Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B./Physical review. B

Repulsive Tomonaga-Luttinger liquid in the quasi-one-dimensional alternating spin- 12 antiferromagnet NaVOPO4

S. S. Islam, Prashanta K. Mukharjee, Pabitra Kumar Biswas⃰, Mark T. F. Telling, Y. Skourski, K. M. Ranjith, M. Baenitz, Yuji Inagaki, Yuji Furukawa, Alexander A. Tsirlin, R. Nath

Published Feb 20, 2024• 3 citations
Publisher

Abstract

We probe the magnetic field-induced Tomonaga-Luttinger liquid (TLL) state in the bond-alternating spin-$1/2$ antiferromagnetic (AFM) chain compound ${\mathrm{NaVOPO}}_{4}$ using thermodynamic as well as local $\ensuremath{\mu}\mathrm{SR}$ and $^{31}\mathrm{P}$ 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 $K$ as a function of the magnetic field. These estimates are crosschecked using magnetization and specific heat data. The field-dependent $K$ lies in the range of $0.4<K<1$ and indicates the repulsive nature of interactions between the spinless fermions, in line with the theoretical predictions. This renders ${\mathrm{NaVOPO}}_{4}$ the first experimental realization of TLL with repulsive fermionic interactions in hitherto studied $S=1/2$ bond-alternating AFM-AFM chain compounds.

DOI
10.1103/physrevb.109.l060406

Related papers

Repulsive Tomonaga-Luttinger Liquid in Quasi-one-dimensional Alternating Spin-$1/2$ Antiferromagnet NaVOPO$_4$

S. S. Islam, Prashanta K. Mukharjee, Pabitra Kumar Biswas⃰ +8 more

We probe the magnetic field-induced Tomonaga-Luttinger liquid (TLL) state in the bond-alternating spin-$1/2$ antiferromagnetic (AFM) chain compound NaVOPO$_4$ using thermodynamic as well as local $μ$SR and $^{31}$P NMR probes down to milli-K temperatures in magnetic fields up to 14~T. The $μ$SR and NMR relaxation rates in the gapless TLL regime decay slowly following characteristic power-law behaviour, enabling us to directly determine the interaction parameter $K$ as a function of the magnetic field. These estimates are cross-checked using magnetization and specific heat data. The field-dependent $K$ lies in the range of $0.4 < K < 1$ and indicates repulsive nature of interactions between the spinless fermions, in line with the theoretical predictions. This renders NaVOPO$_4$ the first experimental realization of TLL with repulsive fermionic interactions in hitherto studied $S=1/2$ bond-alternating AFM-AFM chain compounds.

arXiv:2311.03231•Nov 6, 2023•0 citations

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

Minki Jeong, D. Schmidiger, H. Mayaffre +8 more

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.

arXiv:1604.05252•Physical Review Letters•Sep 1, 2016•39 citations

Attractive Tomonaga-Luttinger Liquid in a Quantum Spin Ladder

Minki Jeong, H. Mayaffre, C. Berthier +3 more

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.

arXiv:1307.0103•Physical Review Letters•Sep 5, 2013•63 citations

Effect of magnetic order on longitudinal Tomonaga-Luttinger liquid spin dynamics in weakly coupled spin- 12 chains

L. Shen, A. Alshemi, E. Campillo +5 more

The quantum many-body interactions in one-dimensional spin-$\frac{1}{2}$ 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 ${\mathrm{SrCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$, a compound which contains weakly coupled spin-$\frac{1}{2}$ 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.

Physical review. B./Physical review. B•Apr 20, 2023•1 citation

Temperature dependence of the NMR relaxation rate 1/T1 for quantum spin chains

Maxime Dupont, Sylvain Capponi, Nicolas Laflorencie

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 NiCl${}_{2}$-4SC(NH${}_{2}$)${}_{2}$ (DTN), made of weakly coupled spin $S=1$ chains, interchain coupling plays an important role at low temperature as it leads to antiferromagnetic long-range order below $1$ 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 $1/{T}_{1}$, a key experimental quantity, and address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime in purely $1$D quantum spins chains. They also comment on the experimental observation of the TLL regime, possibly masked by $3$D long-range order in materials such as DTN.

arXiv:1606.09502•Physical review. B./Physical review. B•Oct 11, 2016•26 citations

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

Kazuki Matsui, Ayato Yagi, Yukihiro Hoshino +4 more

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.

arXiv:1712.06213•Physical review. B./Physical review. B•Dec 8, 2017•15 citations
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 \ensuremathμSR\ensuremath{\mu}\mathrm{SR}\ensuremathμSR and 31P^{31}\mathrm{P}31P NMR probes down to mK temperatures in magnetic fields up to 14 T. The \ensuremathμSR\ensuremath{\mu}\mathrm{SR}\ensuremathμSR 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.
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 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.
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 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.
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.
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 ${H}_{\mathrm{C}}\ensuremath{\simeq}2\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, 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/T11/{T}_{1}1/T1​. 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 KKK was obtained and compared with theoretical calculations based on the spin nematic Tomonaga-Luttinger liquid (TLL) state.