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The 5$d$ transition metal oxides offer a plethora of possibilities to further enrich the fascinating physics of complex 3$d$ compounds by generating novel physical properties at the strong spin-orbit coupling limit. Here, the authors demonstrate that the magnetic correlation length in Sr${}_{2}$IrO${}_{4}$ thin films strongly depends on the film thickness, while it is completely independent of their strain state. This creates the opportunity to fine-tune the magnetic correlation length and may open up important inroads into the stabilization of superconductivity in Sr${}_{2}$IrO${}_{4}$.

We present a combined polarized neutron and x-ray scattering study on two enantiopure langasite single crystals aimed at the determination of their absolute structural and magnetic chiralities and the coupling between them. Our respective data sets unambiguously reveal two samples of opposite structural chirality, where the magnetic handedness is pinned by the structural one. Simple energy considerations of the magnetic exchange and single-ion anisotropy parameters reveal that it is not the Dzyaloshinskii-Moriya interaction but the local single-ion anisotropy on a triangular plaquette which plays a key role in stabilizing one of the two magnetic helices.

Here we investigate antiferromagnetic Eu$_{5}$In$_{2}$Sb$_{6}$, a nonsymmorphic Zintl phase. Our electrical transport data show that Eu$_{5}$In$_{2}$Sb$_{6}$ is remarkably insulating and exhibits an exceptionally large negative magnetoresistance, which is consistent with the presence of magnetic polarons. From {\it ab initio} calculations, the paramagnetic state of Eu$_{5}$In$_{2}$Sb$_{6}$ is a topologically nontrivial semimetal within the generalized gradient approximation (GGA), whereas an insulating state with trivial topological indices is obtained using a modified Becke-Johnson potential. Notably, GGA+U calculations suggest that the antiferromagnetic phase of Eu$_{5}$In$_{2}$Sb$_{6}$ may host an axion insulating state. Our results provide important feedback for theories of topological classification and highlight the potential of realizing clean magnetic narrow-gap semiconductors in Zintl materials., Accepted in npj Quantum Materials. Author list and affiliations corrected

We use resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge to study the effect of hole doping upon the Jeff=1/2 Mott-insulating state in Sr2IrO4, via Rh replacement of the Ir site. The spin-wave gap, associated with XY-type spin-exchange anisotropy, collapses with increasing Rh content, prior to the suppression of the Mott-insulating state and in contrast to electron doping via La substitution of the Sr site. At the same time, despite heavy damping, the d-d excitation spectra retain their overall amplitude and dispersion character. A careful study of the spin-wave spectrum reveals that deviations from the J1-J2-J3 Heisenberg used to model the pristine system disappear at intermediate doping levels. These findings are interpreted in terms of a modulation of Ir-Ir correlations due to the influence of Rh impurities upon nearby Ir wave functions, even as the single-band Jeff=1/2 model remains valid up to full carrier delocalization. They underline the importance of the transition metal site symmetry when doping pseudospin systems such as Sr2IrO4., Comment: 5 pages, 3 figures

${\mathrm{Ba}}_{3}{\mathrm{NbFe}}_{3}{\mathrm{Si}}_{2}{\mathrm{O}}_{14}$ (langasite) is structurally and magnetically single-domain chiral with the magnetic helicity induced through competing symmetric exchange interactions. Using neutron scattering, we show that the spin waves in antiferromagnetic langasite display directional anisotropy. On applying a time-reversal symmetry breaking magnetic field along the $c$ axis, the spin-wave energies differ when the sign is reversed for either the momentum transfer $\ifmmode\pm\else\textpm\fi{}\stackrel{P\vec}{Q}$ or applied magnetic field $\ifmmode\pm\else\textpm\fi{}{\ensuremath{\mu}}_{0}\mathrm{H}$. When the field is applied within the crystallographic $ab$ plane, the spin-wave dispersion is directionally isotropic and symmetric in $\ifmmode\pm\else\textpm\fi{}{\ensuremath{\mu}}_{0}\mathrm{H}$. However, a directional anisotropy is observed in the spin-wave intensity. We discuss this directional anisotropy in the dispersion in langasite in terms of a field-induced precession of the dynamic unit cell staggered magnetization resulting from a broken twofold symmetry. Directional anisotropy, often referred to as nonreciprocal responses, can occur in antiferromagnetic phases in the absence of the Dzyaloshinskii-Moriya interaction or other effects resulting from spin-orbit coupling.

