Negative magnetization and magnetic ordering of rare earth and transition metal sublattices in NdFe0.5Cr0.5O3.

We investigate the effect of alloying at the 3dtransition metal site of a rare-earth-transition metal oxide, by considering NdFe0.5Cr0.5O3mixed perovskite with two equal and random distribution of 3d ions, Cr and Fe, interacting with an early 4f rare earth ion, Nd. Employing temperature- and field- dependent magnetization measurements, temperature-dependent x-ray diffraction, neutron powder diffraction, and Raman spectroscopy, we characterize its structural and magnetic properties. Our study reveals bipolar magnetic switching (arising from negative magnetization) and magnetocaloric effect which underline the potential of the studied mixed perovskite in device application. The neutron diffraction study shows the absence of spin reorientation transition over the entire temperature range of 1.5-320 K, although both parent compounds exhibit spin orientation transition. We discuss the microscopic origin of this curious behavior. The neutron diffraction results also reveal the ordering of Nd spins at an unusually high temperature of about 40 K, which is corroborated by Raman measurements.

Strain control of a bandwidth-driven spin reorientation in Ca3Ru2O7.

The layered-ruthenate family of materials possess an intricate interplay of structural, electronic and magnetic degrees of freedom that yields a plethora of delicately balanced ground states. This is exemplified by Ca3Ru2O7, which hosts a coupled transition in which the lattice parameters jump, the Fermi surface partially gaps and the spins undergo a 90∘ in-plane reorientation. Here, we show how the transition is driven by a lattice strain that tunes the electronic bandwidth. We apply uniaxial stress to single crystals of Ca3Ru2O7, using neutron and resonant x-ray scattering to simultaneously probe the structural and magnetic responses. These measurements demonstrate that the transition can be driven by externally induced strain, stimulating the development of a theoretical model in which an internal strain is generated self-consistently to lower the electronic energy. We understand the strain to act by modifying tilts and rotations of the RuO6 octahedra, which directly influences the nearest-neighbour hopping. Our results offer a blueprint for uncovering the driving force behind coupled phase transitions, as well as a route to controlling them.

Emergence of a Magnetostructural Dipolar Glass in the Quadruple Perovskite Dy_{1-δ}Mn_{7+δ}O_{12}.

We show that a polar, pseudo-Jahn-Teller instability exists for the underbonded rare-earth A-site cations in the quadruple perovskite Dy_{1-δ}Mn_{7+δ}O_{12}, which leads to the spontaneous formation of a dipolar glass. This observation alone expands the applicability of pseudo-Jahn-Teller physics in perovskite-derived materials, for which it is typically confined to B-site cations. We demonstrate that the dipolar glass order parameter is coupled to a ferrimagnetic order parameter via strain, leading to a first order magnetostructural phase transition that can be tuned by magnetic field. This phenomenology may emerge in a broad range of perovskite-derived materials in which A-site cation ordering and octahedral tilting are mutually tied to meet the criteria of structural stability.

Spontaneous Rotation of Ferrimagnetism Driven by Antiferromagnetic Spin Canting.

Spin-reorientation phase transitions that involve the rotation of a crystal's magnetization have been well characterized in distorted-perovskite oxides such as orthoferrites. In these systems spin reorientation occurs due to competing rare-earth and transition metal anisotropies coupled via f-d exchange. Here, we demonstrate an alternative paradigm for spin reorientation in distorted perovskites. We show that the R_{2}CuMnMn_{4}O_{12} (R=Y or Dy) triple A-site columnar-ordered quadruple perovskites have three ordered magnetic phases and up to two spin-reorientation phase transitions. Unlike the spin-reorientation phenomena in other distorted perovskites, these transitions are independent of rare-earth magnetism, but are instead driven by an instability towards antiferromagnetic spin canting likely originating in frustrated Heisenberg exchange interactions, and the competition between Dzyaloshinskii-Moriya and single-ion anisotropies.

Author Correction: Electric and antiferromagnetic chiral textures at multiferroic domain walls.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Electric and antiferromagnetic chiral textures at multiferroic domain walls.

