Fragmentation in spin ice from magnetic charge injection.

The complexity embedded in condensed matter fertilizes the discovery of new states of matter, enriched by ingredients like frustration. Illustrating examples in magnetic systems are Kitaev spin liquids, skyrmions phases, or spin ices. These unconventional ground states support exotic excitations, for example the magnetic charges in spin ices, also called monopoles. Here, we propose a mechanism to inject monopoles in a spin ice at equilibrium through a staggered magnetic field. We show theoretically, and demonstrate experimentally in the Ho2Ir2O7 pyrochlore iridate, that it results in the stabilization of a monopole crystal, which exhibits magnetic fragmentation. In this new state of matter, the magnetic moment fragments into an ordered part and a persistently fluctuating one. Compared to conventional spin ices, the different nature of the excitations in this fragmented state opens the way to tunable field-induced and dynamical behaviors.Exploring unconventional magnetism facilities both fundamental understanding of materials and their real applications. Here the authors demonstrate that a magnetic monopole crystal is stabilized by a staggered magnetic field in the pyrochlore iridate Ho2Ir2O7, leading to a fragmented magnetization.

Coupled multiferroic domain switching in the canted conical spin spiral system Mn2GeO4.

Despite remarkable progress in developing multifunctional materials, spin-driven ferroelectrics featuring both spontaneous magnetization and electric polarization are still rare. Among such ferromagnetic ferroelectrics are conical spin spiral magnets with a simultaneous reversal of magnetization and electric polarization that is still little understood. Such materials can feature various multiferroic domains that complicates their study. Here we study the multiferroic domains in ferromagnetic ferroelectric Mn2GeO4 using neutron diffraction, and show that it features a double-Q conical magnetic structure that, apart from trivial 180o commensurate magnetic domains, can be described by ferromagnetic and ferroelectric domains only. We show unconventional magnetoelectric couplings such as the magnetic-field-driven reversal of ferroelectric polarization with no change of spin-helicity, and present a phenomenological theory that successfully explains the magnetoelectric coupling. Our measurements establish Mn2GeO4 as a conceptually simple multiferroic in which the magnetic-field-driven flop of conical spin spirals leads to the simultaneous reversal of magnetization and electric polarization.

Anisotropy-Tuned Magnetic Order in Pyrochlore Iridates.

The magnetic behavior of polycrystalline samples of Er(2)Ir(2)O(7) and Tb(2)Ir(2)O(7) pyrochlores is studied by magnetization measurements and neutron diffraction. Both compounds undergo a magnetic transition at 140 and 130 K, respectively, associated with an ordering of the Ir sublattice, signaled by thermomagnetic hysteresis. In Tb(2)Ir(2)O(7), we show that the Ir molecular field leads the Tb magnetic moments to order below 40 K in the all-in-all-out magnetic arrangement. No sign of magnetic long-range order on the Er sublattice is evidenced in Er(2)Ir(2)O(7) down to 0.6 K where a spin freezing is detected. These contrasting behaviors result from the competition between the Ir molecular field and the different single-ion anisotropy of the rare-earth elements on which it is acting. Additionally, this strongly supports the all-in-all-out iridium magnetic order.

Spin-stripe phase in a frustrated zigzag spin-1/2 chain.

Motifs of periodic modulations are encountered in a variety of natural systems, where at least two rival states are present. In strongly correlated electron systems, such behaviour has typically been associated with competition between short- and long-range interactions, for example, between exchange and dipole-dipole interactions in the case of ferromagnetic thin films. Here we show that spin-stripe textures may develop also in antiferromagnets, where long-range dipole-dipole magnetic interactions are absent. A comprehensive analysis of magnetic susceptibility, high-field magnetization, specific heat and neutron diffraction measurements unveils ß-TeVO4 as a nearly perfect realization of a frustrated (zigzag) ferromagnetic spin-1/2 chain. Notably, a narrow spin-stripe phase develops at elevated magnetic fields due to weak frustrated short-range interchain exchange interactions, possibly assisted by the symmetry-allowed electric polarization. This concept provides an alternative route for the stripe formation in strongly correlated electron systems and may help understanding of other widespread, yet still elusive, stripe-related phenomena.

