Magnetic Phase Diagram of Cu$_{4-x}$Zn$_x$(OH)$_6$FBr Studied by Neutron-Diffraction and $\mu$SR Techniques
Yuan Wei1,2†, Xiaoyan Ma1,2†, Zili Feng1,3, Devashibhai Adroja4,5, Adrian Hillier4, Pabitra Biswas4, Anatoliy Senyshyn6, Andreas Hoser7, Jia-Wei Mei8, Zi Yang Meng1,9,10, Huiqian Luo1,10*, Youguo Shi1,10*, and Shiliang Li1,2,10*
1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China 3Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan 4ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot Oxon OX11 0QX, United Kingdom 5Highly Correlated Matter Research Group, Physics Department, University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa 6Heinz Maier-Leibnitz Zentrum (MLZ), Technische Universität München, Garching D-85747, Germany 7Helmholtz-Zentrum Berlin für Materialien und Energie, D-14109 Berlin, Germany 8Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China 9Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China 10Songshan Lake Materials Laboratory, Dongguan 523808, China
Abstract：We systematically investigate the magnetic properties of Cu$_{4-x}$Zn$_x$(OH)$_6$FBr using the neutron diffraction and muon spin rotation and relaxation (μSR) techniques. Neutron-diffraction measurements suggest that the long-range magnetic order and the orthorhombic nuclear structure in the $x = 0$ sample can persist up to $x = 0.23$ and 0.43, respectively. The temperature dependence of the zero-field μSR spectra provides two characteristic temperatures, $T_{A_0}$ and $T_{\lambda}$, which are associated with the initial drop close to zero time and the long-time exponential decay of the muon relaxation, respectively. Comparison between $T_{A_0}$ and $T_{\rm M}$ from previously reported magnetic-susceptibility measurements suggest that the former comes from the short-range interlayer-spin clusters that persist up to $x = 0.82$. On the other hand, the doping level where $T_{\lambda}$ becomes zero is about 0.66, which is much higher than threshold of the long-range order, i.e., $\sim$0.4. Our results suggest that the change in the nuclear structure may alter the spin dynamics of the kagome layers and a gapped quantum-spin-liquid state may exist above $x = 0.66$ with the perfect kagome planes.
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