Magnetic ordering and spin dynamics in potassium jarosite: A Heisenberg kagomé lattice antiferromagnet

Abstract

The spin dynamics of the Heisenberg kagom\'e lattice antiferromagnet, potassium jarosite ${\mathrm{KFe}}_{3}(\mathrm{OH}{)}_{6}({\mathrm{SO}}_{4}{)}_{2},$ have been investigated by means of NMR. The NMR spectra confirm the long-range magnetic ordering below 65 K and the $\mathbf{q}=0$ type $120\ifmmode^\circ\else\textdegree\fi{}$ spin structure with positive chirality in the ordered phase. Though the Heisenberg kagom\'e lattice antiferromagnet is considered theoretically to remain disordered down to zero temperature due to the continuous degeneracy of the ground state, the long-range magnetic ordering at the finite temperature is realized in this compound due to the weak anisotropy. The spin-lattice relaxation rate, ${1/T}_{1},$ in the ordered phase decreases sharply with lowering temperature. The experimental rate is well explained by the two-magnon process of the spin waves having an energy gap of 15 K. The temperature dependence of the sublattice magnetization also supports the existence of the spin wave. These are the first experimental evidence that the low-energy excitation in the frustrated classical kagom\'e lattice antiferromagnet is described by the spin wave. We calculate the spin wave in the $\mathbf{q}=0$ type $120\ifmmode^\circ\else\textdegree\fi{}$ spin structure with weak single-ion-type anisotropy, and discuss the characteristics of the spin fluctuations in the Heisenberg kagom\'e lattice antiferromagnet.