MnSb2O6: a polar magnet with a chiral crystal structure.

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 MnSb(2)O(6), a trigonal oxide with a chiral crystal structure. Unlike all other known cases, the MnSb(2)O(6) magnetic structure is based on corotating 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 stabilized by out-of-plane anisotropy. MnSb(2)O(6) is predicted to be multiferroic with a unique ferroelectric switching mechanism.

X-ray imaging and multiferroic coupling of cycloidal magnetic domains in ferroelectric monodomain BiFeO3.

Magnetic domains at the surface of a ferroelectric monodomain BiFeO(3) 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=(δ,δ,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° vortex structure.

Giant tunability of ferroelectric polarization in GdMn2O5.

Giant tunability of ferroelectric polarization (ΔP=5000 µC/m2) in the multiferroic GdMn2O5 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 GdMn2O5, 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 GdMn2O5. This finding provides a new handle in achieving enhanced magnetoelectric functionality.

Magneto-orbital helices as a route to coupling magnetism and ferroelectricity in multiferroic CaMn7O12.

Orbital physics drives a rich phenomenology in transition-metal oxides, providing the microscopic underpinning for effects such as Colossal Magnetoresistance. In particular, magnetic and lattice degrees of freedom are coupled through orbital ordering, and it has long been hoped that this coupling could be exploited to create high-temperature multiferroics with large values of the electrical polarization. Here we report an unprecedented magneto-orbital texture in multiferroic CaMn(7)O(12), found to give rise to the largest magnetically induced ferroelectric polarization measured to date. X-ray diffraction characterization of the structural modulation in these 'magneto-orbital helices', and analysis of magnetic exchange shows that orbital order is crucial in stabilising a chiral magnetic structure, thus allowing for electric polarization. Additionally, the presence of a global structural rotation enables the coupling between this polarization and magnetic helicity required for multiferroicity. These novel principles open up the possibility of discovering new multiferroics with even larger polarization and higher transition temperatures.

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.

Cu3Nb2O8: a multiferroic with chiral coupling to the crystal structure.

By combining bulk properties, neutron diffraction, and nonresonant x-ray diffraction measurements, we demonstrate that the new multiferroic Cu(3)Nb(2)O(8) becomes polar simultaneously with the appearance of generalized 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.

Slow magnetic order-order transition in the spin chain antiferromagnet Ca3Co2O6.

Using powder neutron diffraction, we have discovered an unusual magnetic order-order transition in the Ising spin chain compound Ca3Co2O6. On lowering the temperature, an antiferromagnetic phase with a propagation vector k=(0.5,-0.5,1) emerges from a higher temperature spin density wave structure with k=(0,0,1.01). This transition occurs over an unprecedented time scale of several hours and is never complete.

One-dimensional magnetic fluctuations in the spin-2 triangular lattice alpha-NaMnO2.

The S=2 anisotropic triangular lattice alpha-NaMnO2 is studied by neutron inelastic scattering. Antiferromagnetic order occurs at T< or =45 K with opening of a spin gap. The spectral weight of the magnetic dynamics above the gap (Delta approximately equal to 7.5 meV) has been analyzed by the single-mode approximation. Excellent agreement with the experiment is achieved when a dominant exchange interaction (|J|/k(B) approximately 73 K), along the monoclinic b axis and a sizable easy-axis magnetic anisotropy (|D|/k(B) approximately 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.

Magnetic correlations in the extended kagome YBaCo4O7 probed by single-crystal neutron scattering.

We have studied the frustrated system YBaCo4O7.0 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 Néel ordering transition. Experimental data reveal 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 acts as an external "field."

Nature of the magnetic order in Ca3Co2O6.

