Complex field-induced states in Linarite PbCuSO${}_4$(OH)${}_2$ with a variety of high-order exotic SDW${}_p$ states

Abstract

Low-temperature neutron diffraction and NMR studies of field-induced phases in linarite are presented for magnetic fields $H\parallel b$ axis. A two-step spin-flop transition is observed as well as a transition transforming a helical magnetic ground state into an unusual magnetic phase with sine-wave modulated moments $\parallel H$. An effective ${\tilde{J}}_1$-${\tilde{J}}_2$ single-chain model with a magnetization-dependent frustration ratio ${\alpha }_{\mathrm{eff}}=-{\tilde{J}}_2/{\tilde{J}}_1$ is proposed. The latter is governed by skew interchain couplings and shifted to the vicinity of the ferromagnetic critical point. It explains qualitatively the observation of a rich variety of exotic (for strongly correlated cuprate spin-1/2 Heisenberg systems) longitudinal collinear spin-density wave SDW${}_p$ states ($9\ge p\ge 2$).