Skip to main content
SpringerLink
Log in

Spin-\(1/2\) Ladders

  • Chapter
  • First Online:
Statics and Dynamics of Weakly Coupled Antiferromagnetic Spin-1/2 Ladders in a Magnetic Field

Part of the book series: Springer Theses ((Springer Theses))

  • 497 Accesses

Abstract

The physics of quantum spin systems depends strongly on their microscopic characteristics. In fact, a large variety of phenomena can appear depending on the local spin \(S\), the type of interaction and the geometry of the system. The external environment is also very important. For instance, applying a magnetic field or pressure on the system can lead to even richer physics. Various combinations of internal constraints as well as external conditions have been investigated theoretically for many years [3].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    This phase is also called quantum disordered [15]. It appears in other antiferromagnetic systems such as frustrated antiferromagnets.

  2. 2.

    These parameters were the first outputs from the NMR measurements, which were later refined to the values from Ref. [22]. Note that small changes in these values do not affect the main results of the calculations.

  3. 3.

    More precisely, the Landé factor is different for each ladder forming the compound and varies with their orientation with respect to the magnetic field.

References

  1. I. Affleck, Phys. Rev. B 41, 6697 (1990)

    Article  ADS  Google Scholar 

  2. F. Anfuso, M. Garst, A. Rosch, O. Heyer, T. Lorenz, C. Rüegg, K. Krämer, Spin-spin correlation of the spin-ladder compound bcpb mesured by magnetostriction and comparison to quantum monte carlo results. Phys. Rev. B 77, 235113 (2008)

    Article  ADS  Google Scholar 

  3. A. Auerbach, Interacting Electrons and Quantum Magnetism, 2nd edn. (Springer, Berlin, 1998)

    Google Scholar 

  4. M. Azuma, Z. Hiroi, M. Takano, K. Ishida, Y. Kitaoka, Phys. Rev. Lett. 73, 3463 (1994)

    Article  ADS  Google Scholar 

  5. T. Barnes, E. Dagotto, J. Riera, E.S. Swanson, Excitation spectrum of heisenberg spin ladders. Phys. Rev. B 47, 3196 (1993)

    Article  ADS  Google Scholar 

  6. P. Bouillot, C. Kollath, A.M. Läuchli, M. Zvonarev, B. Thielemann, C. Rüegg, E. Orignac, R. Citro, M. Klanjšek, C. Berthier, M. Horvatić, T. Giamarchi, Statics and dynamics of weakly coupled antiferromagnetic spin-\(\frac{1}{2}\) ladders in a magnetic field. Phys. Rev. B 83, 054407 (2011)

    Article  ADS  Google Scholar 

  7. R. Calemczuk, J. Riera, D. Poilblanc, J.-P. Boucher, G. Chaboussant, L. Lévy, O. Piovesana, Thermodynamic properties of the spin-1/2 antiferromagnetic ladder \({\rm {Cu}}_2({\rm {C}}_5{\rm {H}}_{12}{\rm {N}}_2)_2{\rm {Cl}}_4\) under magnetic field. Eur. Phys. J. B 7, 171 (1999)

    Google Scholar 

  8. S. Capponi, D. Poilblanc, Thermodynamic properties of the coupled dimer system \({\rm {Cu}}_2({\rm {C}}_5{\rm {H}}_{12}{\rm {N}}_2)_2{\rm {Cl}}_4\). Phys. Rev. B 75, 092406 (2007)

    Article  ADS  Google Scholar 

  9. G. Chaboussant, M.-H. Julien, Y. Fagot-Revurat, M. Hanson, L.P. Lévy, C. Berthier, M. Horvatic, O. Piovesana, Zero temperature phase transitions in spin-ladders: phase diagram and dynamical studies of \({\rm {Cu}}_2({\rm {C}}_5{\rm {H}}_{12}{\rm {N}}_2)_2{\rm {Cl}}_4\). Eur. Phys. J. B 6, 167 (1998)

