Magnetic properties of the $S=\frac{1}{2}$ quasisquare lattice antiferromagnet CuF${}_{2}$(H${}_{2}$O)${}_{2}$(pyz) (pyz $=$ pyrazine) investigated by neutron scattering

Magnetic properties of the $S = \frac{1}{2}$ quasisquare lattice antiferromagnet CuF $_{2}$ (H $_{2}$ O) $_{2}$ (pyz) (pyz $=$ pyrazine) investigated by neutron scattering

C. H. Wang, M. D. Lumsden, R. S. Fishman, G. Ehlers, T. Hong, W. Tian, H. Cao, A. Podlesnyak, C. Dunmars, J. A. Schlueter, J. L. Manson, and A. D. Christianson

Phys. Rev. B 86, 064439 – Published 27 August 2012

Abstract

We have performed elastic and inelastic neutron scattering experiments on single crystal samples of the coordination polymer compound CuF $_{2}$ (H $_{2}$ O) $_{2}$ (pyz) (pyz = pyrazine) to study the magnetic structure and excitations. The elastic neutron diffraction measurements indicate a collinear antiferromagnetic structure with moments oriented along the [0.7 0 1] real-space direction and an ordered moment of 0.60 $\pm$ 0.03 $μ_{B} /$ Cu. This value is significantly smaller than the single-ion magnetic moment, reflecting the presence of strong quantum fluctuations. The spin wave dispersion from magnetic zone center to the zone boundary points (0.5 1.5 0) and (0.5 0 1.5) can be described by a two-dimensional Heisenberg model with a nearest-neighbor magnetic exchange constant $J_{2 D} = 0.934$ $\pm$ 0.0025 meV. The interlayer interaction $J_{perp}$ in this compound is less than 1.5 $%$ of $J_{2 D}$ . The spin excitation energy at the (0.5 0.5 0.5) zone boundary point is reduced when compared to the (0.5 1 0.5) zone boundary point by $\sim$ 10.3 $%$ $\pm$ 1.4 $%$ . This zone boundary dispersion is consistent with quantum Monte Carlo and series expansion calculations for the $S = \frac{1}{2}$ Heisenberg square lattice antiferromagnet, which include corrections for quantum fluctuations to linear spin wave theory.

Received 23 May 2012

DOI:https://doi.org/10.1103/PhysRevB.86.064439

Authors & Affiliations

C. H. Wang¹, M. D. Lumsden¹, R. S. Fishman¹, G. Ehlers¹, T. Hong¹, W. Tian¹, H. Cao¹, A. Podlesnyak¹, C. Dunmars², J. A. Schlueter², J. L. Manson³, and A. D. Christianson¹

¹Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Material Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
³Department of Chemistry and Biochemistry, Eastern Washington University, Cheney, Washington 99004, USA

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Vol. 86, Iss. 6 — 1 August 2012

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Images

Figure 1
Temperature dependence of magnetic Bragg peaks: (a) (0.5 1 0) and (b) ( $- 0.5$ 0 1) for CuF $_{2}$ (D $_{2}$ O) $_{2}$ ( $d_{4}$ -pyz). Insets display the temperature-dependent peak intensity. Solid lines are guides to the eye. The data were collected on the HB-1 triple-axis instrument in the $H$ $K$ 0 and $H$ 0 $L$ scattering planes, respectively.Reuse & Permissions
Figure 2
The observed intensity plotted as a function of calculated intensity for CuF $_{2}$ (D $_{2}$ O) $_{2}$ ( $d_{4}$ -pyz) at $T = 0.25$ K. Nuclear and magnetic reflections are denoted by diamonds and circles, respectively. The solid line is a guide to the eye. The data were collected on HB-1 in different scattering planes. The insets depict different views of the unit cell. The arrows on Cu atoms indicate the magnetic-moment configuration. The 2D magnetic behavior of CuF $_{2}$ (D $_{2}$ O) $_{2}$ ( $d_{4}$ -pyz) originates in the $b c$ plane.Reuse & Permissions
Figure 3
(a) Constant- $E$ scans along (0.5 $K$ 0) collected in the $H K$ 0 scattering plane at $T = 1.5$ K by the CG-4C spectrometer. (b) Constant- $Q$ scans collected in the $H K$ 0 scattering plane at $T = 1.5$ K by the CG-4C spectrometer. The solid lines in both panels are fits with Gaussians.Reuse & Permissions
Figure 4
Inelastic neutron scattering data from the time-of-flight spectrometer CNCS. (a) Contour map of intensity in the $H$ 0 $L$ scattering plane with $Δ E = 0.25$ meV and $T = 1.5$ K. Background scattering determined from an empty sample holder measurement has been subtracted. (b) The spin wave dispersion along the (1.5 0 $L$ ) direction. The data were collected at $T = 1.5$ K, with $E_{i} = 3$ meV. Background scattering determined from an empty sample holder measurement has been subtracted. (c) Low-energy spin wave dispersion along the (0 0 $L$ ) direction in the high-resolution mode at $T = 1.5$ K with $E_{i} = 1.5$ meV. Intensities in all panels are given in arbitrary units. The integration range is indicated along with the specified direction at the top of each panel. Note that the dispersion was found to be independent of the value of $H$ , and as such the integration range over $H$ was chosen to be large to increase statistics.Reuse & Permissions
Figure 5
Summary of the spin wave dispersion for CuF $_{2}$ (D $_{2}$ O) $_{2}$ ( $d_{4}$ -pyz). The data were collected using CNCS (solid circles), CG-4C (solid squares), and HB-1A (solid triangles). The solid line represents the dispersion of the Heisenberg linear spin wave theory with a nearest-neighbor interaction. The dash-dotted line represents the results of series expansion to higher order.[8] The inset depicts the $b c$ plane. The dashed lines show the square lattice with a nearest-neighbor exchange interaction.Reuse & Permissions
Figure 6
Constant- $Q$ scans along the zone boundary points ranging from (0 1 $- 0.5$ ) to (0 0.5 $- 0.5$ ). The solid line are fits to a Gaussian. The data were collected on HB-1A.Reuse & Permissions

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