Frustrated cuprate route from antiferromagnetic to ferromagnetic spin-1/2 Heisenberg chains: Li2ZrCuO4 as a missing link near the quantum critical point

Frustrated Extended Bose-Hubbard Model and Deconfined Quantum Critical Points with Optical Lattices at the Antimagic Wavelength

The study of geometrically frustrated many-body quantum systems is of central importance to uncover novel quantum mechanical effects. We design a scheme where ultracold bosons trapped in a one-dimensional state-dependent optical lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of the Hamiltonian parameters based on Cesium atoms, further show large tunability of contact and nearest-neighbor interactions. For pure contact repulsion, we discover the presence of two phases peculiar to frustrated quantum magnets: the bond-order-wave insulator with broken inversion symmetry and a chiral superfluid. When the nearest-neighbor repulsion becomes sizable, a further density-wave insulator with broken translational symmetry can appear. We show that the phase transition between the two spontaneously symmetry-broken phases is continuous, thus representing a one-dimensional deconfined quantum critical point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. Our results provide a solid ground to unveil the novel quantum physics induced by the interplay of nonlocal interactions, geometrical frustration, and quantum fluctuations.

Realizing Persistent Zero Area Compressibility over a Wide Pressure Range in Cu2 GeO4 by Microscopic Orthogonal-Braiding Strategy

Zero area compressibility (ZAC) is an extremely rare mechanical response that exhibits an invariant two-dimensional size under hydrostatic pressure. All known ZAC materials are constructed from units in two dimensions as a whole. Here, we propose another strategy to obtain the ZAC by microscopically orthogonal-braiding one-dimensional zero compressibility strips. Accordingly, ZAC is identified in a copper-based compound with a planar [CuO4 ] unit, Cu2 GeO4 , that possesses an area compressibility as low as 1.58(26) TPa-1 over a wide pressure range from ≈0 GPa to 21.22 GPa. Based on our structural analysis, the subtle counterbalance between the shrinkage of [CuO4 ] and the expansion effect from the increase in the [CuO4 ]-[CuO4 ] dihedral angle attributes to the ZAC response. High-pressure Raman spectroscopy, in combination with first-principles calculations, shows that the electron transfer from in-plane bonding dx 2 -y 2 to out-of-plane nonbonding dz 2 orbitals within copper atoms causes the counterintuitive extension of the [CuO4 ]-[CuO4 ] dihedral angle under pressure. Our study provides an understanding on the pressure-induced structural evolution of copper-based oxides at an electronic level and facilitates a new avenue for the exploration of high-dimensional anomalous mechanical materials.

Quantum phase transitions in skewed ladder systems

In this brief review, we introduce a new spin ladder system called skewed spin ladders and discuss the exotic quantum phases of this system. The spin ladders studied are the 5/7, 3/4 and 3/5 systems corresponding to alternately fused 5 and 7 membered rings; 3 and 4 membered rings; and 3 and 5 membered rings. These ladders show completely different behaviour as the Hamiltonian model parameter is changed. When the Hamiltonian parameter is increased the 5/7 ladder switches from an initial singlet ground state to progressively higher spin ground state and then to a reentrant singlet state before finally settling to the highest spin ground state whose spin equals the number of unit cells in the system. The 3/4 ladder goes from a singlet ground state to a high spin ground state with each unit cell contributing spin 1 to the state, as the model parameter is increased. The 3/5 ladder shows a singlet ground state for small parameters and high spin ground state for intermediate values of the parameter and for still higher parameters, a reentrant singlet ground state. They can also show interesting magnetization plateaus as illustrated by studies on a specific spin ladder.

Quantum Phase Diagram of a Frustrated Spin-1/2 Ferro-Antiferromagnetic Normal Ladder

In this work, we consider a frustrated two-leg spin-1/2 ladder composed of Heisenberg ferromagnetic and antiferromagnetic spin-1/2 chains, and nearest spins from different legs interact via Heisenberg type rung exchange interactions that can be either ferromagnetic or antiferromagnetic in nature. The competing exchange interactions in the system lead to five different quantum phases like ferromagnetic, non-collinear ferrimagnetic (NCF), m - 1 / 4 ${m - 1/4}$ , antiferromagnetic and dimer phases. The  quantum phase diagram is constructed for the Heisenberg spin-1/2 model and the phases are characterized using the correlation functions which are calculated by the density matrix renormalization group method. We also analyze the  stability of m - 1 / 4 ${m - 1/4}$ phase and calculate the pitch angle θ ${\left( \theta \right)}$ in the NCF phase.

