Disordered ground state in the three-dimensional face-centred frustrated spin-$\frac{5}{2}$ system MnSn(OH)${}_{\text{6}}$

Frustrated magnetism in face-centred cubic (fcc) magnetic sublattices remains underexplored but holds considerable potential for exotic magnetic behaviour. Here we report on the crystal structure, magnetic and thermodynamic properties of the $A$-site-vacant double hydroxide perovskite MnSn(OH)${}_6$. Despite dominant antiferromagnetic interactions among Mn${}^{2+}$ moments, evidenced by a negative Curie-Weiss temperature, the lack of a sharp thermodynamic transition down to 350$$mK implies the absence of long-range magnetic order. However, a broad hump in the specific heat at 1.6$$K suggests short-range correlations. Neutron diffraction at low temperatures confirms the presence of three-dimensional antiferromagnetic correlations, manifested as diffuse magnetic scattering with a correlation length $\xi =24.66$Å and magnetic propagation vectors $\mathbf{k}=(\frac{1}{2}\frac{1}{2}\frac{1}{2})$ and $(00.6250)$ at 20$$mK.