Chirality, a foundational concept throughout science, may arise at ferromagnetic domain walls1 and in related objects such as skyrmions2. However, chiral textures should also exist in other types of ferroic materials, such as antiferromagnets, for which theory predicts that they should move faster for lower power3, and ferroelectrics, where they should be extremely small and possess unusual topologies4,5. Here, we report the concomitant observation of antiferromagnetic and electric chiral textures at domain walls in the room-temperature ferroelectric antiferromagnet BiFeO3. Combining reciprocal and real-space characterization techniques, we reveal the presence of periodic chiral antiferromagnetic objects along the domain walls as well as a priori energetically unfavourable chiral ferroelectric domain walls. We discuss the mechanisms underlying their formation and their relevance for electrically controlled topological oxide electronics and spintronics.

Direct Observation of Anapoles by Neutron Diffraction.

The scope of magnetic neutron scattering has been expanded by the observation of electronic Dirac dipoles (anapoles) that are polar (parity odd) and magnetic (time odd). A zero-magnetization ferromagnet Sm_{0.976}Gd_{0.024}Al_{2} with a diamond-type structure presents Dirac multipoles at basis-forbidden reflections that include the standard (2, 2, 2) reflection. Magnetic amplitudes measured at four such reflections are in full accord with a structure factor calculated from the appropriate magnetic space group.

Vesignieite: An S=1/2 Kagome Antiferromagnet with Dominant Third-Neighbor Exchange.

The spin-1/2 kagome antiferromagnet is an archetypal frustrated system predicted to host a variety of exotic magnetic states. We show using neutron scattering measurements that deuterated vesignieite BaCu_{3}V_{2}O_{8}(OD)_{2}, a fully stoichiometric S=1/2 kagome magnet with <1% lattice distortion, orders magnetically at T_{N}=9 K into a multi-k coplanar variant of the predicted triple-k octahedral structure. We find that this structure is stabilized by a dominant antiferromagnetic third-neighbor exchange J_{3} with minor first- or second-neighbor exchanges. The spin-wave spectrum is well described by a J_{3}-only model including a tiny symmetric exchange anisotropy.

Evolution of Magneto-Orbital order Upon B-Site Electron Doping in Na_{1-x}Ca_{x}Mn_{7}O_{12} Quadruple Perovskite Manganites.

We present the discovery and refinement by neutron powder diffraction of a new magnetic phase in the Na_{1-x}Ca_{x}Mn_{7}O_{12} 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.

Electronic and magnetic properties of multiferroic ScFeO3 available from diffraction experiments.

Electronic and magnetic properties of ferric ions (3d 5) in multiferroic ScFeO3 are puzzling, in part because they are different from the only other multiferroic known to possess the same polar chemical structure, BiFeO3. Open questions about ScFeO3 can be addressed by confronting observations with results for G-type antiferromagnetism allowed by the lithium niobate (LiNbO3)-like parent R3c structure. Calculated structure factors for resonant x-ray diffraction include all charge-like quadrupoles allowed by symmetry, and if experimental results for ScFeO3 subsequently imply they are different from zero then ferric ions cannot be in the high-spin 6S state. The same type of experiment can reveal the moment direction in the G-type antiferromagnetism, according to our calculations, and thereby contribute to understanding magnetic anisotropy. Furthermore, structure factors for magnetic neutron diffraction by ScFeO3 include Dirac multipoles that are time-odd and parity-odd, e.g. dipoles that are often called anapoles or toroidal moments. Apart from Dirac multipoles, the conventional approach to the interpretation of neutron Bragg diffraction data will be inadequate if ferric ions (Fe3+) are not in the high-spin 6S state, because the scattering amplitude includes more than simple dipole moments in the general case.

Neutron scattering by Dirac multipoles.

Scattering by magnetic charge formed by Dirac multipoles that are magnetic and polar is examined in the context of materials with properties that challenge conventional concepts. An order parameter composed of Dirac quadrupoles has been revealed in the pseudo-gap phase of ceramic, high-T c superconductors on the basis of Kerr effect and magnetic neutron Bragg diffraction measurements. Construction of Dirac quadrupoles that emerge from centrosymmetric sites used by Cu ions in the ceramic superconductor Hg1201 is illustrated, together with selection rules for excitations that will feature in neutron inelastic scattering, and RIXS experiments. We report magnetic scattering amplitudes for diffraction by polar multipoles that have universal value, because they are not specific to ceramic superconductors. To illustrate this attribute, we consider neutron Bragg diffraction from a magnetically ordered iridate (Sr2IrO4) and discuss shortcomings in published interpretations of diffraction data.

Magnetodielectric detection of magnetic quadrupole order in Ba(TiO)Cu4(PO4)4 with Cu4O12 square cupolas.

