The correct stacking of hexagonal layers is used to obtain accurate estimates for the exchange and anisotropy parameters of the geometrically-frustrated antiferromagnet CuFeO$_2$. Those parameters are highly constrained by the stability of a collinear metamagnetic phase between fields of 13.5 and 20 T. Constrained fits of the spin-wave frequencies of the collinear $\uudd $ phase below 7 T are used to identify the magnetic unit cell of the metamagnetic $\uuudd $ phase, which contains two hexagonal layers and 10 Fe$^{3+}$ spins.
The spin wave excitations of the geometrically frustrated triangular lattice antiferromagnet (TLA) $\rm CuFeO_2$ have been measured using high resolution inelastic neutron scattering. Antiferromagnetic interactions up to third nearest neighbors in the ab plane (J_1, J_2, J_3, with $J_2/J_1 \approx 0.44$ and $J_3/J_1 \approx 0.57$), as well as out-of-plane coupling (J_z, with $J_z/J_1 \approx 0.29$) are required to describe the spin wave dispersion relations, indicating a three dimensional character of the magnetic interactions. Two energy dips in the spin wave dispersion occur at the incommens…
Dielectric responses have been investigated on the triangular-lattice antiferromagnet CuFeO2 and its site-diluted analogs CuFe1-xAlxO2 (x=0.01 and 0.02) with and without application of magnetic field. We have found a ferroelectric behavior at zero magnetic field for x=0.02. At any doping level, the onset field of the ferroelectricity always coincides with that of the noncollinear magnetic structure while the transition field dramatically decreases to zero field with Al doping. The results imply the further possibility of producing the ferroelectricity by modifying the frustrated spin structure…
Magnetoelectric and magnetoelastic phenomena correlated with a phase transition into noncollinear magnetic phase have been investigated for single crystals of CuFeO2 with a frustrated triangular lattice. CuFeO2 exhibits several long-wavelength magnetic structures related to the spin frustration, and it is found that finite electric polarization, namely inversion symmetry breaking, occurs with noncollinear but not at collinear magnetic phases. This result demonstrates that the noncollinear spin structure is a key role to induce electric polarization, and suggests that frustrated magnets which o…
We have investigated spin-wave excitations in a four-sublattice (4SL) magnetic ground state of a frustrated magnet CuFeO2, in which `electromagnon' (electric-field-active magnon) excitation has been discovered by recent terahertz time-domain spectroscopy [Seki et al. Phys. Rev. Lett. 105 097207 (2010)]. In previous study, we have identified two spin-wave branches in the 4SL phase by means of inelastic neutron scattering measurements under applied uniaxial pressure. [T. Nakajima et al. J. Phys. Soc. Jpn. 80 014714 (2011) ] In the present study, we have performed high-energy-resolution inelastic…
Coupling between spin and lattice degrees of freedom are important in geometrically frustrated magnets where they can lead to degeneracy lifting and novel orders. We show that moderate spin-lattice couplings in triangular and Kagome antiferromagnets can induce complex colinear magnetic orders. When classical Heisenberg spins on the triangular lattice are coupled to Einstein phonons, a rich variety of phases emerge, including the experimentally observed four sublattice state and the five sublattice 1/5th plateau state seen in the magneto-electric material CuFeO$_2$. In addition we predict magne…
Biquadratic {\it antisymmetric} exchange terms of the form $ - [C_{ij} e^α_{ij}({\bf s}_i\times{\bf s}_j)_z]^2$, where ${\bf e}_{ij}$ is the unit vector connecting sites $i$ and $j$ and $α= x,y$, due partially to magnetoelectric coupling effects, are shown to be responsible for the spin-flop helical phase in CuFeO$_2$ at low magnetic field and temperature. Usual biquadratic {\it symmetric} exchange, likely due to magnetoelastic coupling, is found to support the stability of axial magnetic states at higher fields in this nearly-Heisenberg like stacked triangular antiferromagnet. A model Hamilto…
The high magnetic field behaviour of the triangular lattice antiferromagnet CuFeO_2 is studied using single crystal neutron diffraction measurements in a field of up to 14.5 T and also by magnetisation measurements in a field of up to 12 T. At low temperature, two well-defined first order magnetic phase transitions are found in this range of applied magnetic field (H // c): at H_c1=7.6(3)/7.1(3) T and H_c2=13.2(1)/12.7(1) T when ramping the field up/down. In a field above H_c2 the magnetic Bragg peaks show unusual history dependence. In zero field T_N1=14.2(1) K separates a high temperature pa…
By means of neutron scattering measurements, we have investigated spin-wave excitation in a collinear four-sublattice (4SL) magnetic ground state of a triangular lattice antiferromagnet CuFeO2, which has been of recent interest as a strongly frustrated magnet, a spin-lattice coupled system and a multiferroic. To avoid mixing of spin-wave spectrum from magnetic domains having three different orientations reflecting trigonal symmetry of the crystal structure, we have applied uniaxial pressure on [1-10] direction of a single crystal CuFeO2. By elastic neutron scattering measurements, we have foun…
This paper examines the relation between the spin-wave instabilities of collinear magnetic phases and the resulting non-collinear phases for a geometrically-frustrated triangular-lattice antiferromagnet in the high spin limit. Using a combination of phenomenological and Monte-Carlo techniques, we demonstrate that the instability wave-vector with the strongest intensity in the collinear phase determines the wave-vector of a cycloid or the dominant elastic peak of a more complex non-collinear phase. Our results are related to the observed multi-ferroic phase of Al-doped CuFeO$_2$.
