Energy- and crystal momentum-resolved study of laser-induced femtosecond magnetism

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 21, 2009, Pages

  Zhang, G P ^a   Bai, Yihua ^a   George, Thomas F ^b  

^a INDIANA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF MISSOURI ST LOUIS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954728502     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.214415     Document Type: Article

References (43)

1. E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, Phys. Rev. Lett. 76, 4250 (1996). 10.1103/PhysRevLett.76.4250
2. L. Guidoni, E. Beaurepaire, and J.-Y. Bigot, Phys. Rev. Lett. 89, 017401 (2002). 10.1103/PhysRevLett.89.017401
3. G. P. Zhang, W. Hübner, E. Beaurepaire, and J.-Y. Bigot, Top. Appl. Phys. 83, 245 (2002). 10.1007/3-540-40907-6-8
4. J.-Y. Bigot, L. Guidoni, E. Beaurepaire, and P. N. Saeta, Phys. Rev. Lett. 93, 077401 (2004) 10.1103/PhysRevLett.93.077401
5. M. Vomir, L. H. F. Andrade, L. Guidoni, E. Beaurepaire, and J.-Y. Bigot, Phys. Rev. Lett. 94, 237601 (2005) 10.1103/PhysRevLett.94.237601
6. I. Radu, G. Woltersdorf, M. Kiessling, A. Melnikov, U. Bovensiepen, J.-U. Thiele, and C. H. Back, Phys. Rev. Lett. 102, 117201 (2009) 10.1103/PhysRevLett.102.117201
7. B. Koopmans, M. van Kampen, J. T. Kohlhepp, and W. J. M. de Jonge, Phys. Rev. Lett. 85, 844 (2000) 10.1103/PhysRevLett.85.844
8. C. Stamm, T. Kachel, N. Pontius, R. Mitzner, T. Quast, K. Holldack, S. Khan, C. Lupulescu, E. F. Aziz, M. Wietstruk, H. A. Dürr, and W. Eberhardt, Nature Mater. 6, 740 (2007) 10.1038/nmat1985
9. G. M. Müller, J. Walowski, M. Djordjevic, G. X. Miao, A. Gupta, A. V. Ramos, K. Gehrke, V. Moshnyaga, K. Samwer, J. Schmalhorst, A. Thomas, A. Hütten, G. Reiss, J. S. Moodera, and M. Münzenberg, Nature Mater. 8, 56 (2009). 10.1038/nmat2341
10. G. P. Zhang and W. Hübner, Phys. Rev. Lett. 85, 3025 (2000) 10.1103/PhysRevLett.85.3025
11. W. Hübner and G. P. Zhang, Phys. Rev. B 58, R5920 (1998) 10.1103/PhysRevB.58.R5920
12. G. P. Zhang and W. Hübner, J. Appl. Phys. 85, 5657 (1999). 10.1063/1.369831
13. P. M. Oppeneer and A. Liebsch, J. Phys.: Condens. Matter 16, 5519 (2004). 10.1088/0953-8984/16/30/013
14. A. Vernes and P. Weinberger, Phys. Rev. B 71, 165108 (2005). 10.1103/PhysRevB.71.165108
15. C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, Phys. Rev. Lett. 99, 047601 (2007). 10.1103/PhysRevLett. 99.047601
16. J. Hohlfeld, C. D. Stanciu, and A. Rebei, Appl. Phys. Lett. 94, 152504 (2009). 10.1063/1.3119313
17. G. P. Zhang, W. Hübner, G. Lefkidis, Y. Bai, and T. F. George, Nat. Phys. 5, 499 (2009). 10.1038/nphys1315
18. D. Steiauf and M. Fähnle, Phys. Rev. B 79, 140401 (R) (2009) 10.1103/PhysRevB.79.140401
19. R. J. Elliott, Phys. Rev. 96, 266 (1954) 10.1103/PhysRev.96.266
20. Y. Yafet, Solid State Phys. 14, 1 (1963) 10.1016/S0081-1947(08)60259-3
21. A paper by Koopmans suggests that the total amount of angular-momentum transfer is limited by the number of photons involved in the laser field. For details, see B. Koopmans, M. van Kampen, and W. J. M. deJonge, J. Phys.: Condens. Matter 15, S723 (2003). 10.1088/0953-8984/15/5/324
22. J.-Y. Bigot, M. Vomir, and E. Beaurepaire, Nat. Phys. 5, 515 (2009). 10.1038/nphys1285
23. G. P. Zhang, Phys. Rev. Lett. 101, 187203 (2008). 10.1103/PhysRevLett. 101.187203
24. G. P. Zhang and T. F. George, Phys. Rev. B 78, 052407 (2008). 10.1103/PhysRevB.78.052407
25. M. I. Kurkin, N. B. Bakulina, and R. V. Pisarev, Phys. Rev. B 78, 134430 (2008). 10.1103/PhysRevB.78.134430
26. M. Pickel, A. B. Schmidt, F. Giesen, J. Braun, J. Minár, H. Ebert, M. Donath, and M. Weinelt, Phys. Rev. Lett. 101, 066402 (2008). 10.1103/PhysRevLett.101.066402
