Luttinger liquid behavior in the alternating spin-chain system copper nitrate

We determine the phase diagram of copper nitrate $\text{Cu}{\left({\text{NO}}_3\right)}_2·2.5{\mathrm{D}}_2\text{O}$ in the context of quantum phase transitions and novel states of matter. We establish this compound as an ideal candidate to study quasi-1D Luttinger liquids, 3D Bose-Einstein-Condensation of triplons, and the crossover between 1D and 3D physics. Magnetocaloric effect, magnetization, and neutron scattering data provide clear evidence for transitions into a Luttinger liquid regime and a 3D long-range ordered phase as a function of field and temperature. Theoretical simulations of this model material allow us to fully establish the phase diagram and to discuss it in the context of dimerized spin systems.

Figure 1

Magnetocaloric effect $-\frac{1}{T}\frac{\delta Q_{\text{MCE}}\left(H\right)}{d\left({\mu }_{0}H\right)}$ of copper nitrate (a) and the corresponding entropy $S$ (b) at different bath temperatures. The data at 290 mK are compared to the results of exact diagonalization (ED) simulations; for details see text.

Figure 2

Magnetization $M\left(H\right)$ and the field derivative $dM/d{\mu }_{0}H$ of copper nitrate. $M\left(H\right)$ calculated via exact diagonalization (ED) is included; for details see text.

Figure 3

Magnetization $M\left(T\right)$ and the temperature derivative at 2.95 (a), 4.1 (b), 3.1 (c), and 3.92 T (d) obtained from MCE data. The purple lines indicate the transition into the LRO phase, while the blue lines mark the transition into the LL regime.

Figure 4

Phase diagram of copper nitrate for applied magnetic fields along the $b$ direction. The dotted line is a guide to the eye. The contour plot represents the data $-\frac{1}{T}\frac{\delta Q_{\text{MCE}}\left(H\right)}{d\left({\mu }_{0}H\right)}$. The crosses indicate local maxima in the heat capacity obtained from exact diagonalization simulations. They represent crossovers between the QD, QC, and the fully polarized regime; for details see text.