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

Abstract

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.

12 pages, 8 figures included

References in corpus (6)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum Criticality in Heavy Fermion Metals
• Bose-Einstein Condensation in Magnetic Insulators
• Diverging thermal expansion of the spin-ladder system (C${}_5$H${}_{12}$N)${}_2$CuBr${}_4$
• Critical properties and Bose Einstein Condensation in dimer spin systems
• Thermodynamics of the coupled spin-dimer system TlCuCl3 close to a quantum phase transition

Cited by in corpus (4)

• Controlling Luttinger liquid physics in spin ladders under a magnetic field
• Thermodynamics of the Spin Luttinger-Liquid in a Model Ladder Material
• Neutron scattering evidence for isolated spin-1/2 ladders in (C${}_5$D${}_{12}$N)${}_2$CuBr${}_4$
• Dimensional crossover in quantum critical metallic magnets