Magnet with Ferromagnetic Nearest-Neighbor and Antiferromagnetic Next-Nearest-Neighbor Exchange Interactions

Magnetic properties of $Pb[Cu(SO_4)(OH)_2]$ (linarite) natural single crystals were studied by magnetization and specific heat measurements. The angular dependences of magnetization were revealed which correlated with the regularities of the crystal structure. At about 2.8 K this quasi-one-dimensional Heisenberg system undergoes a phase transition to the long-range antiferromagnetic order with antiparallel magnetic moments aligned probably along the b-axis. The antiferromagnetic order is evidenced by the metamagnetic transition and pronounced λ-type anomaly at $T_N$ in the specific heat. Using phenomenological modeling based on a quantum transfer-matrix method, we argue that at higher temperatures linarite is a quasi-one-dimensional system with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange interactions.