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I present a tensorial approach to the description of $\vec{k}/-\vec{k}$-symmetric, time-reversal-odd splitting of electronic bands in magnetic materials, which can be of non-relativistic origin and was recently given the name of `altermagnetism'. I demonstrate that tensors provide a general framework to discuss magnetic symmetry using both spin groups and magnetic point groups, which have often been contrasted in recent literature. I also provide a natural classification of altermagnets in terms of the lowest-order tensorial forms that are permitted in each of the 69 altermagnetic point groups. This approach clarifies the connection between altermagnetism and well-known bulk properties, establishing that the vast majority of altermagnetic materials must also be piezomagnetic and MOKE-active, and provides a rational criterion to search for potential altermagnets among known materials and to test them when the magnetic structure is unknown or ambiguous., Comment: 23 pages, 6 figures, 5 tables. V2 with updated chronology (introduction) and references

Lensless coherent x-ray imaging techniques have great potential for high-resolution imaging of magnetic systems with a variety of in-situ perturbations. Despite many investigations of ferromagnets, extending these techniques to the study of other magnetic materials, primarily antiferromagnets, is lacking. Here, we demonstrate the first (to our knowledge) study of an antiferromagnet using holographic imaging through the "holography with extended reference by autocorrelation linear differential operation" technique. Energy-dependent contrast with both linearly and circularly polarised x-rays are demonstrated. Antiferromagnetic domains and topological textures are studied in the presence of applied magnetic fields, demonstrating quasi-cyclic domain reconfiguration up to 500 mT., Comment: 14 pages, 6 figures

We report a detailed study of the magnetic field switching of ferrotoroidal/multiferroic domains in the Y-type hexaferrite compound Ba$_{0.5}$Sr$_{1.5}$Mg$_2$Fe$_{12}$O$_{22}$. By combining data from SQUID magnetometry, magneto-current measurements, and resonant X-ray scattering experiments, we arrive at a complete description of the deterministic switching, which involves the formation of a temperature-dependent mixed state in low magnetic fields. This mechanism is likely to be shared by other members of the hexaferrite family, and presents a challenge for the development of high-speed read-write memory devices based on these materials., Comment: 20 pages, 7 figures, 2 tables

Whirling topological textures play a key role in exotic phases of magnetic materials and offer promise for logic and memory applications. In antiferromagnets, these textures exhibit enhanced stability and faster dynamics with respect to ferromagnetic counterparts, but they are also difficult to study due to their vanishing net magnetic moment. One technique that meets the demand of highly sensitive vectorial magnetic field sensing with negligible backaction is diamond quantum magnetometry. Here, we show that the archetypal antiferromagnet, hematite, hosts a rich tapestry of monopolar, dipolar and quadrupolar emergent magnetic charge distributions. The direct readout of the previously inaccessible vorticity of an antiferromagnetic spin texture provides the crucial connection to its magnetic charge through a duality relation. Our work defines a novel paradigmatic class of magnetic systems to explore two-dimensional monopolar physics, and highlights the transformative role that diamond quantum magnetometry could play in exploring emergent phenomena in quantum materials.

Antiferromagnets hosting real-space topological spin textures are promising platforms to model fundamental ultrafast phenomena and explore spintronics. However, to date, they have only been fabricated epitaxially on specific symmetry-matched crystalline substrates, to preserve their intrinsic magneto-crystalline order. This curtails their integration with dissimilar supports, markedly restricting the scope of fundamental and applied investigations. Here, we circumvent this limitation by designing detachable crystalline antiferromagnetic nanomembranes of $\alpha$-Fe$_{2}$O$_{3}$, that can be transferred onto other desirable supports after growth. We develop transmission-based antiferromagnetic vector-mapping to show that these nanomembranes harbour rich topological phenomenology at room temperature. Moreover, we exploit their extreme flexibility to demonstrate three-dimensional reconfiguration of antiferromagnetic properties, driven locally via flexure-induced strains. This allows us to spatially design antiferromagnetic states outside their typical thermal stability window. Integration of such freestanding antiferromagnetic layers with flat or curved nanostructures could enable spin texture designs tailored by magnetoelastic-/geometric-effects in the quasi-static and dynamical regimes, opening new explorations into curvilinear antiferromagnetism and unconventional computing., Comment: 17 pages, 4 figures

