Coexistence of Long-Range Order and Spin Fluctuation in Geometrically Frustrated Clinoatacamite ${\mathrm{Cu}}_2\mathrm{Cl}(\mathrm{OH}{)}_3$

Muon spin rotation experiments are carried out on clinoatacamite, ${\mathrm{Cu}}_2\mathrm{Cl}(\mathrm{OH}{)}_3$, which is a new geometrically frustrated system featuring a three-dimensional network of corner-sharing tetrahedral $3d$ ${\mathrm{Cu}}^{2+}$ spins. A long-range antiferromagnetic order occurs below 18.1 K with a surprisingly small entropy release of about $0.05R\ln 2/\mathrm{Cu}$. Below 6.5 K, the static long-range order transforms abruptly into a metastable state with nearly complete depolarization of muon spins which suggests strong fluctuation. The system then enters a state in which partial long-range order and spin fluctuation coexist down to the lowest experimentally attainable temperature of 20 mK. This work presents a novel system for studying geometric frustration.

Figure 1

The specific heat per mol formula of clinoatacamite ${\mathrm{Cu}}_2\mathrm{Cl}(\mathrm{OH}{)}_3$ at ZF (filled circles) and 5 T (open circles), and entropy per mol Cu spin (open squares). The inset is an enlarged view of two anomalies at 6.2 and 6.4 K.

Figure 2

Depolarization of muon spins at typical temperatures. (a) short-term spectra; and (b) long-term spectra. The broad gray lines are fitted curves. For a clear view, the oscillations of the fitted curves in (b) for $t<1\mu \mathrm{s}$ are omitted.

Figure 3

Phase diagram for the magnetic transitions in clinoatacamite (the lower part depicts the rapid decrease of the baseline of the polarization spectra around 5.7 K).

Figure 4

(a) Temperature dependence of a slow relaxation ${\Lambda }_{\mathrm{S}}$ (open triangles) and its proportion $P_{\mathrm{S}}$ (open diamonds). (b) Temperature dependence of rapid relaxation ${\Lambda }_{\mathrm{Q}}$ (open circles) and the transverse field relaxation $\lambda$ (open squares).

Figure 5

Longitudinal field $\mu \mathrm{SR}$ at 5.7 K [thick solid lines are fitted curves using Eq. (3)].