Anisotropic Elliott–Yafet theory and application to KC8 potassium intercalated graphite
Bence G. Márkus
Department of Physics, Budapest University of Technology and Economics and MTA-BME Lendület Spintronics Research Group (PROSPIN), P.O. Box 91, 1521 Budapest, Hungary
Search for more papers by this authorLénárd Szolnoki
Department of Physics, Budapest University of Technology and Economics and MTA-BME Lendület Spintronics Research Group (PROSPIN), P.O. Box 91, 1521 Budapest, Hungary
Search for more papers by this authorDávid Iván
Department of Physics, Budapest University of Technology and Economics and MTA-BME Lendület Spintronics Research Group (PROSPIN), P.O. Box 91, 1521 Budapest, Hungary
Search for more papers by this authorBalázs Dóra
Department of Theoretical Physics, Budapest University of Technology and Economics and MTA-BME Lendület Exotic Quantum Phases Group (Momentum), P.O. Box 91, 1521 Budapest, Hungary
Search for more papers by this authorPéter Szirmai
Institute of Physics of Complex Matter, FBS Swiss Federal Institute of Technology (EPFL), 1015 Lausanne, Switzerland
Search for more papers by this authorBálint Náfrádi
Institute of Physics of Complex Matter, FBS Swiss Federal Institute of Technology (EPFL), 1015 Lausanne, Switzerland
Search for more papers by this authorLászló Forró
Institute of Physics of Complex Matter, FBS Swiss Federal Institute of Technology (EPFL), 1015 Lausanne, Switzerland
Search for more papers by this authorCorresponding Author
Ferenc Simon
Department of Physics, Budapest University of Technology and Economics and MTA-BME Lendület Spintronics Research Group (PROSPIN), P.O. Box 91, 1521 Budapest, Hungary
Corresponding author: e-mail [email protected], Phone: +36-1-463-1215, Fax: +36-1-463-4180Search for more papers by this authorBence G. Márkus
Department of Physics, Budapest University of Technology and Economics and MTA-BME Lendület Spintronics Research Group (PROSPIN), P.O. Box 91, 1521 Budapest, Hungary
Search for more papers by this authorLénárd Szolnoki
Department of Physics, Budapest University of Technology and Economics and MTA-BME Lendület Spintronics Research Group (PROSPIN), P.O. Box 91, 1521 Budapest, Hungary
Search for more papers by this authorDávid Iván
Department of Physics, Budapest University of Technology and Economics and MTA-BME Lendület Spintronics Research Group (PROSPIN), P.O. Box 91, 1521 Budapest, Hungary
Search for more papers by this authorBalázs Dóra
Department of Theoretical Physics, Budapest University of Technology and Economics and MTA-BME Lendület Exotic Quantum Phases Group (Momentum), P.O. Box 91, 1521 Budapest, Hungary
Search for more papers by this authorPéter Szirmai
Institute of Physics of Complex Matter, FBS Swiss Federal Institute of Technology (EPFL), 1015 Lausanne, Switzerland
Search for more papers by this authorBálint Náfrádi
Institute of Physics of Complex Matter, FBS Swiss Federal Institute of Technology (EPFL), 1015 Lausanne, Switzerland
Search for more papers by this authorLászló Forró
Institute of Physics of Complex Matter, FBS Swiss Federal Institute of Technology (EPFL), 1015 Lausanne, Switzerland
Search for more papers by this authorCorresponding Author
Ferenc Simon
Department of Physics, Budapest University of Technology and Economics and MTA-BME Lendület Spintronics Research Group (PROSPIN), P.O. Box 91, 1521 Budapest, Hungary
Corresponding author: e-mail [email protected], Phone: +36-1-463-1215, Fax: +36-1-463-4180Search for more papers by this authorAbstract
We report electron spin resonance (ESR) measurements on stage-I potassium intercalated graphite (KC
). Angular dependent measurements show that the spin–lattice relaxation time is longer when the magnetic field is perpendicular to the graphene layer as compared to when the magnetic field is in the plane. This anisotropy is analyzed in the framework of the Elliott–Yafet theory of spin-relaxation in metals. The analysis considers an anisotropic spin–orbit Hamiltonian and the first order perturbative treatment of Elliott is reproduced for this model Hamiltonian. The result provides an experimental input for the first-principles theories of spin–orbit interaction in layered carbon and thus to a better understanding of spin-relaxation phenomena in graphene and in other layered materials as well.