Twisting in bilayers introduces structural chirality with two enantiomers, i.e., left- and right-hand bilayers, depending on the oriented twist angle. The interplay between this global chirality and additional degrees of freedom, such as magnetic ordering and the local octahedral chirality arising from the geometry of the bonds, can yield striking phenomena. In this work, we focus on collinear antiferromagnetic CrI$_3$ twisted homo-bilayers, which are characterized by a staggered octahedral chirality in each monolayer. Using symmetry analysis, density functional theory and tight-binding model calculations we show that layers twisting can lower the structural and magnetic point-group symmetries, thus activating pyroelectricity and the magneto-optical Kerr effect, which would otherwise be absent in untwisted antiferromagnetic homo-bilayers. Interestingly, both electric polarization and Kerr angle are controllable by the twist angle and their sign is reversed when switching from left- to right-twisted bilayers. We further unveil the occurrence of unconventional vortices with spin textures that alternate opposite chiralities in momentum space. These findings demonstrate that the interplay between twisting and octahedral chirality in magnetic bilayers and related van der Waals heterostructures represents an extraordinary resource for tailoring their physical properties for spintronic and optoelectronic applications., Comment: Accepted by PRB; 15 pages, 9 figures, and 4 tables in main text; 10 pages, 8 figures, and 1 table in supplemental material

Topologically protected whirling magnetic textures could emerge as data carriers in next-generation post-Moore computing. Such textures are abundantly observed in ferromagnets (FMs); however, their antiferromagnetic (AFM) counterparts are expected to be even more relevant for device applications, as they promise ultra-fast, deflection-free dynamics whilst being robust against external fields. Unfortunately, they have remained elusive, hence identifying materials hosting such textures is key to developing this technology. Here, we present comprehensive micromagnetic and analytical models investigating topological textures in the broad material class of A-type antiferromagnets, specifically focusing on the prototypical case of $\alpha \text{-Fe}_2 \text{O}_3$,an emerging candidate for AFM spintronics. By exploiting a symmetry breaking interfacial Dzyaloshinskii-Moriya interaction (iDMI), it is possible to stabilize a wide topological family, including AFM (anti)merons and bimerons and the hitherto undiscovered AFM skyrmions. Whilst iDMI enforces homochirality and improves the stability of these textures, the widely tunable anisotropy and exchange interactions enable unprecedented control of their core dimensions. We then present a unifying framework to model the scaling of texture sizes based on a simple dimensional analysis. As the parameters required to host and tune homochiral AFM textures may be obtained by rational materials design of $\alpha \text{-Fe}_2 \text{O}_3$, it could emerge as a promising platform to initiate AFM topological spintronics., Comment: 17 pages, 9 figures. Submitted to Physical Review X

Long-range ordering of magnetic dipoles in bulk materials gives rise to a broad range of magnetic structures, from simple collinear ferromagnets and antiferromagnets, to complex magnetic helicoidal textures stabilized by competing exchange interactions. In contrast, in the context of dipolar order in dielectric crystals, only parallel (ferroelectric) and antiparallel (antiferroelectric) collinear alignments of electric dipoles are typically considered. Here, we report an observation of incommensurate helical ordering of electric dipoles by light hole-doping of the quadruple perovskite BiMn7O12. In analogy with magnetism, the electric dipole helicoidal texture is also stabilized by competing instabilities. Specifically, orbital ordering and lone electron pair stereochemical activity compete, giving rise to phase transitions from a non-chiral cubic structure, to an incommensurate electric dipole and orbital helix, via an intermediate density wave.

