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A new member of the descloizite family, a cobalt vanadate, SrCo(VO4)(OH), has been synthesized as large single crystals using high-temperature and high-pressure hydrothermal methods. SrCo(VO4)(OH) crystallizes in the orthorhombic crystal system in space group P212121 with the following unit cell parameters: a = 6.0157(2) A, b = 7.645(2) A, c = 9.291(3) A, V = 427.29(2) A3, and Z = 4. It contains one-dimensional Co-O-Co chains of edge-sharing CoO6 octahedra along the a-axis connected to each other via VO4 tetrahedra along the b-axis forming a three-dimensional structure. The magnetic susceptibility of SrCo(VO4)(OH) indicates an antiferromagnetic transition at 10 K as well as unusually large spin orbit coupling. Single-crystal magnetic measurements in all three main crystallographic directions displayed a significant anisotropy in both temperature- and field-dependent data. Single-crystal neutron diffraction at 4 K was used to characterize the magnetically ordered state. The Co2+ magnetic spins are arranged in a staggered configuration along the chain direction, with a canting angle that follows the tipping of the CoO6 octahedra. The net magnetization along the chain direction, resulting in ferromagnetic coupling of the a-axis spin components in each chain, is compensated by an antiferromagnetic interaction between nearest neighbor chains. A metamagnetic transition appears in the isothermal magnetization data at 2 K along the chain direction, which seems to correspond to a co-alignment of the spin directions of the nearest neighbor chain. We propose a phenomenological spin Hamiltonian that describes the canted spin configuration of the ground state and the metamagnetic transition in SrCo(VO4)(OH).

Due to the strong coupling between magnetism and ferroelectricity, ${({\mathrm{ND}}_{4})}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$ exhibits several intriguing magnetic and electric phases. In this Letter, we include higher-order onsite anisotropic spin interactions to explain the ferroelectric phase transitions of ${({\mathrm{ND}}_{4})}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$ in a magnetic field and to produce the large weights of high-order harmonic components in the cycloid structure that are observed from neutron diffraction experiments. Moreover, we predict a new ferroelectric phase sandwiched between the FE II and FE III phases in a magnetic field. By emphasizing the importance of the higher-order spin anisotropic interactions, our work provides a framework to understand multiferroic materials with rich phase diagrams.

By developing models of increasing complexity, we show that a model without single-ion anisotropy (SIA) cannot explain the magnetic properties of ${J}_{\mathrm{eff}}=1/2 {\mathrm{Tb}}^{3+}$ moments in the orthorhombically distorted, honeycomb material ${\mathrm{Tb}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Ga}}_{9}$. In four different models for the magnetization of a single honeycomb layer, the only sources of anisotropy are symmetric exchange interactions ${J}_{n\ensuremath{\alpha}\ensuremath{\beta}}={J}_{n\ensuremath{\beta}\ensuremath{\alpha}}$ along three different bonds $n$, an anisotropic $\underline{g}$ tensor, and a Dzyalloshinskii-Moriya interaction (asymmetric exchange) that produces the observed canted moment along $\mathbf{b}$. With 21 parameters, the best such model yields ${\ensuremath{\chi}}^{2}=0.065$, which is substantially smaller than ${\ensuremath{\chi}}^{2}=0.112$ obtained using a Heisenberg model containing six parameters including easy-axis anisotropy. However, models without SIA fail to reproduce the linear dependence of the magnetization with a field perpendicular to the Ising axis while predicting a saturation magnetization that is far too low. Due to the complex crystal-field environments, we argue that SIA is necessary to study low-symmetry, three-dimensional ${J}_{\mathrm{eff}}=1/2$ materials containing ${\mathrm{Tb}}^{3+}$ ions.

We report a comprehensive inelastic neutron scattering study of the hybrid molecule-based multiferroic compound $({\mathrm{ND}}_{4}{)}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$ in the zero-field incommensurate cycloidal phase and the high-field quasicollinear phase. The spontaneous electric polarization changes its direction concurrently with the field-induced magnetic transition, from mostly aligned with the crystallographic $a$ axis to the $c$ axis. To account for such a change in polarization direction, the underlying multiferroic mechanism was proposed to switch from the spin-current model induced via the inverse Dzyaloshinskii-Moriya interaction to the $p\text{\ensuremath{-}}d$ hybridization model. We perform a detailed analysis of the inelastic neutron data of $({\mathrm{ND}}_{4}{)}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$ using linear spin-wave theory to quantify magnetic interaction strengths and investigate the possible impact of different multiferroic mechanisms on the magnetic couplings. Our result reveals that the spin dynamics of both multiferroic phases can be well described by a Heisenberg Hamiltonian with easy-plane anisotropy. We do not find notable differences between the optimal model parameters of the two phases. The hierarchy of exchange couplings and the balance among frustrated interactions remain the same between two phases, suggesting that magnetic interactions in $({\mathrm{ND}}_{4}{)}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$ are much more robust than the electric polarization in response to delicate reorganizations of the electronic degrees of freedom in an applied magnetic field.

