Abstract
Magnetoelastic properties of the spin-1/2 Ising-Heisenberg model on doubly decorated planar lattices partially amenable to lattice vibrations are examined within the framework of the harmonic approximation and decoration-iteration transformation. It is shown that the magnetoelastic coupling may lead to a spontaneous distortion of the vibrating decorating atoms and the mutual interplay between quantum spin fluctuations and local lattice deformations enhances typical quantum features like the quantum reduction of the magnetization in the ground state of the quantum antiferromagnetic phase, while it does not affect the ground-state behaviour of the classical ferromagnetic phase. It also turns out that the spontaneous distortion is responsible for a much more pronounced reduction of the critical temperature in the quantum antiferromagnetic phase than in the classical ferromagnetic phase.
Similar content being viewed by others
References
D.C. Mattis, in The Many-Body Problem: An Encyclopedia of Exactly Solved Models in One Dimension (World Scientific, Singapore, 1993)
D.A. Lavis, G.M. Bell, in Statistical Mechanics of Lattice Systems (Springer, Berlin, 1999)
H.T. Diep, H. Giacomini, in Frustrated Spin Systems, edited by H.T. Diep (World Scientific, Singapore, 2004)
F.Y. Wu, in Exactly Solved Models: A Journey in Statistical Mechanics (World Scientific, Singapore, 2009)
R. O’Handley, in Modern Magnetic Materials: Principles and Applications (Wiley, New York, 2000)
O.K. Rice, J. Chem. Phys. 22, 1535 (1954)
C. Domb, J. Chem. Phys. 24, 783 (1956)
C.P. Bean, D.S. Rodbell, Phys. Rev. 126, 10 (1962)
D.C. Mattis, T.D. Schultz, Phys. Rev. 129, 175 (1963)
G.E. Baker, J.W. Essam, Phys. Rev. Lett. 24, 447 (1970)
L. Gunther, D.J. Bergman, Y. Imry, Phys. Rev. Lett. 27, 558 (1971)
N. Matsudaira, J. Phys. Soc. Jpn 25, 1225 (1968)
S.R. Salinas, J. Phys. C: Solid State Phys. 7, 241 (1974)
K.A. Penson, Phys. Rev. B 8, 2119 (1973)
Y. Imry, Phys. Rev. Lett. 33, 1304 (1974)
D.J. Bergman, B.I. Halperin, Phys. Rev. B 13, 2145 (1976)
M.E. Fisher, Phys. Rev. 176, 257 (1968)
P. Pincus, Solid State Commun. 9, 1971 (1971)
G. Beni, P. Pincus, J. Chem. Phys. 57, 3531 (1972)
J.H. Taylor, G. Müller, Physica A 130, 1 (1985)
K. Okamoto, Solid State Commun. 83, 1039 (1992)
O. Derzhko, J. Richter, O. Zaburannyi, J. Phys.: Condens. Matter 12, 8661 (2000)
I.G. Enting, J. Phys. A 6, 170 (1973)
S.R. Salinas, J. Phys. A 6, 1527 (1973)
B.S. Lee, Prog. Theor. Phys. 50, 2093 (1973)
M. Barma, Phys. Rev. B 12, 2710 (1975)
K.A. Penson, A. Holz, K.H. Bennemann, Phys. Rev. B 13, 433 (1976)
M. Marchand, A. Caille, J. Appl. Phys. 57, 3346 (1985)
T.A. Kaplan, Phys. Rev. B 80, 012407 (2009)
T.A. Kaplan, Phys. Rev. B 80, E229906 (2009)
E. Orignac, R. Citro, Phys. Rev. B 71, 214419 (2005)
E. Pytte, Ann. Phys. 32, 377 (1965)
E. Pytte, Phys. Rev. B 10, 4637 (1974)
G. Beni, J. Chem. Phys. 58, 3200 (1973)
