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arXiv:1008.3922 · Physical Review Letters

Field-Induced Tomonaga-Luttinger Liquid Phase of a Two-Leg Spin-1/2 Ladder with Strong Leg Interactions

Tao Hong, Y. H. Kim, Chisa Hotta, Y. Takano, Grant W. Tremelling, Mark M. Turnbull, C.P. Landee, H. J. Kang, Niels Bech Christensen, Kim Lefmann, Kai Phillip Schmidt, Götz Silvester Uhrig, C. Broholm

Published Sep 23, 2010• 106 citations
arXivHTMLPDF

Abstract

We study the magnetic-field-induced quantum phase transition from a gapped quantum phase that has no magnetic long-range order into a gapless phase in the spin-1/2 ladder compound bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). At temperatures below about 1 K, the specific heat in the gapless phase attains an asymptotic linear temperature dependence, characteristic of a Tomonaga-Luttinger liquid. Inelastic neutron scattering and the specific heat measurements in both phases are in good agreement with theoretical calculations, demonstrating that DIMPY is the first model material for an S=1/2 two-leg spin ladder in the strong-leg regime.

DOI
10.1103/physrevlett.105.137207

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Magnetic excitations in the strong-leg quantum spin ladder compound (C7H10N)2CuBr4{({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}(C7​H10​N)2​CuBr4​ (known as DIMPY) in the field-induced Tomonaga-Luttinger spin-liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual nonlinear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact-diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe their ESR observability to the uniform Dzyaloshinskii-Moriya interaction.
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.
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<K<2 range, which signifies attractive interaction between the spinless fermions in the Tomonaga-Luttinger liquid.
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.
Using micromechanical force magnetometry, we have measured the magnetization of the strong-leg spin-1/2 ladder compound (C(7)H(10)N)(2)CuBr(2) at temperatures down to 45 mK. Low-temperature magnetic susceptibility as a function of field exhibits a maximum near the critical field H(c) at which the magnon gap vanishes, as expected for a gapped one-dimensional antiferromagnet. Above H(c) a clear minimum appears in the magnetization as a function of temperature, as predicted by theory. In this field region, the susceptibility in conjunction with our specific-heat data yields the Wilson ratio R(W). The result supports the relation R(W)=4K, where K is the Tomonaga-Luttinger-liquid parameter.
The thermodynamics and transport properties of strong-rail ladder systems are investigated by means of Green's function theory. It is shown that the magnetic behavior clearly manifests a typical antiferromagnetism with gapped or gapless low-lying excitations, which is in agreement with the experimental results. In addition, the temperature-field-induced phase diagram is explored, and we demonstrate a Luttinger liquid behavior in the window h(c) (marking the ending of the M=0 plateau)<h<h(s) (saturation magnetic field) within a narrow range of temperature. The spin liquid phase is uncovered for h<h(c) upon cooling down to zero temperature. It is also shown that the rung entanglement entropy is a good indicator for detecting the field-driven quantum criticality. Meanwhile, the magnetic susceptibility, the specific heat, and the thermal (spin) Drude weights are calculated to characterize the plentiful quantum phases, in which the thermal insulating and conducting behaviors can be controlled by magnetic fields.