Topological defects have been playgrounds for many emergent phenomena in complex matter such as superfluids, liquid crystals, and early universe. Recently, vortex-like topological defects with six interlocked structural antiphase and ferroelectric domains merging into a vortex core were revealed in multiferroic hexagonal manganites. Numerous vortices are found to form an intriguing self-organized network. Thus, it is imperative to find out the magnetic nature of these vortices. Using cryogenic magnetic force microscopy, we discovered unprecedented alternating net moments at domain walls around vortices that can correlate over the entire vortex network in hexagonal ErMnO 3. The collective nature of domain wall magnetism originates from the uncompensated Er 3+ moments and the correlated organization of the vortex network. Furthermore, our proposed model indicates a fascinating phenomenon of field-controllable spin chirality. Our results demonstrate a new route to achieving magnetoelectric coupling at domain walls in single-phase multiferroics, which may be harnessed for nanoscale multifunctional devices. 2 Multiferroics are materials with coexisting magnetism and ferroelectricity 1. The cross-coupling between two ferroic orders can result in giant magnetoelectric coupling for potential applications 2-5. Because formation of domains is the hallmark of any ferroic order 6 , it is of both fundamental and technological interests to visualize cross-coupled domains or walls in multiferroics. Hexagonal (h-) REMnO 3 (RE = Sc, Y, Ho, … Lu) are multiferroics with coexistence of ferroelectricity (T C ≈ 1200-1500 K) 7 and antiferromagnetism (T N ≈ 70-120 K) 8. The ferroelectricity is induced by structural instability called trimerization 9,10 , which lifts presumably the frustration of antiferromagnetic interactions of Mn 3+ spins on triangular lattice. Indeed, a 120º antiferromagnetic order of Mn 3+ spin in the ab-plane sets in below T N. Recently, an intriguing 6-state vortex domain structure in YMnO 3 is revealed by transmission electron microscopy, conductive atomic force microscopy and piezoresponse force microscopy (PFM) at room temperature 11-13. The formation of 6-state vortices originates from the cyclic arrangement of 6 interlocked structural antiphase (α, β, γ) and ferroelectric (+/−) ground states (i.e. α + , β-, γ + , α-, β + , γ-) 11,14. The intriguing network of vortex-antivortex pairs has a profound connection to graph theory, where 6-valent planer graphs with even-gons are two-proper-colorable 15. Using second harmonic generation optics, it has been claimed that ferroelectric domain walls (DWs) in millimeter-size YMnO 3 tend to pin antiferromagnetic DWs, but free antiferromagnetic DWs also exist 16. Thus, it is of great interest to find out the magnetic nature of vortex domains and DWs. However, this has been an experimental challenge, particularly due to the lack of suitable high resolution imaging technique of antiferromagnetic domains or DWs for h-REMnO 3 at low temperatures (supplementary discussion 1). T...

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TbMnO3 is an orthorhombic insulator where incommensurate spin order for temperature T(N)<41 K is accompanied by ferroelectric order for T<28 K. To understand this, we establish the magnetic structure above and below the ferroelectric transition using neutron diffraction. In the paraelectric phase, the spin structure is incommensurate and longitudinally modulated. In the ferroelectric phase, however, there is a transverse incommensurate spiral. We show that the spiral breaks spatial inversion symmetry and can account for magnetoelectricity in TbMnO3.

We report inelastic neutron scattering measurements on Na2IrO3, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zig-zag magnetic order. The onset of long-range magnetic order below TN = 15.3 K is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90• Ir-O-Ir bonds required for dominant Kitaev exchange. [6,7], in which edge-sharing IrO 6 octahedra form a honeycomb lattice [see Fig. 1b)], have been predicted to display novel magnetic states for composite spin-orbital moments coupled via frustrated exchanges. The exchange between neighboring Ir moments (called S i,j , S=1/2) is proposed to be [2]where J K > 0 is an Ising ferromagnetic (FM) term arising from superexchange via the Ir-O-Ir bond, and J 1 > 0 is the antiferromagnetic (AFM) Heisenberg exchange via direct Ir-Ir 5d overlap. Due to the strong spin-orbital admixture the Kitaev term J K couples only the components in the direction γ, normal to the plane of the Ir-O-Ir bond [8,9]. Because of the orthogonal geometry, different spin components along the cubic axes (γ = x, y, z) of the IrO 6 octahedron are coupled for the three bonds emerging out of each site in the honeycomb lattice. This leads to the strongly-frustrated Kitaev-Heisenberg (KH) model [2], which has conventional Néel order [see Fig. 3a)] for large J 1 , a stripy collinear AFM phase [see Fig. 3c)] for 0.4 α 0.8, where α = J K / (J K + 2J 1 ) (exact ground state at α = 1/2), and a quantum spin liquid with Majorana fermion excitations [10] at large J K (α 0.8). Measurements of the spin excitations are very important to determine the overall energy scale and the relevant magnetic interactions, however because Ir is a strong neutron absorber inelastic neutron scattering (INS) experiments are very challenging. Using an optimized setup we here report the first observation of dispersive spin wave excitations of Ir moments via INS. We show that the dispersion can be quantitatively accounted for by including substantial further-neighbor in-plane exchanges, which in turn stabilize zig-zag order. To inform future ab initio studies of microscopic models of the interactions we combine single-crystal xray diffraction with density functional calculations to determine precisely the oxygen positions, which are key in mediating the exchange and controlling the spin-orbital admixture via crystal field effects. We propose a revised crystal structure with much more symmetric IrO 6 octahedra, but with substantial departures from the ideal 90• Ir-O-Ir bonds required for dominant Kitaev exchange [9], and with frequent structural stacking faults. This differs from the currentlyadopted model, used by several band-structure calculations [14,15], with asymme...