    Article  ADS  Google Scholar 

  10. G. Chaboussant, M.-H. Julien, Y. Fagot-Revurat, M.E. Hanson, L.P. Lévy, C. Berthier, M. Horvatić, O. Piovesana, Eur. Phys. J. B 6, 167 (1998)

    Article  ADS  Google Scholar 

  11. R. Chitra, T. Giamarchi, Phys. Rev. B 55, 5816 (1997)

    Article  ADS  Google Scholar 

  12. M. Clémancey, H. Mayaffre, C. Berthier, M. Horvatić, J.-B. Fouet, S. Miyahara, F. Mila, B. Chiari, O. Piovesana, Field-induced staggered magnetization and magnetic ordering in \({\rm {Cu}}_2({\rm {C}}_5{\rm {H}}_{12}{\rm {N}}_2)_2{\rm {Cl}}_4\). Phys. Rev. Lett. 97, 167204 (2006)

    Article  ADS  Google Scholar 

  13. E. Dagotto, T.M. Rice, Science 271, 5249 (1996)

    Article  Google Scholar 

  14. A. Furusaki, S.C. Zhang, Phys. Rev. B 60, 1175 (1999)

    Article  ADS  Google Scholar 

  15. T. Giamarchi, C. Rüegg, O. Tchernyshyov, Bose-Einstein condensation in magnetic insulators. Nat. Phys. 4, 198–204 (2008)

    Article  Google Scholar 

  16. T. Giamarchi, A.M. Tsvelik, Phys. Rev. B 59, 11398 (1999)

    Article  ADS  Google Scholar 

  17. S. Gopalan, T.M. Rice, M. Sigrist, Phys. Rev. B 49, 8901 (1994)

    Article  ADS  Google Scholar 

  18. F.D.M. Haldane, Phys. Rev. Lett. 50, 1153 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  19. P.H. Hammar, D.H. Reich, C. Broholm, F. Trouw, Phys. Rev. B 57, 7846 (1998)

    Article  ADS  Google Scholar 

  20. T. Hikihara, A. Furusaki, Spin correlations in the two-leg antiferromagnetic ladder in a magnetic field. Phys. Rev. B 63, 134438 (2000)

    Article  ADS  Google Scholar 

  21. G.I. Japaridze, E. Pogosyan, Magnetization plateau in the \(s=1/2\) spin ladder with alternating rung exchange. J. Phys. Condens. Matter 18, 9297 (2006)

    Google Scholar 

  22. M. Klanjšek, H. Mayaffre, C. Berthier, M. Horvatić, B. Chiari, O. Piovesana, P. Bouillot, C. Kollath, E. Orignac, R. Citro, T. Giamarchi, Controlling luttinger liquid physics in spin ladders under a magnetic field. Phys. Rev. Lett. 101, 137207 (2008)

    Article  ADS  Google Scholar 

  23. C. Knetter, K.P. Schmidt, M. Grüninger, G.S. Uhrig, Fractional and integer excitations in quantum antiferromagnetic spin 1/2 ladders. Phys. Rev. Lett. 87, 167204 (2001)

    Article  ADS  Google Scholar 

  24. T. Lorenz, O. Heyer, M. Garst, F. Anfuso, A. Rosch, Ch. Rüegg, K. Krämer, Diverging thermal expansion of the spin-ladder system \(({\rm {C}}_{5}{\rm {H}}_{12}{\rm {N}})_{2}{\rm {CuBr}}_{4}\). Phys. Rev. Lett. 100, 067208 (2008)

    Article  ADS  Google Scholar 

  25. Y. Maeda, C. Hotta, M. Oshikawa, Universal temperature dependence of the magnetization of gapped spin chains. Phys. Rev. Lett. 99, 057205 (2007)