We present a detailed powder and single-crystal neutron diffraction study of the spin chain compound Ca3Co2O6. Below 25 K, the system orders magnetically with a modulated partially disordered antiferromagnetic structure. We give a description of the magnetic interactions in the system which is consistent with this magnetic structure. Our study also reveals that the long-range magnetic order coexists with a shorter-range order with a correlation length scale of approximately 180 angstroms in the ab plane. Remarkably, on cooling, the volume of material exhibiting short-range order increases at the expense of the long-range order.

Electric field switching of antiferromagnetic domains in YMn2O5: a probe of the multiferroic mechanism.

We employ neutron spherical polarimetry to determine the nature and population of the coexisting antiferromagnetic domains in multiferroic YMn2O5. By applying an electric field, we prove that reversing the electrical polarization results in the population inversion of two types of in-plane domains, related to each other by inversion. Our results are completely consistent with the exchange-striction mechanism of ferroelectricity, and support a unified model where cycloidal ordering is induced by coupling to the main magnetic order parameter.

Enhanced ferroelectric polarization by induced Dy spin order in multiferroic DyMnO3.

Neutron powder diffraction and single crystal x-ray resonant magnetic scattering measurements suggest that Dy plays an active role in enhancing the ferroelectric polarization in multiferroic DyMnO3 above T(Dy)(N)=6.5 K. We observe the evolution of an incommensurate ordering of Dy moments with the same periodicity as the Mn spiral ordering. It closely tracks the evolution of the ferroelectric polarization. Below T(Dy)(N), where Dy spins order commensurately, the polarization decreases to values similar for those of TbMnO3. The higher P(s) found just above T(Dy)(N) arises from the contribution of Dy spins so as to effectively increase the amplitude of the Mn spin spiral.

Ferroelectricity induced by acentric spin-density waves in YMn2O5.

The commensurate and incommensurate magnetic structures of the magnetoelectric system YMn2O5, as determined from neutron diffraction, were found to be spin-density waves lacking a global center of symmetry. We propose a model, based on a simple magnetoelastic coupling to the lattice, which enables us to predict the polarization based entirely on the observed magnetic structure. Our data accurately reproduce the temperature dependence of the spontaneous polarization, particularly its sign reversal at the commensurate-incommensurate transition.

Cu(HCO2)2(pym) (pym = pyrimidine): low-dimensional magnetic behavior and long-range ordering in a quantum-spin lattice.

We synthesized and structurally and magnetically characterized the novel 3D coordination polymer Cu(HCO2)2(pym) (pym = pyrimidine). The compound crystallizes in the monoclinic space group C2/c with a = 14.4639(8) A, b = 7.7209(4) A, c = 8.5172(5) A, beta = 126.076(2) degrees, and V= 768.76(7) A3. In the structure buckled layers of Cu(HCO2)2 are interconnected by pym ligands to afford 1D Cu-pym-Cu chains. Bulk magnetic susceptibility measurements show a broad maximum at 25 K that is indicative of short-range magnetic ordering. Between 12 and 300 K a least-squares fit of the chi(T) data to a mean-field-corrected antiferromagnetic chain model yielded excellent agreement for g = 2.224(3), J/kB = -26.9(2) K, and zJ'/kB = -1.1(3) K. Below approximately 3 K a transition to long-range magnetic ordering is observed, as suggested by a sharp and sudden decrease in chi(T). This result is corroborated by muon spin relaxation measurements that show oscillations in the muon asymmetry below T(N) = 2.802(1) K and rapidly fluctuating moments above T(N).

Structural anomalies and multiferroic behavior in magnetically frustrated TbMn2O5.

We have studied the magnetostructural phase diagram of multiferroic TbMn2O5 as a function of temperature and magnetic field by neutron diffraction. Dielectric and magnetic anomalies are found to be associated with steps in the magnetic propagation vector, including a rare example of a commensurate-incommensurate transition on cooling below 24 K, and in the structural parameters. The geometrically frustrated magnetic structure is stabilized by "canted antiferroelectric" displacements of the Mn3+ ions, an example of the magnetic Jahn-Teller effect. The Tb moments order ferromagnetically at low temperatures in an applied field, while the Mn magnetic structure is largely unchanged.