Single-crystal neutron diffraction, inelastic neutron scattering, bulk magnetization measurements, and first-principles calculations are used to investigate the magnetic properties of the honeycomb lattice ${\mathrm{Tb}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Ga}}_{9}$. While the $Rln2$ magnetic contribution to the low-temperature entropy indicates a ${J}_{\mathrm{eff}}=1/2$ moment for the lowest-energy crystal-field doublet, the ${\mathrm{Tb}}^{3+}$ ions form a canted antiferromagnetic structure below 12.5 K. Due to the Dzyaloshinskii-Moriya interactions, the Tb moments in the $ab$ plane are slightly canted towards $\mathbf{b}$ with a canted moment of 1.22 ${\ensuremath{\mu}}_{\mathrm{B}}$ per formula unit. A minimal $xxz$ spin Hamiltonian is used to simultaneously fit the spin-wave frequencies along the high-symmetry directions and the field dependence of the magnetization along the three crystallographic axes. Long-range magnetic interactions for both in-plane and out-of-plane couplings up to the second nearest neighbors are needed to account for the observed static and dynamic properties. The $z$ component of the exchange interactions between Tb moments is larger than the $x$ and $y$ components. This compound also exhibits bond-dependent exchange with negligible nearest-neighbor exchange coupling between moments parallel and perpendicular to the $4f$ orbitals. Despite the ${J}_{\mathrm{eff}}=1/2$ moments, the spin Hamiltonian is denominated by a large in-plane anisotropy ${K}_{z}\ensuremath{\sim}\ensuremath{-}1\phantom{\rule{4pt}{0ex}}\mathrm{meV}$. DFT calculations confirm the antiferromagnetic ground state and the substantial interplane coupling at larger Tb-Tb distances.

We report the magnetic field dependence of the THz absorption and non-reciprocal directional dichroism spectra of BiFeO$_3$ measured on the three principal crystal cuts for fields applied along the three principal directions of each cut. From the systematic study of the light polarization dependence we deduced the optical selection rules of the spin-wave excitations. Our THz data, combined with small-angle neutron scattering results showed that i) an in-plane magnetic field rotates the $\mathbf{q}$ vectors of the cycloids perpendicular to the magnetic field, and ii) the selection rules are mostly determined by the orientation of the $\mathbf{q}$ vector with respect to the electromagnetic fields. We observed a magnetic field history dependent change in the strength and the frequency of the spin-wave modes, which we attributed to the change of the orientation and the length of the cycloidal $\mathbf{q}$ vector, respectively. Finally, we compared our experimental data with the results of linear spin-wave theory that reproduces the magnetic field dependence of the spin-wave frequencies and most of the selection rules, from which we identified the spin-polarization coupling terms relevant for the optical magnetoelectric effect.

The entropy stabilized oxide ${\mathrm{Mg}}_{0.2}{\mathrm{Co}}_{0.2}{\mathrm{Ni}}_{0.2}{\mathrm{Cu}}_{0.2}{\mathrm{Zn}}_{0.2}\mathrm{O}$ exhibits antiferromagnetic order and magnetic excitations, as revealed by recent neutron scattering experiments. This observation raises the question of the nature of spin-wave excitations in such disordered systems. Here, we investigate theoretically the magnetic ground state and the spin-wave excitations using linear spin-wave theory in combination with the supercell approximation to take into account the extreme disorder in this magnetic system. We find that the experimentally observed antiferromagnetic structure can be stabilized by a rhombohedral distortion together with large second-nearest-neighbor interactions. Our calculations show that the spin-wave spectrum consists of a well-defined low energy coherent spectrum in the background of an incoherent continuum that extends to higher energies.