    Article  ADS  Google Scholar 

  26. F. Mila, Eur. Phys. J. B 6, 201 (1998)

    Article  ADS  Google Scholar 

  27. B. Normand, Ch. Rüegg, Complete bond-operator theory of the two-chain spin ladder. Phys. Rev. B 83, 054415 (2011)

    Article  ADS  Google Scholar 

  28. S. Notbohm, P. Ribeiro, B. Lake, D.A. Tennant, K.P. Schmidt, G.S. Uhrig, C. Hess, R. Klingeler, G. Behr, B. Büchner, M. Reehuis, R.I. Bewley, C.D. Frost, P. Manuel, R.S. Eccleston, One- and two-triplon spectra of a cuprate ladder. Phys. Rev. Lett. 98, 027403 (2007)

    Article  ADS  Google Scholar 

  29. E. Orignac, R. Citro, T. Giamarchi, Phys. Rev. B 75, 140403(R) (2007)

    Google Scholar 

  30. B.R. Patyal, B.L. Scott, R.D. Willett, Crystal-structure, magnetic-susceptibility, and EPR studies of \(({\rm {C}}_{5}{\rm {H}}_{12}{\rm {N}})_{2}{\rm {CuBr}}_{4}\): a novel monomer system showing spin diffusion. Phys. Rev. B 41, 1657 (1990)

    Article  ADS  Google Scholar 

  31. M. Reigrotzki, H. Tsunetsugu, T.M. Rice, J. Phys. Condens. Matter 6, 9235 (1994)

    Google Scholar 

  32. Ch. Rüegg, K. Kiefer, B. Thielemann, D.F. McMorrow, V. Zapf, B. Normand, M.B. Zvonarev, P. Bouillot, C. Kollath, T. Giamarchi, S. Capponi, D. Poilblanc, D. Biner, K.W. Krämer, Thermodynamics of the spin luttinger liquid in a model ladder material. Phys. Rev. Lett. 101, 247202 (2008)

    Article  ADS  Google Scholar 

  33. S. Sachdev, T. Senthil, R. Shankar, Phys. Rev. B 50, 258 (1994)

    Google Scholar 

  34. A.T. Savici, G.E. Granroth, C.L. Broholm, D.M. Pajerowski, C.M. Brown, D.R. Talham, M.W. Meisel, K.P. Schmidt, G.S. Uhrig, S.E. Nagler, Neutron scattering evidence for isolated spin-1/2 ladders in BPCD. Phys. Rev. B 80, 094411 (2009)

    Article  ADS  Google Scholar 

  35. H.J. Schulz, Phys. Rev. B 34, 6372 (1986)

    Article  ADS  Google Scholar 

  36. M.B. Stone, Y. Chen, J. Rittner, H. Yardimci, D.H. Reich, C. Broholm, D.V. Ferraris, T. Lectka, Frustrated three-dimensional quantum spin liquid in CuHpCl. Phys. Rev. B 65, 064423 (2001)

    Article  ADS  Google Scholar 

  37. O.P. Sushkov, V.N. Kotov, Bound states of magnons in the \(s=1/2\) quantum spin ladder. Phys. Rev. Lett. 81, 1941 (1998)

    Article  ADS  Google Scholar 

  38. M. Tachiki, T. Yamada, Spin ordering in spin-pair system. J. Phys. Soc. Jpn. 28, 1413–1425 (1970)

    Article  ADS  Google Scholar 

  39. M. Tachiki, T. Yamada, S. Maekawa, J. Phys. Soc. Jpn. 29, 663 (1970)

    Article  ADS  Google Scholar 

  40. B. Thielemann, Ch. Rüegg, K. Kiefer, H.M. Rønnow, B. Normand, P. Bouillot, C. Kollath, E. Orignac, R. Citro, T. Giamarchi, A.M. Läuchli, D. Biner, K.W. Krämer, F. Wolff-Fabris, V. S. Zapf, M. Jaime, J. Stahn, N.B. Christensen, B. Grenier, D.F. McMorrow, J. Mesot, Field-controlled magnetic order in the quantum spin-ladder system \(({\rm {Hpip}})_{2}{\rm {CuBr}}_{4}\). Phys. Rev. B 79, 020408(R) (2009)

