Thermodynamic properties of the coupled dimer system ${\mathrm{Cu}}_2{\left({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2\right)}_2{\mathrm{Cl}}_4$

We reexamine the thermodynamic properties of the coupled dimer system ${\mathrm{Cu}}_2{\left({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2\right)}_2{\mathrm{Cl}}_4$ under magnetic field in the light of recent NMR experiments [Clémancey et al., Phys. Rev. Lett. 97, 167204 (2006)], suggesting the existence of a finite Dzyaloshinskii-Moriya interaction. We show that including such a spin anisotropy greatly improves the fit of the magnetization curve and gives the correct trend of the insofar unexplained anomalous behavior of the specific heat in magnetic field at low temperature.

Figure 1

(Color online) Uniform magnetization per site, $m_z$, vs magnetic field $h$ (in tesla) for various cluster sizes. (a) $D=0$: $m_z$ exhibits finite-size plateaus at rational values multiple of $1∕N$ that disappear in the thermodynamic limit. (b) Finite $D$: we obtain continuous curves (since $S_z$ is not conserved any more) which show very small finite-size effects. The square-root singularity disappears and the magnetization curves become smooth.

Figure 2

(Color online) Normalized magnetization along magnetic field $m_z$: experimental data are taken from Ref. 9; numerical results are presented for various $D$ (in units of $J_{\perp }$) and $N=20$ spins (lines are guides to the eye). In the specific case $D=0$, we plot an extrapolation (see text). The best agreement with experiment is obtained for $D\simeq 0.05J_{\perp }$.

Figure 3

(Color online) Magnetic specific heat vs temperature for various magnetic fields $h$ (in tesla): experimental data (symbols) are taken from Ref. 6; exact numerical results are presented for $D=0$ (dashed lines, obtained with 20 spins) and $D=0.05J_{\perp }$ (solid lines, obtained with 16 spins), showing a better agreement.

Figure 4

(Color online) Magnetic specific heat for $h=10\mathrm{T}$ obtained numerically for various $D∕J_{\perp }=0$, 0.05, 0.1, and 0.15 with 16 spins. As $D$ increases, we observe that both the low-temperature peak intensity and position increase.

Figure 5

(Color online) Magnetic specific heat for $h=0$ (a) and $h=9\mathrm{T}$ (b) obtained numerically for $D∕J_{\perp }=0$ (solid and dashed lines) and 0.05 (dot-dashed lines) with $N=12$ and $N=16$ spins. Note that in (a) all four curves are indistinguishable.