Nuclear Magnetic Resonance Study of theS=1/2Heisenberg LadderCu2(C5H12N2)2Cl4: Quantum Phase Transition and Critical Dynamics

We present an extensive NMR study of the spin-1/2 antiferromagnetic Heisenberg ladder $\mathrm{Cu}{}_2({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2{)}_2\mathrm{Cl}{}_4$ in a magnetic field range 4.5–16.7 T. By measuring the proton NMR relaxation rate $1/T_1$ and varying the magnetic field around the critical field $H_{c1\mathrm{}}=\Delta /g{\mu }_B\approx 7.5\mathrm{T}$, we have studied the transition from a gapped spin liquid ground state to a gapless magnetic regime which can be described as a Luttinger liquid. We identify an intermediate regime $T\ge |{H-H}_{c1\mathrm{}}|$, where the spin dynamics is (possibly) only controlled by the $T=0\mathrm{}$ critical point $H_{c1\mathrm{}}$.