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Fragile ground state and rigid field-induced structures in the zigzag ladder compound <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>BaDy</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>
We report on a sequence of field-induced transitions in the zigzag ladder compound ${\mathrm{BaDy}}_{2}{\mathrm{O}}_{4}$ studied with powder neutron diffraction and magnetization measurements. In agreement with the previously published results, the low-temperature zero-field structure is characterized by two half-integer propagation vectors ${\mathbf{k}}_{1}=[\frac{1}{2}\phantom{\rule{0.16em}{0ex}}0\phantom{\rule{0.16em}{0ex}}\frac{1}{2}]$ and ${\mathbf{k}}_{2}=[\frac{1}{2}\phantom{\rule{0.16em}{0ex}}\frac{1}{2}\phantom{\rule{0.16em}{0ex}}\frac{1}{2}]$. However, on application of an external magnetic …