M.C. Cross, D.S. Fisher, Phys. Rev. B 19, 402 (1979)
G.S. Uhrig, Phys. Rev. B 57, R14004 (1998)
D. Augier, D. Poilblanc, Eur. Phys. J. B 1, 19 (1998)
H. Onishi, S. Miyashita, J. Phys. Soc. Jpn 72, 392 (2003)
S. Akiyama, Ch. Yasuda, J. Phys. Soc. Jpn 80, 104709 (2011)
J. Strečka, M. Jacščur, Phys. Rev. B 66, 174415 (2002)
J. Strečka, M. Jacščur, Acta Phys. Slovaca 56, 65 (2006)
J. Strečka, L. Čanová, M. Jaščur, M. Hagiwara, Phys. Rev. B 78, 024427 (2008)
D.X. Yao, Y.L. Loh, E.W. Carlson, M. Ma, Phys. Rev. B 78, 024428 (2008)
J.S. Valverde, O. Rojas, S.M. de Souza, Phys. Rev. E 79, 041101 (2009)
J. Strečka, L. Čanová, K. Minami, Phys. Rev. E 79, 051103 (2009)
J. Strečka, L. Čanová, K. Minami, Phys. Rev. E 83, E069904 (2011)
Z.-Y. Sun, L. Li, N. Li, K.-L. Yao, J. Liu, B. Luo, G.-H. Du, H.-N. Li, Europhys. Lett. 95, 30008 (2011)
S. Bellucci, V. Ohanyan, Eur. Phys. J. B 75, 531 (2010)
J. Lu, W.T.A. Harrison, A.J. Jacobson, Chem. Commun. 399 (1996)
Y. Miyazato, M. Ohba, H. Okawa, Bull. Chem. Soc. Jpn 78, 1646 (2005)
M. Verdauger, Polyhedron 20, 1115 (2001)
J. Černák, M. Orendač, I. Potočňák, J. Chomič, A. Orendáčová, J. Skoršepa, A. Feher, Coord. Chem. Rev. 224, 51 (2002)
R. Lescouezec, L.M. Toma, J. Vaissermann, M. Verdaguer, F.S. Delgado, C. Ruiz-Pérez, F. Lloret, M. Julve, Coord. Chem. Rev. 249, 2691 (2005)
M.E. Fisher, Phys. Rev. 113, 969 (1959)
O. Rojas, J.S. Valverde, S.M. de Souza, Physica A 388, 1419 (2009)
J. Strečka, Phys. Lett. A 374, 3718 (2010)
J. Strečka, in On the Theory of Generalized Algebraic Transformations (LAP LAMBERT Academic Publishing, Saarbrücken, 2010)
L. Onsager, Phys. Rev. 65, 117 (1944)
R.M.F. Houtappel, Physica 16, 425 (1950)
H.N.V. Temperley, Proc. Roy. Soc. A 203, 202 (1950)
C. Domb, Adv. Phys. 9, 149 (1960)
B.M. McCoy, T.T. Wu, The Two-Dimensional Ising Model (Harvard University Press, Cambridge, 1973)
J.H. Barry, M. Khatun, T. Tanaka, Phys. Rev. B 37, 5193 (1988)
M. Khatun, J.H. Barry, T. Tanaka, Phys. Rev. B 42, 4398 (1990)
J.H. Barry, T. Tanaka, M. Khatun, C.H. Múnera, Phys. Rev. B 44, 2595 (1991)
J.H. Barry, M. Khatun, Phys. Rev. B 51, 5840 (1995)
C.N. Yang, Phys. Rev. 85, 808 (1952)
K.Y. Lin, Chinese J. Phys. 30, 287 (1992)
H.B. Callen, Phys. Lett. 4, 161 (1963)
M. Suzuki, Phys. Lett. 19, 267 (1965)
F.C. SáBarreto, I.P. Fittipaldi, B. Zeks, Ferroelectrics 39, 1103 (1981)
F.C. SáBarreto, I.P. Fittipaldi, Physica A 129, 360 (1985)
T. Balcerzak, J. Magn. Magn. Mater. 246, 213 (2002)
O. Rojas, J. Strečka, S.M. de Souza, unpublished results
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Strečka, J., Rojas, O. & de Souza, S.M. Spontaneous distortion in the spin-1/2 Ising-Heisenberg model on decorated planar lattices with a magnetoelastic coupling. Eur. Phys. J. B 85, 54 (2012). https://doi.org/10.1140/epjb/e2011-20733-5
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2011-20733-5