Incommensurate dynamic correlations in the quasi-two-dimensional spin liquid BiCu${}_{2}$PO${}_{6}$

Incommensurate dynamic correlations in the quasi-two-dimensional spin liquid BiCu $_{2}$ PO $_{6}$

K. W. Plumb, Zahra Yamani, M. Matsuda, G. J. Shu, B. Koteswararao, F. C. Chou, and Young-June Kim

Phys. Rev. B 88, 024402 – Published 2 July 2013

Abstract

We report detailed inelastic neutron-scattering measurements on single crystals of the frustrated two-leg ladder ${BiCu}_{2} {PO}_{6}$ , whose ground state is described as a spin liquid phase with no long-range order down to 6 K. Two branches of steeply dispersing long-lived spin excitations are observed with excitation gaps of $Δ_{1} = 1.90 (9)$ meV and $Δ_{2} = 3.95 (8)$ meV. Significant frustrating next-nearest-neighbor interactions along the ladder leg drive the minimum of each excitation branch to incommensurate wave vectors $ζ_{1} = 0.574 π$ and $ζ_{2} = 0.553 π$ for the lower and upper energy branches, respectively. The temperature dependence of the excitation spectrum near the gap energy is consistent with thermal activation into singly and doubly degenerate excited states. The observed magnetic excitation spectrum as well as earlier thermodynamic data could be consistently explained by the presence of strong anisotropic interactions in the ground-state Hamiltonian.

Received 25 January 2013

DOI:https://doi.org/10.1103/PhysRevB.88.024402

Authors & Affiliations

K. W. Plumb^1,*, Zahra Yamani², M. Matsuda³, G. J. Shu⁴, B. Koteswararao⁴, F. C. Chou⁴, and Young-June Kim^1,†

¹Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
²Canadian Neutron Beam Centre, National Research Council, Chalk River Laboratories, Chalk River, Ontario K0J 1P0, Canada
³Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁴Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan

^*kplumb@physics.utoronto.ca
^†yjkim@physics.utoronto.ca

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Vol. 88, Iss. 2 — 1 July 2013

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Images

Figure 1
(a) Schematic representation of the crystal structure of ${BiCu}_{2} {PO}_{6}$ . The unit cell is orthorhombic, space group $P n m a$ , with $a = 11.755$ Å, $b = 5.16$ Å, and $c = 7.79$ Å at 6 K.[23] (b) Perspective view of the ladder unit in the $b$ – $c$ plane. (c) Projection into the $a$ – $c$ plane showing the zig-zag chains of ${Cu}^{2+}$ ions.Reuse & Permissions
Figure 2
Representative constant-q scans. Data in panels (a)–(d) were obtained on C5 with the sample aligned in the $(0, k, l)$ scattering plane and a collimation of 33'-48'-51'-144'. Data in panels (e) and (f) were obtained on HB1 with the sample aligned in the $(h, k, 2 k$ ) scattering plane and a collimation of 48'-40'-40'-120'. All data were collected at $T = 6$ K. The solid black lines are the results of a global fit to the single mode approximation; gold and blue filled areas show the contribution from each mode including resolution effects.Reuse & Permissions
Figure 3
Constant energy transfer scans around the gap energy. Data were obtained on HB1 with a collimation of 48'-20'-20'-60'. All data were collected at $T = 6$ K. The solid black lines are the results of a global fit to the single mode approximation.Reuse & Permissions
Figure 4
(a–c) Inelastic neutron-scattering intensity map for $T = 6$ K constructed by linear interpolation of a series of constant scans. All data have been corrected for the isotropic ${Cu}^{2+}$ form factor. Solid and dashed gray lines show the dispersion relation, Eq. (1), using the parameters obtained from the single mode approximation fit. Solid white symbols in panel (c) show the fitted peak positions of resolution limited mode. (d) Structure factor data obtained at $T = 6$ K, for equal-time spin correlations along the chain $b^{*}$ direction, calculated by numerically integrating constant-q scans for $ω > 0.5$ meV. (e–f) Measured first moment as a function of wave vector along the rung $c^{*}$ direction and perpendicular to the planes of the ladders, along $a^{*}$ . Solid lines are fits as described in the text.Reuse & Permissions
Figure 5
Temperature dependence of spin excitations near the incommensurate wave vector at (0,1.425,1), data collected on C5. (a) A series of representative constant-q scans; data have been offset for clarity; solid lines are fit to the resolution convolved cross section. (b–d) Results of fit to resolution convolved Lorentzian scattering cross section. Solid and dashed lines in panel (b) are fit to the population thermalization factor from RPA theory. The solid and dashed lines in panel (c) are fit to exponential activated behavior as described in the text.Reuse & Permissions

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