In the quest for post-CMOS technologies, ferromagnetic skyrmions and their anti-particles have shown great promise as topologically protected solitonic information carriers in memory-in-logic or neuromorphic devices. However, the presence of dipolar fields in ferromagnets, restricting the formation of ultra-small topological textures, and the deleterious skyrmion Hall effect when driven by spin torques have thus far inhibited their practical implementations. Antiferromagnetic analogues, which are predicted to demonstrate relativistic dynamics, fast deflection-free motion and size scaling have recently come into intense focus, but their experimental realizations in natural antiferromagnetic systems are yet to emerge. Here, we demonstrate a family of topological antiferromagnetic spin-textures in $\alpha$-Fe$_2$O$_3$ - an earth-abundant oxide insulator - capped with a Pt over-layer. By exploiting a first-order analogue of the Kibble-Zurek mechanism, we stabilize exotic merons-antimerons (half-skyrmions), and bimerons, which can be erased by magnetic fields and re-generated by temperature cycling. These structures have characteristic sizes of the order ~100 nm that can be chemically controlled via precise tuning of the exchange and anisotropy, with pathways to further scaling. Driven by current-based spin torques from the heavy-metal over-layer, some of these AFM textures could emerge as prime candidates for low-energy antiferromagnetic spintronics at room temperature., Comment: 18 pages, 4 figures

Strain engineering is widely used to manipulate the electronic and magnetic properties of complex materials. An attractive route to control magnetism with strain is provided by the piezomagnetic effect, whereby the staggered spin structure of an antiferromagnet is decompensated by breaking the crystal field symmetry, which induces a ferrimagnetic polarization. Piezomagnetism is especially attractive because unlike magnetostriction it couples strain and magnetization at linear order, and allows for bi-directional control suitable for memory and spintronics applications. However, its use in functional devices has so far been hindered by the slow speed and large uniaxial strains required. Here, we show that the essential features of piezomagnetism can be reproduced with optical phonons alone, which can be driven by light to large amplitudes without changing the volume and hence beyond the elastic limits of the material. We exploit nonlinear, three-phonon mixing to induce the desired crystal field distortions in the antiferromagnet CoF$_2$. Through this effect, we generate a ferrimagnetic moment of 0.2 $\mu_B$ per unit cell, nearly three orders of magnitude larger than achieved with mechanical strain., Comment: 27 pages, 12 figures

The spin-Hall effect describes the interconversion of charge currents and spin currents, enabling highly efficient manipulation of magnetization for spintronics. Symmetry conditions generally restrict polarizations of these spin currents to be orthogonal to both the charge and spin flows. Spin polarizations can deviate from such direction in nonmagnetic materials only when the crystalline symmetry is reduced11. Here we experimentally show control of the spin polarization direction by using a non-collinear antiferromagnet Mn$_{3}$GaN, in which the triangular spin structure creates a low magnetic symmetry state while maintaining a high crystalline symmetry. We demonstrate that epitaxial Mn3GaN/Permalloy heterostructures can generate unique types of spinHall torques at room temperature corresponding to unconventional spin polarizations collinear to spin currents or charge currents which are forbidden in any sample with two-fold rotational symmetry. Our results demonstrate an approach based on spin-structure design for controlling spinorbit torque, paving the way for further progress in the emergent field of antiferromagnetic spintronics.

Using micromagnetic simulations, we have modelled the formation of imprinted merons and anti-merons in cobalt overlayers of different thickness (1-8 nm), stabilised by interfacial exchange with antiferromagnetic vortices in $\alpha$-Fe2O3. Structures similar to those observed experimentally could be obtained with reasonable exchange parameters, also in the presence of surface roughness. We produce simulated meron|antimeron images by magnetic force microscopy (MFM) and nitrogen-vacancy (N-V) centre microscopy, and established signatures of these topological structures in different experimental configurations., Comment: 11 pages, 7 figures, Published in Physical Review B, 26 February 2020

Ba$_{3}$NbFe$_{3}$Si$_{2}$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 $\pm$ $\vec{Q}$ or applied magnetic field $\pm$ $\mu_{0}$H. When the field is applied within the crystallographic $ab$-plane, the spin wave dispersion is directionally \textit{isotropic} and symmetric in $\pm$ $\mu_{0}$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. Directional anisotropy, or often referred to as non reciprocal responses, can occur in antiferromagnetic phases in the absence of the Dzyaloshinskii-Moriya interaction or other effects resulting from spin-orbit coupling., Comment: (6 pages, 4 figures, to be published in Phys. Rev. B)

