Proton relaxation and the dynamics of the S=1/2 antiferromagnetic Heisenberg chain

Proton spin-lattice relaxation times have been measured in the quasi-one-dimensional $s=\frac{1}{2}$ Heisenberg antiferromagnetic compounds CuSe ${\mathrm{O}}_{4}$ \ifmmode\cdot\else\textperiodcentered\fi{}5 ${\mathrm{H}}_{2}$ O and CuS ${\mathrm{O}}_{4}$ \ifmmode\cdot\else\textperiodcentered\fi{}5 ${\mathrm{H}}_{2}$ O, in order to study the magnetic field dependence of the 1D quantum spin dynamics at various temperatures. Information is obtained on the low-frequency behavior of the spin autocorrelation functions for the linear chains. The transverse component shows at high $T$ a marked decrease with magnetic field above the saturation field ${B}_{c}$ . Towards lower temperatures a pronounced maximum just below ${B}_{c}$ develops and the decrease above ${B}_{c}$ becomes more abrupt. The longitudinal component behaves more smoothly near and above ${B}_{c}$ . The field dependence of the relaxation rates is well explained at all nonzero temperatures by finite-chain calculations. For $T=0$ we present analytical calculations of autocorrelation functions based on the predominance of a two-parameter spin-wave continuum for the quantum spin dynamics yielding a nondivergent behavior at $\ensuremath{\omega}=0$ and $B=0$ . Exact results are obtained for fields above ${B}_{c}$ . Further, an effective $\mathrm{XY}$ approach is used for low but finite $T$ . Here, good agreement is found with the proton relaxation data for very low temperatures.Proton spin-lattice relaxation times have been measured in the quasi-one-dimensional $s=\frac{1}{2}$ Heisenberg antiferromagnetic compounds CuSe${\mathrm{O}}_{4}$\ifmmode\cdot\else\textperiodcentered\fi{}5${\mathrm{H}}_{2}$O and CuS${\mathrm{O}}_{4}$\ifmmode\cdot\else\textperiodcentered\fi{}5${\mathrm{H}}_{2}$O, in order to study the magnetic field dependence of the 1D quantum spin dynamics at various temperatures. Information is obtained on the low-frequency behavior of the spin autocorrelation functions for the linear chains. The transverse component shows at high $T$ a marked decrease with magnetic field above the saturation field ${B}_{c}$. Towards lower temperatures a pronounced maximum just below ${B}_{c}$ develops and the decrease above ${B}_{c}$ becomes more abrupt. The longitudinal component behaves more smoothly near and above ${B}_{c}$. The field dependence of the relaxation rates is well explained at all nonzero temperatures by finite-chain calculations. For $T=0$ we present analytical calculations of autocorrelation functions based on the predominance of a two-parameter spin-wave continuum for the quantum spin dynamics yielding a nondivergent behavior at $\ensuremath{\omega}=0$ and $B=0$. Exact results are obtained for fields above ${B}_{c}$. Further, an effective $\mathrm{XY}$ approach is used for low but finite $T$. Here, good agreement is found with the proton relaxation data for very low temperatures.

Physical review. B, Condensed matterDec 1, 198037 citations

Nuclear Magnetic Resonance Study of the S=1/2 Heisenberg Ladder Cu2(C5H12N2)2Cl4 : Quantum Phase Transition and Critical Dynamics

G. Chaboussant, Y. Fagot‐Révurat, M.-H. Julien +5 more

We present an extensive NMR study of the spin-1/2 antiferromagnetic Heisenberg ladder $\mathrm{Cu}{}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}\mathrm{Cl}{}_{4}$ in a magnetic field range 4.5--16.7 T. By measuring the proton NMR relaxation rate $1/{T}_{1}$ and varying the magnetic field around the critical field ${H}_{c1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\Delta}/g{\ensuremath{\mu}}_{B}\ensuremath{\approx}7.5\mathrm{T}$, we have studied the transition from a gapped spin liquid ground state to a gapless magnetic regime which can be described as a Luttinger liquid. We identify an intermediate regime $T\ensuremath{\ge}|{H\ensuremath{-}H}_{c1}|$, where the spin dynamics is (possibly) only controlled by the $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ critical point ${H}_{c1}$ .We present an extensive NMR study of the spin-1/2 antiferromagnetic Heisenberg ladder $\mathrm{Cu}{}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}\mathrm{Cl}{}_{4}$ in a magnetic field range 4.5--16.7 T. By measuring the proton NMR relaxation rate $1/{T}_{1}$ and varying the magnetic field around the critical field ${H}_{c1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\Delta}/g{\ensuremath{\mu}}_{B}\ensuremath{\approx}7.5\mathrm{T}$, we have studied the transition from a gapped spin liquid ground state to a gapless magnetic regime which can be described as a Luttinger liquid. We identify an intermediate regime $T\ensuremath{\ge}|{H\ensuremath{-}H}_{c1}|$, where the spin dynamics is (possibly) only controlled by the $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ critical point ${H}_{c1}$.

arXiv:cond-mat/9711124Physical Review LettersMar 23, 1998108 citations

Proton spin-lattice relaxation times have been measured in the quasi-one-dimensional

s=\frac{1}{2}

Heisenberg antiferromagnetic compounds CuSe

{\mathrm{O}}_{4}

\ifmmode\cdot\else\textperiodcentered\fi{}5

{\mathrm{H}}_{2}

O and CuS

{\mathrm{O}}_{4}

\ifmmode\cdot\else\textperiodcentered\fi{}5

{\mathrm{H}}_{2}

O, in order to study the magnetic field dependence of the 1D quantum spin dynamics at various temperatures. Information is obtained on the low-frequency behavior of the spin autocorrelation functions for the linear chains. The transverse component shows at high

T

a marked decrease with magnetic field above the saturation field

{B}_{c}

. Towards lower temperatures a pronounced maximum just below

{B}_{c}

develops and the decrease above

{B}_{c}

becomes more abrupt. The longitudinal component behaves more smoothly near and above

{B}_{c}

. The field dependence of the relaxation rates is well explained at all nonzero temperatures by finite-chain calculations. For

T=0

we present analytical calculations of autocorrelation functions based on the predominance of a two-parameter spin-wave continuum for the quantum spin dynamics yielding a nondivergent behavior at $\ensuremath{\omega}=0$ and

B=0

. Exact results are obtained for fields above

{B}_{c}

. Further, an effective

\mathrm{XY}

approach is used for low but finite

T

. Here, good agreement is found with the proton relaxation data for very low temperatures.

We present an extensive NMR study of the spin-1/2 antiferromagnetic Heisenberg ladder

\mathrm{Cu}{}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}\mathrm{Cl}{}_{4}

in a magnetic field range 4.5--16.7 T. By measuring the proton NMR relaxation rate

1/{T}_{1}

and varying the magnetic field around the critical field ${H}_{c1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\Delta}/g{\ensuremath{\mu}}_{B}\ensuremath{\approx}7.5\mathrm{T}$, we have studied the transition from a gapped spin liquid ground state to a gapless magnetic regime which can be described as a Luttinger liquid. We identify an intermediate regime $T\ensuremath{\ge}|{H\ensuremath{-}H}_{c1}|$, where the spin dynamics is (possibly) only controlled by the

T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

critical point

{H}_{c1}