An experimental setup to perform high-pressure resonant X-ray scattering (RXS) experiments at low temperature on I16 at Diamond Light Source is presented. The setup consists of a membrane-driven diamond anvil cell, a panoramic dome and an optical system that allows pressure to be measured in situ using the ruby fluorescence method. The membrane cell, inspired by the Merrill–Bassett design, presents an asymmetric layout in order to operate in a back-scattering geometry, with a panoramic aperture of 100° in the top and a bottom half dedicated to the regulation and measurement of pressure. It is specially designed to be mounted on the cold finger of a 4 K closed-cycle cryostat and actuated at low-temperature by pumping helium into the gas membrane. The main parts of the body are machined from a CuBe alloy (BERYLCO 25) and, when assembled, it presents an approximate height of 20–21 mm and fits into a 57 mm diameter. This system allows different materials to be probed using RXS in a range of temperatures between 30 and 300 K and has been tested up to 20 GPa using anvils with a culet diameter of 500 µm under quasi-cryogenic conditions. Detailed descriptions of different parts of the setup, operation and the developed methodology are provided here, along with some preliminary experimental results.

The presence of domains in ferroic materials can negatively affect their macroscopic properties and hence their usefulness in device applications. From an experimental perspective, the measurement of materials comprising multiple domains can complicate the interpretation of the material properties and their underlying mechanisms. In general, BiFeO3 films tend to grow with multiple magnetic domains and often contain multiple ferroelectric- and ferroelastic-domain variants. By growing (111)-oriented BiFeO3 films on an orthorhombic TbScO3 substrate, we are able to overcome this and, by exploiting the magnetoelastic coupling between the magnetic and crystal structures, bias the growth of a given magnetic-, ferroelectric-, and structural-domain film. We further demonstrate the coupling of the magnetic structure to the ferroelectric polarization by showing that the magnetic polarity in this domain is inverted upon 180∘ ferroelectric switching.

We review the magnetic and orbital ordered states in ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$ by performing resonant elastic x-ray scattering (REXS) at the Ru ${\mathrm{L}}_{2,3}$ edges. In principle, the point symmetry at Ru sites does not constrain the direction of the magnetic moment below ${T}_{N}$. However early measurements reported the ordered moment entirely along the $\stackrel{P\vec}{b}$ orthorhombic axis. Taking advantage of the large resonant enhancement of the magnetic scattering close to the Ru ${\mathrm{L}}_{2}$ and ${\mathrm{L}}_{3}$ absorption edges, we monitored the azimuthal, thermal, and energy dependence of the REXS intensity and find that a canting (${m}_{c}\ensuremath{\simeq}0.1{m}_{b}$) along the $\stackrel{P\vec}{c}$-orthorhombic axis is present. No signal was found for ${m}_{a}$ despite this component also being allowed by symmetry. Such findings are interpreted by a microscopic model Hamiltonian and pose new constraints on the parameters describing the model. Using the same technique we reviewed the accepted orbital ordering picture. We detected no symmetry breaking associated with the signal increase at the ``so-called'' orbital ordering temperature ($\ensuremath{\simeq}260$ K). We did not find any changes of the orbital pattern even through the antiferromagnetic transition, suggesting that, if any, only a complex rearrangement of the orbitals, not directly measurable using linearly polarized light, can take place.

The chemical and magnetic structures of the series of compounds ${\mathrm{Ca}}_{2\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{RuO}}_{4}$ $[x=0$, 0.05(1), 0.07(1), 0.12(1)] have been investigated using neutron diffraction and resonant elastic x-ray scattering. Upon La doping, the low-temperature S-$Pbca$ space group of the parent compound is retained in all insulating samples $[x\ensuremath{\le}0.07(1)]$, but with significant changes to the atomic positions within the unit cell. These changes can be characterized in terms of the local ${\mathrm{RuO}}_{6}$ octahedral coordination: with increasing doping, the structure, crudely speaking, evolves from an orthorhombic unit cell with compressed octahedra to a quasitetragonal unit cell with elongated ones. The magnetic structure on the other hand, is found to be robust, with the basic $\mathbf{k}=(0,0,0)$, $\mathbf{b}$-axis antiferromagnetic order of the parent compound preserved below the critical La doping concentration of $x\ensuremath{\approx}0.11$. The only effects of La doping on the magnetic structure are to suppress the A-centred mode, favoring the B mode instead, and to reduce the N\'eel temperature somewhat. Our results are discussed with reference to previous experimental reports on the effects of cation substitution on the ${d}^{4}$ Mott insulator ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$, as well as with regard to theoretical studies on the evolution of its electronic and magnetic structure. In particular, our results rule out the presence of a proposed ferromagnetic phase, and suggest that the structural effects associated with La substitution play an important role in the physics of the system.