In vortex-like spin arrangements, multiple spins can combine into emergent multipole moments. Such multipole moments have broken space-inversion and time-reversal symmetries, and can therefore exhibit linear magnetoelectric (ME) activity. Three types of such multipole moments are known: toroidal; monopole; and quadrupole moments. So far, however, the ME activity of these multipole moments has only been established experimentally for the toroidal moment. Here we propose a magnetic square cupola cluster, in which four corner-sharing square-coordinated metal-ligand fragments form a noncoplanar buckled structure, as a promising structural unit that carries an ME-active multipole moment. We substantiate this idea by observing clear magnetodielectric signals associated with an antiferroic ME-active magnetic quadrupole order in the real material Ba(TiO)Cu4(PO4)4. The present result serves as a useful guide for exploring and designing new ME-active materials based on vortex-like spin arrangements.

Ordered state of magnetic charge in the pseudo-gap phase of a cuprate superconductor (HgBa2CuO(4+δ)).

A symmetry-based interpretation of published experimental results demonstrates that the pseudo-gap phase of underdoped HgBa2CuO(4+δ) (Hg1201) possesses an ordered state of magnetic charge epitomized by Cu magnetic monopoles. Magnetic properties of one-layer Hg1201 and two-layer YBa2Cu3O(6+x) (YBCO) cuprates have much in common, because their pseudo-gap phases possess the same magnetic space-group, e.g. both underdoped cuprates allow the magneto-electric (Kerr) effect. Differences in their properties stem from different Cu site symmetries, leaving Cu magnetic monopoles forbidden in YBCO. Resonant x-ray Bragg diffraction experiments can complement the wealth of information available from neutron diffraction experiments on five Hg1201 samples on which our findings are based. In the case of Hg1201 emergence of the pseudo-gap phase, with time-reversal violation, is accompanied by a reduction of Cu site symmetry that includes loss of a centre of inversion symmetry. In consequence, parity-odd x-ray absorption events herald the onset of the enigmatic phase, and we predict dependence of corresponding Bragg spots on magneto-electric multipoles, including the monopole, and the azimuthal angle (crystal rotation about the Bragg wavevector).

Ferro-type order of magneto-electric quadrupoles as an order-parameter for the pseudo-gap phase of a cuprate superconductor.

There is general agreement within the community of researchers that investigate high-Tc materials that it is most important to understand the pseudo-gap phase. To this end, many experiments on various cuprates have been reported. Two prominent investigations-Kerr effect and neutron Bragg diffraction-imply that underdoped YBCO samples possess long-range magnetic order of an unusual kind. However, other measurements do not support the existence of magnetic order. Here we show that the Kerr effect and magnetic Bragg diffraction data are individual manifestations of ordered magneto-electric quadrupoles at Cu sites. While the use of magneto-electric multipoles is new in studies of the electronic properties of cuprates, they are not unknown in other materials, including an investigation with x-rays of the parent compound CuO. We exploit the recent prediction that neutrons are deflected by magneto-electric multipoles. The outcome of our study is a theory for the order-parameter of the pseudo-gap phase without the aforementioned conflict with other measurements, and the first experimental evidence that neutrons interact with multipoles belonging to a state of magnetic charge.

Field-tunable spin-density-wave phases in Sr3Ru2O7.

The conduction electrons in a metal experience competing interactions with each other and the atomic nuclei. This competition can lead to many types of magnetic order in metals. For example, in chromium the electrons order to form a spin-density-wave (SDW) antiferromagnetic state. A magnetic field may be used to perturb or tune materials with delicately balanced electronic interactions. Here, we show that the application of a magnetic field can induce SDW magnetic order in a quasi-2D metamagnetic metal, where none exists in the absence of the field. We use magnetic neutron scattering to show that the application of a large (B ≈ 8 T) magnetic field to the perovskite metal Sr3Ru2O7 (refs 3-7) can be used to tune the material through two magnetically ordered SDW states. The ordered states exist over relatively small ranges in field (≲0.4 T), suggesting that their origin is due to a new mechanism related to the electronic fine structure near the Fermi energy, possibly combined with the stabilizing effect of magnetic fluctuations. The magnetic field direction is shown to control the SDW domain populations, which naturally explains the strong resistivity anisotropy or 'electronic nematic' behaviour observed in this material.

Strange magnetic multipoles and neutron diffraction by an iridate perovskite (Sr2IrO4).