By employing resonant X-ray microdiffraction, we image the magnetisation and magnetic polarity domains of the Y-type hexaferrite Ba$_{0.5}$Sr$_{1.5}$Mg$_2$Fe$_{12}$O$_{22}$. We show that the magnetic polarity domain structure can be controlled by both magnetic and electric fields, and that full inversion of these domains can be achieved simply by reversal of an applied magnetic field in the absence of an electric field bias. Furthermore, we demonstrate that the diffraction intensity measured in different X-ray polarisation channels cannot be reproduced by the accepted model for the polar magnetic structure, known as the 2-fan transverse conical (TC) model. We propose a modification to this model, which achieves good quantitative agreement with all of our data. We show that the deviations from the TC model are large, and may be the result of an internal magnetic chirality, most likely inherited from the parent helical (non-polar) phase., Comment: 9 figures

We present the magnetic structure of $\mathrm{TmMn_3O_6}$, solved via neutron powder diffraction - the first such study of any $R\mathrm{Mn_3O_6}$ A-site columnar-ordered quadruple perovskite to be reported. We demonstrate that long range magnetic order develops below 74 K, and at 28 K a spin-flop transition occurs driven by $f$-$d$ exchange and rare earth single ion anisotropy. In both magnetic phases the magnetic structure may be described as a collinear ferrimagnet, contrary to conventional theories of magnetic order in the manganite perovskites. Instead, we show that these magnetic structures can be understood to arise due to ferro-orbital order, the A, A$'$ and A$''$ site point symmetry, $mm2$, and the dominance of A-B exchange over both A-A and B-B exchange, which together are unique to the $R\mathrm{Mn_3O_6}$ perovskites., Comment: 11 pages, 5 figures

The presence of domains in ferroic materials can negatively affect their macroscopic properties and hence their usefulness in device applications. From an experimental perspective, measuring materials comprising multiple domains can complicate the interpretation of material properties and their underlying mechanisms. In general, BiFeO$_3$ films tend to grow with multiple magnetic domains and often contain multiple ferroelectric and ferroelastic domain variants. By growing (111)-oriented BiFeO$_3$ films on an orthorhombic TbScO$_3$ 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 polarisation by showing the magnetic polarity in this domain is inverted upon 180$^\circ$ ferroelectric switching, Comment: 8 pages, 3 figures

We present the discovery and refinement by neutron powder diffraction of a new magnetic phase in the Na1-xCaxMn7O12 quadruple perovskite phase diagram, which is the incommensurate analogue of the well-known pseudo-CE phase of the simple perovskite manganites. We demonstrate that incommensurate magnetic order arises in quadruple perovskites due to the exchange interactions between A and B sites. Furthermore, by constructing a simple mean field Heisenberg exchange model that generically describes both simple and quadruple perovskite systems, we show that this new magnetic phase unifies a picture of the interplay between charge, magnetic and orbital ordering across a wide range of compounds., Comment: Accepted for publication in Physical Review Letters

Vortices are among the simplest topological structures, and occur whenever a flow field `whirls' around a one-dimensional core. They are ubiquitous to many branches of physics, from fluid dynamics to superconductivity and superfluidity, and are even predicted by some unified theories of particle interactions, where they might explain some of the largest-scale structures seen in today's Universe. In the crystalline state, vortex formation is rare, since it is generally hampered by long-range interactions: in ferroic materials (ferromagnetic and ferroelectric), vortices are only observed when the effects of the dipole-dipole interaction is modified by confinement at the nanoscale, or when the parameter associated with the vorticity does not couple directly with strain. Here, we present the discovery of a novel form of vortices in antiferromagnetic (AFM) hematite ($\alpha$-Fe$_2$O$_3$) epitaxial films, in which the primary whirling parameter is the staggered magnetisation. Remarkably, ferromagnetic (FM) topological objects with the same vorticity and winding number of the $\alpha$-Fe$_2$O$_3$ vortices are imprinted onto an ultra-thin Co ferromagnetic over-layer by interfacial exchange. Our data suggest that the ferromagnetic vortices may be merons (half-skyrmions, carrying an out-of-plane core magnetisation), and indicate that the vortex/meron pairs can be manipulated by the application of an in-plane magnetic field, H$_{\parallel}$, giving rise to large-scale vortex-antivortex annihilation., Comment: 16 pages, 4 figures

