Eur. Phys. J. B 6, 167-181 (1998)
https://doi.org/10.1007/s100510050539

Zero temperature phase transitions in spin-ladders: Phase diagram and dynamical studies of C_u2(C₅H₁₂N₂)₂Cl₄

¹ Grenoble High Magnetic Field Laboratory, CNRS and MPI-FKF, BP 166, 38042 Grenoble, France
² Institut Universitaire de France and Université Joseph Fourier, BP 53, 38400 St Martin d'Hères, France
³ Laboratoire de Spectrométrie Physique, Université Joseph Fourier, BP 87, 38402 St Martin d'Hères, France
⁴ Dipartimento di Chimica, Università di Perugia, 06100 Perugia, Italy

Corresponding author: ^a levy@grenet.fr

Received: 13 March 1998
Accepted: 21 July 1998
Published online: 15 November 1998

Abstract

In a magnetic field, spin-ladders undergo two zero-temperature phase transitions at the critical fields and . 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 and ). 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.