Abstract
In chap. 2, we have seen that the physics of weakly coupled spin ladders is particularly rich. In the following, we explore the diversity of their phase diagram, pictured in Fig. 2.2, by computing several physical quantities such as the magnetization, the rung state density and the specific heat. In particular, we test the LL low energy prediction and evaluate the related crossover to the quantum critical regime. Furthermore we discuss the effect of the 3D interladder coupling computing the staggered magnetization in the 3D-ordered phase and its critical temperature. We finally discuss the NMR relaxation rate in the LL gapless regime related to the low energy dynamics. All of these physical quantities are computed for the BPCB parameters (see Sect. 2.2). Hence they can be directly compared to the experiments on BPCB discussed in detail at the end of this chapter.
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- 1.
The perturbative expression of the ground state in the spin liquid regime and the corresponding singlet and triplet densities are given in Appendix A.
- 2.
An additional scaling factor \(7.47\,\mathrm{mJ/gK}\) has to be applied on the theoretical specific heat (per rung) to convert to the experimental units.
- 3.
\(g=2.17\) for the experimental settings of ND measurements.
References
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)
T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004)
T. Giamarchi, C. Rüegg, O. Tchernyshyov, Bose-einstein condensation in magnetic insulators. Nat. Phys. 4, 198–204 (2008)
T. Giamarchi, A.M. Tsvelik, Phys. Rev. B 59, 11398 (1999)
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)
S. Lukyanov, A.B. Zamolodchikov, Nucl. Phys. B 493, 571 (1997)
Y. Maeda, C. Hotta, M. Oshikawa, Universal temperature dependence of the magnetization of gapped spin chains. Phys. Rev. Lett. 99, 057205 (2007)
B. Normand, Ch. Rüegg, Complete bond-operator theory of the two-chain spin ladder. Phys. Rev. B 83, 054415 (2011)
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)
S. Sachdev, T. Senthil, R. Shankar, Phys. Rev. B 50, 258 (1994)
D.J. Scalapino, Y. Imry, P. Pincus, Phys. Rev. B 11, 2042 (1975)
C.P. Slichter, Principles of Magnetic Resonance (Springer, Berlin, 1980)
S. Suga, J. Phys. Soc. Jpn. 77, 074717 (2008)
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 (Hpip)\(_2\)CuBr\(_4\). Phys. Rev. B 79, 020408(R) (2009)
S. Todo, A. Shibasaki, Improved chain mean-field theory for quasi-one-dimensional quantum magnets. Phys. Rev. B 78, 224411 (2008)
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)
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 \((c_{5}h_{12}n)_{2}cubr_{4}\). Phys. Rev. B 82, 054431 (2010)
X. Wang, L. Yu, Magnetic-field effects on two-legheisenberg antiferromagnetic ladders: thermodynamic properties. Phys. Rev. Lett. 84, 5399–5402 (2000)
Z. Weihong, V. Kotov, J. Oitmaa, Two-chain spin ladder with frustrating second-neighbor interactions. Phys. Rev. B 57, 11439–11445 (1998)
S. Wessel, M. Olshanii, S. Haas, Field-induced magnetic order in quantum spin liquids. Phys. Rev. Lett. 87, 206407 (2001)
C. Yasuda, S. Todo, K. Hukushima, F. Alet, M. Keller, M. Troyer, H. Takayama, Néel temperature of quasi-low-dimensional heisenberg antiferromagnets. Phys. Rev. Lett. 94, 217201 (2005)
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Bouillot, P. (2013). Static Properties and NMR Relaxation Rate. 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_4
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