We study Ising antiferromagnets that have nearest-neighbour interactions on multilayer triangular lattices with frustrated ($abc$ and $abab$) stacking, and make comparisons with the unfrustrated ($aaa$) stacking. If interlayer couplings are much weaker than in-plane ones, the paramagnetic phase of models with frustrated stackings has a classical spin-liquid regime at low temperature, in which correlations are strong both within and between planes, but there is no long-range order. We investigate this regime using Monte Carlo simulations and by mapping the spin models to coupled height models, …
Spin correlations in the geometrically frustrated RBaCo4O7 compounds, usually described as an alternating stacking of Kagome and triangular layers on a hexagonal lattice, have been studied by mean-field approach and by Monte-Carlo simulations. The behavior of the system was modelled with an isotropic Heisenberg Hamiltonian as a function of the relevant parameter Jout/Jin, representing the ratio between exchange integrals inside the Kagome layers, Jin, and between Kagome and triangular layers, Jout. This ratio can be varied in real systems by appropriate chemical substitutions. At the mean-fiel…
Artificial spin ice is a frustrated magnetic two-dimensional nano-material, recently employed to study variety of tailor-designed unusual collective behaviours. Recently proposed extensions to three dimensions are based on self-assembly techniques and allow little control over geometry and disorder. We present a viable design for the realization of a three-dimensional artificial spin ice with the same level of precision and control allowed by lithographic nano-fabrication of the popular two-dimensional case. Our geometry is based on layering already available two-dimensional artificial spin ic…
We have successfully synthesized three quasi-2D geometrically frustrated magnetic compounds (α-MCr_2O_4, M=Ca, Sr, Ba) using the spark-plasma-sintering technique. All these members of the α-MCr_2O_4 family consist of the stacking planar triangular lattices of Cr$^{3+}$ spins (${\rm S}=3/2$), separated by non-magnetic alkaline earth ions. Their corresponding magnetic susceptibility, specific heat, dielectric permittivity and ferroelectric polarization are systematically investigated. A long-range magnetic ordering arises below the Néel temperature (around 40K) in each member of the α-MCr_2O_4 f…
The recently discovered material Cs$_3$Fe$_2$Br$_9$ contains Fe$_2$Br$_9$ bi-octahedra forming triangular layers with hexagonal stacking along the $c$ axis. In contrast to isostructural Cr-based compounds, the zero-field ground state is not a nonmagnetic $S=0$ singlet-dimer state. Instead, the Fe$_2$Br$_9$ bi-octahedra host semiclassical $S=5/2$ Fe$^{3+}$ spins with a pronounced easy-axis anisotropy along $c$ and interestingly, the intra-dimer spins are ordered ferromagnetically. The high degree of magnetic frustration due to (various) competing intra- and inter-dimer couplings leads to a surp…
We report the nature of magnetic structure, microscopic spin-spin correlations and their dependence on the underlying crystal structure of the geometrically frustrated layered spin-3/2 maple-leaf-lattice (MLL) antiferromagnet Na2Mn3O7 by a comprehensive neutron diffraction study. Crystal structural studies by x-ray and neutron diffractions reveal that the MLL layers (constituted by Mn3O72- units) are well separated by non-magnetic Na layers. The studies also conclude the presence of stacking faults (in-plane sliding of magnetic MLL layers) as well as a distortion in the MLL of Mn4+. Temperatur…
We have studied the frustrated system YBaCo4O7 generally described as an alternating stacking of Kagome and triangular layers of magnetic ions on a trigonal lattice, by single crystal neutron diffraction experiments above the Neel ordering transition. Experimental data reveals pronounced magnetic diffuse scattering, which is successfully modeled by direct Monte-Carlo simulations. Long-range magnetic correlations are found along the c-axis, due to the presence of corner-sharing bipyramids, creating quasi one-dimensional order at finite temperature. In contrast, in the Kagome layers ab-plane, th…
