Kagome Planes Research Articles

Selectively doping barlowite for quantum spin liquid: A first-principles study

Barlowite $Cu_4(OH)_6FBr$ is a newly found mineral containing $Cu^{2+}$ kagome planes. Despite similarities in many aspects to Herbertsmithite $Cu_3Zn(OH)_6Cl_2$, the well-known quantum spin liquid (QSL) candidate, intrinsic Barlowite turns out not to be a QSL, possibly due to the presence of $Cu^{2+}$ ions in between kagome planes that induce interkagome magnetic interaction [PRL, 113, 227203 (2014)]. Using first-principles calculation, we systematically study the feasibility of selective substitution of the interkagome Cu ions with isovalent nonmagnetic ions. Unlike previous speculation of using larger dopants, such as $Cd^{2+}$ and $Ca^{2+}$, we identify the most ideal stoichiometric doping elements to be Mg and Zn in forming $Cu_3Mg(OH)_6FBr$ and $Cu_3Zn(OH)_6FBr$ with the highest site selectivity and smallest lattice distortion. The equilibirium anti-site disorder in Mg/Zn- doped Barlowite is estimated to be one order of magnitude lower than that in Herbertsmithite. The single-electron band structure and orbital component analysis show that the proposed selective doping effectively mitigates the difference between Barlowite and Herbertsmithite.

A two-dimensional spin liquid in quantum kagome ice

Actively sought since the turn of the century, two-dimensional quantum spin liquids (QSLs) are exotic phases of matter where magnetic moments remain disordered even at zero temperature. Despite ongoing searches, QSLs remain elusive, due to a lack of concrete knowledge of the microscopic mechanisms that inhibit magnetic order in materials. Here we study a model for a broad class of frustrated magnetic rare-earth pyrochlore materials called quantum spin ices. When subject to an external magnetic field along the [111] crystallographic direction, the resulting interactions contain a mix of geometric frustration and quantum fluctuations in decoupled two-dimensional kagome planes. Using quantum Monte Carlo simulations, we identify a set of interactions sufficient to promote a groundstate with no magnetic long-range order, and a gap to excitations, consistent with a Z2 spin liquid phase. This suggests an experimental procedure to search for two-dimensional QSLs within a class of pyrochlore quantum spin ice materials.

Magnetic properties of a family of quinternary oxalates

We report on the magnetic properties of four isomorphous compounds of a family of quinternary oxalates down to 60 mK. In all these materials, the magnetic FeII ions with a strong magneto-crystalline anisotropy form a distorted kagome lattice, topologically equivalent to a perfect kagome one if nearest-neighbor interactions only are considered. All the compounds order at low temperature in an antiferromagnetic arrangement with magnetic moments at 120{\deg}. A remarkable magnetic behavior emerges below the N\'eel temperature in three compounds (with inter-kagome-layer Zr, Sn, Fe but not with Al): the spin anisotropy combined with a low exchange path network connectivity lead to domain walls intersecting the kagome planes through strings of free spins. These produce an unfamiliar slow spin dynamics in the ordered phase observed by AC susceptibility, evolving from exchange-released spin-flips towards a cooperative behavior on decreasing the temperature.

Gapless spin liquid ground state in the S = 1/2 vanadium oxyfluoride kagome antiferromagnet [NH4]2[C7H14N][V7O6F18

The vanadium oxyfluoride [NH(4)](2)[C(7)H(14)N][V(7)O(6)F(18)] (DQVOF) is a geometrically frustrated magnetic bilayer material. The structure consists of S = 1/2 kagome planes of V(4+) d(1) ions with S = 1 V(3+) d(2) ions located between the kagome layers. Muon spin relaxation measurements demonstrate the absence of spin freezing down to 40 mK despite an energy scale of 60 K for antiferromagnetic exchange interactions. From magnetization and heat capacity measurements we conclude that the S = 1 spins of the interplane V(3+) ions are weakly coupled to the kagome layers, such that DQVOF can be viewed as an experimental model for S = 1/2 kagome physics, and that it displays a gapless spin liquid ground state.