A theory describing how ferroic properties can emerge transiently in the ultra-fast regime by breaking symmetry with light through three-phonon coupling is presented. Particular emphasis is placed on the special case when two exactly degenerate mid-infra-red or THz phonons are resonantly pumped, since this situation can give rise to an exactly rectified ferroic response with damping envelopes of ~ 1 ps or less. Light-induced ferroelectricity and ferromagnetism are discussed in this context, and a number of candidate materials that could display these phenomena are proposed. The same analysis is also applied to the interpretation of previous femto-magnetism experiments, performed in different frequency ranges (visible and near-infrared), but sharing similar symmetry characteristics., Comment: 10 pages

We present an implementation of time-dependent density functional perturbation theory for spin fluctuations, based on planewaves and pseudopotentials. We compute the dynamic spin susceptibility self-consistently by solving the time-dependent Sternheimer equation, within the adiabatic local density approximation to the exchange and correlation kernel. We demonstrate our implementation by calculating the spin susceptibility of representative elemental transition metals, namely bcc Fe, fcc Ni and bcc Cr. The calculated magnon dispersion relations of Fe and Ni are in agreement with previous work. The calculated spin susceptibility of Cr exhibits a soft-paramagnon instability, indicating the tendency of the Cr spins to condense in a incommensurate spin density wave phase, in agreement with experiment.

Through analysis of variable temperature neutron powder diffraction data, we present solutions for the magnetic structures of SrMn$_7$O$_{12}$, CdMn$_7$O$_{12}$, and PbMn$_7$O$_{12}$ in all long-range ordered phases. The three compounds were found to have magnetic structures analogous to that reported for CaMn$_7$O$_{12}$. They all feature a higher temperature lock-in phase with \emph{commensurate} magneto-orbital coupling, and a delocked, multi-\textbf{k} magnetic ground state where \emph{incommensurate} magneto-orbital coupling gives rise to a constant-moment magnetic helix with modulated spin helicity. CdMn$_7$O$_{12}$ represents a special case in which the orbital modulation is commensurate with the crystal lattice and involves stacking of fully and partially polarized orbital states. Our results provide a robust confirmation of the phenomenological model for magneto-orbital coupling previously presented for CaMn$_7$O$_{12}$. Furthermore, we show that the model is universal to the $A^{2+}$ quadruple perovskite manganites synthesised to date, and that it is tunable by selection of the $A$-site ionic radius.

We have directly imaged reversible electrical switching of the cycloidal rotation direction (magnetic polarity) in a (111)-BiFeO3 epitaxial-film device at room temperature by non-resonant x-ray magnetic scattering. Consistent with previous reports, fully relaxed (111)-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., Comment: 6 pages, 5 figures; corrected figure 4

We investigate polarization memory effects in single-crystal CuFeO2, which has a magnetically-induced ferroelectric phase at low temperatures and applied B fields between 7.5 and 13 T. Following electrical poling of the ferroelectric phase, we find that the nonpolar collinear antiferromagnetic ground state at B = 0 T retains a strong memory of the polarization magnitude and direction, such that upon re-entering the ferroelectric phase a net polarization of comparable magnitude to the initial polarization is recovered in the absence of external bias. This memory effect is very robust: in pulsed-magnetic-field measurements, several pulses into the ferroelectric phase with reverse bias are required to switch the polarization direction, with significant switching only seen after the system is driven out of the ferroelectric phase and ground state either magnetically (by application of B > 13 T) or thermally. The memory effect is also largely insensitive to the magnetoelastic domain composition, since no change in the memory effect is observed for a sample driven into a single-domain state by application of stress in the [1-10] direction. On the basis of Monte Carlo simulations of the ground state spin configurations, we propose that the memory effect is due to the existence of helical domain walls within the nonpolar collinear antiferromagnetic ground state, which would retain the helicity of the polar phase for certain magnetothermal histories., Comment: 9 pages, 7 figures

The D2O ice VI to ice XV hydrogen ordering phase transition at ambient pressure is investigated in detail with neutron diffraction. The lattice constants are found to be sensitive indicators for hydrogen ordering. The a and b lattice constants contract whereas a pronounced expansion in c is found upon hydrogen ordering. Overall, the hydrogen ordering transition goes along with a small increase in volume which explains why the phase transition is more difficult to observe upon cooling under pressure. Slow-cooling ice VI at 1.4 GPa gives essentially fully hydrogen-disordered ice VI. Consistent with earlier studies, the ice XV obtained after slow-cooling at ambient pressure is best described with P-1 space group symmetry. Using a new computational approach, we achieve the atomistic reconstruction of a supercell structure that is consistent with the average partially ordered structure derived from Rietveld refinements. This shows that C-type networks are most prevalent in ice XV but other structural motifs outside of the classifications of the fully hydrogen-ordered networks are identified as well. The recently proposed Pmmn structural model for ice XV is found to be incompatible with our diffraction data and we argue that only structural models that are capable of describing full hydrogen order should be used., Comment: 19 pages, 8 figures

