Correlated impurities and intrinsic spin-liquid physics in the kagome material herbertsmithite

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Correlated impurities and intrinsic spin-liquid physics in the kagome material herbertsmithite

Tian-Heng Han, M. R. Norman, J.-J. Wen, Jose A. Rodriguez-Rivera, Joel S. Helton, Collin Broholm, and Young S. Lee

Phys. Rev. B 94, 060409(R) – Published 18 August 2016

Abstract

Low energy inelastic neutron scattering on single crystals of the kagome spin-liquid compound ${ZnCu}_{3} {(OD)}_{6} {Cl}_{2}$ (herbertsmithite) reveals antiferromagnetic correlations between impurity spins for energy transfers $ℏ ω < 0.8 meV (\sim J / 20)$ . The momentum dependence differs significantly from higher energy scattering which arises from the intrinsic kagome spins. The low energy fluctuations are characterized by diffuse scattering near wave vectors (100) and $(00 \frac{3}{2})$ , which is consistent with antiferromagnetic correlations between pairs of nearest-neighbor Cu impurities on adjacent triangular (Zn) interlayers. The corresponding impurity lattice resembles a simple cubic lattice in the dilute limit below the percolation threshold. Such an impurity model can describe prior neutron, NMR, and specific heat data. The low energy neutron data are consistent with the presence of a small spin gap $(Δ \sim 0.7 meV)$ in the kagome layers, similar to that recently observed by NMR. The ability to distinguish the scattering due to Cu impurities from that of the planar kagome Cu spins provides an important avenue for probing intrinsic spin-liquid physics.

Received 18 December 2015

DOI:https://doi.org/10.1103/PhysRevB.94.060409

Physics Subject Headings (PhySH)

Antiferromagnetism Frustrated magnetism

Kagome lattice

Heisenberg model Inelastic neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tian-Heng Han^1,2,*, M. R. Norman¹, J.-J. Wen^3,4, Jose A. Rodriguez-Rivera^5,6, Joel S. Helton^5,7, Collin Broholm^5,8, and Young S. Lee^3,4,†

¹Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
²James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
³Department of Applied Physics, Stanford University, Stanford, California 94305, USA
⁴Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
⁵NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
⁶Department of Materials Science, University of Maryland, College Park, Maryland 20742, USA
⁷Department of Physics, The United States Naval Academy, Annapolis, Maryland 21402, USA
⁸Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA

^*tianheng@alum.mit.edu
^†youngsl@stanford.edu

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Issue

Vol. 94, Iss. 6 — 1 August 2016

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Images

Figure 1
Inelastic neutron data on herbertsmithite in the $(H K 0)$ scattering plane at $T = 2 K$ for (a) $ℏ ω = 0.4 meV$ and (b) $ℏ ω = 1.3 meV$ . Data taken in the $(H H L)$ scattering plane for (d) $ℏ ω = 0.4 meV$ and (e) $ℏ ω = 1.3 meV$ . The bright spots at (110) and (003) arise from structural Bragg peaks. The diffuse spots at (100), $(00 \frac{3}{2})$ , and $(\frac{1}{2} \frac{1}{2} 0)$ are magnetic in origin. Note that the $(00 \frac{3}{2})$ diffuse spot is particularly pronounced at 0.4 meV, while the magnetic scattering at 1.3 meV is nearly independent of $L$ . Plots of the calculated $S (Q)$ in (c) the $(H K 0)$ and (f) the $(H H L)$ planes, representing antiferromagnetically correlated nearest-neighbor impurities on the interlayer sites, as described in the text.
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Figure 2
(a) Proposed model of the antiferromagnetically correlated nearest-neighbor Cu impurities which give rise to the low energy scattering. The blue spheres are the intrinsic kagome Cu sites. The red spheres denote the Zn interlayer sites. The green ovals indicate interlayer sites which have Cu impurities on nearest-neighbor locations. These moments are fluctuating with AF correlations. In our sample, only about 15% of the Zn sites have a Cu impurity. (b) The effective connectivity of the impurity lattice as a simple cubic lattice. Here, the red bonds indicate the NN impurity-impurity bonds identified in the structure factor calculations. The blue spheres and bonds indicate the intrinsic kagome layers.
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Figure 3
Line scan through the data obtained by subtracting the data along $(00 L)$ at 0.4 meV acquired at $T = 20 K$ from the data at $T = 2 K$ . Here, to improve statistics, an integration width of $\pm 0.15$ was used along the $(H H 0)$ direction. The blue dashed line denotes a fit to these data involving only the correlator between nearest-neighbor impurities $f_{3}$ . The red solid line denotes a fit that also includes the correlator between the impurity and the nearest spins on the kagome layers $f_{1}$ , however, the contribution of $f_{1}$ is found to be small. Error bars indicate $1 σ$ .
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Figure 4
(a) Specific heat vs temperature in herbertsmithite [2]. The solid curve denotes the equation described in the text based on the impurity model, with an assumed impurity concentration of 12%, whereas the dashed curve is the estimated kagome contribution (these data were taken on a powder sample, different from the single crystals used for the neutron measurements, as discussed further in the Supplemental Material [32]). (b) A measure of the intrinsic scattering $S_{kagome} (ω)$ obtained after subtracting the impurity contribution as described in the text. These data are integrated over a large region in reciprocal space. The red line is fit to $1 + tanh (\frac{ω - Δ}{Γ})$ with $Δ = 0.63 (4) meV$ and $Γ = 0.19 (7) meV$ . Inset: A reciprocal space map of the integration regions used to obtain $S_{imp} (ω)$ [green box near (200)] and $S_{kag + imp} (ω)$ [red box near (100)].
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