Institute of Theoretical and Applied Physics, Jiangsu Key Laboratory of Thin Films, School of Physical Science and Technology, Soochow University, Suzhou, China

Di Gennaro, Marco ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures

Giantomassi, Matteo ; UCLouvain, Institute of Condensed Matter and Nanosciences (IMCN), Louvain-la-Neuve, Belgium

Verstraete, Matthieu ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures

Xu, Bin ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures ; Institute of Theoretical and Applied Physics, Jiangsu Key Laboratory of Thin Films, School of Physical Science and Technology, Soochow University, Suzhou, China

Language :

English

Title :

Ab initio calculation of thermoelectric properties in 3d ferromagnets based on spin-dependent electron-phonon coupling

Publication date :

April 2023

Journal title :

New Journal of Physics

ISSN :

1367-2630

Publisher :

Institute of Physics

Volume :

Issue :

Pages :

043022

Peer reviewed :

Peer Reviewed verified by ORBi

Tags :

CÉCI : Consortium des Équipements de Calcul Intensif
Tier-1 supercomputer

Additional URL :

https://iopscience.iop.org/article/10.1088/1367-2630/accca1

Funders :

FWB - Fédération Wallonie-Bruxelles
NSCF - National Natural Science Foundation of China
F.R.S.-FNRS - Fonds de la Recherche Scientifique

Funding text :

This work is supported by the National Natural Science Foundation of China under Grant No. 12074277, Natural Science Foundation of Jiangsu Province (BK20201404), the startup fund from Soochow University and the support from Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions. MJV acknowledges funding by the Belgian FNRS (PdR Grant No. T.0103.19—ALPS), ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and the CONNECT Excellence of Science Project Number 40007563 funded by FWO and FNRS. MDG acknowledges Klanik SA.

Available on ORBi :

