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 (0.638μ(B)) is in the monoclinic ac plane forming an angle with the a axis of 27(2)°, while the other component (0.833μ(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.
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).
We present a detailed study in the paramagnetic regime of the frustrated s = 1/2 spin-compound linarite, PbCuSO4(OH)2, with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange interactions. Our data reveal highly anisotropic values for the saturation field along the crystallographic main directions, with ∼ 7.6, ∼ 10.5 and ∼ 8.5 T for the a, b, and c axes, respectively. In the paramagnetic regime, this behavior is explained mainly by the anisotropy of the g-factor but leaving room for an easy-axis exchange anisotropy. Within the isotropic J1-J2 spin model our experimental data are described by various theoretical approaches yielding values for the exchange interactions J1 ∼ -100 K and J2 ∼ 36 K. These main intrachain exchange integrals are significantly larger as compared to the values derived in two previous studies in the literature and shift the frustration ratio α = J2/|J1| ≈ 0.36 of linarite closer to the 1D critical point at 0.25. Electron spin resonance (ESR) and nuclear magnetic resonance (NMR) measurements further prove that the static susceptibility is dominated by the intrinsic spin susceptibility. The Knight shift as well as the broadening of the linewidth in ESR and NMR at elevated temperatures indicate a highly frustrated system with the onset of magnetic correlations far above the magnetic ordering temperature TN = 2.75(5) K, in agreement with the calculated exchange constants.
We present a comprehensive macroscopic thermodynamic study of the quasi-one-dimensional (1D) s = 1 2 frustrated spin-chain system linarite. Susceptibility, magnetization, specific heat, magnetocaloric effect, magnetostriction, and thermal-expansion measurements were performed to characterize the magnetic phase diagram. In particular, for magnetic fields along the b axis five different magnetic regions have been detected, some of them exhibiting short-range-order effects. The experimental magnetic entropy and magnetization are compared to a theoretical modelling of these quantities using DMRG and TMRG approaches. Within the framework of a purely 1D isotropic model Hamiltonian, only a qualitative agreement between theory and the experimental data can be achieved. Instead, it is demonstrated that a significant symmetric anisotropic exchange of about 10 % is necessary to account for the basic experimental observations, including the 3D saturation field, and which in turn might stabilize a triatic (three-magnon) multipolar phase.
Here we present inelastic neutron scattering measurements from the frustrated, quantum spin-1/2 chain material linarite, PbCuSO4(OH)2. Time of flight data, taken at 0.5 K and zero applied magnetic field reveals low-energy dispersive spin wave excitations below 1.5 meV both parallel and perpendicular to the Cu-chain direction. From this we confirm that the interchain couplings within linarite are around 10 % of the nearest neighbour intrachain interactions. We analyse the data within both linear spin-wave theory and density matrix renormalisation group theories and establish the main magnetic exchange interactions and the simplest realistic Hamiltonian for this material.
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