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)₂CuBr₄ 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)₂CuBr₄. 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, 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 χ, which diverges as χ∼1/√T at the critical fields and thus leads to a strong softening of the crystal.