    Google Scholar 

  41. B. Thielemann, Ch. Rüegg, H.M. Rønnow, A.M. Läuchli, J.-S. Caux, B. Normand, D. Biner, K.W. Krämer, H.-U. Güdel, J. Stahn, K. Habicht, K. Kiefer, M. Boehm, D.F. McMorrow, J. Mesot, Direct observation of magnon fractionalization in the quantum spin ladder. Phys. Rev. Lett. 102, 107204 (2009)

    Article  ADS  Google Scholar 

  42. M. Troyer, H. Tsunetsugu, D. Würtz, Thermodynamics and spin gap of the Heisenberg ladder calculated by the look-ahead Lanczos algorithm. Phys. Rev. B 50, 13515 (1994)

    Article  ADS  Google Scholar 

  43. US Naval Research Laboratory, Crystal Lattice Structures (2008), http://cst-www.nrl.navy.mil/lattice/index.html

  44. M. Usami, S. Suga, Critical properties of \(s=\frac{1}{2}\) heisenberg ladders in magnetic fields. Phys. Rev. B 58, 14401–14406 (1998)

    Article  ADS  Google Scholar 

  45. E. Čižmár, M. Ozerov, J. Wosnitza, B. Thielemann, K.W. Krämer, Ch. Rüegg, O. Piovesana, M. Klanjšek, M. Horvatić, C. Berthier, S.A. Zvyagin, Anisotropy of magnetic interactions in the spin-ladder compound \(({\rm {C}}_{5}{\rm {H}}_{12}{\rm {N}})_{2}{\rm {CuBr}}_{4}\). Phys. Rev. B 82, 054431 (2010)

    Article  ADS  Google Scholar 

  46. X. Wang, Yu. Lu, Magnetic-field effects on two-leg Heisenberg antiferromagnetic ladders: thermodynamic properties. Phys. Rev. Lett. 84, 5399–5402 (2000)

    Article  ADS  Google Scholar 

  47. B.C. Watson, V.N. Kotov, M.W. Meisel, D.W. Hall, G.E. Granroth, W.T. Montfrooij, S.E. Nagler, D.A. Jensen, R. Backov, M.A. Petruska, G.E. Fanucci, D.R. Talham, He magnetic spin ladder \(\rm (C_{5}H_{12}N)_{2}CuBr_{4}\): high field magnetization and scaling near quantum criticality. Phys. Rev. Lett. 86, 5168 (2001)

    Google Scholar 

  48. Z. Weihong, V. Kotov, J. Oitmaa, Two-chain spin ladder with frustrating second-neighbor interactions. Phys. Rev. B 57, 11439–11445 (1998)

    Article  ADS  Google Scholar 

  49. S. Wessel, M. Olshanii, S. Haas, Field-induced magnetic order in quantum spin liquids. Phys. Rev. Lett. 87, 206407 (2001)

    Article  ADS  Google Scholar 

  50. F.C. Zhang, T.M. Rice, Phys. Rev. B 37, 3759 (1988)

    Article  ADS  Google Scholar 

  51. W. Zheng, C.J. Hamer, R.R.P. Singh, S. Trebst, H. Monien, Linked cluster series expansions for two-particle bound states. Phys. Rev. B 63, 144410 (2001)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DPMC-MaNEP, University of Geneva, 1211, Geneva, Switzerland

    Pierre Bouillot

Authors
  1. Pierre Bouillot
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pierre Bouillot .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bouillot, P. (2013). Spin-\(1/2\) Ladders. In: Statics and Dynamics of Weakly Coupled Antiferromagnetic Spin-1/2 Ladders in a Magnetic Field. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33808-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33808-3_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33807-6

  • Online ISBN: 978-3-642-33808-3

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation