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arXiv:1712.06213 · Physical review. B./Physical review. B

Rb-NMR study of the quasi-one-dimensional competing spin-chain compound Rb2Cu2Mo3O12

Kazuki Matsui, Ayato Yagi, Yukihiro Hoshino, Sochiro Atarashi, Masashi Hase, T. Sasaki, Takayuki Goto

Published Dec 8, 2017• 15 citations
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Abstract

A Rb-NMR study has been performed on the quasi-one-dimensional competing spin chain $\mathrm{R}{\mathrm{b}}_{2}\mathrm{C}{\mathrm{u}}_{2}\mathrm{M}{\mathrm{o}}_{3}{\mathrm{O}}_{12}$ with ferromagnetic and antiferromagnetic exchange interactions on nearest-neighboring and next-nearest neighboring spins, respectively. The system changes from a gapped ground state at zero field to a gapless state at ${H}_{\mathrm{C}}\ensuremath{\simeq}2\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, where the existence of magnetic order below 1 K was demonstrated by a broadening of the NMR spectrum, associated with a critical divergence of $1/{T}_{1}$. In the higher-temperature region, ${T}_{1}^{\ensuremath{-}1}$ showed a power-law-type temperature dependence, from which the field dependence of the Luttinger parameter $K$ was obtained and compared with theoretical calculations based on the spin nematic Tomonaga-Luttinger liquid (TLL) state.

DOI
10.1103/physrevb.96.220402

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A Rb-NMR study has been performed on the quasi-one-dimensional competing spin chain Rb2Cu2Mo3O12\mathrm{R}{\mathrm{b}}_{2}\mathrm{C}{\mathrm{u}}_{2}\mathrm{M}{\mathrm{o}}_{3}{\mathrm{O}}_{12}Rb2​Cu2​Mo3​O12​ with ferromagnetic and antiferromagnetic exchange interactions on nearest-neighboring and next-nearest neighboring spins, respectively. The system changes from a gapped ground state at zero field to a gapless state at HC\ensuremath≃2T{H}_{\mathrm{C}}\ensuremath{\simeq}2\phantom{\rule{0.16em}{0ex}}\mathrm{T}HC​\ensuremath≃2T, where the existence of magnetic order below 1 K was demonstrated by a broadening of the NMR spectrum, associated with a critical divergence of 1/T11/{T}_{1}1/T1​. In the higher-temperature region, T1\ensuremath−1{T}_{1}^{\ensuremath{-}1}T1\ensuremath−1​ showed a power-law-type temperature dependence, from which the field dependence of the Luttinger parameter KKK was obtained and compared with theoretical calculations based on the spin nematic Tomonaga-Luttinger liquid (TLL) state.
Quasi-one-dimensional S = 1/2 Heisenberg system Rb2Cu2Mo3O12 described by the J1 - J2 model with the nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic exchange interactions have been investigated by 87/85Rb-NMR under extended field range up to 18 T. From the thermal-activation-type temperature dependence of l/T1, opening of the spin excitation gap was confirmed under the low field below 2 T. With increasing the field, the system becomes gapless, and the gap opens again in the high field saturation region, where the field dependence of the gap size showed the coherent excitation of the neighbouring two spins.
Quasi-one-dimensional (1D) antiferromagnets are good candidates to realize a Tomonaga-Luttinger liquid (TLL), describing 1D interacting quantum systems, provided 3D coupling remains small as compared to temperature. In systems such as NiCl2{}_{2}2​-4SC(NH2{}_{2}2​)2{}_{2}2​ (DTN), made of weakly coupled spin S=1S=1S=1 chains, interchain coupling plays an important role at low temperature as it leads to antiferromagnetic long-range order below 111 K, corresponding to a Bose-Einstein condensate of magnons. Using time-dependent numerical simulations at finite temperature, the authors compute here the nuclear magnetic resonance (NMR) relaxation rate 1/T11/{T}_{1}1/T1​, a key experimental quantity, and address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime in purely 111D quantum spins chains. They also comment on the experimental observation of the TLL regime, possibly masked by 333D long-range order in materials such as DTN.
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.
By means of nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system ${\mathrm{NiCl}}_{2}\mathrm{\text{\ensuremath{-}}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}$ and the spin-ladder system (C5H12N)2CuBr4({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}(C5​H12​N)2​CuBr4​. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.
The quantum many-body interactions in one-dimensional spin-12\frac{1}{2}21​ systems are subject to Tomonaga-Luttinger liquid (TLL) physics, which predict an array of multiparticle excitations that form continua in momentum-energy space. Here we use inelastic neutron spectroscopy to study the TLL spin dynamics in SrCo2V2O8{\mathrm{SrCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}SrCo2​V2​O8​, a compound which contains weakly coupled spin-12\frac{1}{2}21​ chains of Co atoms, at 0.05 K and in a longitudinal magnetic field up to 9.0 T. The measurements were performed above 3.9 T, where the ground-state N\'eel antiferromagnetic (AFM) order is completely suppressed and the multiparticle excitations are exclusively of the TLL type. In this region and below 7.0 T, the longitudinal TLL mode---psinon/antipsinon (P/AP)---is unexpectedly well described by a damped harmonic oscillator (DHO) while approaching the zone center defining the static spin-spin correlations. A non-DHO-type, continuumlike signal is seen at higher fields, but deviations from the ideal one-dimensional TLL still remain. This change in the P/AP mode coincides with the phase transition between the longitudinal spin density wave (LSDW) and transverse AFM order. Inside the LSDW state, the DHO-type P/AP spectral weight increases and the linewidth broadens as the magnetic order parameter decreases. These results reveal the impact of three-dimensional magnetic order on the TLL spin dynamics; they call for beyond-mean-field treatment for the interchain exchange interactions.
The spin-1/21/21/2 ferromagnetic XXZ chain is a prototypical many-body quantum model, exactly solvable via the integrable Bethe ansatz method, hosting a Tomonaga-Luttinger spin liquid. However, its clear experimental realizations remain absent. Here, we present a thorough investigation of the magnetism of the structurally disorder-free compound LuCu(OH)3SO4\mathrm{LuCu}{(\mathrm{OH})}_{3}{\mathrm{SO}}_{4}LuCu(OH)3​SO4​. By conducting magnetization and electron-spin-resonance measurements on the single-crystal sample, we establish that the title compound approximates the spin-1/21/21/2 ferromagnetic XXZ chain model with a nearest-neighbor exchange strength of ${J}_{1}\ensuremath{\sim}65\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and an easy-plane anisotropy of $\ensuremath{\sim}0.994$. The specific heat demonstrates a distinctive power-law behavior at low magnetic fields (with energy scales $\ensuremath{\le}0.02{J}_{1}$) and low temperatures $(T\ensuremath{\le}0.03{J}_{1})$. This behavior is consistent with the expectations of the ideal spin-1/21/21/2 ferromagnetic XXZ chain model, thereby supporting the formation of a gapless Tomonaga-Luttinger spin liquid in LuCu(OH)3SO4\mathrm{LuCu}{(\mathrm{OH})}_{3}{\mathrm{SO}}_{4}LuCu(OH)3​SO4​.