  Neutron diffraction is used to investigate the field-induced,
antiferromagnetically ordered state in the two-leg spin-ladder material
(Hpip)2CuBr4. This "classical" phase, a consequence of weak interladder
coupling, is nevertheless highly unconventional: its properties are influenced
strongly by the spin Luttinger-liquid state of the ladder subunits. We
determine directly the order parameter (transverse magnetization), the ordering
temperature, the spin structure, and the critical exponents around the
transition. We introduce a minimal, microscopic model for the interladder
coupling and calculate the quantum fluctuation corrections to the mean-field
interaction.
