We present a combined neutron diffraction and bulk thermodynamic study of the natural mineral linarite ${\mathrm{PbCuSO}}_{4}(\mathrm{OH}{)}_{2}$, this way establishing the nature of the ground-state magnetic order. An incommensurate magnetic ordering with a propagation vector $\mathbit{k}=(0,0.186,\frac{1}{2})$ was found below ${T}_{N}=2.8\text{ }\text{ }\mathrm{K}$ in a zero magnetic field. The analysis of the neutron diffraction data yields an elliptical helical structure, where one component ($0.638{\ensuremath{\mu}}_{B}$) is in the monoclinic $ac$ plane forming an angle with the $a$ axis of 27(2)\ifmmode^\circ\else\textdegree\fi{}, while the other component ($0.833{\ensuremath{\mu}}_{B}$) 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.

Magnetic Frustration in a Quantum Spin Chain: The Case of Linarite PbCuSO 4 ( OH ) 2

We present a detailed study in the paramagnetic regime of the frustrated $s=1/2$ spin-compound linarite PbCuSO${}_{4}$(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 $\ensuremath{\sim}$7.6, $\ensuremath{\sim}$10.5, and $\ensuremath{\sim}$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 ${J}_{1}$-${J}_{2}$ spin model, our experimental data are described by various theoretical approaches, yielding values for the exchange interactions ${J}_{1}\ensuremath{\sim}\ensuremath{-}100$ K and ${J}_{2}$ $\ensuremath{\sim}$ 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 $\ensuremath{\alpha}={J}_{2}/|{J}_{1}|$ $\ensuremath{\approx}$ 0.36 of linarite closer to the one-dimensional 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 ${T}_{\mathrm{N}}$ $=$ 2.75(5) K, in agreement with the calculated exchange constants.

/pdf/magnetic-properties-and-exchange-integrals-of-the-frustrated-4ziblox346.pdf

Magnetic properties and exchange integrals of the frustrated chain cuprate linarite PbCuSO4(OH)2

It is generally difficult experimentally to distinguish magnetic multipolar orders in spin systems. Recently, it was proposed that the temperature dependence of the nuclear magnetic resonance relaxation rate $1/{T}_{1}$ can involve an indirect but clear signature of the field-induced spin nematic or multipolar Tomonaga-Luttinger (TL) liquid phase [M. Sato, T. Momoi, and A. Furusaki, Phys. Rev. B 79, 060406(R) (2009)]. In this paper, we evaluate accurately the field and temperature dependence of $1/{T}_{1}$ in spin-$\frac{1}{2}$ frustrated ${J}_{1}$-${J}_{2}$ chains combining field-theoretical techniques with numerical data. Our results demonstrate that isotherms of $1/{T}_{1}$ as a function of magnetic field also exhibit distinctive nonmonotonic behavior in spin nematic TL liquid, in contrast with the standard TL liquid in the spin-$\frac{1}{2}$ Heisenberg chain. The relevance of our results to quasi-one-dimensional edge-sharing cuprate magnets, such as ${\mathrm{LiCuVO}}_{4}$, is discussed.

Field and temperature dependence of NMR relaxation rate in the magnetic quadrupolar liquid phase of spin- 1 2 frustrated ferromagnetic chains

The discovery of magnetism by the ancient Greeks was enabled by the natural occurrence of lodestone -- a magnetized version of the mineral magnetite. Nowadays, natural minerals continue to inspire the search for novel magnetic materials with quantum-critical behavior or exotic ground states such as spin liquids. The recent surge of interest in magnetic frustration and quantum magnetism was largely encouraged by crystalline structures of natural minerals realizing pyrochlore, kagome, or triangular arrangements of magnetic ions. As a result, names like azurite, jarosite, volborthite, and others, which were barely known beyond the mineralogical community a few decades ago, found their way into cutting-edge research in solid-state physics. In some cases, the structures of natural minerals are too complex to be synthesized artificially in a chemistry lab, especially in single-crystalline form, and there is a growing number of examples demonstrating the potential of natural specimens for experimental investigations in the field of quantum magnetism. On many other occasions, minerals may guide chemists in the synthesis of novel compounds with unusual magnetic properties. The present review attempts to embrace this quickly emerging interdisciplinary field that bridges mineralogy with low-temperature condensed-matter physics and quantum chemistry.

Quantum Magnetism in Minerals

Magnetic and dielectric properties have been studied for single- and polycrystalline samples of PbCuSO 4 (OH) 2 with quasi-one-dimensional spin-1/2 chains composed of edge-sharing CuO 4 square planes called CuO 2 ribbon chains. The dielectric constant and polarization measurements indicate that a ferroelectric transition takes place simultaneously with magnetic transition at the Neel temperature T N ∼2.8 K. From the magnetization curves of the single crystalline sample at 2 K, spin flop transition is found at H c ∼2.5 T for the H ∥CuO 2 plane. On the basis of detailed magnetization and dielectric constant measurements, the possible magnetic structure and the origin of the ferroelectricity of the compound are discussed.

Multiferroic Behavior in the Quasi-One-Dimensional Frustrated Spin-1/2 System PbCuSO4(OH)2 with CuO2 Ribbon Chains

Zero-field susceptibility and specific heat of Pb[Cu(SO4)(OH)2] (linarite) single crystal were measured. In order to verify that linarite is a quasi-one-dimensional system with competing nearest-neighbour and next-nearest-neighbour in-chain exchange interaction (J1 ≈ –30 K, J2 ≈ 15 K), theoretical results based on electronic structure calculations within the LDA and a phenomenological modelling using the finite-temperature transfer-matrix method are taken into account. The possibility of various ground states is discussed in terms of the screened onsite repulsion Us: commensurate Neel or spin-Peierls phases versus incommensurate spiral states with acute or obtuse pitch angles. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Quasi-one-dimensional S=1/2 magnet Pb[Cu(SO4)(OH)2] frustration due to competing in-chain exchange

https://www2.cpfs.mpg.de/fplo/pub/PhysStatSol_3_220.pdf

Quasi-one-dimensional S = 1/2 magnet Pb[Cu(SO4)(OH)2]: frustration due to competing in-chain exchange

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Quasi-one-dimensional S=1/2 magnet Pb[Cu(SO4)(OH)2] frustration due to competing in-chain exchange

Quasi-one-dimensional S = 1/2 magnet Pb[Cu(SO4)(OH)2]: frustration due to competing in-chain exchange