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

We present a thorough density functional theory study of the magneto-electric (ME) effect in Cr$_{2}$O$_{3}$. The spin-lattice ME tensor $\alpha$ was determined in the low-field and spin flop (SF) phases, using the method of dynamical magnetic charges, and found to be the sum of three distinct components. Two of them, a large relativistic "cycloidal" term and a small longitudinal term, are independent on the spin orientation. The third, only active in the SF phases is also of relativistic origin and arises from magnetic-field-induced chirality, leading to a non-toroidal ME response., Comment: 5 pages with 2 figures, 2 pages supplementary material

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., Comment: 5 pages, 3 figures

We present measurements of conductance hysteresis on CH3NH3PbI3 perovskite thin films, performed using the double-wave method, in order to investigate the possibility of a ferroelectric response. A strong frequency dependence of the hysteresis is observed in the range of 0.1 Hz to 150 Hz, with a hysteretic charge density in excess of 1000 {\mu}C/cm2 at frequencies below 0.4 Hz - a behaviour uncharacteristic of a ferroelectric response. We show that the observed hysteretic conductance, as well as the presence of a double arc in the impedance spectroscopy, can be fully explained by the migration of mobile ions under bias on a timescale of seconds. Our measurements place an upper limit of approximately 1 {\mu}C/cm2 on any intrinsic frequency-independent polarisation, ruling out ferroelectricity as the main cause of current-voltage hysteresis and providing further evidence of the importance of ionic migration in modifying the efficiency of CH3NH3PbI3 devices.

We study the electronic and magnetic structures of multiferroic CaMn$_7$O$_{12}$ by first-principle calculations, based on the experimentally determined modulated crystal structure. We confirm the presence of a 3$d$ orbital modulation of the Mn2 (Mn$^{3+}$) sites, previously inferred from the Jahn-Teller crystal distortions. Our results indicate that in the multiferroic phase the magnetic structure of the Mn3 (Mn$^{4+}$) sites is anharmonically modulated via orbitally-mediated coupling with the structural modulation, and that the Dzyaloshinskii-Moriya and exchange striction mechanisms contribute equally to the polarization

We have investigated the magnetic structure and ferroelectricity in RbFe(MoO$_4$)$_2$ via first-principles calculations. Phenomenological analyses have shown that ferroelectricity may arise due to both the triangular chirality of the magnetic structure, and through coupling between the magnetic helicity and the ferroaxial structural distortion. Indeed, it was recently proposed that the structural distortion plays a key role in stabilising the chiral magnetic structure itself. We have determined the relative contribution of the two mechanisms via \emph{ab-initio} calculations. Whilst the structural axiality does induce the magnetic helix by modulating the symmetric exchange interactions, the electric polarization is largely due to the in-plane spin triangular chirality, with both electronic and ionic contributions being of relativistic origin. At the microscopic level, we interpret the polarization as a secondary steric consequence of the inverse Dzyaloshinskii-Moriya mechanism and accordingly explain why the ferroaxial component of the electric polarization must be small.

Magneto-electric coupling in pyroelectric CaBaCo$_4$O$_7$ is investigated using ab-intio calculations and Landau theory. The former shows that exchange-striction is strong enough to produce a giant change in electric polarization upon ferrimagnetic ordering, comparable to the experimentally determined value of ~17 mC/m$^2$ . Furthermore, Landau theory demonstrates that magneto-elastic coupling in CaBaCo$_4$O$_7$ is responsible for the strong magneto-electric coupling appearing close to the magnetic phase transition.