We present a comprehensive neutron scattering study of the breathing pyrochlore magnet LiGaCr_{4}S_{8}. We observe an unconventional magnetic excitation spectrum with a separation of high- and low-energy spin dynamics in the correlated paramagnetic regime above a spin-freezing transition at 12(2) K. By fitting to magnetic diffuse-scattering data, we parametrize the spin Hamiltonian. We find that interactions are ferromagnetic within the large and small tetrahedra of the breathing pyrochlore lattice, but antiferromagnetic further-neighbor interactions are also essential to explain our data, in qualitative agreement with density-functional-theory predictions [Ghosh et al., npj Quantum Mater. 4, 63 (2019)2397-464810.1038/s41535-019-0202-z]. We explain the origin of geometrical frustration in LiGaCr_{4}S_{8} in terms of net antiferromagnetic coupling between emergent tetrahedral spin clusters that occupy a face-centered-cubic lattice. Our results provide insight into the emergence of frustration in the presence of strong further-neighbor couplings, and a blueprint for the determination of magnetic interactions in classical spin liquids.

Using THz spectroscopy, we show that the spin-wave spectrum of multiferroic BiFeO$_3$ in its high-field canted antiferromagnetic state is well described by a spin model that violates rhombohedral symmetry. We demonstrate that the monoclinic distortion of the canted antiferromagnetic state is induced by the single-ion magnetoelastic coupling between the lattice and the two nearly anti-parallel spins. The revised spin model for BiFeO$_3$ contains two new single-ion anisotropy terms that violate rhombohedral symmetry and depend on the direction of the magnetic field., Comment: 28 pages (main & supplementary), 2 figures (main article), 15 figures (supplementary material)

Single crystals of a honeycomb lattice antiferromagnet, ${\mathrm{Tb}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Ga}}_{9}$, were synthesized, and the physical properties have been studied. From magnetometry, a long-range antiferromagnetic ordering at $\ensuremath{\approx}12.5$ K with highly anisotropic magnetic behavior was found. Neutron powder diffraction confirms that the Tb spins lie along the $\mathbf{a}$-axis, parallel to the shortest Tb-Tb contact. Two field-induced spin-flip transitions are observed when the field is applied parallel to this axis, separated by a plateau corresponding roughly to $M\ensuremath{\approx}{M}_{\mathrm{s}}/2$. Transport measurements show the resistivity to be metallic with a discontinuity at the onset of N\'eel order. Heat capacity shows a $\ensuremath{\lambda}$-like transition confirming the bulk nature of the magnetism. We propose a phenomenological spin Hamiltonian that describes the magnetization plateau as a result of strong Ising character arising from a quasidoublet ground state of the ${\mathrm{Tb}}^{3+}$ ion in a site of ${C}_{s}$ symmetry and expressing a significant bond-dependent anisotropy.

Thin flakes of Cr1/3NbS2 are fabricated successfully via microexfoliation techniques. Temperature-dependent and field-dependent magnetizations of thin flakes with various thicknesses are investigat...

Owing to their overall low energy scales, flexible molecular architectures, and ease of chemical substitution, molecule-based multiferroics are extraordinarily responsive to external stimuli and exhibit remarkably rich phase diagrams. Even so, the stability and microscopic properties of various magnetic states in close proximity to quantum critical points are highly under-explored in these materials. Inspired by these opportunities, we combined pulsed-field magnetization, first-principles calculations, and numerical simulations to reveal the magnetic field–temperature (B–T) phase diagram of multiferroic (NH4)2FeCl5⋅H2O. In this system, a network of intermolecular hydrogen and halogen bonds creates a competing set of exchange interactions that generates additional structure in the phase diagram—both in the vicinity of the spin flop and near the 30 T transition to the fully saturated state. Consequently, the phase diagrams of (NH4)2FeCl5⋅H2O and its deuterated analog are much more complex than those of other molecule-based multiferroics. The entire series of coupled electric and magnetic transitions can be accessed with a powered magnet, opening the door to exploration and control of properties in this and related materials.