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.

Antiferromagnetic and ferromagnetic spintronics and the role of in-chain and inter-chain interaction on spin transport in the Heisenberg ferromagnet

Spin-transport and current-induced torques in ferromagnet heterostructures given by a ferromagnetic domain wall are investigated. Furthermore, the continuum spin conductivity is studied in a frustrated spin system given by the Heisenberg model with ferromagnetic in-chain interaction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_1<0$$\end{document}J1<0 between nearest neighbors and antiferromagnetic next-nearest-neighbor in-chain interaction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_2>0$$\end{document}J2>0 with aim to investigate the effect of the phase diagram of the critical ion single anisotropy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_c$$\end{document}Dc as a function of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_2$$\end{document}J2 on conductivity. We consider the model with the moderate strength of the frustrating parameter such that in-chain spin-spin correlations that are predominantly ferromagnetic. In addition, we consider two inter-chain couplings \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_{\perp ,y}$$\end{document}J⊥,y and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_{\perp ,z}$$\end{document}J⊥,z, corresponding to the two axes perpendicular to chain where ferromagnetic as well as antiferromagnetic interactions are taken into account.

Quantum phases and thermodynamics of a frustrated spin-1/2 ladder with alternate Ising-Heisenberg rung interactions

We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either isotropicS-type or discrete anisotropicσ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, bothSandσ-type of spins are anti-ferromagnetically aligned with each other, two nearestSspins along the rung form an anisotropic singlet bond whereas two nearestσspins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like specific heatC_v(T), magnetic susceptibilityχ(T) and thermal entropyS(T) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed fromχ(T) andC_v(T) curves.

Signatures of a magnetic field-induced unconventional nematic liquid in the frustrated and anisotropic spin-chain cuprate LiCuSbO4

Modern theories of quantum magnetism predict exotic multipolar states in weakly interacting strongly frustrated spin-1/2 Heisenberg chains with ferromagnetic nearest neighbor (NN) inchain exchange in high magnetic fields. Experimentally these states remained elusive so far. Here we report strong indications of a magnetic field-induced nematic liquid arising above a field of ~13 T in the edge-sharing chain cuprate LiSbCuO₄ ≡ LiCuSbO₄. This interpretation is based on the observation of a field induced spin-gap in the measurements of the ⁷Li NMR spin relaxation rate T ₁^-1 as well as a contrasting field-dependent power-law behavior of T ₁^-1 vs. T and is further supported by static magnetization and ESR data. An underlying theoretical microscopic approach favoring a nematic scenario is based essentially on the NN XYZ exchange anisotropy within a model for frustrated spin-1/2 chains and is investigated by the DMRG technique. The employed exchange parameters are justified qualitatively by electronic structure calculations for LiCuSbO₄.

Numerical study of incommensurate and decoupled phases of spin-1/2 chains with isotropic exchange J1, J2 between first and second neighbors

The spin-1/2 chain with isotropic exchange J1, J2 > 0 between first and second neighbors is frustrated for either sign of J1 and has a singlet ground state (GS) for J1/J2 ⩾ -4. Its rich quantum phase diagram supports gapless, gapped, commensurate (C), incommensurate (IC) and other phases. Critical points J1/J2 are evaluated using exact diagonalization and density matrix renormalization group calculations. The wave vector qG of spin correlations is related to GS degeneracy and obtained as the peak of the spin structure factor S(q). Variable qG indicates IC phases in two J1/J2 intervals, [-4, - 1.24] and [0.44, 2], and a C-IC point at J1/J2 = 2. The decoupled C phase in [-1.24, 0.44] has constant qG = π/2, nondegenerate GS, and a lowest triplet state with broken spin density on sublattices of odd and even numbered sites. The lowest triplet and singlet excitations, E m and Eσ, are degenerate in finite systems at specific frustration J1/J2. Level crossing extrapolates in the thermodynamic limit to the same critical points as qG. The S(q) peak diverges at qG = π in the gapless phase with J1/J2 > 4.148 and quasi-long-range order (QLRO(π)). S(q) diverges at ±π/2 in the decoupled phase with QLRO(π/2), but is finite in gapped phases with finite-range correlations. Numerical results and field theory agree at small J2/J1 but disagree for the decoupled phase with weak exchange J1 between sublattices. Two related models are summarized: one has an exact gapless decoupled phase with QLRO(π/2) and no IC phases; the other has a single IC phase without a decoupled phase in between.