The candidate magnetoelectric Pb3Mn7O15 has a structure consisting of 1/3 filled Kagome layers linked by ribbons of edge-sharing octahedra in the stacking direction. Previous reports have indicated a complex hexagonal-orthorhombic structural transition upon cooling to room temperature, although its origins are uncertain. Here both structures are revisited using a combination of neutron and synchrotron X-ray diffraction data. Large shifts of oxygen positions are detected which show that the interlayer sites and those which occupy voids in the kagome lattice are trivially charge ordered in both …
Recently, the mixed transition metal oxides of the form Li(Ni1-y-zCoyMnz)O2, have become the center of attention as promising candidates for novel battery material. These materials have also revealed very interesting magnetic properties due to the alternate stacking of planes of metal oxides on a 2D triangular lattice and the Li-layers. The title compound, Li(Ni0.8Co0.1Mn0.1)O2, has been investigated by both magnetometry and measurements and μ+SR. We find the evolution of localized magnetic moments with decreasing temperature below 70 K. The magnetic ground state (T = 2 K) is, however, shown t…
The layered β-NaMnO2, a promising Na-ion energy-storage material has been investigated for its triangular lattice capability to promote complex magnetic configurations that may release symmetry restrictions for the coexistence of ferroelectric and magnetic orders. The complexity of the neutron powder diffraction patterns underlines that the routinely adopted commensurate structural models are inadequate. Instead, a single-phase superspace symmetry description is necessary, demonstrating that the material crystallizes in a compositionally modulated q= (0.077(1), 0, 0) structure. Here, Mn3+ Jahn…
We use the coupled cluster method (CCM) to study a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg antiferromagnet on a bilayer honeycomb lattice with $AA$ stacking. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor antiferromagnetic (AFM) exchange interactions are present in each layer, with respective exchange coupling constants $J_{1}>0$ and $J_{2} \equiv κJ_{1} > 0$. The two layers are coupled with NN AFM exchanges with coupling strength $J_{1}^{\perp}\equiv δJ_{1}>0$. We calculate to high orders of approximation within the CCM the zero-field trans…
The layered honeycomb magnet alpha-RuCl3 has been proposed as a candidate to realize a Kitaev spin model with strongly frustrated, bond-dependent, anisotropic interactions between spin-orbit entangled jeff=1/2 Ru4+ magnetic moments. Here we report a detailed study of the three-dimensional crystal structure using x-ray diffraction on untwinned crystals combined with structural relaxation calculations. We consider several models for the stacking of honeycomb layers and find evidence for a crystal structure with a monoclinic unit cell corresponding to a stacking of layers with a unidirectional in…
We report x-ray diffraction, magnetic susceptibility, heat capacity, $^{1}$H nuclear magnetic resonance (NMR), and muon spin relaxation ($μ$SR) measurements, as well as density-functional band-structure calculations for the frustrated $S=3/2$ triangular lattice Heisenberg antiferromagnet (TLHAF) $α$-HCrO$_{2}$ (trigonal, space group: $R\bar{3}m$). This compound undergoes a clear magnetic transition at $T_{\rm N} \simeq 22.5$~K, as seen from the drop in the muon paramagnetic fraction and concurrent anomalies in the magnetic susceptibility and specific heat. Local probes (NMR and $μ$SR) reveal a…
Spin $\frac{1}{2}$ honeycomb materials have gained substantial interest due to their exotic magnetism and possible application in quantum computing. However, in all current materials out-of-plane interactions are interfering with the in-plane order, hence a true 2D magnetic honeycomb system is still of demand. Here, we report the exfoliation of the magnetic semiconductor $α$-RuCl$_3$ into the first halide monolayers and the magnetic characterization of the spin $\frac{1}{2}$ honeycomb arrangement of turbostratically stacked RuCl$_3$ monolayers. The exfoliation is based on a reductive lithiatio…
We report $^{23}$Na and $^{59}$Co nuclear magnetic (NMR) and quadrupolar resonance (NQR) studies for the $x=2/3$ phase of the lamellar oxide Na$_{x}$CoO$_{2}$, which allowed us to establish reliably the atomic order of the Na layers and their stacking between the CoO$_{2}$ slabs. We evidence that the Na$^{+}$ order stabilizes filled non magnetic Co$^{3+}$ ions on 25% of the cobalt sites arranged in a triangular sublattice. The transferred holes are delocalized on the 75% complementary cobalt sites which unexpectedly display a planar cobalt kagomé structure. These experimental results resolve a…
