Abstract
We have measured the nuclear spin-lattice relaxation of ${}^{59}$Co in the geometrically frustrated Ising-type spin-chain system Ca${}_{3}$Co${}_{2}$O${}_{6}$ as a function of temperature and applied magnetic field. In the nearly-saturated ferrimagnetic and ferromagnetic regimes considered here, the field-dependent energy scales governing the spin-lattice relaxation rates reflect the energy cost of a spin flip in the Co ions adjacent to the probed nuclei. This results in a thermally activated form for the nuclear relaxation rates, which can be exploited as a local probe of the exchange interactions. In particular, the measurements enable the values of intra- and interchain exchange constants ${J}_{1}$, ${J}_{2}+{J}_{3}$ to be directly extracted from the data. By using a quasi-one-dimensional model, we then determine the value of ${J}_{2}$ consistent with the spin-density-wave order observed in zero field.
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