Observation of S = 1/2 quasi-1D magnetic and magneto-dielectric behavior in a cubic SrCuTe2O6

We investigate the magnetic, thermal, and dielectric properties of SrCuTe2O6, which is isostructural to PbCuTe2O6, a recently found, Cu-based 3D frustrated magnet with a corner-sharing triangular spin network having dominant first and second nearest neighbor (nn) couplings (Koteswararao et al 2014 Phys. Rev. B 90 035141). Although SrCuTe2O6 has a structurally similar spin network, the magnetic data exhibit the characteristic features of a typical quasi-1D magnet, which mainly resulted from the magnetically dominant third nn coupling, uniform chains. The magnetic properties of this system are studied via magnetization (M), heat capacity (C p ), dielectric constant ([Formula: see text]), and measurements along with ab initio band structure calculations. The magnetic susceptibility [Formula: see text] data show a broad maximum at 32 K and the system orders at low temperatures [Formula: see text] K and [Formula: see text] K, respectively. The analysis of the [Formula: see text] data gives an intra-chain coupling, [Formula: see text], to be about  ≈  -  42 K with non-negligible frustrated inter-chain couplings ([Formula: see text] and [Formula: see text]). The hopping parameters obtained from the LDA band structure calculations also suggest the presence of coupled uniform chains. The observation of simultaneous anomalies in [Formula: see text] at [Formula: see text] and [Formula: see text] suggests the presence of a magneto-dielectric effect in SrCuTe2O6. A magnetic phase diagram is also built based on the M, C p , and [Formula: see text] results.

Structural and magnetic properties of the low-dimensional fluoride β-FeF3(H2O)2·H2O

We have reinvestigated the crystal structure of the low-dimensional fluoride β-FeF₃(H₂O)₂·H₂O using high resolution neutron and X-ray diffraction data.

Spin-flop and antiferromagnetic phases of the ferromagnetic half-twist ladder compounds Ba3Cu3In4O12 and Ba3Cu3Sc4O12

The title compounds have dominant ferromagnetic exchange interactions within one-dimensional (1D) half-twist ladders of s = 1/2 Cu(2+) ions and antiferromagnetic (AFM) interactions between ladders, leading to ordered 3D phases at temperatures below 20 K. Here we show that a microscopic 1D model of the paramagnetic (PM) phase combined with a phenomenological model based on sublattice magnetization describes the observed temperature and field dependent magnetism. The model identifies AFM, spin-flop and PM phases whose boundaries have sharp features in the experimental magnetization M(T,H) and specific heat C(P)(T,H). Exact diagonalization of the 1D model, possible for 24 spins due to special structural features of half-twist ladders, yields the magnetization and spin susceptibility of the PM phase. AFM interactions between ladders are included at the mean-field level using the field, H(AF), obtained from modelling the ordered phases. Isotropic exchange J1 =- 135 K and g-tensor g = 2.1 within ladders, plus exchange and anisotropy fields H(AF) and H(A), describe the ordered phases and are almost quantitative for the PM phase.

Ca(2)Y(2)Cu(5)O(10): the first frustrated quasi-1D ferromagnet close to criticality

Ca(2)Y(2)Cu(5)O(10) is built up from edge-shared CuO(4) plaquettes forming spin chains. From inelastic neutron scattering data we extract an in-chain nearest-neighbor exchange J(1)≈-170  K and the frustrating next-neighbor J(2)≈32  K interactions, both significantly larger than previous estimates. The ratio α=|J(2)/J(1)|=0.19±0.01 places the system close to the critical point α(c)=0.25 of the J(1)-J(2) chain but in the 1D ferromagnetic regime. We establish that the vicinity to criticality only marginally affects the dispersion and coherence of the spin-wave-like magnetic excitations but instead results in a dramatic T dependence of high-energy Zhang-Rice singlet excitation intensities.