Evidence for an internal-field-induced spin-flop configuration in the extended kagome YBaCo4O7

The spin structure and spin dynamics in the extended kagome frustrated antiferromagnet YBaCo${}_{4}$O${}_{7}$ have been investigated using zero field and low applied field ${}^{59}$Co NMR. The YBaCo${}_{4}$O${}_{7}$ lattice is made up of bipyramid Co-ion units that form alternating planes of edge-sharing spin triangles and corner-sharing kagome spin triangles in an unusual exchange topology. Our low-temperature spin configuration results, based on hyperfine field orientations, are consistent with those from neutron scattering for the triangle spins which order antiferromagnetically below 106 K. For the kagome spins at low temperatures the static hyperfine fields are found to be oriented orthogonal to those of the triangle spins in a spin-flop configuration that is in disagreement with the neutron findings. Nuclear relaxation rate measurements made as a function of temperature show that inhomogeneous dynamic spin disorder occurs in kagome planes well below the N\'eel point.

Low-energy spin dynamics of the s = 1/2 kagome system herbertsmithite

The low-energy (ϵ = ħω < 1 meV), low-temperature (T = 0.05 K) spin dynamics of the s = 1/2 kagome candidate herbertsmithite are probed in the presence of magnetic fields up to 2.5 T. The zero-field spectra reveal a very weak continuum of scattering at T = 10 K and a broad inelastic peak centred at ϵmax = 0.2 meV at lower temperatures, T < 1 K. The broad peak is found to be strongly damped, with a liquid-like structure factor implying correlations at length scales up to r = 6 Å. The field dependence of the peak appears to follow the Zeeman splitting of s = 1/2 excitations, consistent with the weakly split ‘doublets’ observed in low-temperature specific heat. A possible explanation of these observations is a short-range correlated state involving defect spins between the kagome planes and moments in the kagome layers.

Topological phases in layered pyrochlore oxide thin films along the [111] direction

We theoretically study a multi-band Hubbard model of pyrochlore oxides of the form A$_2$B$_2$O$_7$, where B is a heavy transition metal ion with strong spin-orbit coupling, in a thin film geometry orientated along the [111] direction. Along this direction, the pyrochlore lattice consists of alternating kagome and triangular lattice planes of B ions. We consider a single kagome layer, a bilayer, and the two different trilayers. As a function of the strength of the spin-orbit coupling, the direct and indirect $d$-orbital hopping, and the band filling, we identify a number of scenarios where a non-interacting time-reversal invariant Z$_2$ topological phase is expected and we suggest some candidate materials. We study the interactions in the half-filled $d$-shell within Hatree-Fock theory and identify parameter regimes where a zero magnetic field Chern insulator with Chern number $\pm1$ can be found. The most promising geometries for topological phases appear to be the bilayer which supports both a Z$_2$ topological insulator and a Chern insulator, and the triangular-kagome-triangular trilayer which supports a relatively robust Chern insulator phase.

High-Field Magnetism of the S=5/2 Kagome-Lattice Antiferromagnet KFe3(OH)6(SO4)2 for the Magnetic Field in the Kagome-Plane

We have performed electron spin resonance (ESR) and magnetization measurements on single crystals of K-Fe-jarosite along the a-axis (in the kagome-plane). We have calculated the resonance branches and the magnetization curve using a spin Hamiltonian including the interlayer exchange and the Dzyaloshinsky-Moriya (DM) interactions. By putting the same parameter values for the analyses along the c-axis (normal to the kagome plane), the calculated results show satisfactory agreement with the experimental ones. As a result, we have successfully explained all the experimental results with one set of the intra- and the inter-plane exchange and the DM interaction parameters.

Exotic Magnetism of NovelS= 1 Kagome Lattice Antiferromagnet KV3Ge2O9

Single crystals of the novel vanadium oxide compound KV 3 Ge 2 O 9 have been synthesized. This compound has a hexagonal unit cell with the space group P 6 3 / m m c . Its lattice constants are a = 5.8624(4) A and c = 13.7094(7) A. KV 3 Ge 2 O 9 contains layers of edge-shared VO 6 octahedra, where V 3+ ions with an S = 1 spin form kagome lattice layers separated by double layers of GeO 4 tetrahedra. The magnetic susceptibility shows a broad maximum at approximately 70 K, suggesting that magnetic transition is suppressed in spite of the presence of strong antiferromagnetic interactions. Below approximately 20 K, the susceptibility under a magnetic field perpendicular to the kagome plane steeply drops toward zero, while the in-plane susceptibility diverges with reduction in temperature.

