Controlling Luttinger Liquid Physics in Spin Ladders under a Magnetic Field

We present a ${}^{14}\mathrm{N}$ nuclear magnetic resonance study of a single crystal of ${\mathrm{CuBr}}_4({\mathrm{C}}_5{\mathrm{H}}_{12}\mathrm{N}{)}_2$ (BPCB) consisting of weakly coupled spin-$1/2$ Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate $T_1^{-1}$ at 250 mK and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to weak interladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and the Luttinger liquid model tested in detail over the whole fermion band.