Frustrated magnetic planes with intricate interaction pathways in the mineral langite Cu4(OH)6SO4 · 2H2O Stefan Lebernegg,1, ∗ Alexander A. Tsirlin,2, 3 Oleg Janson,4 G¨unther J. Redhammer,5 and Helge Rosner1, y 1Max Planck Institute for Chemical Physics of Solids, N¨othnitzerStr. 40, 01187 Dresden, Germany 2National Institute of Chemical Physics and Biophysics, 12618 Tallinn, Estonia 3Experimental Physics VI, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, 86135 Augsburg, Germany 4Institute of Solid State Physics, Technical University Vienna, Wiedner Hauptstr. 8{10/138, 1040 Vienna, Austria 5Department of Materials Sciences & Physics, University Salzburg, Hellbrunnerstr. 34, 5020 Salzburg, Austria (Dated: October 3, 2018) Magnetic and crystallographic properties of the mineral langite Cu4(OH)6SO4 ·2H2O are reported. 1 2+ Its layered crystal structure features a peculiar spatial arrangement of spin- 2 Cu ions that arises from a combination of corner- and edge-sharing chains. Experimentally, langite orders antiferromagnetically at TN ' 5:7 K as revealed by magnetization and specific heat measurements. Despite this very low energy scale of the magnetic transition, langite features significantly stronger couplings on the order of 50-70 K. Half of the Cu2+ spins are weakly coupled and saturate around 12 T, where the magnetization reaches 0.5 µB /Cu. These findings are rationalized by density-functional band-structure calculations suggesting a complex interplay of frustrated exchange couplings in the magnetic planes. A simplified model of coupled magnetic sublattices explains the experimental features qualitatively. To start from reliable structural data, the crystal structure of langite in the 100{280 K temperature range has been determined by single-crystal x-ray diffraction, and the hydrogen positions were refined computationally. PACS numbers: 75.50.Ee,75.10.Jm,71.20.Ps,61.50.Ks I. INTRODUCTION of spin chains, those with edge- and corner-sharing ge- ometries, are placed next to each other within one material. Spin systems comprising several magnetic Low-dimensional magnets show unique diversity of sublattices with different dimensionalities and energy crystal structures and associated spin lattices, where a scales may have very unusual low-temperature proper- plethora of quantum phenomena can be observed.1{3 The ties. When two sublattices are weakly coupled, they physics of quantum spin chains has been actively ex- are, to a certain extent, independent, hence two mag- plored in Cu2+ compounds featuring chains of corner- or netic transitions manifesting the ordering within each edge-sharing CuO plaquette units. The corner-sharing 4 of the sublattices could be observed. On the other geometry results in uniform spin chains with a negligi- hand, the ordering within one sublattice will neces- bly small second-neighbor coupling, as in Sr CuO ,4,5 2 3 sarily depend on the other sublattice, because three- AgCuVO 6 and KCuMoO (OH).7 The edge-sharing ge- 4 4 dimensional (3D) long-range order typically involves in- ometry is by far more common. It gives rise to com- teractions between the sublattices. Unusual manifesta- peting nearest-neighbor and next-nearest-neighbor cou- tions of quantum order-from-disorder have been observed plings, where the former (J ) is typically ferromagnetic, 1 in Sr Cu O Cl 21{25 featuring interpenetrating square while the latter (J ) is antiferromagnetic. Such J − J 2 3 4 2 2 1 2 lattices with drastically different exchange couplings. In frustrated spin chains develop incommensurate spin cor- CuP O , where spins, arranged on a planar square lat- relations and helical magnetic order,8,9 although few in- 2 6 tice, coexist with uniform spin chains, very strong spin stances of ferromagnetic intrachain spin order are known fluctuations are observed even below the N´eeltemper- as well.10,11 The helical spin arrangement observed in 12 13 ature TN , and the value of TN is unusually low for a simple binary compounds CuCl2 and CuBr2 and in 26 14 quasi-two-dimensional (2D) antiferromagnet. The co- arXiv:1506.08562v3 [cond-mat.str-el] 9 Feb 2017 more complex materials like linarite PbCu(OH) SO , 2 4 existence of corner- and edge-sharing Cu2+ chains could all being frustrated J − J spin chains, may trigger elec- 1 2 be even more interesting because of the different nature tric polarization induced by the magnetic order, thus of spin correlations, which are expected to be antiferro- leading to multiferroic behavior.15{17 Additionally, small magnetic collinear and helical, for the corner- and edge- interactions beyond the isotropic Heisenberg model lead sharing chains, respectively. to an intricate magnetic phase diagram, including mul- tipolar (three-magnon) phases, which has been studied The respective magnetic ground state of these com- 18 recently. However, the complex interplay of frustration pounds depends very subtly on the interplay of vari- and anisotropy needs further investigations on different ous exchange