The hexaferrites are known to exhibit a wide range of magnetic structures, some of which are connected to important technological applications and display magnetoelectric properties. We present data on the low field magnetic structures stabilised in a Y-type hexaferrite as observed by resonant soft X-ray diffraction. The helical spin block arrangement that is present in zero applied magnetic field becomes fan-like as a field is applied in plane. The propagation vectors associated with each fan structure are studied as a function of field, and a new magnetic phase is reported. Mean field calculations indicate this phase should stabilise close to the boundary of the previously reported phases., Comment: 10 pages, 7 figures

Structural and magnetic chiralities are found to coexist in a small group of materials in which they produce intriguing phenomenologies such as the recently discovered skyrmion phases. Here, we describe a previously unknown manifestation of this interplay in MnSb2O6, a trigonal oxide with a chiral crystal structure. Unlike all other known cases, the MnSb2O6 magnetic structure is based on co-rotating cycloids rather than helices. The coupling to the structural chirality is provided by a magnetic axial vector, related to the so-called vector chirality. We show that this unique arrangement is the magnetic ground state of the symmetric-exchange Hamiltonian, based on ab-initio theoretical calculations of the Heisenberg exchange interactions, and is stabilised by out-of-plane anisotropy. MnSb2O6 is predicted to be multiferroic with a unique ferroelectric switching mechanism., Comment: Accepted for publication in Physical Review Letters

Magnetic domains at the surface of a ferroelectric monodomain BiFeO3 single crystal have been imaged by hard X-ray magnetic scattering. Magnetic domains up to several hundred microns in size have been observed, corresponding to cycloidal modulations of the magnetization along the wave-vector k=2\pi(\delta,\delta,0) and symmetry equivalent directions. The rotation direction of the magnetization in all magnetic domains, determined by diffraction of circularly polarized light, was found to be unique and in agreement with predictions of a combined approach based on a spin-model complemented by relativistic density-functional simulations. Imaging of the surface shows that the largest adjacent domains display a 120 degree vortex structure., Comment: Published in Physical Review Letters

Orbitally ordered states evolving coincidentally with structural distortions and magnetic ordering provide a novel route to controlling electronic and magnetic properties of materials through external fields. We report an unprecedented magneto-orbital helix in CaMn7O12, found to give rise to the largest magnetically induced ferroelectric polarisation measured to date. Characterisation of the structural modulation using x-ray diffraction, and analysis of magnetic exchange shows that orbital order is crucial in stabilising a chiral magnetic structure, thus allowing for electric polarisation. Additionally, the presence of a global structural rotation enables the coupling between this polarisation and magnetic helicity required for multiferrocitiy. These novel principles open up the possibility of discovering new high-temperature multiferroics., Comment: Submitted to Nature Communications

The coupling of magnetic chiralities to the ferroelectric polarisation in multiferroic RbFe(MoO$_4$)$_2$ is investigated by neutron spherical polarimetry. Because of the axiality of the crystal structure below $T_\textrm{c}$ = 190 K, helicity and triangular chirality are symmetric-exchange coupled, explaining the onset of the ferroelectricity in this proper-screw magnetic structure - a mechanism that can be generalised to other systems with "ferroaxial" distortions in the crystal structure. With an applied electric field we demonstrate control of the chiralities in both structural domains simultaneously., Comment: 5 pages, 4 figures

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 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 deg Ir-O-Ir bonds required for dominant Kitaev exchange., Comment: 12 pages; fixed typos

In rhombohedral CaMn7O12, an improper ferroelectric polarization of magnitude 2870 {\mu}C m-2 is induced by an incommensurate helical magnetic structure that evolves below TN1 = 90 K. The electric polarization was found to be constrained to the high symmetry three-fold rotation axis of the crystal structure, perpendicular to the in-plane rotation of the magnetic moments. The multiferroicity is explained by the ferroaxial coupling mechanism, which in CaMn7O12 gives rise to the largest magnetically induced, electric polarization measured to date., Comment: 10 pages, 4 figures, and 1 table. Submitted to Physical Review Letters

By combining bulk properties, neutron diffraction and non-resonant X-ray diffraction measurements, we demonstrate that the new multiferroic Cu$_3$Nb$_2$O$_8$ becomes polar simultaneously with the appearance of generalised helicoidal magnetic ordering. The electrical polarization is oriented perpendicularly to the common plane of rotation of the spins --- an observation that cannot be reconciled with the "conventional" theory developed for cycloidal multiferroics. Our results are consistent with coupling between a macroscopic structural rotation, which is allowed in the paramagnetic group, and magnetically-induced structural chirality., Comment: This article is in print with Physical Review Letters

