We have systematically studied the magnetic properties of Cu$_{4-x}$Zn$_x$(OH)$_6$FBr by the neutron diffraction and muon spin rotation and relaxation ($\mu$SR) 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 (ZF) $\mu$SR spectra provide two characteristic temperatures, $T_{A0}$ and $T_{\lambda}$. Comparison between $T_{A0}$ and $T_M$ 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.

中文翻译：

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通过中子衍射和 μSR 技术研究的 Cu4-x Zn x (OH)6FBr 的磁相图

我们通过中子衍射和μ子自旋旋转和弛豫（$\mu$SR）技术系统地研究了Cu$_{4-x}$Zn$_x$(OH)$_6$FBr的磁性。中子衍射测量表明，$x$ = 0 样品中的长程磁序和正交核结构可以分别持续到 $x$ = 0.23 和 0.43。零场 (ZF) $\mu$SR 光谱的温度依赖性提供了两个特征温度，$T_{A0}$ 和 $T_{\lambda}$。$T_{A0}$ 和先前报告的磁化率测量值的 $T_M$ 之间的比较表明，前者来自短程层间自旋簇，其持续时间高达 $x$ = 0.82。另一方面，$T_{\lambda}$ 变为零的掺杂水平约为 0.66，远高于长程有序的阈值，即，$\sim$ 0.4。我们的结果表明，核结构的变化可能会改变 kagome 层的自旋动力学，并且在 $x$ = 0.66 以上可能存在有间隙的量子自旋液体状态，具有完美的 kagome 平面。