integrals, including possible frustration and 19,20 systems as, e.g., LiCuVO4. strong quantum fluctuations. In particular, in edge- One may naturally ask what happens when two types sharing geometries (with Cu{O{Cu bond angles near 2 90◦) the leading exchange integrals and, thus, the actual II. METHODS magnetic model are often difficult to establish due to a pronounced dependency of the exchange on the struc- All experiments have been performed on a natural sam- tural details: Small changes of bond angles or minor ple (Fig.1) of langite from the Podlipa and Reinera mine, changes of the local Cu{O environment, e.g. by attached Lubietova, Slovakia. The sample quality was first thor- 27,28 H-atoms, may even swap the ground state qualita- oughly controlled by laboratory powder X-ray diffraction tively. Owing to the high complexity of the structure- (XRD) (Huber G670 Guinier camera, CuKα 1 radiation, properties relation in these compounds, the combination ImagePlate detector, 2θ = 3 − 100◦ angle range). of experimental investigations with theoretical methods Single-crystal X-ray diffraction between 100 and 280 K appeared to be very successful to disentangle the com- was performed on a Bruker SMART APEX CCD- plicated interplay. In particular, in recent years den- diffractometer equipped with a Cryosteam liquid nitro- sity functional calculations have developed to a valuable gen low-temperature device. A single crystal, selected on tool, establishing accurate magnetic models on micro- 13,29,30 the basis of its optical properties (sharp extinctions, reg- scopic grounds, even for involved geometries like ular shape and homogeneity in color) was glued on top of coupled edge-sharing chains or various magnetic sublat- a glass capillary (0.1 mm). Intensity data were collected tices in a single compound. with graphite-monochromatized MoKα radiation (50 kV, 30 mA). The crystal-to-detector distance was 40 mm and The coexistence of the edge- and corner-sharing the detector was positioned at −28◦ 2Θ using an !-scan geometries is rather common for Cu2+ minerals. In mode strategy at four different '-positions (0◦, 90◦, 180◦ antlerite31 and szenicsite,32 one edge-sharing chain and 270◦). 630 frames with ∆! = 0.3◦ were acquired for is encompassed by two corner-sharing chains that each run. The 3D data were integrated and corrected together form a three-leg spin ladder. The edge- for Lorentz polarization and background effects using and corner-sharing chains can also form infinite the APEX2 software (Bruker { Nonius, 2004). Struc- layers, as in deloryite Cu (UO )(MoO ) (OH) ,33 4 2 4 2 6 ture solution (using Patterson methods) and subsequent derriksite Cu (UO )(SeO ) (OH) ,34 niedermayrite 4 2 3 2 6 weighted full-matrix least-square refinements on F 2 were Cu Cd(SO ) (OH) ,35 and langite Cu (OH) SO ·2H O. 4 4 2 6 4 6 4 2 done with SHELXL-9738 as implemented in the program The crystal structure of the latter mineral is shown in suite WinGX 1.64.39 Fig.1. Layers of alternating edge- and corner-sharing All further experiments were performed on a powder chains (Fig.1, right) are well separated by SO 4 sulphate groups and water molecules. A somewhat similar sample since the natural crystals are very small and frag- structure without water molecules has been reported ile as well as strongly intergrown, preventing us from col- 36,37 lecting a sufficient amount of single crystallites for mag- for the mineral brochantite Cu4(OH)6SO4 that, however, features a much smaller interlayer separation, netic and specific heat measurements. Magnetization hence substantial interlayer couplings can be expected. measurements were done on a Quantum Design (QD) In this paper, we focus on the magnetism of langite, SQUID MPMS in magnetic fields up to 5 T and using the where individual structural planes should be very weakly vibrating sample magnetometer (VSM) setup of Quan- coupled magnetically and sufficiently pure natural tum Design PPMS up to 14 T in the temperature range samples of this mineral are available. of 1.6{300 K. Heat capacity data were acquired with the QD PPMS in fields up to 14 T. We also show that, in contrast to our expectations, in- Electronic structure calculations within density func- dividual structural chains in this material cannot be con- tional theory (DFT) were performed with the full- 40 sidered as weakly coupled magnetic chains. On the other potential local-orbital code FPLO9.07-41 on the 100 K hand, two sublattices formed by the structural chains of crystal structure in combination with the local density 41 either type, can be distinguished in the overall very in- approximation (LDA), generalized gradient approxi- 42 43,44 tricate spin lattice. These sublattices reveal drastically mation (GGA) and the DFT+U method. A 4×4×4 different magnetic couplings and facilitate the description k-mesh was employed for LDA and GGA runs while su- of the complex low-temperature magnetism on a qualita- per cells used for DFT+U calculations were computed tive microscopic level.