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Elastic constants and ultrasound attenuation in the spin-liquid phase of Cs2CuCl4

S. Streib, P. Kopietz, P. T. Cong, B. Wolf, M. Lang, N. van Well, F. Ritter, and W. Assmus
Phys. Rev. B 91, 041108(R) – Published 9 January 2015
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    Abstract

    The spin excitations in the spin-liquid phase of the anisotropic triangular lattice quantum antiferromagnet Cs2CuCl4 have been shown to propagate dominantly along the crystallographic b axis. To test this dimensional reduction scenario, we have performed ultrasound experiments in the spin-liquid phase of Cs2CuCl4 probing the elastic constant c22 and the sound attenuation along the b axis as a function of an external magnetic field along the a axis. We show that our data can be quantitatively explained within the framework of a nearest-neighbor spin-1/2 Heisenberg chain, where fermions are introduced via the Jordan-Wigner transformation and the spin-phonon interaction arises from the usual exchange-striction mechanism.

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    • Received 16 September 2014

    DOI:https://doi.org/10.1103/PhysRevB.91.041108

    ©2015 American Physical Society

    Authors & Affiliations

    S. Streib and P. Kopietz

    • Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt, Germany

    P. T. Cong, B. Wolf, M. Lang, N. van Well, F. Ritter, and W. Assmus

    • Physikalisches Institut, Universität Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt, Germany

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    Vol. 91, Iss. 4 — 15 January 2015

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    • Figure 1
      Figure 1

      Part of the anisotropic triangular lattice formed by the spins in Cs2CuCl4. The largest exchange coupling J connects nearest-neighbor spins along the crystallographic b axis. The corresponding elastic constant is denoted by c22. In this work we consider only the case where the magnetic field B is along the a axis perpendicular to the plane of the lattice.

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    • Figure 2
      Figure 2

      Comparison of the Hartree-Fock result for the magnetization curve s(h) of the Heisenberg chain (without phonons) at T=0 with the exact Bethe ansatz [23]. Inset: Renormalization Z(h) of the nearest-neighbor hopping.

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    • Figure 3
      Figure 3

      Comparison of theory and experiment for the relative change of the sound velocity of the c22 mode: (a) in the ordered phase (T=50mK) with coupling constants g1=0 and g2=−1.2×10−3, (b) in the spin-liquid phase (T=1K) with coupling constants g1=0 and g2=−1.1×10−3. In the fitting procedure we have allowed a constant offset for Δc/c which is necessary due to a small anomaly in the experimental data close to zero magnetic field.

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    • Figure 4
      Figure 4

      Experimental results for the relative change Δγ of the sound attenuation of the c22 mode as a function of the magnetic field for three different temperatures.

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    • Figure 5
      Figure 5

      (a) Damping γq for different values of r=c/(Jb) as a function of the magnetic field at temperature T/J=0.05. (b) Corresponding contribution c(1) to Δc/c defined in Eq. (13).

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