Complex Field-Induced States in LinaritePbCuSO4(OH)2with a Variety of High-Order Exotic Spin-Density Wave States

Abstract

Low-temperature neutron diffraction and NMR studies of field-induced phases in linarite are presented for magnetic fields H∥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 ∥H. An effective J[over ˜]_{1}-J[over ˜]_{2} single-chain model with a magnetization-dependent frustration ratio α_{eff}=-J[over ˜]_{2}/J[over ˜]_{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 longitudinal collinear spin-density wave, SDW_{p}, states (9≥p≥2).

Dynamics of linarite: Observations of magnetic excitations

“…Clearly, these calculations reproduce the salient features of the low energy branch of the experimental spin excitation spectra. Thus, relatively good agreement is found when modeling the data with the exchange interactions J 1 , J 2 and J ic , as determined from susceptibility χ(T ), magnetization M (H) and inelastic neutron diffraction INS, indicating that the model used to describe the magnetic coupling in linarite is robust 17,30 , see Tab. I.…”

“…This gives two coupled J 1 -J 2 chains with α ≈ 0.36 and J ic = 0.05|J 1 |. For linarite this interchain coupling was revealed to be a critical component into the multipolar ordering at high magnetic fields 17 . While the incommensurate propagation vector component (in units [H, K, L]) along the chain has been found to be K = 0.186 in zero field, for a single J 1 -J 2 chain with α ≈ 0.36 a value K = 0.367 would be predicted.…”

“…Further, the diagonal interchain coupling plays an important role, although the details are not yet fully understood: some coupling is required to establish long-range order, but above a small critical interchain coupling it can also destroy any isotropic multipolar phase 9,16 . However, with specific exchange anisotropies a stabilization of the spin-nematic phase can be achieved 17,18 . Together, the Hamiltonian, including diagonal interchain coupling, J ic , between chains l, l ′ , is written aŝ…”

“…Unfortunately, for many of the candidates for exhibiting multipolar phases, the involved AFM magnetic couplings and thus the saturation field are quite large, making it difficult to probe the multipolar phases. In this respect, linarite, PbCuSO 4 (OH) 2 , is a promising spin-multipolar candidate as the Cu 2+ ions form a quasi-1D S = 1/2 spinchain along the crystallographic b-axis 17,[30][31][32][33] . The material crystallizes in a monoclinic space group P 2 1 /m with lattice parameters 31,32,34 (at 1.8 K) a = 9.682Å, b = 5.646Å, c = 4.683Å, and β = 102.65 • (Fig.…”

“…We have recently presented an extensive thermodynamic investigation of linarite, establishing a rich and detailed phase diagram along each of the principal directions 17,[31][32][33] . Below T N = 2.8 K linarite shows magnetic long range order at zero field.…”