Refining the Spin Hamiltonian in the Spin-12Kagome Lattice AntiferromagnetZnCu3(OH)6Cl2Using Single Crystals

We report thermodynamic measurements of the S=1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2, a promising candidate system with a spin-liquid ground state. Using single crystal samples, the magnetic susceptibility both perpendicular and parallel to the kagome plane has been measured. A small, temperature-dependent anisotropy has been observed, where χ(z)/χ(p)>1 at high temperatures and χ(z)/χ(p)<1 at low temperatures. Fits of the high-temperature data to a Curie-Weiss model also reveal an anisotropy. By comparing with theoretical calculations, the presence of a small easy-axis exchange anisotropy can be deduced as the primary perturbation to the dominant Heisenberg nearest neighbor interaction. These results have great bearing on the interpretation of theoretical calculations based on the kagome Heisenberg antiferromagnet model to the experiments on ZnCu3(OH)6Cl2.

Domain-Wall Spin Dynamics in Kagome Antiferromagnets

We report magnetization and neutron scattering measurements down to 60 mK on a new family of Fe based kagome antiferromagnets, in which a strong local spin anisotropy combined with a low exchange path network connectivity lead to domain walls intersecting the kagome planes through strings of free spins. These produce unfamiliar slow spin dynamics in the ordered phase, evolving from exchange-released spin flips towards a cooperative behavior on decreasing the temperature, probably due to the onset of long-range dipolar interaction. A domain structure of independent magnetic grains is obtained that could be generic to other frustrated magnets.

Spin-liquid ground state in the frustrated kagome antiferromagnet MgCu3(OH)6Cl2

We report muSR experiments on Mg{x}Cu{4-x}(OH)6Cl2 with x \sim 1, a new material isostructural to Herbertsmithite exhibiting regular kagome planes of spin 1/2 (Cu^{2+}), and therefore a candidate for a spin liquid ground state. We evidence the absence of any magnetic ordering down to 20 mK (\sim J/10^4). We investigate in detail the spin dynamics on well characterized samples in zero and applied longitudinal fields and propose a low T defect based interpretation to explain the unconventional dynamics observed in the quantum spin liquid phase.

Local spin susceptibility of theS=12kagome lattice in ZnCu3(OD)6Cl2

We report single-crystal 2-D NMR investigation of the nearly ideal spin S=1/2 kagome lattice ZnCu3(OD)6Cl2. We successfully identify 2-D NMR signals originating from the nearest-neighbors of Cu2+ defects occupying Zn sites. From the 2-D Knight shift measurements, we demonstrate that weakly interacting Cu2+ spins at these defects cause the large Curie-Weiss enhancement toward T=0 commonly observed in the bulk susceptibility data. We estimate the intrinsic spin susceptibility of the kagome planes by subtracting defect contributions, and explore several scenarios.

Dzyaloshinskii-Moriya interaction and spin reorientation transition in the frustrated kagome lattice antiferromagnet

Magnetization, specific heat, and neutron scattering measurements were performed to study a magnetic transition in jarosite, a spin-5/2 kagome lattice antiferromagnet. When a magnetic field is applied perpendicular to the kagome plane, magnetizations in the ordered state show a sudden increase at a critical field H_c, indicative of the transition from antiferromagnetic to ferromagnetic states. This sudden increase arises as the spins on alternate kagome planes rotate 180 degrees to ferromagnetically align the canted moments along the field direction. The canted moment on a single kagome plane is a result of the Dzyaloshinskii-Moriya interaction. For H < H_c, the weak ferromagnetic interlayer coupling forces the spins to align in such an arrangement that the canted components on any two adjacent layers are equal and opposite, yielding a zero net magnetic moment. For H > H_c, the Zeeman energy overcomes the interlayer coupling causing the spins on the alternate layers to rotate, aligning the canted moments along the field direction. Neutron scattering measurements provide the first direct evidence of this 180-degree spin rotation at the transition.

Classical topological order in kagome ice

We examine the onset of classical topological order in a nearest neighbour kagome icemodel. Using Monte Carlo simulations, we characterize the topological sectors of theground state using a nonlocal cut measure which circumscribes the toroidal geometry of thesimulation cell. We demonstrate that simulations which employ global loop updates thatare allowed to wind around the periodic boundaries cause the topological sector tofluctuate, while restricted local loop updates freeze the simulation into one topologicalsector. The freezing into one topological sector can also be observed in the susceptibility ofthe real magnetic spin vectors projected onto the kagome plane. The ability of thesusceptibility to distinguish between fluctuating and non-fluctuating topological sectorsshould motivate its use as a local probe of topological order in a variety of related systems.

