Spin-spin correlations of the spin-ladder compound (C5H12N)2CuBr4 measured by magnetostriction and comparison to quantum Monte Carlo results

Magnetostriction and thermal expansion of the spin-ladder compound piperidinium copper bromide (C5H12N)(2)CuBr4 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 (C5H12N)(2)CuBr4. 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 [ 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, nonrelativistic 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 similar to 1/root T at the critical fields and thus leads to a strong softening of the crystal.