Magnetic Frustration in a Quantum Spin Chain: The Case of Linarite ${\mathrm{PbCuSO}}_4(\mathrm{OH}{)}_2$

We present a combined neutron diffraction and bulk thermodynamic study of the natural mineral linarite ${\mathrm{PbCuSO}}_4(\mathrm{OH}{)}_2$, this way establishing the nature of the ground-state magnetic order. An incommensurate magnetic ordering with a propagation vector $\mathit{k}=(0,0.186,\frac{1}{2})$ was found below $T_N=2.8\mathrm{K}$ in a zero magnetic field. The analysis of the neutron diffraction data yields an elliptical helical structure, where one component ($0.638{\mu }_B$) is in the monoclinic $ac$ plane forming an angle with the $a$ axis of 27(2)°, while the other component ($0.833{\mu }_B$) points along the $b$ axis. From a detailed thermodynamic study of bulk linarite in magnetic fields up to 12 T, applied along the chain direction, a very rich magnetic phase diagram is established, with multiple field-induced phases, and possibly short-range-order effects occurring in high fields. Our data establish linarite as a model compound of the frustrated one-dimensional spin chain, with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. Long-range magnetic order is brought about by interchain coupling 1 order of magnitude smaller than the intrachain coupling.

Figure 1

(a) The magnetic peak $(0,0.186,\frac{1}{2})$ of linarite at temperatures below and above $T_N$ from rocking scans, with omega defining the angle of sample rotation. (b) Temperature dependence of the integrated intensity of the magnetic Bragg peak $(0,0.186,\frac{1}{2})$.

Figure 2

The magnetic structure of linarite. Only the ${\mathrm{Cu}}^{2+}$ ions and the oxygen atoms O4 and O5 are shown. The two differently colored arrows symbolize the spins on the two copper sites: Cu1 (red) and Cu2 (green).

Figure 3

Susceptibility (top) and specific heat (bottom; data in different fields shifted for clarity) for linarite with the magnetic field $B\parallel b$ axis. The inset shows the transition at $T_{\mathrm{cp}}$ in the specific-heat data for a magnetic field of 7 T.

Figure 4

(a) Detailed view of the magnetization of linarite with the hysteretic transition between the fields $B_s$ and $B_e$ and (b) the nonadiabatic MCE with the anomalies at the phase boundary $(T_3,B_3)$ and the signatures at $B_{\mathrm{cp}}$; for details, see the text. (c) Magnetic phase diagram of linarite for a magnetic field $B$ along the $b$ axis.