Spin-$\frac{1}{2}$ $XXZ$ Chain System ${\mathrm{Cs}}_2{\mathrm{CoCl}}_4$ in a Transverse Magnetic Field

Comparing high-resolution specific heat and thermal expansion measurements to exact finite-size diagonalization, we demonstrate that ${\mathrm{Cs}}_2{\mathrm{CoCl}}_4$ for a magnetic field along the crystallographic $b$ axis realizes the spin-$\frac{1}{2}$ $XXZ$ chain in a transverse field. Exploiting both thermal as well as virtual excitations of higher crystal-field states, we find that the spin chain is in the $XY$ limit with an anisotropy $J_z/J_{\perp }\approx 0.12$, substantially smaller than previously believed. A spin-flop Ising quantum phase transition occurs at a critical field of ${\mu }_0{H}_b^{\mathrm{cr}}\approx 2\mathrm{T}$ before around 3.5 T the description in terms of an effective spin-$\frac{1}{2}$ chain becomes inapplicable.

Figure 1

Phase diagram of ${\mathrm{Cs}}_2{\mathrm{CoCl}}_4$ for a magnetic field along the $b$ axis. An extended regime (1D $XXZ$) is described by the spin-$\frac{1}{2}$ $XXZ$ chain Hamiltonian in a transverse field (4). Crossover lines are characteristic for Ising criticality $T\sim |H_b-H_b^{\mathrm{cr}}{|}^{\nu z}$ with $\nu z=1$ and extrapolate to a critical field ${\mu }_0{H}_b^{\mathrm{cr}}\approx 2\mathrm{T}$.

Figure 2

Specific heat (a) and $b$-axis thermal expansion (b) of ${\mathrm{Cs}}_2{\mathrm{CoCl}}_4$ in zero field (symbols). Both quantities can be decomposed into three contributions attributed to the phonons (long-dashed line), the Schottky anomaly (dash-dotted line), and the $XXZ$ chain (short-dashed line).

Figure 3

Specific heat (a) and $b$-axis thermal expansion (b) of ${\mathrm{Cs}}_2{\mathrm{CoCl}}_4$ (symbols) for different magnetic fields $H_b$. The solid lines are best fits to theory.