since 12 May 2023

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Bibliography

Bridgman P W 1918 Thermo-Electromotive force, Peltier heat, and Thomson heat under pressure Proc. Am. Acad. Arts Sci. 53 269 10.2307/25129992
Onsager L 1931 Reciprocal relations in irreversible processes. II Phys. Rev. 38 2265 10.1103/PhysRev.38.2265
Xu B Di Gennaro M Verstraete M J 2020 Thermoelectric properties of elemental metals from first-principles electron-phonon coupling Phys. Rev. B 102 155128 10.1103/PhysRevB.102.155128
Allen P B 1976 Fermi-surface harmonics: a general method for nonspherical problems application to Boltzmann and Eliashberg equations Phys. Rev. B 13 1416 10.1103/PhysRevB.13.1416
Li W 2015 Electrical transport limited by electron-phonon coupling from Boltzmann transport equation: an ab initio study of Si, Al and MoS 2 Phys. Rev. B 92 075405 10.1103/PhysRevB.92.075405
Mustafa J I Bernardi M Neaton J B Louie S G 2016 Ab initio electronic relaxation times and transport in noble metals Phys. Rev. B 94 155105 10.1103/PhysRevB.94.155105
Rittweger F Hinsche N F Mertig I 2017 Phonon limited electronic transport in Pb J. Phys.: Condens. Matter 29 355501 10.1088/1361-648X/aa7b56
Verstraete M J 2013 Ab initio calculation of spin-dependent electron-phonon coupling in iron and cobalt J. Phys.: Condens. Matter 25 136001 10.1088/0953-8984/25/13/136001
Sha X Cohen R E 2011 First-principles studies of electrical resistivity of iron under pressure J. Phys.: Condens. Matter 23 075401 10.1088/0953-8984/23/7/075401
Ebert H Mankovsky S Chadova K Polesya S Minar J Koedderitzsch D 2015 Calculating linear-response functions for finite temperatures on the basis of the alloy analogy model Phys. Rev. B 91 165132 10.1103/PhysRevB.91.165132
Wagenknecht D Šmejkal L Kašpar Z Sinova J Jungwirth T Kudrnovský J Carva K Turek I 2019 Temperature-dependent resistivity and anomalous hall effect in nimnsb from first principles Phys. Rev. B 99 174433 10.1103/PhysRevB.99.174433
Koedderitzsch D Chadova K Minar J Ebert H 2013 Impact of finite temperatures and correlations on the anomalous hall conductivity from ab initio theory New J. Phys. 15 053009 10.1088/1367-2630/15/5/053009
Raquet B Viret M Sondergard E Cespedes O Mamy R 2002 Electron-magnon scattering and magnetic resistivity in 3d ferromagnets Phys. Rev. B 66 024433 10.1103/PhysRevB.66.024433
Watzman S J Duine R A Tserkovnyak Y Boona S R Jin H Prakash A Zheng Y Heremans J P 2016 Magnon-drag thermopower and nernst coefficient in Fe, Co and Ni Phys. Rev. B 94 144407 10.1103/PhysRevB.94.144407
Blatt F J Schroeder P A Foiles C L Greig D 1976 Thermoelectric Power of Metals Berlin Springer
Gambino D Malyi O I Wang Z Alling B Zunger A 2022 Density functional description of spin, lattice and spin-lattice dynamics in antiferromagnetic and paramagnetic phases at finite temperatures Phys. Rev. B 106 134406 10.1103/PhysRevB.106.134406
Hohenberg P Kohn W 1964 Density functional theory (DFT) Phys. Rev. 136 B864 10.1103/PhysRev.136.B864
Kohn W Sham L J 1965 Self-consistent equations including exchange and correlation effects Phys. Rev. 140 A1133 10.1103/PhysRev.140.A1133
Gonze X Lee C 1997 Dynamical matrices, born effective charges, dielectric permittivity tensors and interatomic force constants from density-functional perturbation theory Phys. Rev. B 55 10355 10.1103/PhysRevB.55.10355
Gonze X 1997 First-principles responses of solids to atomic displacements and homogeneous electric fields: implementation of a conjugate-gradient algorithm Phys. Rev. B 55 10337 10.1103/PhysRevB.55.10337
Gonze X 2005 A brief introduction to the abinit software package Z. Kristallogr. 220 558 62 558-62 10.1524/zkri.220.5.558.65066
Gonze X et al 2016 Recent developments in the abinit software package Comput. Phys. Commun. 205 106 31 106-31 10.1016/j.cpc.2016.04.003
Gonze X et al 2020 The abinit project: impact, environment and recent developments Comput. Phys. Commun. 248 107042 10.1016/j.cpc.2019.107042
Hamann D R 2013 Optimized norm-conserving Vanderbilt pseudopotentials Phys. Rev. B 88 085117 10.1103/PhysRevB.88.085117
van Setten M J Giantomassi M Bousquet E Verstraete M J Hamann D R Gonze X Rignanese G-M 2018 The pseudoDojo: training and grading a 85 element optimized norm-conserving pseudopotential table Comput. Phys. Commun. 226 39 54 39-54 10.1016/j.cpc.2018.01.012
Madsen G K Singh D J 2006 Boltztrap. a code for calculating band-structure dependent quantities Comput. Phys. Commun. 175 67 71 67-71 10.1016/j.cpc.2006.03.007
