Spin-wave interaction in two-dimensional ferromagnets with dipolar forces

Physical Review B - Condensed Matter and Materials Physics

Volumn 77, Issue 14, 2008, Pages

  Syromyatnikov, A V ^a  

^a PETERSBURG NUCLEAR PHYSICS INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 43049109489     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.77.144433     Document Type: Article

References (34)

1. K. De'Bell, A. B. MacIsaac, and J. P. Whitehead, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.72.225 72, 225 (2000).
2. P. J. Jensen and K. H. Bennemann, Surf. Sci. Rep. SSREDI 0167-5729 10.1016/j.surfrep.2006.02.001 61, 129 (2007).
3. N. D. Mermin and H. Wagner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.17.1133 17, 1133 (1966).
4. S. V. Maleev, Sov. Phys. JETP 43, 1240 (1976). 0038-5646
5. C. Pich and F. Schwabl, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.7957 47, 7957 (1993).
6. B. P. Toperverg and A. G. Yashenkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48.16505 48, 16505 (1993).
7. T. S. Rahman and D. L. Mills, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.20.1173 20, 1173 (1979).
8. A. I. Akhiezer, V. G. Bar'yakhtar, and S. V. Peletminskii, Spin Waves (North-Holland, Amsterdam, 1968).
9. A. Kashuba, A. Abanov, and V. L. Pokrovsky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.2554 77, 2554 (1996).
10. A. Abanov, A. Kashuba, and V. L. Pokrovsky, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.56.3181 56, 3181 (1997).
11. A. V. Syromyatnikov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74. 014435 74, 014435 (2006).
12. J. R. Tessman, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.96.1192 96, 1192 (1954).
13. J. H. van Vleck, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.52.1178 52, 1178 (1937).
14. F. Keffer and T. Oguchi, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.117. 718 117, 718 (1960).
15. F. Keffer, Handbook of Physics (Springer, Berlin, 1966), Vol. 18, Pt. 2.
16. M. Dantziger, B. Glinsmann, S. Scheffler, B. Zimmermann, and P. J. Jensen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.094416 66, 094416 (2002).
17. C. L. Henley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62. 2056 62, 2056 (1989).
18. J. Villain, R. Bidaux, J. P. Carton, and R. Conte, J. Phys. (Paris) JOPQAG 0302-0738 10.1051/jphys:0198000410110126300 41, 1263 (1980).
19. S. Prakash and C. L. Henley, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.42.6574 42, 6574 (1990).
20. K. De'Bell, A. B. MacIsaac, I. N. Booth, and J. P. Whitehead, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.55.15108 55, 15108 (1997).
21. A. Carbognani, E. Rastelli, S. Regina, and A. Tassi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.1015 62, 1015 (2000).
22. R. N. Costa Filho, M. G. Cottam, and G. A. Farias, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.6545 62, 6545 (2000).
23. F. Dyson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.102.1217 102, 1217 (1956).
24. F. Dyson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.102.1230 102, 1230 (1956).
25. S. V. Maleev, Sov. Phys. JETP 6, 776 (1958). 0038-5646
26. M. H. Cohen and F. Keffer, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.99.1128 99, 1128 (1955).
27. Thermal corrections to the gap proportional to ω03 Tln [T/ (S ω0)] / D2 from the Hartree-Fock diagram and from the loop diagram discussed in Sec. 3 cancel each other. As a result, the thermal correction to the square of the gap for S∼1 is much smaller, ω03 T3/2 / D5/2 (see discussion in Sec. 3). To find it, one should take into account O (k2) corrections in the expansion of the dipolar tensor Qk ρβ, which depend on the lattice type.
28. Although TC given by Eq. 51 can differ several times from the real value of the Curie temperature (Ref.), this precision is sufficient for our estimations.
29. Notice that even at large enough dipolar characteristic energy ω0 (remains small as compared to the exchange value), say, at ω0 ≈0.1J, we have Sln { 4πS (D/ [S ω0]) 3/2 } only for pretty large spins S8.
30. A. B. Harris, D. Kumar, B. I. Halperin, and P. C. Hohenberg, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.3.961 3, 961 (1971).
31. P. D. Loly, 07281 Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003- 4916(70)90003-5 56, 40 (1970).
32. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed., Landau and Lifshitz Course of Theoretical Physics Vol. 5 (Butterworth-Heinemann, Oxford, 1980), Pt. 1.
33. A. B. Harris, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.143.353 143, 353 (1966).
34. A. Grechnev, V. Y. Irkhin, M. I. Katsnelson, and O. Eriksson, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.024427 71, 024427 (2005).