In spinels ACr2O4 (A=Mg, Zn), realization of the classical pyrochlore Heisenberg antiferromagnet model is complicated by a strong spin-lattice coupling: the extensive degeneracy of the ground state is lifted by a magneto-structural transition at TN = 12.5 K. We study the resulting low-temperature low-symmetry crystal structure by synchrotron x-ray diffraction. The consistent features of x-ray low-temperature patterns are explained by the tetragonal model of Ehrenberg et al. [Pow. Diff. 17, 230 (2002)], while other features depend on sample or cooling protocol. A complex, partially ordered magnetic state is studied by neutron diffraction and spherical neutron polarimetry. Multiple magnetic domains of configuration arms of the propagation vectors k1 = (1/2 1/2 0), k2 = (1 0 1/2 ) appear. The ordered moment reaches 1.94(3) μB/Cr3+ for k1 and 2.08(3) μB/Cr3+ for k2, if equal amount of the k1 and k2 phases is assumed. The magnetic arrangements have the dominant components along the [110] and [1−10] diagonals and a smaller c component.We use inelastic neutron scattering to investigate the spin excitations, which comprise a mixture of dispersive spin waves propagating from the magnetic Bragg peaks and resonance modes centered at equal energy steps of 4.5 meV.We interpret these as acoustic and optical spin wave branches, but show that the neutron scattering cross sections of transitions within a unit of two corner-sharing tetrahedra match the observed intensity distribution of the resonances. The distinctive fingerprint of clusterlike excitations in the optical spin wave branches suggests that propagating excitations are localized by the complex crystal structure and magnetic orders.

We observed a hump-like feature in Hall effects of SrRuO$_3$ ultrathin films, and systematically investigated it with controlling thicknesses, temperatures and magnetic fields. The hump-like feature is extremely stable, even surviving as a magnetic field is tilted by as much as 85$^\circ$. Based on the atomic-level structural analysis of a SrRuO$_3$ ultrathin film with a theoretical calculation, we reveal that atomic rumplings at the thin-film surface enhance Dzyaloshinskii-Moriya interaction, which can generate stable chiral spin textures and a hump-like Hall effect. Moreover, temperature dependent resonant X-ray measurements at Ru L-edge under a magnetic field showed that the intensity modulation of unexpected peaks was correlated with the hump region in the Hall effect. We verify that the two-dimensional property of ultrathin films generates stable non-coplanar spin textures having a magnetic order in a ferromagnetic oxide material.

We have directly imaged reversible electrical switching of the cycloidal rotation direction (magnetic polarity) in a (111)pc-BiFeO3 epitaxial-film device at room temperature by non-resonant x-ray magnetic scattering. Consistent with previous reports, fully relaxed (111)pc-BiFeO3 epitaxial films consisting of a single ferroelectric domain were found to comprise a sub-micron-scale mosaic of magneto-elastic domains, all sharing a common direction of the magnetic polarity, which was found to switch reversibly upon reversal of the ferroelectric polarization without any measurable change of the magneto-elastic domain population. A real-space polarimetry map of our device clearly distinguished between regions of the sample electrically addressed into the two magnetic states with a resolution of a few tens of micron. Contrary to the general belief that the magneto-electric coupling in BiFeO3 is weak, we find that electrical switching has a dramatic effect on the magnetic structure, with the magnetic moments rotating on average by 90 degrees at every cycle.

The metal-insulator transition (MIT) in transition-metal-oxide is fertile ground for exploring intriguing physics and potential device applications. Here, an atomic-scale MIT triggered by surface termination conversion in SrRuO3 ultrathin films is reported. Uniform and effective termination engineering at the SrRuO3 (001) surface can be realized via a self-limiting water-leaching process. As the surface termination converts from SrO to RuO2 , a highly insulating and nonferromagnetic phase emerges within the topmost SrRuO3 monolayer. Such a spatially confined MIT is corroborated by systematic characterizations on electrical transport, magnetism, and scanning tunneling spectroscopy. Density functional theory calculations and X-ray linear dichroism further suggest that the surface termination conversion breaks the local octahedral symmetry of the crystal field. The resultant modulation in 4d orbital occupancy stabilizes a nonferromagnetic insulating surface state. This work introduces a new paradigm to stimulate and tune exotic functionalities of oxide heterostructures with atomic precision.

