Identification of Nuclear Relaxation Processes in a Gapped Quantum Magnet:1HNMR in theS=12Heisenberg LadderCu2(C5H12N2)2Cl4

The ${}^1\mathrm{H}$ hyperfine shift $K$ and NMR relaxation rate $T_1^{-1\mathrm{}}$ have been measured as a function of temperature in the $S=1\mathrm{}/2$ Heisenberg antiferromagnetic ladder compound ${\mathrm{Cu}}_2({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2{)}_2{\mathrm{Cl}}_4$. The presence of a spin gap $\Delta \simeq J_{\perp }{-J}_{\parallel }$ in this strongly coupled ladder ( $J_{\parallel }<J_{\perp }$) is supported by the $K$ and $T_1^{-1\mathrm{}}$ results. By comparing $T_1^{-1\mathrm{}}$ at two different ${}^1\mathrm{H}$ sites, we infer the evolution of the spectral functions $S_z(q,{\omega }_n)$ and $S_{\perp }(q,{\omega }_n)$. When the gap is significantly reduced by the magnetic field, two different channels of nuclear relaxation, specific to gapped antiferromagnets, are identified and are in agreement with theoretical predictions.