Spin-spin correlations of the spin-ladder compound (C$_5$H$_{12}$N)$_2$CuBr$_4$ measured by magnetostriction and comparison to Quantum Monte Carlo results

Details Spin-spin correlations of the spin-ladder compound (C$_5$H$_{12}$N)$_2$CuBr$_4$ measured by magnetostriction and comparison to Quantum Monte Carlo results Spin-spin correlations of the spin-ladder compound (C$_5$H$_{12}$N)$_2$CuBr$_4$ measured by magnetostriction and comparison to Quantum Monte Carlo results

2008-03-07

arxiv.org/abs/0803.1072v1

Phys. Rev. B 77, 235113 (2008)

Physics

Condensed Matter

Strongly Correlated Electrons

12 pages, 8 figures included

Scientific paper

10.1103/PhysRevB.77.235113

Magnetostriction and thermal expansion of the spin-ladder compound piperidinium copper bromide (C$_5$H$_{12}$N)$_2$CuBr$_4$ are analyzed in detail. We find perfect agreement between experiments and the theory of a two-leg spin ladder Hamiltonian for more than a decade in temperature and in a wide range of magnetic fields. Relating the magnetostriction along different crystallographic directions to two static spin-spin correlation functions, which we compute with Quantum Monte Carlo, allows us to reconstruct the magnetoelastic couplings of (C$_5$H$_{12}$N)$_2$CuBr$_4$. We especially focus on the quantum critical behavior near the two critical magnetic fields $H_{c1}$ and $H_{c2}$, which is characterized by strong singularities rooted in the low dimensionality of the critical spin-system. Extending our discussion in Lorenz et al [Phys. Rev. Lett., 100, 067208 (2008)], we show explicitly that the thermal expansion near the upper critical field $H_{c2}$ is quantitatively described by a parameter-free theory of one-dimensional, non-relativistic Fermions. We also point out that there exists a singular quantum critical correction to the elastic moduli. This correction is proportional to the magnetic susceptibility $\chi$ which diverges as $\chi \sim 1/\sqrt{T}$ at the critical fields and thus leads to a strong softening of the crystal.

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