The insulating ternary oxide YbFe$_2$O$_4$ displays an unusual frustration-driven incommensurate charge-ordering (CO) transition, linked to possible ferroelectricity. Based on high-resolution synchrotron data, we report a detailed structural model showing that the CO phase is an incommensurate charge-density wave and cannot be ferroelectric, since the electrical dipole moments are also incommensurately modulated. The change between continuous and "spotty" helices of scattering at the CO transition is attributed to three-dimensional fluctuations of the direction of the ordering wavevector., Comment: 7 pages, 6 figures

We report resonant X-ray scattering measurements on the orbitally-degenerate triangular metallic antiferromagnet 2H-AgNiO2 to probe the spontaneous transition to a triple-cell superstructure at temperatures below 365 K. We observe a strong resonant enhancement of the supercell reflections through the Ni K-edge. The empirically extracted K-edge shift between the crystallographically-distinct Ni sites of 2.5(3) eV is much larger than the value expected from the shift in final states, and implies a core-level shift of ~1 eV, thus providing direct evidence for the onset of spontaneous honeycomb charge order in the triangular Ni layers. We also provide band-structure calculations that explain quantitatively the observed edge shifts in terms of changes in the Ni electronic energy levels due to charge order and hybridization with the surrounding oxygens., Comment: 5 pages, 4 figures

We have investigated the spin fluctuations in the langasite compound Ba3NbFe3Si2O14 in both the ordered state and as a function of temperature. The low temperature magnetic structure is defined by a spiral phase characterized by magnetic Bragg peaks at q=(0,0,tau ~ 1/7) onset at TN=27 K as previously reported by Marty et al. The nature of the fluctuations and temperature dependence of the order parameter is consistent with a classical second order phase transition for a two dimensional triangular antiferromagnet. We will show that the physical properties and energy scales including the ordering wavevector, Curie-Weiss temperature, and the spin-waves can be explained through the use of only symmetric exchange constants without the need for the Dzyaloshinskii-Moriya interaction. This is accomplished through a set of ``helical" exchange pathways along the c direction imposed by the chiral crystal structure and naturally explains the magnetic diffuse scattering which displays a strong vector chirality up to high temperatures well above the ordering temperature. This illustrates a strong coupling between magnetic and crystalline chirality in this compound., Comment: 16 pages, 16 figures, submitted to Physical Review B

The S=2 anisotropic triangular lattice alpha-NaMnO2 is studied by neutron inelastic scattering. Antiferromagnetic order occurs at T ~ 45 K with opening of a spin gap. The spectral weight of the magnetic dynamics above the gap (Delta ~ 7.5 meV) has been analysed by the single-mode approximation. Excellent agreement with the experiment is achieved when a dominant exchange interaction (|J|/k_B ~ 73 K), along the monoclinic b-axis and a sizeable easy-axis magnetic anisotropy (|D|/k_B ~ 3 K) are considered. Despite earlier suggestions for two-dimensional spin interactions, the dynamics illustrate strongly coupled antiferromagnetic S=2 chains and cancellation of the interchain exchange due to the lattice topology. alpha-NaMnO2 therefore represents a model system where the geometric frustration is resolved through the lowering of the dimensionality of the spin interactions., Comment: 4 pages, 4 figures, to be published in Physical Review Letters

A new phase of ice, named ice XV, has been identified and its structure determined by neutron diffraction. Ice XV is the hydrogen-ordered counterpart of ice VI and is thermodynamically stable at temperatures below ~130 K in the 0.8 to 1.5 GPa pressure range. The regions of stability in the medium pressure range of the phase diagram have thus been finally mapped, with only hydrogen-ordered phases stable at 0 K. The ordered ice XV structure is antiferroelectric, in clear disagreement with recent theoretical calculations predicting ferroelectric ordering.

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, the spin-spin correlation function -displaying a short-range 120 degrees configuration- decays rapidly as typically found in spin-liquids. YBaCo4O7 experimentally realizes a new class of two-dimensional frustrated systems where the strong out-of-plane coupling does not lift the in-plane degeneracy, but instead act as an external "field".