Zero temperature phase transitions in spin-ladders: Phase diagram and dynamical studies of Cu<Subscript>2</Subscript>(C<Subscript>5</Subscript>H<Subscript>12</Subscript>N<Subscript>2</Subscript>)<Subscript>2</Subscript>Cl<Subscript>4></Subscript>

In a magnetic field, spin-ladders undergo two zero-temperature phase transitions at the critical fields H<Subscript>c1</Subscript> and H<Subscript>c2</Subscript>. An experimental review of static and dynamical properties of spin-ladders close to these critical points is presented. The scaling functions, universal to all quantum critical points in one-dimension, are extracted from (a) the thermodynamic quantities (magnetization) and (b) the dynamical functions (NMR relaxation). A simple mapping of strongly coupled spin ladders in a magnetic field on the exactly solvable XXZ model enables to make detailed fits and gives an overall understanding of a broad class of quantum magnets in their gapless phase (between H<Subscript>c1</Subscript> and H<Subscript>c2</Subscript>). In this phase, the low temperature divergence of the NMR relaxation demonstrates its Luttinger liquid nature as well as the novel quantum critical regime at higher temperature. The general behavior close these quantum critical points can be tied to known models of quantum magnetism. Copyright EDP Sciences, Springer-Verlag 1998