27. T. Kampfrath, R. G. Ulbrich, F. Leuenberger, M. Münzenberg, B. Sass, and W. Felsch, Phys. Rev. B 65, 104429 (2002). 10.1103/PhysRevB.65.104429
28. One should not confuse the variational method with perturbation theory. See the variational method in A. Messiah, Quantum Mechanics (Dover, New York, 1999), Chap. No., p. 762; see the perturbation method in Chapters XVI and XVII in the same book.
29. P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and J. Luitz, WIEN2K, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Technische Universität Wien, Austria, 2001).
30. T. Hartenstein, G. Lefkidis, W. Hübner, G. P. Zhang, and Y. Bai, J. Appl. Phys. 105, 07D305 (2009) 10.1063/1.3058704
31. G. P. Zhang, Y. Bai, W. Hübner, G. Lefkidis, and T. F. George, J. Appl. Phys. 103, 07B113 (2008). 10.1063/1.2837248
32. For other methods to compute the dipole transition matrix in solids, please refer to G. F. Bertsch, J.-I. Iwata, A. Rubio, and K. Yabana, Phys. Rev. B 62, 7998 (2000) 10.1103/PhysRevB.62.7998
33. R. Resta and D. Vanderbilt, in Physics of Ferroelectrics: a Modern Perspective, edited by, K. M. Rabe,,, C. H. Ahn,, and, J.-M. Triscone, (Springer-Verlag, Berlin, 2007), pp. 31-68 10.1007/978-3-540-34591-6-2
34. I. Souza, J. Iniguez, and D. Vanderbilt, Phys. Rev. B 69, 085106 (2004) 10.1103/PhysRevB.69.085106
35. R. Resta, Phys. Rev. Lett. 80, 1800 (1998). 10.1103/PhysRevLett.80.1800
36. S. Sharma, J. K. Dewhurst, and C. Ambrosch-Draxl, Phys. Rev. B 67, 165332 (2003). 10.1103/PhysRevB.67.165332
37. C. Ambrosch-Draxl and J. O. Sofo, Comput. Phys. Commun. 175, 1 (2006). 10.1016/j.cpc.2006.03.005
38. We have not included the relativistic corrections in the momentum operator as Wang and Callaway have already pointed out that the matrix element is small [C. S. Wang and J. Callaway, Phys. Rev. B 9, 4897 (1974)]. 10.1103/PhysRevB.9.4897
39. Note that the coefficients are spin-orbit coupling dependent. As a result, the transition-matrix element contains the mixed spin-up and spin-down components. One should not confuse the following three matrices: (a) the matrix formed within the LAPW basis, (b) the matrix formed within the spin-polarized basis, and (c) the matrix formed within the spin-polarized basis with the presence of spin-orbit coupling.
40. There is no intrinsic limitation in our scheme. As far as the DFT works, the scheme will work. If the laser is too strong and melts the sample then our scheme will break down as does the experimental one. We only consider the electron dynamics and work on the time scale of several hundred femtoseconds before the phonon is strongly activated. We can not use temperature concept during the laser excitation: temperature is a statistical concept and should not be used within a few hundred fs.
41. The small magnetization change is due to a weak laser field used in our simulation. If we use a strong laser, the demagnetization will of course be larger. There are two reasons why we choose a weak laser. First, when excited with a weak laser field, all the states, that make substantial magnetic contribution will make substantial contributions to the magnetic changes when the laser field becomes strong. But the other way around is not necessarily true. We use linearly polarized light in the present work. In metals, polarity does not play a big role since the orbital moment is small. Since our sample is a metal, there is no big effect on the results, which is already known from experiments. The laser affects the system through the second term as explained in our paper (Ref.).
42. C. Ambrosch-Draxl, P. Novak, D. J. Singh, and P. Blaha (private communications).
43. D. Singh and L. Nordstrom, Planewaves, Pseudopotentials and the LAPW Method, 2nd ed. (Springer, Berlin, 2006).