Striped magnetic ground state of the kagome lattice in ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$

We have experimentally identified a different magnetic ground state for the kagome lattice, in the perfectly hexagonal ${\mathrm{Fe}}^{2+}$ ($3d^6,S=2$) compound ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$. A representational symmetry analysis of neutron diffraction data shows that below $T_N=3.5$ K, the spins on $\frac{2}{3}$ of the magnetic ions order into canted antiferromagnetic chains, separated by the remaining $\frac{1}{3}$ which are geometrically frustrated and show no long-range order down to at least $T=0.1$ K. Mössbauer spectroscopy confirms that there is no static order on the latter $\frac{1}{3}$ of the magnetic ions—i.e., they are in a liquidlike rather than a frozen state—down to at least 1.65 K. A heavily Mn-doped sample ${\mathrm{Fe}}_{1.45}{\mathrm{Mn}}_{2.55}{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$ has the same magnetic structure. Although the propagation vector $q=\left(0,\frac{1}{2},\frac{1}{2}\right)$ breaks hexagonal symmetry, we see no evidence for magnetostriction in the form of a lattice distortion within the resolution of our data. We discuss the relationship to partially frustrated magnetic order on the pyrochlore lattice of ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, and to theoretical models that predict symmetry breaking ground states for perfect kagome lattices.

Figure 1

$P\overline{3}m1$ structure of ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$, showing edge-sharing ${\mathrm{FeO}}_6$ (gold) and ${\mathrm{SnO}}_6$ (silver) octahedra in the oxide layer; Fe (gold), Sn (silver), and O (red) atoms in the stannide layer; and ${\mathrm{SiO}}_4$ tetrahedra (blue) in between.

Figure 2

Final Rietveld fit (black) to 1.6 K NPD data (red) from ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$, using the ${\mathrm{\Gamma }}_1$ irreducible representation ($R_p=0.121,R_{wp}=0.128$). Peak markers from top to bottom correspond to the nuclear and magnetic components of ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$, and a $<1$ wt% ${\mathrm{SnO}}_2$ impurity. The inset shows the fit to magnetic peaks only (10 K data subtracted from 1.6 K data) at low angles.

Figure 3

Final refined magnetic structure of ${\mathrm{Fe}}_4{\mathrm{Si}}_2{\mathrm{Sn}}_7{\mathrm{O}}_{16}$, showing the Fe atoms in a single kagome layer at $z=\frac{1}{2}$. The nuclear unit cell is shown as dotted black lines. The $z$-axis component refined to zero, and moments on the sites with no vector drawn refined to zero. The moments in the surrounding layers at $z=\pm 1c$ are AFM with respect to those shown. Dotted lines show nearest-neighbor ($J_1$, black) second-nearest-neighbor ($J_2$, green), and diagonal ($J_d$, blue) magnetic exchange pathways (see text for details).

Figure 4

Mössbauer spectra above (5 K) and below (1.8 K) $T_N$. For the 5 K pattern, the total fit is shown by the magenta line, as well as the two subspectra from Fe in the $1a$ (red) and $3f$ (green) sites. For the 1.8 K pattern, the same colors are used, except that the contribution from iron in the $3f$ site is now split into nonmagnetic (green) and magnetic (teal).