Swedenborgite ${\mathrm{Ca}}_{0.5}{\mathrm{Y}}_{0.5}{\mathrm{BaCo}}_4{\mathrm{O}}_7$ (CYBCO) with geometrically frustrated kagome and triangular lattices exhibits a disordered ground state in spite of strong antiferromagnetic couplings between the Co spins. The character of the disordered state has been debated due to ambiguous Co states in the triangular layers. Here, we perform single-crystal diffuse neutron scattering experiments to fully characterize the short-range spin correlations in CYBCO. Through reverse Monte Carlo and self-consistent Gaussian approximation analyses, we confirm that the Co ions in both the kagome and triangular layers are magnetic, and the interlayer couplings, together with the lattice distortion, promote an incommensurate magnetic order that is suppressed possibly by exchange disorder. Our work clarifies the short-range spin correlations in CYBCO and establishes a general correspondence between unequal interactions and incommensurate spin correlations on the swedenborgite lattice.

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• Frustrated magnetism
• Kagome lattice
• Quasi elastic neutron scattering