Experimental Observation of the $1/3$ Magnetization Plateau in the Diamond-Chain Compound ${\mathrm{Cu}}_3({\mathrm{CO}}_3{)}_2(\mathrm{OH}{)}_2$

The magnetic susceptibility, high field magnetization, and specific heat measurements of ${\mathrm{Cu}}_3({\mathrm{CO}}_3{)}_2(\mathrm{OH}{)}_2$, which is a model substance for the frustrating diamond spin chain model, have been performed using single crystals. Two broad peaks are observed at around 20 and 5 K in both magnetic susceptibility and specific heat results. The magnetization curve has a clear plateau at one third of the saturation magnetization. The experimental results are examined in terms of theoretical expectations based on exact diagonalization and density matrix renormalization group methods. An origin of magnetic anisotropy is also discussed.

Figure 1

(a) The distorted diamond chain. Solid circles represent spin $1/2$ coupled by exchange interactions $J_1$, $J_2$, and $J_3$. (b) Schematic view of the crystal structure of the azurite ${\mathrm{Cu}}_3({\mathrm{CO}}_3{)}_2(\mathrm{OH}{)}_2$ along the $b$ axis.

Figure 2

The high field magnetization curves of ${\mathrm{Cu}}_3({\mathrm{CO}}_3{)}_2(\mathrm{OH}{)}_2$ measured below 4.2 K. The magnetic field was applied along the $b$ axis (a) and perpendicular to the $b$ axis (b), respectively.

Figure 3

The temperature dependence of the magnetic susceptibilities for $H\parallel b$ and $H\perp b$. The solid line is the best fitted result of high temperature series calculation using the parameters shown in figure. The inset is the low temperature part of the magnetic susceptibility. The diamagnetic contribution from core electrons is subtracted in this figure.

Figure 4

The temperature dependence of the low temperature specific heat. Inset is the specific heat for the entire temperature range. A broken line is a guide for the eyes to make an anomaly at around 18 K clearer. Note that a lattice contribution is not subtracted.

Figure 5

The best fitting result for the magnetization curve at 1.5 K for $H\parallel b$ with the theoretical dotted line using $J_1:J_2:J_3=1:1.25:0.45$.