A theoretical investigation of a plausible construct for electronic structure in iridate perovskites demonstrates the existence of magnetic multipoles hitherto not identified. The strange multipoles, which are parity-even, time-odd and even rank tensors, are absent from the so-called j(eff) = 1/2 model. We prove that the strange multipoles contribute to magnetic neutron diffraction, and we estimate their contribution to intensities of Bragg spots for Sr(2)IrO(4). The construct encompasses the j(eff) = 1/2 model, and it is consistent with the known magnetic structure, ordered magnetic moment, and published resonant x-ray Bragg diffraction data. Over and above time-odd quadrupoles and hexadecapoles, whose contribution changes neutron Bragg intensities by an order of magnitude, according to our estimates, are relatively small triakontadipoles recently proposed as the primary magnetic order-parameter of Sr(2)IrO(4).

Magnetically driven suppression of nematic order in an iron-based superconductor.

A theory of superconductivity in the iron-based materials requires an understanding of the phase diagram of the normal state. In these compounds, superconductivity emerges when stripe spin density wave (SDW) order is suppressed by doping, pressure or atomic disorder. This magnetic order is often pre-empted by nematic order, whose origin is yet to be resolved. One scenario is that nematic order is driven by orbital ordering of the iron 3d electrons that triggers stripe SDW order. Another is that magnetic interactions produce a spin-nematic phase, which then induces orbital order. Here we report the observation by neutron powder diffraction of an additional fourfold-symmetric phase in Ba1-xNaxFe2As2 close to the suppression of SDW order, which is consistent with the predictions of magnetically driven models of nematic order.

Symmetry-protected hidden order and magnetic neutron Bragg diffraction by URu2Si2.

We investigate how the order parameter of a continuous phase transition can be protected from view by symmetry in a magnetic crystal. The symmetry in question forbids atomic displacements and formation of magnetic dipoles, rendering the order parameter invisible in standard x-ray and magnetic neutron Bragg diffraction. Analysis of the allowed magnetic space-groups reveals exact properties of the hidden order parameter. We demonstrate that Bragg spots forbidden by the chemical structure can unveil magnetic hidden order. The method is applied to URu2Si2, which has been thoroughly investigated in the past few decades using all manner of experimental techniques. Starting from the established chemical structure of URu2Si2, we have performed a critical analysis of available data for magnetic neutron Bragg diffraction.

Magnetic symmetries in neutron and resonant x-ray Bragg diffraction patterns of four iridium oxides.

The magnetic properties of Sr(2)IrO(4), Na(2)IrO(3), Sr(3)Ir(2)O(7) and CaIrO(3) are discussed, principally in the light of experimental data in recent literature for Bragg intensities measured in x-ray diffraction with enhancement at iridium L-absorption edges. The electronic structure factors we report, which incorporate parity-even and acentric entities, serve the immediate purpose of making full use of crystal and magnetic symmetry to refine our knowledge of the magnetic properties of the four iridates from resonant x-ray diffraction data. They also offer a platform on which to interpret future investigations, using dichroic signals, resonant x-ray diffraction and neutron diffraction, for example, as well as ab initio calculations of electronic structure. Unit-cell structure factors, suitable for x-ray Bragg diffraction enhanced by an electric dipole-electric dipole (E1-E1) event, reveal exactly which iridium multipoles are visible, e.g., a magnetic dipole parallel to the crystal c-axis (z-axis) and an electric quadrupole with yz-like symmetry in the specific case of CaIrO(3). Magnetic space-groups are assigned to Sr(2)IrO(4), Sr(3)Ir(2)O(7) and CaIrO(3), namely, P(I)cca, P(A)ban and Cm'cm', respectively, in the Belov-Neronova-Smirnova notation. The assignment for Sr(2)IrO(4) is possible because of our new high-resolution neutron diffraction data, gathered on a powder sample. In addition, the new data are used to show that the ordered magnetic moment of an Ir(4+) ion in Sr(2)IrO(4) does not exceed 0.29(4) µ(B). Na(2)IrO(3) has two candidate magnetic space-groups that are not resolved with currently available resonant x-ray data.

Giant improper ferroelectricity in the ferroaxial magnet CaMn7O12.

In rhombohedral CaMn7O12, an improper ferroelectric polarization of magnitude 2870 µC m(-2) is induced by an incommensurate helical magnetic structure that evolves below T(N1)=90 K. The electric polarization was found to be constrained to the high symmetry threefold 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.