The physical properties of epitaxial films can fundamentally differ from those of bulk single crystals even above the critical thickness. By a combination of non-resonant x-ray magnetic scattering, neutron diffraction and vector-mapped x-ray magnetic linear dichroism photoemission electron microscopy, we show that epitaxial (111)-BiFeO3 films support sub-micron antiferromagnetic domains, which are magneto-elastically coupled to a coherent crystallographic monoclinic twin structure. This unique texture, which is absent in bulk single crystals, should enable control of magnetism in BiFeO3 film devices via epitaxial strain., 5 pages, 3 figures

The layered honeycomb magnet $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ has been theoretically proposed as a candidate to display unconventional magnetic behaviour associated with Kitaev interactions between spin-orbit entangled ${j}_{\mathrm{eff}}=1/2$ magnetic moments on a honeycomb lattice. Here we report single crystal magnetic resonant x-ray diffraction combined with powder magnetic neutron diffraction to reveal an incommensurate magnetic order in the honeycomb layers with Ir magnetic moments counterrotating on nearest-neighbor sites. This unexpected type of magnetic structure for a honeycomb magnet cannot be explained by a spin Hamiltonian with dominant isotropic (Heisenberg) couplings. The magnetic structure shares many key features with the magnetic order in the structural polytypes $\ensuremath{\beta}$- and $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$, understood theoretically to be stabilized by dominant Kitaev interactions between Ir moments located on the vertices of three-dimensional hyperhoneycomb and stripyhoneycomb lattices, respectively. Based on this analogy and a theoretical soft-spin analysis of magnetic ground states for candidate spin Hamiltonians, we propose that Kitaev interactions also dominate in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$, indicative of universal Kitaev physics across all three members of the harmonic honeycomb family of ${\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ polytypes.

The layered perovskite Ca3-xSrxMn2O7 is shown to exhibit a switching from a material exhibiting uniaxial negative to positive thermal expansion as a function of x. The switching is shown to be related to two closely competing phases with different symmetries. The negative thermal expansion (NTE) effect is maximized when the solid solution is tuned closest to this region of phase space but is switched off suddenly on passing though the transition. Our results show for the first time that, by understanding the symmetry of the competing phases alone, one may achieve unprecedented chemical control of this unusual property.

Through a combination of neutron diffraction and Landau theory we describe the spin ordering in the ground state of the quadruple perovskite manganite CaMn7O12 - a magnetic multiferroic supporting an incommensurate orbital density wave that onsets above the magnetic ordering temperature, TN1 = 90 K. The multi-k magnetic structure in the ground state was found to be a nearly-constant-moment helix with modulated spin helicity, which oscillates in phase with the orbital occupancies on the Mn3+ sites via trilinear magneto-orbital coupling. Our phenomenological model also shows that, above TN2 = 48 K, the primary magnetic order parameter is locked into the orbital wave by an admixture of helical and collinear spin density wave structures. Furthermore, our model naturally explains the lack of a sharp dielectric anomaly at TN1 and the unusual temperature dependence of the electrical polarisation., Comment: Accepted for publication in Physical Review B, Rapid Communications

The high-resolution temperature-dependent diffuse X-ray scattering from an Na0.5Bi0.5TiO3 perovskite-based single crystal is measured on the approach to the polymorphic phase transition. The previously unseen topological features of the diffuse scattering and their temperature evolution are reported., The results of high-resolution measurements of the diffuse X-ray scattering produced by a perovskite-based Na0.5Bi0.5TiO3 ferroelectric single crystal between 40 and 620 K are reported. The study was designed as an attempt to resolve numerous controversies regarding the average structure of Na0.5Bi0.5TiO3, such as the mechanism of the phase transitions between the tetragonal, P4bm, and rhombohedral | monoclinic, R3c | Cc, space groups and the correlation between structural changes and macroscopic physical properties. The starting point was to search for any transformations of structural disorder in the temperature range of thermal depoling (420–480 K), where the average structure is known to remain unchanged. The intensity distribution around the {032} pseudocubic reflection was collected using a PILATUS 100K detector at the I16 beamline of the Diamond Light Source (UK). The data revealed previously unknown features of the diffuse scattering, including a system of dual asymmetric L-shaped diffuse scattering streaks. The topology, temperature dependence, and relationship between Bragg and diffuse intensities suggest the presence of complex microstructure in the low-temperature R3c | Cc phase. This microstructure may be formed by the persistence of the higher-temperature P4bm phase, built into a lower-temperature R3c | Cc matrix, accompanied by the related long-range strain fields. Finally, it is shown that a correlation between the temperature dependence of the X-ray scattering features and the temperature regime of thermal depoling is present.

