Magnetic frustration in a quantum spin chain: the case of linarite PbCuSO4(OH)2

Terahertz Vibrational Dynamics and DFT Calculations for the Quantum Spin Chain Linarite, PbCuSO4(OH)2

The low-dimensional quantum-magnet, linarite, PbCuS4(OH)2, has been investigated using terahertz (THz) spectroscopy coupled with detailed density functional theory (DFT) calculations in order to explore the effects of the temperature on its lattice vibrations. Linarite is characterized by largely isolated CuO chains propagating along the crystallographic b-axis, which at very low temperatures are responsible for exotic, quasi-1D magnetism in this material. To better understand the synergy between the structural bonds and lattice oscillations that contribute to these chains, polarized THz spectroscopic measurements were performed. Consolidating these results with detailed DFT calculations has revealed that the anisotropic vibrational motion for the THz modes is correlated with extreme motion associated with the crystallographic b-axis. An unexpected feature observed in the infrared spectrum is attributed to subtle lattice distortions which break the centro-symmetry in linarite at high temperatures. This phenomenon has not previously been observed in linarite and likely results from anharmonicity in lattice oscillations.

Quasi-One-Dimensional Linarite-Type PbCu(SeO4)(OH)2 with Competing Nearest-Neighbor and Next-Nearest-Neighbor Intrachain Exchange Interactions

PbCu(SeO₄)(OH)₂, the selenate sibling of the mineral linarite, was synthesized hydrothermally, investigated in measurements of magnetization M, specific heat C_p and dielectric permittivity ε, and analyzed within density functional theory formalism. This quasi-one-dimensional compound evidences formation of a short-range correlation regime at T* ~ 8 K and experiences a long-range magnetic order at T_N = 4.3 K. A magnetization saturation of approximately 1 µ_B is reached at µ₀H_flip ~ 16 T preceded by a jump at µ₀H_flop = 2.4 T. Additionally, there are multiple indicators of the formation of an additional electrically active phase above the Neel temperature, which suggests that PbCu(SeO₄)(OH)₂ is a multiferroic system.

Linarite from Cap Garonne

Linarite, PbCuSO4(OH)2, crystallizes as secondary mineral in form of clusters of crystals in Mine du Pradet at Cap Garonne in France. A tiny single crystal was isolated and its structure was refined from synchrotron diffraction data (λ = 0.049592 nm): P121/m1, a = 467.75(2), b = 563.48(4), c = 967.64(5) pm, β = 102.647(5)°, wR = 0.0544, 819 F 2 values and 56 variables. The proton positions were also refined. The Cu2+ cations are located within Cu(OH)2 ribbons and exhibit pronounced Jahn-Teller distortion (d(Cu–O): 2 × 191.9, 2 × 197.3 and 2 × 252.8 pm). The Cu(OH)2 ribbons are condensed with the sulfate tetrahedra and the lead cations. The latter are coordinated to eight oxygen atoms in a slightly anisotropic manner. Calculations of the electron localization function (ELF) of PbO (litharge), PbSO4 (anglesite) and PbCuSO4(OH)2 (linarite) show pronounced lone-pair character for PbO but rather isotropic ELF values around the lead cations in PbSO4 and PbCuSO4(OH)2.

Measuring the excitations in a new S = 1/2 quantum spin chain material with competing interactions

Recently a new one-dimensional (1D) quantum spin chain system has been reported: catena-dichloro(2-Cl-3Mpy)copper(II), (where 2-Cl-3Mpy=2-chloro-3-methylpyridine). Preliminary calculations and bulk magnetic property measurements indicate that this system does not undergo magnetic ordering down to 1.8 K and is a prime candidate for investigating frustration in a J ₁/J ₂ system (where the nearest neighbour interactions, J ₁, are ferromagnetic and the next nearest neighbour interactions, J ₂, are antiferromagnetic). Calculations predicted three possible magnetic interaction strengths for J ₁ below 6 meV depending on the orientation of the ligand. For one of the predicted J ₁ values, the existence of a quantum critical point is implied. A deuterated sample of catena-dichloro(2-Cl-3Mpy)copper(II) was synthesised and the excitations measured using inelastic neutron scattering. Scattering indicated the most likely scenario involves spin-chains where each chain consists of only one of the three possible magnetic excitations in this material, rather than the completely random array of exchange interactions within each chain as predicted by Herringer et al (2014 Chem. Eur. J. 20 8355-62). This indicates the possibility of tuning the chemical structure to favour a system which may exhibit a quantum critical point.