References
- 1 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666–669 (2004).
- 2 A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109–162 (2009).
- 3 I. Žutić, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323–134 (2004).
- 4 N. Tombros, C. Józsa, M. Popinciuc, H. T. Jonkman, and B. J. van Wees, Nature 448, 571–574 (2007).
- 5 W. Han and R. K. Kawakami, Phys. Rev. Lett. 107, 047207 (2011).
- 6 T. Y. Yang, J. Balakrishnan, F. Volmer, A. Avsar, M. Jaiswal, J. Samm, S. R. Ali, A. Pachoud, M. Zeng, M. Popinciuc, G. Güntherodt, B. Beschoten, and B. Özyilmaz, Phys. Rev. Lett. 107, 047206 (2011).
- 7 D. Kochan, S. Irmer, M. Gmitra, and J. Fabian, Phys. Rev. Lett. 115, 196601 (2015).
- 8 B. Náfrádi, M. Choucair, P. D. Southon, C. J. Kepert, and L. Forró, Chem. Eur. J. 21, 770–777 (2015).
- 9 A. Grüneis, C. Attaccalite, A. Rubio, D. V. Vyalikh, S. L. Molodtsov, J. Fink, R. Follath, W. Eberhardt, B. Büchner, and T. Pichler, Phys. Rev. B 79, 205106 (2009).
- 10 A. Grüneis, C. Attaccalite, A. Rubio, D. V. Vyalikh, S. L. Molodtsov, J. Fink, R. Follath, W. Eberhardt, B. Büchner, and T. Pichler, Phys. Rev. B 80, 075431 (2009).
- 11 Z. H. Pan, J. Camacho, M. Upton, A. Fedorov, A. Walters, C. Howard, M. Ellerby, and T. Valla, Phys. Rev. Lett. 106, 187002 (2011).
- 12 J. C. Chacón-Torres, L. Wirtz, and T. Pichler, ACS Nano 7(10), 9249–9259 (2013).
- 13 J. C. Chacón-Torres, L. Wirtz, and T. Pichler, Phys. Status Solidi B 251(12), 2337–2355 (2014).
- 14 M. S. Dresselhaus and G. Dresselhaus, Adv. Phys. 30, 1–186 (1981).
- 15 G. Fábián, B. Dóra, Á. Antal, L. Szolnoki, L. Korecz, A. Rockenbauer, N. M. Nemes, L. Forró, and F. Simon, Phys. Rev. B 85, 235405 (2012).
- 16 K. A. Müller and R. Kleiner, Phys. Lett. 1(3), 98–100 (1962).
- 17 J. Poitrenaud, Rev. Phys. Appl. (France) 5, 275–281 (1970).
- 18 P. Lauginie, H. Estrade, J. Conard, D. Guerard, P. Lagrange, and M. E. Makrini, Physica B 99, 514–520 (1980).
- 19 R. J. Elliott, Phys. Rev. 96(2), 266–279 (1954).
- 20 W. Rüdorff and E. Schulze, Z. Anorg. Allg. Chem. 227, 156–171 (1954).
- 21 A. Hérold, Bull. Soc. Chim. Fr. 3, 999 (1955).
- 22 R. C. Croft, Q. Rev. Chem. Soc. 14, 1–45 (1960).
- 23 G. Feher and A. F. Kip, Phys. Rev. 95, 337–348 (1955).
- 24 F. J. Dyson, Phys. Rev. 98, 349–359 (1955).
- 25 L. Walmsley, G. Ceotto, J. H. Castilho, and C. Rettori, Synth. Met. 30, 97–107 (1989).
- 26 C. P. Slichter, Principles of Magnetic Resonance (Springer, New York, 1989).
- 27 L. Walmsley, J. Magn. Reson. A 122, 209–213 (1996).
- 28 Y. Yafet, Solid State Phys. 14, 1–98 (1963).
- 29 H. A. Kramers, Proc. Amsterdam Acad. 33, 959 (1930).