Single crystal neutron diffraction is combined with synchrotron x-ray scattering to identify the different superlattice phases present in ${\text{Cs}}_{0.8}{\text{Fe}}_{1.6}{\text{Se}}_{2}$. A combination of single crystal refinements and first principles modeling are used to provide structural solutions for the $\sqrt{5}\ifmmode\times\else\texttimes\fi{}\sqrt{5}$ and $\sqrt{2}\ifmmode\times\else\texttimes\fi{}\sqrt{2}$ superlattice phases. The $\sqrt{5}\ifmmode\times\else\texttimes\fi{}\sqrt{5}$ superlattice structure is predominantly composed of ordered Fe vacancies and Fe distortions, whereas the $\sqrt{2}\ifmmode\times\else\texttimes\fi{}\sqrt{2}$ superlattice is composed of ordered Cs vacancies. The Cs vacancies only order within the plane, causing Bragg rods in reciprocal space. By mapping x-ray diffraction measurements with narrow spatial resolution over the surface of the sample, the structural domain pattern was determined, consistent with the notion of a majority antiferromagnetic $\sqrt{5}\ifmmode\times\else\texttimes\fi{}\sqrt{5}$ phase and a superconducting $\sqrt{2}\ifmmode\times\else\texttimes\fi{}\sqrt{2}$ phase.

Using a combined approach of neutron powder diffraction and single-crystal magnetic resonant xray diffraction, the authors determine the complex incommensurate magnetic ground state of $\ensuremath{\beta}$-Li${}_{2}$IrO${}_{3}$.

Materials that realize Kitaev spin models with bond-dependent anisotropic interactions have long been searched for, as the resulting frustration effects are predicted to stabilize novel forms of magnetic order or quantum spin liquids. Here, we explore the magnetism of $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$, which has the topology of a three-dimensional Kitaev lattice of interconnected Ir honeycombs. Using magnetic resonant x-ray diffraction, we find a complex, yet highly symmetric incommensurate magnetic structure with noncoplanar and counterrotating Ir moments. We propose a minimal Kitaev-Heisenberg Hamiltonian that naturally accounts for all key features of the observed magnetic structure. Our results provide strong evidence that $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ realizes a spin Hamiltonian with dominant Kitaev interactions.

We report hard (14 keV) x-ray diffraction measurements on three compositions ($x=0.11,0.12,0.13)$ of the high-temperature superconductor ${\text{La}}_{2\ensuremath{-}x}$${\text{Sr}}_{x}$${\text{CuO}}_{4}$. All samples show charge density wave (CDW) order with onset temperatures in the range 51--80 K and ordering wave vectors close to (0.23,0,0.5). The CDW is strongest with the longest in-plane correlation length near 1/8 doping. On entering the superconducting state the CDW is suppressed, demonstrating the strong competition between the charge order and superconductivity. CDW order coexists with incommensurate magnetic order and the wave vectors of the two modulations have the simple relationship ${\mathbit{\ensuremath{\delta}}}_{\mathrm{charge}}=2{\mathbit{\ensuremath{\delta}}}_{\mathrm{spin}}$. The intensity of the CDW Bragg peak tracks the intensity of the low-energy (quasielastic) spin fluctuations. We present a phase diagram of ${\text{La}}_{2\ensuremath{-}x}$${\text{Sr}}_{x}$${\text{CuO}}_{4}$ including the pseudogap phase, CDW, and magnetic order.

