Physical review. B, Condensed matter

Transverse susceptibility of the one-dimensional antiferromagnetic XY model. Application to Cs2 Co Cl4

Philip M. Duxbury, J. Oitmaa, Michael N. Barber, Andries van der Bilt, Kyong O. Joung, Richard L. Carlin

Published Nov 1, 1981• 58 citations

Abstract

The transverse susceptibility of the one-dimensional antiferromagnetic $\mathrm{XY}$ model is calculated for a sequence of finite chains with periodic boundary conditions. The infinite-chain susceptibility is obtained by extrapolation, and good convergence is found for most temperatures. The results are compared with the $c$-axis susceptibility of ${\mathrm{Cs}}_{2}$Co${\mathrm{Cl}}_{4}$, which has been measured over the temperature interval 40 mK-4.2 K. The agreement is excellent, confirming that this compound can be well approximated by a set of weakly coupled antiferromagnetic $\mathrm{XY}$ chains.

DOI: 10.1103/physrevb.24.5149

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Physical review. B, Condensed matter

Transverse susceptibility of the one-dimensional antiferromagnetic XY model. Application to Cs2 Co Cl4

Philip M. Duxbury, J. Oitmaa, Michael N. Barber, Andries van der Bilt, Kyong O. Joung, Richard L. Carlin

Published Nov 1, 1981• 58 citations

Publisher

Abstract

The transverse susceptibility of the one-dimensional antiferromagnetic

\mathrm{XY}

model is calculated for a sequence of finite chains with periodic boundary conditions. The infinite-chain susceptibility is obtained by extrapolation, and good convergence is found for most temperatures. The results are compared with the

c

-axis susceptibility of

{\mathrm{Cs}}_{2}

{\mathrm{Cl}}_{4}

, which has been measured over the temperature interval 40 mK-4.2 K. The agreement is excellent, confirming that this compound can be well approximated by a set of weakly coupled antiferromagnetic

\mathrm{XY}

chains.

DOI: 10.1103/physrevb.24.5149

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S=1 antiferromagnetic Heisenberg chain in a magnetic field

Tôru Sakai, Minoru Takahashi

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Physical review. B, Condensed matterJun 1, 1991150 citations

The transverse susceptibility of the one-dimensional antiferromagnetic

\mathrm{XY}

c

-axis susceptibility of

{\mathrm{Cs}}_{2}

{\mathrm{Cl}}_{4}

, which has been measured over the temperature interval 40 mK-4.2 K. The agreement is excellent, confirming that this compound can be well approximated by a set of weakly coupled antiferromagnetic

\mathrm{XY}

chains.

We calculate precise numerical values for the nondivergent direct or staggered zero-temperature susceptibilities of the one-dimensional,

S=\frac{1}{2}

, transverse Ising model at the critical field and for the isotropic

\mathrm{XY}

model in zero field which have not been previously determined analytically. Our method is based on a rigorous approach to calculate dynamic correlation functions for these models. We also investigate the exact nature of the divergenices in the

q

-dependent susceptibilities. Our results are compared with existing predictions of approximate analytic approaches and numerical finite-chain calculations. Our result for the

\mathrm{XY}

case is directly relevant for the interpretation of recent susceptibility measurements on the quasi-one-dimensional magnetic compound

{\mathrm{Cs}}_{2}

{\mathrm{CoCl}}_{4}

Magnetic susceptibility is measured on the one-dimensional spin 1/2 antiferromagnets

{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}

and

\mathrm{Sr}{\mathrm{CuO}}_{2}

using single crystals. Large, nearly contamination-free single crystals enable us to measure the intrinsic spin susceptibility over a wide temperature range between 5 and 800 K. The results are in excellent agreement with the recent calculation by Eggert, Affleck, and Takahashi, and the exchange interaction energy

J

is estimated to be $2200\ifmmode\pm\else\textpm\fi{}200$ and $2100\ifmmode\pm\else\textpm\fi{}200\mathrm{K}$, respectively. In

{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}

, an isotropic susceptibility drop is observed below about 20 K, which is also consistent with the result of this rigorous calculation.

{\mathrm{CsNiCl}}_{3}

, which displays a Haldane gap, is revealed.

{\mathit{H}}_{\mathit{c}1}

(=\ensuremath{\Delta}), where \ensuremath{\Delta} is the Haldane gap. It is also found that the transverse spin correlation has the asymptotic form 〈

{\mathit{S}}_{0}^{\mathit{x}}

{\mathit{S}}_{\mathit{r}}^{\mathit{x}}

〉\ensuremath{\sim}(-1

{)}^{\mathit{r}}

${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\eta}}}$, and the transverse staggered susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{st}}^{\mathit{x}\mathit{x}}$ diverges between

{\mathit{H}}_{\mathit{c}1}

and

{\mathit{H}}_{\mathit{c}2}

(=4). The exponent \ensuremath{\eta} has a minimum (\ensuremath{\eta}\ensuremath{\simeq}0.3) at magnetization m\ensuremath{\simeq}1/3 and \ensuremath{\eta}\ensuremath{\simeq}0.5 at

{\mathit{H}}_{\mathit{c}1}

and

{\mathit{H}}_{\mathit{c}2}

. If the system is quasi-one-dimensional, even small interchain couplings can create a canted N\'eel order, within a mean-field approximation for interchain interactions. This is consistent with a recent NMR measurement for Ni(

{\mathrm{C}}_{2}

{\mathrm{H}}_{8}

{\mathrm{N}}_{2}

{)}_{2}

{\mathrm{NO}}_{2}

(

{\mathrm{ClO}}_{4}

) (NENP) at low temperature.