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arXiv:1604.05252 · Physical Review Letters

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

Minki Jeong, D. Schmidiger, H. Mayaffre, M. Klanjšek, C. Berthier, W. Knafo, G. Ballon, Baptiste Vignolle, S. Krämer, A. Zheludev, M. Horvatić

Published Sep 1, 2016• 39 citations
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Abstract

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.

DOI
10.1103/physrevlett.117.106402

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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.
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Repulsive Tomonaga-Luttinger Liquid in Quasi-one-dimensional Alternating Spin-1/21/21/2 Antiferromagnet NaVOPO4_44​
We probe the magnetic field-induced Tomonaga-Luttinger liquid (TLL) state in the bond-alternating spin-1/21/21/2 antiferromagnetic (AFM) chain compound NaVOPO4_44​ using thermodynamic as well as local μμμSR and 31^{31}31P NMR probes down to milli-K temperatures in magnetic fields up to 14~T. The μμμSR and NMR relaxation rates in the gapless TLL regime decay slowly following characteristic power-law behaviour, enabling us to directly determine the interaction parameter KKK as a function of the magnetic field. These estimates are cross-checked using magnetization and specific heat data. The field-dependent KKK lies in the range of 0.4<K<10.4 < K < 10.4<K<1 and indicates repulsive nature of interactions between the spinless fermions, in line with the theoretical predictions. This renders NaVOPO4_44​ the first experimental realization of TLL with repulsive fermionic interactions in hitherto studied S=1/2S=1/2S=1/2 bond-alternating AFM-AFM chain compounds.
We probe the magnetic field-induced Tomonaga-Luttinger liquid (TLL) state in the bond-alternating spin-1/21/21/2 antiferromagnetic (AFM) chain compound NaVOPO4{\mathrm{NaVOPO}}_{4}NaVOPO4​ using thermodynamic as well as local $\ensuremath{\mu}\mathrm{SR}$ and 31P^{31}\mathrm{P}31P NMR probes down to mK temperatures in magnetic fields up to 14 T. The $\ensuremath{\mu}\mathrm{SR}$ and NMR relaxation rates in the gapless TLL regime decay slowly following characteristic power-law behavior, enabling us to directly determine the interaction parameter KKK as a function of the magnetic field. These estimates are crosschecked using magnetization and specific heat data. The field-dependent KKK lies in the range of 0.4<K<10.4<K<10.4<K<1 and indicates the repulsive nature of interactions between the spinless fermions, in line with the theoretical predictions. This renders NaVOPO4{\mathrm{NaVOPO}}_{4}NaVOPO4​ the first experimental realization of TLL with repulsive fermionic interactions in hitherto studied S=1/2S=1/2S=1/2 bond-alternating AFM-AFM chain compounds.
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.
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.
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.