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Incommensurate antiferromagnetic order in the manifoldly-frustrated SrTb$_2$O$_4$ with transition temperature up to 4.28 K

The N$\acute{\rm e}$el temperature of the new frustrated family of Sr\emph{RE}$_2$O$_4$ (\emph{RE} = rare earth) compounds is yet limited to $\sim$ 0.9 K, which more or less hampers a complete understanding of the relevant magnetic frustrations and spin interactions. Here we report on a new frustrated member to the family, SrTb$_2$O$_4$ with a record $T_{\rm N}$ = 4.28(2) K, and an experimental study of the magnetic interacting and frustrating mechanisms by polarized and unpolarized neutron scattering. The compound SrTb$_2$O$_4$ displays an incommensurate antiferromagnetic (AFM) order with a transverse wave vector \textbf{Q}$^{\rm 0.5 K}_{\rm AFM}$ = (0.5924(1), 0.0059(1), 0) albeit with partially-ordered moments, 1.92(6) $μ_{\rm B}$ at 0.5 K, stemming from only one of the two inequivalent Tb sites mainly by virtue of their different octahedral distortions. The localized moments are confined to the \emph{bc} plane, 11.9(66)$^\circ$ away from the \emph{b} axis probably by single-ion anisotropy. We reveal that this AFM order is dominated mainly by dipole-dipole interactions and disclose that the octahedral distortion, nearest-neighbour (NN) ferromagnetic (FM) arrangement, different next NN FM and AFM configurations, and in-plane anisotropic spin correlations are vital to the magnetic structure and associated multiple frustrations. The discovery of the thus far highest AFM transition temperature renders SrTb$_2$O$_4$ a new friendly frustrated platform in the family for exploring the nature of magnetic interactions and frustrations.