Magnetic-Order Crossover in Coupled Spin Ladders.

We report a novel crossover behavior in the long-range-ordered phase of a prototypical spin-1/2 Heisenberg antiferromagnetic ladder compound (C_{7}H_{10}N)_{2}CuBr_{4}. The staggered order was previously evidenced from a continuous and symmetric splitting of ^{14}N NMR spectral lines on lowering the temperature below T_{c}≃330 mK, with a saturation towards ≃150 mK. Unexpectedly, the split lines begin to further separate away below T^{*}∼100 mK, while the linewidth and the line shape remain completely invariable. This crossover behavior is further corroborated by the NMR relaxation rate T_{1}^{-1} measurements. A very strong suppression reflecting the ordering, T_{1}^{-1}∼T^{5.5}, observed above T^{*}, is replaced by T_{1}^{-1}∼T below T^{*}. These original NMR features are indicative of the unconventional nature of the crossover, which may arise from a unique arrangement of the ladders into a spatially anisotropic and frustrated coupling network.

Emergent Interacting Spin Islands in a Depleted Strong-Leg Heisenberg Ladder.

Properties of the depleted Heisenberg spin ladder material series (C_{7}H_{10}N)_{2}Cu_{1-z}Zn_{z}Br_{4} have been studied by the combination of magnetic measurements and neutron spectroscopy. Disorder-induced degrees of freedom lead to a specific magnetic response, described in terms of emergent strongly interacting "spin island" objects. The structure and dynamics of the spin islands is studied by high-resolution inelastic neutron scattering. This allows us to determine their spatial shape and to observe their mutual interactions, manifested by strong spectral in-gap contributions.

Dichotomy between Attractive and Repulsive Tomonaga-Luttinger Liquids in Spin Ladders.

We present a direct NMR method to determine whether the interactions in a Tomonaga-Luttinger liquid (TLL) state of a spin-1/2 Heisenberg antiferromagnetic ladder are attractive or repulsive. For the strong-leg spin ladder compound (C_{7}H_{10}N)_{2}CuBr_{4} we find that the isothermal magnetic field dependence of the NMR relaxation rate T_{1}^{-1}(H) displays a concave curve between the two critical fields bounding the TLL regime. This is in sharp contrast to the convex curve previously reported for a strong-rung ladder, (C_{5}H_{12}N)_{2}CuBr_{4}. We show that the concavity and the convexity of T_{1}^{-1}(H), which is a fingerprint of spin fluctuations, directly reflect the attractive and repulsive fermionic interactions in the TLL, respectively. The interaction sign is alternatively determined from an indirect method combining bulk magnetization and specific heat data.

Attractive Tomonaga-Luttinger liquid in a quantum spin ladder.

We present NMR measurements of a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)2CuBr4 under magnetic fields up to 15 T in the temperature range from 1.2 K down to 50 mK. From the splitting of NMR lines, we determine the phase boundary and the order parameter of the low-temperature (three-dimensional) long-range-ordered phase. In the Tomonaga-Luttinger regime above the ordered phase, NMR relaxation reflects characteristic power-law decay of spin correlation functions as 1/T1∝T(1/2K-1), which allows us to determine the interaction parameter K as a function of field. We find that field-dependent K varies within the 1

Spectrum of a magnetized strong-leg quantum spin ladder.

Inelastic neutron scattering is used to measure the spin excitation spectrum of the Heisenberg S=1/2 ladder material (C7H10N)2CuBr4 in its entirety, both in the gapped spin liquid and the magnetic field-induced Tomonaga-Luttinger spin liquid regimes. A fundamental change of the spin dynamics is observed between these two regimes. Density matrix renormalization group calculations quantitatively reproduce and help understand the observed commensurate and incommensurate excitations. The results validate long-standing quantum field-theoretical predictions but also test the limits of that approach.

Spectral and thermodynamic properties of a strong-leg quantum spin ladder.

The strong-leg S=1/2 Heisenberg spin ladder system (C(7)H(10)N)(2)CuBr(4) is investigated using density matrix renormalization group calculations, inelastic neutron scattering, and bulk magnetothermodynamic measurements. Measurements showed qualitative differences compared to the strong-rung case. A long-lived two-triplon bound state is confirmed to persist across most of the Brillouin zone in a zero field. In applied fields, in the Tomonaga-Luttinger spin-liquid phase, elementary excitations are attractive, rather than repulsive. In the presence of weak interladder interactions, the strong-leg system is considerably more prone to three-dimensional ordering.