Magnetic Frustration in a Quantum Spin Chain: The Case of Linarite PbCuSO₄(OH)₂

We present a combined neutron diffraction and bulk thermodynamic study of the natural mineral linarite PbCuSO₄(OH)₂, this way establishing the nature of the ground-state magnetic order. An incommensurate magnetic ordering with a propagation vector k = (0, 0.186, 1/2) was found below T_N = 2.8 K in a zero magnetic field. The analysis of the neutron diffraction data yields an elliptical helical structure, where one component (0.638 µ_B) is in the monoclinic ac plane forming an angle with the a axis of 27(2)°, while the other component (0.833 µ_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.