The Herbertsmithite Hamiltonian:μSR measurements on single crystals

We present transverse field muon spin rotation/relaxation measurements on single crystals of the spin-1/2 kagome antiferromagnet Herbertsmithite. We find that the spins are more easily polarizedwhen the field is perpendicular to the kagome plane. We demonstrate that the differencein magnetization between the different directions cannot be accounted for byDzyaloshinskii–Moriya-type interactions alone and that anisotropic axial interaction ispresent.

Magnetic-Field-Induced Transitions in Spinel GeCo2O4

The spinel GeCo 2 O 4 has the pyrochlore lattice of Co 2+ ions, in which the kagome and triangular planes stack alternately along the [111] direction. It shows antiferromagnetic ordering below T N ∼21 K with a characteristic wave vector of Q M =(1/2,1/2,1/2). The spin arrangement is ferromagnetic in the kagome and triangular planes and antiferromagnetic between the kagome planes as well as between the triangular planes. GeCo 2 O 4 exhibits a magnetic phase transition at H ∼4 T. Powder neutron diffraction measurements were performed on GeCo 2 O 4 in ambient and magnetic field. Our results are consistent with the magnetic structure model in which the kagome and triangular planes behave independently in magnetic field, that is, the spin arrangement between the triangular planes becomes ferromagnetic above ∼4 T while retaining the antiferromagnetic arrangement between the kagome planes.

Synthesis and characterization of single crystals of the spin-12kagome-lattice antiferromagnets ZnxCu4−x(OH)6Cl2

The Zn-paratacamite family, Zn$_{x}$Cu$_{4-x}$(OH)$_{6}$Cl$_{2}$ for $x \, \geq$ 0.33, is an ideal system for studying spin-1/2 frustrated magnetism in the form of antiferromagnetic Cu$^{2+}$ kagome planes. Here we report a new synthesis method by which high quality millimeter-sized single crystals of Zn-paratacamite have been produced. These crystals have been characterized by metal analysis, x-ray diffraction, neutron diffraction, and thermodynamic measurements. The $x$ = 1 member of the series displays a magnetic susceptibility that is slightly anisotropic at high temperatures with $\chi_{c} \, > \, \chi_{ab}$. Neutron and synchrotron x-ray diffraction experiments confirm the quality of these $x$ = 1 single crystals and indicate no obvious structural transition down to temperatures of T=2 K.

Spin dynamics, short-range order, and spin freezing inY0.5Ca0.5BaCo4O7

Y${}_{0.5}$Ca${}_{0.5}$BaCo${}_{4}$O${}_{7}$ was recently introduced as a possible candidate for capturing some of the predicted classical spin kagome ground-state features. Stimulated by this conjecture, we have taken up a more complete study of the spin correlations in this compound with neutron scattering methods on a powder sample characterized with high-resolution neutron diffraction and the temperature dependence of magnetic susceptibility and specific heat. We have found that the frustrated near-neighbor magnetic correlations involve not only the kagome planes but concern the full Co sublattice, as evidenced by the analysis of the wave-vector dependence of the short-range order. We conclude from our results that the magnetic moments are located on the Co sublattice as a whole and that correlations extend beyond the two-dimensional kagome planes. We identify intriguing dynamical properties, observing high-frequency fluctuations with a Lorentzian linewidth $\ensuremath{\Gamma}\ensuremath{\leqslant}20$ meV at ambient temperature. On cooling a low-frequency ($~$1 meV) dynamical component develops alongside the high-frequency fluctuations, which eventually becomes static at temperatures below $T\ensuremath{\approx}50$ K. The high-frequency response with an overall linewidth of $~$10 meV prevails at $T\ensuremath{\leqslant}2$ K, coincident with a fully elastic short-range-ordered contribution.

A Spin Molecule Model for Geometrically Frustrated Spinel ZnFe2O4

We analyzed the single-crystal neutron scattering data on a frustrated spinel ZnFe 2 O 4 , which is governed by dominant antiferromagnetic third-neighbor exchange interactions J 3 and additional ferromagnetic J 1 [K. Kamazawa et al. : Phys. Rev. B 68 (2003) 024412]. A spin dodecamer model that is formed on the kagome plane is proposed. It is notable that, although J 3 bonds consist of two types of exchange paths Fe–O–Fe–O–Fe and Fe–O–Zn–O–Fe, only the spatial spin correlations corresponding to the former paths are antiferromagnetic while those of all the latter paths are ferromagnetic in the dodecamer. This fact suggests that the frustration is relieved by utilizing the difference of exchange paths even in the same-distant interactions, that is to say, that only specific orbital mixing is selectively enhanced as an origin of the spin molecule.