LaMMB - MagLab Highlight

Thermodynamics of the spin Luttinger-liquid in a model ladder material

- an example for complementary measurements at the Laboraty for Magnetic Measurements at BENSC (LaMMB - MagLab)
Christian Rüegg, Klaus Kiefer, Benedikt Thielemann, et al. Phys. Rev. Letters, Vol.: 101,  Art. No.: 247202 (2008)

The phase diagram in temperature and magnetic field of the metal-organic, two-leg, spin-ladder compound (C5H12N)(2)CuBr4 is studied by measurements of the specific heat and the magnetocaloric effect. We demonstrate the presence of an extended spin Luttinger-liquid phase between two field-induced quantum critical points and over a broad range of temperature. Based on an ideal spin-ladder Hamiltonian, comprehensive numerical modeling of the ladder specific heat yields excellent quantitative agreement with the experimental data across the entire phase diagram.

The white circles in the Figure denote the crossover to the Luttinger-liquid regime based on measurements of the magnetocaloric effect. The special technique used at LaMMB for the very accurate determination of the Luttinger-liquid regime boundary is the quantitative quasi-isothermal magnetocaloric effect. With this powerful method it is possible to directly determine the temperature derivative of the magnetisation dM/dT|B via the relation dM/dT|B=–(dQ/dB)/T, where dQ is the heat generated in the sample by the magnetocaloric effect at a magnetic field change dB. As the magnetization M vs. temperature T is expected to pass an extremum (maximum or minimum) at the crossover to the Luttinger-liquid regime, the zero-transition of dM/dT|B vs. T then indicates the boundary of the Luttinger-liquid regime.

The measurements were performed on the LaMMB - MagLab Instrument CM14.5T.

Field-temperature phase diagram of the spin-ladder compound (Hpip)CuBr4, showing quantum disordered (QD), quantum critical (QC), and spin Luttinger-liquid (LL) phases. The contour plot shows the magnetic specific heat capacity as Cm(T,B)/T. Local maxima from the reduction of the triplet gap by the Zeeman effect are indicated by crosses. Circles denote the LL crossover based on measurements of the magnetocaloric effect, black lines are fits to extract the critical fields. The blue line indicates the onset of 3D long-range order below 100 mK. Inset: lattice structure of (Hpip)CuBr4 in projection along the b-axis, with Cu atoms blue and Br white.