Approaching the Ground State of the Kagomé Antiferromagnet

${\mathrm{Y}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{BaCo}}_4{\mathrm{O}}_7$ contains kagomé layers of Co ions, whose spins are strongly coupled, with a Curie-Weiss temperature of $-2200\mathrm{K}$. At low temperature, $T=1.2\mathrm{K}$, our diffuse neutron scattering study with polarization analysis reveals characteristic spin correlations close to a predicted two-dimensional coplanar ground state with staggered chirality. The absence of three-dimensional long-range antiferromagnetic order indicates negligible coupling between the kagomé layers. The scattering intensities are consistent with high spin $S=3/2$ states of ${\mathrm{Co}}^{2+}$ in the kagomé layers and low spin $S=0$ states for ${\mathrm{Co}}^{3+}$ ions on interlayer sites. Our observations agree with previous Monte Carlo simulations indicating a ground state of effectively short range, staggered chiral spin order.

Figure 1

Infinitely degenerate AF ground states on the kagomé lattice. (a) The $q_0$ structure with uniform chirality; (b) the staggered chiral structure, which has a larger unit cell by $\sqrt{3}\times \sqrt{3}$. The chirality is denoted by the sign inside the triangles; chirality is positive when spins rotate by $+120$ degrees as one goes anticlockwise around a triangle. The dashed ellipses represent thermal fluctuations of zero energy: (a) common spin rotations in an infinite chain; (b) the weathervane defect, a common local spin rotation on a hexagon around the axis of the spins on the edges of the unit cell.

Figure 2

The ${\mathrm{Y}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{BaCo}}_4{\mathrm{O}}_7$ crystal structure. Thicker bonds between the Co2 atoms highlight the kagomé layers. All Co atoms are tetrahedrally coordinated by oxygen, as shown in the polyhedral representation (left), emphasizing the threefold symmetry axis, going through Co1, which allow trimerization of Co2 in the kagomé substructure.

Figure 3

Temperature dependence of the diffuse magnetic scattering; data are calibrated by the spin-incoherent scattering of Co ($0.382\mathrm{b}/\mathrm{sr}$); the separated nuclear coherent scattering, ${\mathbf{I}}_{nc}$, has been rescaled and shifted (bottom part).

Figure 4

Quasielastic broadening due to thermal spin fluctuations. The difference of $S(Q,\omega )$ measured at 150 K and 40 K in time-of-flight mode reveals a loss of elastic intensity (blue) and a relaxation response (red) with a $Q$ dependence consistent with weathervane modes. The vertical line corresponds to the peak of model (iv) in Fig. 5.

Figure 5

Modeling of 1.2 K scattering data. (i) Power law decay of spin correlations in the $q_0$ and $\sqrt{3}\times \sqrt{3}$ structures, respectively (dashed dotted black and solid orange lines); (ii) Fourier analysis (fit, red line), yielding $G_{\sqrt{3}}$ (inset) spin correlations normalized to those of the $\sqrt{3}\times \sqrt{3}$ structure with ideal staggered chirality; (iii) MC data (thick cyan line) for a classical Heisenberg AF at $T/J=0.002$ [4]; (iv) weathervane model (dashed blue line).