Field-induced States and Excitations in the Quasicritical Spin-1/2 Chain Linarite

The mineral linarite, PbCuSO_{4}(OH)_{2}, is a spin-1/2 chain with frustrating nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic exchange interactions. Our inelastic neutron scattering experiments performed above the saturation field establish that the ratio between these exchanges is such that linarite is extremely close to the quantum critical point between spin-multipolar phases and the ferromagnetic state. We show that the predicted quantum multipolar phases are fragile and actually suppressed by a tiny orthorhombic exchange anisotropy and weak interchain interactions in favor of a dipolar fan phase. Including this anisotropy in classical simulations of a nearly critical model explains the field-dependent phase sequence of the phase diagram of linarite, its strong dependence of the magnetic field direction, and the measured variations of the wave vector as well as the staggered and the uniform magnetizations in an applied field.

Dielectric properties of complex magnetic field induced states in PbCuSO4(OH)2

Spin spirals, which coexist with collinear spin order in linarite PbCuSO₄(OH)₂, indicate electrical polarisation textures of spin-multipolar phases. We derive experimental evidence by a detailed investigation of the magnetic-field dependent dielectric and electric polarization properties at low temperatures. Linarite exhibits a quasi-one-dimensional frustrated S = ½ spin chain, which forms 3D spin-spiral order in zero magnetic field for T < 2.85 K. Recently, due to the monoclinic lattice of linarite with CuO₂ ribbon chains, complex magnetic field induced states were found. These spin-multipolar phases, which compete with spin-density waves at low magnetic fields, exist in close vicinity to the transition from the spin spiral into field induced spin polarized state. Via antisymmetric Dzyaloshinskii-Moriya interaction spin-driven ferroelectricity develops in the spin-spirals state. Via electric polarization measurements this allows to prove the transitions into complex magnetic field induced phases. Thorough analyses of the temperature and magnetic field dependent dielectric properties of a naturally grown single crystalline sample provide a detailed (T,H) phase diagrams for the three different crystallographic directions.

Complex Field-Induced States in Linarite PbCuSO4(OH)2 with a Variety of High-Order Exotic Spin-Density Wave States

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).

Modulated minerals as potential ferroic materials

A list of potential (multi-) ferroic systems is derived based on the idea that structure gradients can generate ferroic distortions. Structure gradients are restricted here to structural modulations, which are commonly observed in natural minerals. These minerals contain transition metals and are prone to Jahn-Teller distortions and magnetic instabilities. The list contains mineral groups, which are often available in mineralogical collections.

Magnetic Orderings in Li2Cu(WO4)2 with Tungstate-Bridged Quasi-1D Spin-1/2 Chains

By both experimental measurements and theoretical calculations, we investigated the magnetic and electronic properties of Li2Cu(WO4)2 as a tungstate-bridged quasi-one-dimensional (1D) copper spin-(1/2) chain system. Interestingly, magnetic susceptibility χ(T) and specific heat measurements show that the system undergoes a three-dimensional antiferromagnetic (AF)-like ordering at TN ≈ 3.7 K, below a broad χ(T) maximum at ∼8.9 K indicating a low-dimensional short-range AF spin correlation. Bonner-Fisher model fitting of χ(T) leads to an AF intrachain exchange constant of J/kB = 15.8 ± 0.1 K, and mean-field theory estimation gives an interchain coupling constant of J⊥/kB = 1.6 K, which supports the quasi-1D nature of this spin system. Theoretical evaluation of exchange coupling constants within the generalized gradient approximation (GGA) plus on-site Coulomb interaction (U) shows that the dominant AF exchange interaction is of ∼13.9 K along the a-axis with weak interchain coupling, in agreement with the experimental result of a quasi-1D spin-(1/2) chain system. The GGA+U calculations also predict that Li2Cu(WO4)2 is a charge transfer-type AF semiconductor with a direct band gap of 1.5 eV.

Magnetic and magnetocaloric properties of Dy5Pd2: role of magnetic irreversibility

In this report the origin of giant inverse magnetocaloric effect at low temperature region has been studied in cluster glass intermetallic compound Dy₅Pd₂. In this context the procedure to obtain reversible magnetocaloric effect using Maxwell’s relation has been described.

Persistent spin dynamics intrinsic to amplitude-modulated long-range magnetic order

An incommensurate elliptical helical magnetic structure in the frustrated coupled-spin-chain system FeTe(2)O(5)Br is surprisingly found to persist down to 53(3) mK (T/T(N)~1/200), according to neutron scattering and muon spin relaxation. In this state, finite spin fluctuations at T→0 are evidenced by muon depolarization, which is in agreement with specific-heat data indicating the presence of both gapless and gapped excitations. We thus show that the amplitude-modulated magnetic order intrinsically accommodates contradictory persistent spin dynamics and long-range order and can serve as a model structure to investigate their coexistence.