Madsen G K Carrete J Verstraete M J 2018 Boltztrap2, a program for interpolating band structures and calculating semi-classical transport coefficients Comput. Phys. Commun. 231 140 5 140-5 10.1016/j.cpc.2018.05.010
Allen P B 1978 New method for solving Boltzmann’s equation for electrons in metals Phys. Rev. B 17 3725 10.1103/PhysRevB.17.3725
Erekhinsky M Casanova F Schuller I K Sharoni A 2012 Spin-dependent Seebeck effect in non-local spin valve devices Appl. Phys. Lett. 100 212401 10.1063/1.4717752
Tulapurkar A A Suzuki Y 2010 Contribution of electron-magnon scattering to the spin-dependent Seebeck effect in a ferromagnet Solid State Commun. 150 466 70 466-70 10.1016/j.ssc.2009.12.035
Yamanoi K Yafuso M Miyazaki K Kimura T 2019 Signature of spin-dependent Seebeck effect in dynamical spin injection of metallic bilayer structures J. Phys. Mater. 3 014005 10.1088/2515-7639/ab45cc
Flipse J Bakker F L Slachter A Dejene F K Van Wees B J 2012 Direct observation of the spin-dependent Peltier effect Nat. Nanotechnol. 7 166 8 166-8 10.1038/nnano.2012.2
Slachter A Bakker F L Adam J-P van Wees B J 2010 Thermally driven spin injection from a ferromagnet into a non-magnetic metal Nat. Phys. 6 879 82 879-82 10.1038/nphys1767
Uchida K Takahashi S Harii K Ieda J Koshibae W Ando K Maekawa S Saitoh E 2008 Observation of the spin Seebeck effect Nature 455 778 81 778-81 10.1038/nature07321
Adachi H Uchida K Saitoh E Maekawa S 2013 Theory of the spin Seebeck effect Rep. Prog. Phys. 76 036501 10.1088/0034-4885/76/3/036501
Bauer G E Saitoh E Van Wees B J 2012 Spin caloritronics Nat. Mater. 11 391 9 391-9 10.1038/nmat3301
Rosengaard N M Johansson B 1997 Finite-temperature study of itinerant ferromagnetism in Fe, Co and Ni Phys. Rev. B 55 14975 10.1103/PhysRevB.55.14975
Le Laurent L Barreteau C Markussen T 2019 Magnetocrystalline anisotropy of Fe, Co and Ni slabs from density functional theory and tight-binding models Phys. Rev. B 100 174426 10.1103/PhysRevB.100.174426
Yao Y Kleinman L MacDonald A H Sinova J Jungwirth T Wang D Wang E Niu Q 2004 First principles calculation of anomalous hall conductivity in ferromagnetic bcc Fe Phys. Rev. Lett. 92 037204 10.1103/PhysRevLett.92.037204
Anderson J R Papaconstantopoulos D A Boyer L L Schirber J E 1979 Spin-polarized band-structure calculations for Ni Phys. Rev. B 20 3172 10.1103/PhysRevB.20.3172
Wakabayashi N Scherm R H Smith H G 1982 Lattice dynamic of Ti, Co, Tc and other hcp transition metals Phys. Rev. B 25 5122 10.1103/PhysRevB.25.5122
Brockhouse B N Abou-Helal H E Hallman E D 1967 Lattice vibrations in iron at 296 K Solid State Commun. 5 211 6 211-6 10.1016/0038-1098(67)90258-X
Dal Corso A de Gironcoli S 2000 Ab initio phonon dispersions of Fe and Ni Phys. Rev. B 62 273 10.1103/PhysRevB.62.273
White G K Woods S B 1959 Electrical and thermal resistivity of the transition elements at low temperatures Phil. Trans. R. Soc. A 251 273 302 273-302 10.1098/rsta.1959.0004
Laubitz M J Matsumura T 1973 Transport properties of the ferromagnetic metals. I. cobalt Can. J. Phys. 51 1247 56 1247-56 10.1139/p73-163
Fulkerson W Moore J P McElroy D L 1966 Comparison of the thermal conductivity, electrical resistivity and Seebeck coefficient of a high-purity iron and an armco iron to 1000∘C J. Appl. Phys. 37 2639 53 2639-53 10.1063/1.1782098
Hellwege K H Olsen J L 1985 Electrical Resistivity, Thermoelectrical Power and Optical Properties vol 15b Berlin Springer 10.1007/b 19992
Blatt F J Flood D J Rowe V Schroeder P A Cox J E 1967 Magnon-drag thermopower in iron Phys. Rev. Lett. 18 395 10.1103/PhysRevLett.18.395
MacInnes W M Schröder K 1971 Thermoelectric power of a two-band ferromagnet Phys. Rev. B 4 4091 10.1103/PhysRevB.4.4091
Fletcher R Greig D 1968 The low temperature thermoelectric power of some palladium and platinum alloys Phil. Mag. 17 21 35 21-35 10.1080/14786436808218177
Dejene F K Flipse J Van Wees B J 2012 Spin-dependent Seebeck coefficients of ni 80 fe 20 and co in nanopillar spin valves Phys. Rev. B 86 024436 10.1103/PhysRevB.86.024436
Korenblit I Y Lazarenko Y P 1971 Thermal EMF and thermal resistance of ferromagnetic metals with impurities Sov. Phys-JETP 33 837 42 837-42
Zhou J Liao B Qiu B Huberman S Esfarjani K Dresselhaus M S Chen G 2015 Ab initio optimization of phonon drag effect for lower-temperature thermoelectric energy conversion Proc. Natl Acad. Sci. 112 14777 82 14777-82 10.1073/pnas.1512328112
Pan H Ding Z-K Zeng B-W Luo N-N Zeng J Tang L-M Chen K-Q 2023 Ab initio Boltzmann approach to coupled magnon-phonon thermal transport in ferromagnetic crystals Phys. Rev. B 107 104303 10.1103/PhysRevB.107.104303