Quantum spin liquid in frustrated one-dimensional LiCuSbO4

A quantum magnet, LiCuSbO4, with chains of edge-sharing spin-1/2 CuO6 octahedra is reported. While short-range order is observed for T<10  K, no zero-field phase transition or spin freezing occurs down to 100 mK. Specific heat indicates a distinct high-field phase near the 12 T saturation field. Neutron scattering shows incommensurate spin correlations with q=(0.47±0.01)π/a and places an upper limit of 70  μeV on any spin gap. Exact diagonalization of 16-spin easy-plane spin-1/2 chains with competing ferro- and antiferromagnetic interactions (J1=-75  K, J2=34  K) accounts for the T>2  K data.

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

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.

Chiral order and electromagnetic dynamics in one-dimensional multiferroic cuprates

We show by unbiased numerical calculations that the ferromagnetic nearest-neighbor exchange interaction stabilizes a vector spin chiral order against the quantum fluctuation in a frustrated spin-1/2 chain relevant to multiferroic cuprates, LiCu2O2 and LiCuVO4. Our realistic semiclassical analyses for LiCu2O2 resolve controversies on the helical magnetic structure and unveil the pseudo-Nambu-Goldstone modes as the origin of experimentally observed electromagnons.

Spiral correlations in frustrated one-dimensional spin-1/2 Heisenberg J1-J2-J3 ferromagnets

We use the coupled cluster method for infinite chains complemented by exact diagonalization of finite periodic chains to discuss the influence of a third-neighbor exchange J(3) on the ground state of the spin-½ Heisenberg chain with ferromagnetic nearest-neighbor interaction J(1) and frustrating antiferromagnetic next-nearest-neighbor interaction J(2). A third-neighbor exchange J(3) might be relevant to describe the magnetic properties of the quasi-one-dimensional edge-shared cuprates, such as LiVCuO(4) or LiCu(2)O(2). In particular, we calculate the critical point J(2)(c) as a function of J(3), where the ferromagnetic ground state gives way for a ground state with incommensurate spiral correlations. For antiferromagnetic J(3) the ferro-spiral transition is always continuous and the critical values J(2)(c) of the classical and the quantum model coincide. On the other hand, for ferromagnetic J3 is < or approximately equal to -(0.01...0.02)|J1|. the critical value J(2)(c) of the quantum model is smaller than that of the classical model. Moreover, the transition becomes discontinuous, i.e. the model exhibits a quantum tricritical point. We also calculate the height of the jump of the spiral pitch angle at the discontinuous ferro-spiral transition.

Interaction between the chain and ladder subsystems in (Ca,Sr,La)(14)Cu(24)O(41) compounds

We investigate the influence of structural modulations on the electronic properties of incommensurate (Ca,Sr,La)(14)Cu(24)O(41) compounds by band structure calculations based on density functional theory and the local density approximation (LDA). Using a supercell approach with ten CuO(2) chain and seven Cu(2)O(3) ladder segments, we take into account the major effects of the structural incommensurability. We find that the LDA electronic states show very little response to these modulations. The coupling between the electronic and structural degrees of freedom, hence, can be well described in terms of two independent subsystems. The incommensurate charge density waves (CDWs) in the chains and the ladders are formed independently of each other.

Incommensurate spin-density modulation in a copper oxide chain compound with commensurate charge order

Neutron diffraction has been used to determine the magnetic structure of Na8Cu5O10, a stoichiometric compound containing chains based on edge-sharing CuO4 plaquettes. The chains are doped with 2/5 hole per Cu site and exhibit long-range commensurate charge order with an onset well above room temperature. Below TN=23 K, the neutron data indicate long-range collinear magnetic order with a spin-density modulation whose propagation vector is commensurate along, and incommensurate perpendicular to, the chains. Competing interchain exchange interactions are discussed as a possible origin of the incommensurate magnetic order.

Magnetic ground state of coupled edge-sharing CuO2 spin chains

By means of density functional theory, we investigate the magnetic ground state of edge-sharing CuO2 spin chains, as found in the (La,Ca,Sr)14Cu24O41 system, for instance. Our data rely on spin-polarized electronic structure calculations including on-site interaction [local density approximation plus the multiorbital mean-field Hubbard model (LDA+U)] and an effective model for the interchain coupling. Strong doping dependence of the magnetic order is characteristic for edge-sharing CuO2 spin chains. We determine the ground state magnetic structure as function of the spin-chain filling and quantify the competing exchange interactions.