Giant tunability of ferroelectric polarization ($\ensuremath{\Delta}P=5000\text{ }\text{ }\ensuremath{\mu}\mathrm{C}/{\mathrm{m}}^{2}$) in the multiferroic ${\mathrm{GdMn}}_{2}{\mathrm{O}}_{5}$ with external magnetic fields is discovered. The detailed magnetic model from x-ray magnetic scattering results indicates that the Gd-Mn symmetric exchange striction plays a major role in the tunable ferroelectricity of ${\mathrm{GdMn}}_{2}{\mathrm{O}}_{5}$, which is in distinction from other compounds of the same family. Thus, the highly isotropic nature of Gd spins plays a key role in the giant magnetoelectric coupling in ${\mathrm{GdMn}}_{2}{\mathrm{O}}_{5}$. This finding provides a new handle in achieving enhanced magnetoelectric functionality.

'Forbidden' Bragg reflections of iron orthoborate Fe3BO6 were studied theoretically and experimentally in the vicinity of the iron K edge. Their energy spectra are explained as resulting from the interference of x-rays scattered from two inequivalent crystallographic sites occupied by iron ions. This particular structure property gives rise to complex azimuthal dependences of the reflection intensities in the pre-edge region as they result from the interplay of site specific dipole-quadrupole and quadrupole-quadrupole resonant scattering. Also evidenced is an isotropic character of the absorption spectrum. Self-absorption correction to the diffraction data, as well as possible contributions of thermal vibrations and magnetic order, are discussed. Particular care is given to extracting clean spectra from the data, and it is demonstrated that excellent results can be obtained even from measurements that appear corrupted by several effects such as poor crystal quality and multiple scattering., Comment: 12 pages

The commensurate phase of multiferroic ${\text{HoMn}}_{2}{\text{O}}_{5}$ was studied by x-ray magnetic scattering, both off-resonance and in resonant conditions at the $\text{Ho}\text{ }{L}_{3}$ edge. Below 40 K, magnetic ordering at the Ho sites is induced by the main Mn magnetic order parameter, and its temperature dependence is well accounted for by a simple Curie--Weiss susceptibility model. A lattice distortion of periodicity twice that of the magnetic order is also evidenced. The azimuthal scans confirm the model of the magnetic structure recently refined from neutron diffraction data for both Mn and Ho sites, indicating that the two sublattices interact via magnetic superexchange.

A thorough tensor analysis of the Bragg-forbidden reflection $(00.3{)}_{h}$ in corundum systems having a global center of inversion, such as ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ and $\ensuremath{\alpha}\mathrm{\text{\ensuremath{-}}}{\mathrm{F}\mathrm{e}}_{2}{\mathrm{O}}_{3}$, shows that anomalous x-ray resonant diffraction can access chiral properties related to the dipole-quadrupole ($E1\mathrm{\text{\ensuremath{-}}}E2$) channel via an interference with the pure quadrupole-quadrupole ($E2\mathrm{\text{\ensuremath{-}}}E2$) process. This is also confirmed by independent ab initio numerical simulations. In such a way, it becomes possible to detect chiral quantities in systems where dichroic absorption techniques are ineffective.

At room temperature Cu3Nb2O8 has a centrosymmetric, triclinic crystal structure. If cooled below 24 K, the copper magnetic moments order with a complex, generalized helicoidal magnetic structure that breaks inversion symmetry, giving rise to ferroelectricity. Unusually, the direction of the induced electric polarization vector with respect to the helicoidal spin rotation cannot be reconciled by conventional theories of magneto-electric coupling. Instead, we show that the observed multiferroic properties of Cu3Nb2O8 may be explained through a phenomenological analysis based upon coupling between the magnetic chirality, electric polarity, and a structural axial rotation. Trigonal MnSb2O6 crystallizes with a chiral crystal structure. Typically, magnetic materials with a chiral crystal lattice order with a chiral magnetic structure, where the magnetic exchange interactions and anisotropies follow the symmetry of the lattice. The magnetism of MnSi is a classic example of this scenario, in which exotic skyrmion phases emerge out of a helical magnetic state. To the contrary, we show that the low temperature magnetic structure of MnSb2O6 is cycloidal, described by a magnetic polarity as opposed to a chirality. We demonstrate through ab-initio calculations that this magnetic structure is in fact the ground state of the symmetric-exchange Heisenberg spin Hamiltonian, which has higher symmetry than the underlying crystal lattice. Furthermore, the phenomenology may be understood by considering the coupling between structural chirality, magnetic polarity, and a magnetic axial rotation. As a result, we predict MnSb2O6 to be multiferroic with a weak ferroelectric polarization.