The unusual magnetic properties of La 0.5 Ca 0.5 MnO 3 were found to be associated with structural and magnetic ordering phenomena, resulting from the close interplay between charge, orbital, and magnetic ordering. Analysis of synchrotron x-ray and neutron powder diffraction data indicates that the anomalous and hysteretic behavior of the lattice parameters occurring between T C ϳ225 K and T N ϳ155 K is due to the development of a Jahn-Teller ͑J-T͒ distortion of the MnO 6 octahedra, the d z 2 orbitals being oriented perpendicular to the orthorhombic b axis. We observed an unusual broadening of the x-ray Bragg reflections throughout this temperature region, suggesting that this process occurs in stages. Below T N , the development of well-defined satellite peaks in the x-ray patterns, associated with a transverse modulation with qϭ[1/2Ϫ,0,0], indicates that quasicommensurate ͑ϳ0͒ orbital ordering occurs within the a-c plane as well. The basic structural features of the charge-ordered low-temperature phase were determined from these satellite peaks. The lowtemperature magnetic structure is characterized by systematic broadening of the magnetic peaks associated with the ''Mn ϩ3 '' magnetic sublattice. This phenomenon can be explained by the presence of magnetic domain boundaries, which break the coherence of the spin ordering on the Mn ϩ3 sites while preserving the coherence of the spin ordering on the Mn ϩ4 sublattice as well as the identity of the two sublattices. The striking resemblance between these structures and the structural ''charge ordering'' and ''discommensuration'' domain boundaries, which were recently observed by electron diffraction and real-space imaging, strongly suggests that these two types of structures are the same and implies that, in this system, commensurate long-range charge ordering coexists with quasicommensurate orbital ordering.

The structures of the three ferroelectric phases of BaTi03 have been determined by Rietveld refinement using powder diffraction data collected at a spallation neutron source. The correlation between refined atomic displacements and thermal parameters, which has hampered previous structure determinations, has been partially alleviated by using data which extend over a wide range of d spacings. Data collected at a large number of sample temperatures provide information about the temperature dependence of the ferroelectric displacements and changes in the oxygen octahedra which surround the Ti ions. The temperature dependence of the thermal parameters gives atomic Debye-Waller temperatures that are remarkably similar to those for the cations in the high-Tc superconductors. Our results are insensitive to predictions of a soft-mode displacive model; however, values of the anisotropic thermal parameters do not support the order-disorder model suggested by Comes et al. Powder extinction and profile coefficients from the structural refinements show pronounced minima and maxima, respectively, near the phase transitions and provide information about the temperature dependence of the mosaic structure and the strain in the

The ability to tune material properties using gating by electric fields is at the heart of modern electronic technology. It is also a driving force behind recent advances in two-dimensional systems, such as the observation of gate electric-field-induced superconductivity and metal-insulator transitions. Here, we describe an ionic field-effect transistor (termed an iFET), in which gate-controlled Li ion intercalation modulates the material properties of layered crystals of 1T-TaS2. The strong charge doping induced by the tunable ion intercalation alters the energetics of various charge-ordered states in 1T-TaS2 and produces a series of phase transitions in thin-flake samples with reduced dimensionality. We find that the charge-density wave states in 1T-TaS2 collapse in the two-dimensional limit at critical thicknesses. Meanwhile, at low temperatures, the ionic gating induces multiple phase transitions from Mott-insulator to metal in 1T-TaS2 thin flakes, with five orders of magnitude modulation in resistance, and superconductivity emerges in a textured charge-density wave state induced by ionic gating. Our method of gate-controlled intercalation opens up possibilities in searching for novel states of matter in the extreme charge-carrier-concentration limit.