Absence of long range order in SrDy$_2$O$_4$ frustrated magnet due to trapped defects from a dimensionality crossover

The simultaneous occurence of geometrical frustration and low dimensionality can lead to strongly correlated fluctuating ground states. In the SrLn$_2$O$_4$ compounds, the Ln magnetic ions form one-dimensional (1D) zig-zag chains that have both of these characteristics, offering a playground to study novel states of matter. In SrDy$_2$O$_4$, the two inequivalent Dy$^{3+}$ sites are Ising-like with perpendicular easy-axes, favouring the decoupling of neighbouring zig-zag chains. No long range order is observed down to $T=60$ mK in zero field but diffuse neutron scattering indicates short range correlations that are consistent with those of the 1D Ising zig-zag chain model. AC susceptibility measurements indicate a slowing down of the fluctuations at low temperatures. We attribute this behaviour to the domain walls in the zig-zag chains. Experimental evidence of a dimensionality crossover at low temperatures in SrDy$_2$O$_4$ suggest that the domains walls are trapped because of interchain interactions, precluding long-range order to the lowest temperatures.