Spin order in the Heisenberg kagome antiferromagnet $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$

Spin behaviors on kagome lattices have received increased attention because of their exotic magnetic states. Here, we report magnetic ordering in the $S=2$ kagome antiferromagnet $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$. The compound has been synthesized by selectively replacing the magnetic ions in the triangular planes of its parent compound of deformed pyrochlore $\mathrm{F}{\mathrm{e}}_2{\left(\mathrm{OH}\right)}_3\mathrm{Cl}$ with nonmagnetic Mg. Whereas $\mathrm{F}{\mathrm{e}}_2{\left(\mathrm{OH}\right)}_3\mathrm{Cl}$ showed antiferromagnetic order below $T_{\mathrm{N}}=8.5\mathrm{K}$ with persistent spin fluctuations, $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$ showed an antiferromagnetic transition at an enhanced $T_{\mathrm{N}}$ value of 9.9 K. Susceptibility, high-field magnetization, and neutron-diffraction studies suggest that $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$ is a Heisenberg-like spin system with a ${120}^{\circ }$ nearest-neighbor spin structure confined in the kagome plane and spin-vector chirality of $q=-1$ below $T_{\mathrm{N}}$. Muon spin-rotation/-relaxation studies demonstrate that the persisting spin fluctuations are suppressed relative to $\mathrm{F}{\mathrm{e}}_2{\left(\mathrm{OH}\right)}_3\mathrm{Cl}$. The present paper reports the experimental realization of an $S=2$ kagome antiferromagnet, highlighting a real system with a quasiclassical Heisenberg spin, which may also be a valuable reference system for quantum Heisenberg kagome antiferromagnets.

Figure 1

(a) Crystal structure of $\mathrm{F}{\mathrm{e}}_2{\left(\mathrm{OH}\right)}_3\mathrm{Cl}$, wherein $\mathrm{F}{\mathrm{e}}_{\mathrm{k}}$ and $\mathrm{F}{\mathrm{e}}_{\mathrm{T}}$ denote the $\mathrm{F}{\mathrm{e}}^{2+}$ spins on the alternatively stacked layers of the kagome- and triangular-lattice planes, respectively. The green large balls and the next-largest red balls represent $\mathrm{C}{\mathrm{l}}^{-}$ and ${\mathrm{O}}^{2-}$, respectively. (b) Crystal structure of $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$, wherein the kagome network of the $\mathrm{F}{\mathrm{e}}^{2+}$ ions is illustrated with $\mathrm{M}{\mathrm{g}}^{2+}$ ions located between the kagome planes.

Figure 2

Neutron powder-diffraction pattern (filled circles) for $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OD}\right)}_6\mathrm{C}{\mathrm{l}}_2$ at 300 K with a wavelength of 1.848 43 Å and the result of Rietveld structure refinements showing the calculated (thick solid line) pattern and the difference (thin solid line on the bottom).

Figure 3

Temperature dependence of the dc susceptibilities χ (open circles, left axis) and the inverse susceptibilities 1/χ (open squares, right axis) per mole formula of $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$, measured at 1 T. The blue line represents the Curie-Weiss fit. The inset plot A shows χ−T under 0.1 T. The inset plot B shows the trace of FeO, wherein a small anomaly appeared at ∼200 K in the enlarged differential plot of dχ/dT due to the antiferromagnetic transition of FeO.

Figure 4

Magnetization for less-oxidized sample A and heavier-oxidized sample B at 2 K. Oxidization in the latter produced a notable nonlinear behavior at weak fields, and divergence of FC and ZFC curves.

Figure 5

Temperature dependence of the dc susceptibility curves measured at 1 T for $\mathrm{F}{\mathrm{e}}_2{\left(\mathrm{OH}\right)}_3\mathrm{Cl}$ and $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$.

Figure 6

High-field magnetization per $\mathrm{F}{\mathrm{e}}^{2+}$ spin for $\mathrm{F}{\mathrm{e}}_2{\left(\mathrm{OH}\right)}_3\mathrm{Cl}$ and $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$ at 4.2 and 15 K, respectively. The differential plot dM/dH–H showing two anomalies around $H_{\mathrm{c}1}=5.8\mathrm{T}$ and $H_{\mathrm{c}2}=13\mathrm{T}$ for $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$.

Figure 7

Neutron powder-diffraction patterns for $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OD}\right)}_6\mathrm{C}{\mathrm{l}}_2$ at 2.63 and 300 K with wavelength of 2.470 543 Å, and $\mathrm{F}{\mathrm{e}}_2{\left(\mathrm{OD}\right)}_3\mathrm{Cl}$ at 3.5 K. The inset plot shows the temperature dependence of the intensity of the (0 1 1/2) magnetic peak for $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OD}\right)}_6\mathrm{C}{\mathrm{l}}_2$, and the solid line is a power-law fit.

Figure 8

(a) Possible magnetic structures of ${\mathrm{\Gamma }}_1^{+}\left({\phi }_1\right),{\mathrm{\Gamma }}_3^{+}({\phi }_2+{\phi }_3),{\mathrm{\Gamma }}_5^{+}({\phi }_4+{\phi }_5)$, and ${\mathrm{\Gamma }}_5^{+}({\phi }_7+{\phi }_8)$ for $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OD}\right)}_6\mathrm{C}{\mathrm{l}}_2$. (b) Fitting results for the possible magnetic structures.

Figure 9

ZF and LF μSR asymmetries for polycrystalline $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$ at 1.9, 30, and 200 K.

Figure 10

ZF μSR asymmetries for polycrystalline $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$ at typical temperatures. The inset plot shows the change of depolarization rate λ, depicting a phase transition at $T_{\mathrm{N}}\sim 10\mathrm{K}$.

Figure 11

Comparison of the ZF-μSR asymmetries for polycrystalline $\mathrm{MgF}{\mathrm{e}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$ and $\mathrm{F}{\mathrm{e}}_2{\left(\mathrm{OH}\right)}_3\mathrm{Cl}$ at low temperatures. The inset plot is an enlargement of the short-time asymmetry spectra with the thick line fitted with two frequencies around 20 and 35 MHz, depicting the oscillations due to a magnetic long-range order.

Figure 12

Enhanced $T_{\mathrm{N}}$ in $\mathrm{MgM}{\mathrm{n}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$ as compared to $\mathrm{M}{\mathrm{n}}_2{\left(\mathrm{OH}\right)}_3\mathrm{Cl}$.