Although spin cycloids and helices are quite common, remarkably little is known about the normal modes of a spin cycloid or helix with finite length on a discrete lattice. Based on simple one-dimensional lattice models, we numerically evaluate the normal modes of a spin cycloid or helix produced by either Dzyaloshinskii-Moriya (DM) or competing exchange (CE) interactions. The normal modes depend on the type of interaction and on whether the nearest-neighbor exchange is antiferromagnetic (AF) or ferromagnetic (FM). In the AF/DM and FM/DM cases, there is only a single Goldstone mode; in the AF/CE and FM/CE cases, there are three. For FM exchange, the spin oscillations produced by non-Goldstone modes contain a mixture of tangential and transverse components. For the DM cases, we compare our numerical results with analytic results in the continuum limit. Examples are given of materials that fall into all four cases., Comment: 10 pages, 6 figures

International audience; The antiferromagnetic semiconductor MnTe has recently attracted attention for spintronics and high-performance thermoelectric applications. However, little is known about its vibrational and thermal transport properties and how these might relate to the electronic and magnetic structure, particularly as related to 3d Mn orbital correlations. Here, we calculate a physically justified Coulomb correlation parameter within the DFT+U framework. We couple this framework with the Heisenberg Hamiltonian and first-principles Boltzmann transport to understand the magnetic, vibrational, and phonon thermal transport properties of MnTe. We also perform inelastic neutron and nuclear inelastic x-ray scattering measurements of the total and partial phonon density of states, respectively. Very good agreement is obtained with the measured and calculated phonon density of states, and with available measurements for the band gap, local magnetic moments, Néel temperature, magnon dispersion, thermal conductivity, and phonon dispersion. This study demonstrates that the vibrational and magnetic degrees of freedom are not strongly coupled in MnTe, and provides a more comprehensive picture of this technologically promising material.

Using high-resolution inelastic neutron scattering, we examine the spin dynamics of ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}{\mathrm{WO}}_{4}$ in the collinear AF1, the $ac\text{\ensuremath{-}}b$ spiral AF2, and the $ac$ cycloidal AF5 phases. The spin wave excitations are well described by a Heisenberg model with competing long-range exchange interactions $({J}_{i}$ up to 12th nearest neighbors) and the single-ion anisotropy $K$ induced by the spin-orbit interaction. While the exchange constants are relatively unchanged, the dominant effect of doping is to change the single-ion anisotropy from easy axis $(Kg0)$ in the collinear AF1 phase to easy plane $(Kl0)$ in the two multiferroic phases.

We measured absorption of THz radiation in ${\mathrm{YFeO}}_{3}$ single crystals at a temperature of 3 K in the magnetic field up to 17 T applied in all three crystallographic directions. Two spin-wave modes were observed at the $\mathrm{\ensuremath{\Gamma}}$ point with energies 1.2 meV (9.8 ${\mathrm{cm}}^{\ensuremath{-}1}$) and 2.4 meV (19.3 ${\mathrm{cm}}^{\ensuremath{-}1}$) in zero field. From the magnetic-field dependence of mode energies, we have refined the previously proposed model [S. E. Hahn et al., Phys. Rev. B 89, 014420 (2014)] and quantified the parameters of Dzyaloshinskii-Moriya interactions and single-ion anisotropies.

Electronic phase separation has been increasingly recognized as an important phenomenon in understanding many of the intriguing properties displayed in transition metal oxides. It is believed to produce fascinating functional properties in otherwise chemically homogenous electronic systems, e.g., colossal magnetoresistance manganites and high-${T}_{\mathrm{c}}$ cuprates. While many well-known electronically phase-separated systems are oxides, it has been argued that the same phenomenon should occur in other electronic systems with strong competing interactions. Here we report the observation of electronic phase separation in molecular $({\mathrm{ND}}_{4}{)}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$, a type-II multiferroic. We show that two magnetic phases, one of which is commensurate and the other of which is incommensurate, coexist in this material. Their evolution under applied magnetic field produces emergent properties. In particular, our measurements reveal a field-induced exotic state linked to a direct transition from a paraelectric/paramagnetic phase to a ferroelectric/antiferromagnetic phase, a collective phenomenon that hasn't been seen in other magnetic multiferroics.

Sr$_2$FeOsO$_6$ is an insulating double perovskite compound which undergoes antiferromagnetic transitions at 140 K ($T_{N1}$) and 67 K ($T_{N2}$). To study the underlying electronic and magnetic interactions giving rise to this behavior we have performed inelastic neutron scattering (INS) and resonant inelastic x-ray scattering (RIXS) experiments on polycrystalline samples of Sr$_2$FeOsO$_6$. The INS data reveal that the spectrum of spin excitations remains ungapped below T$_{N1}$, however below T$_{N2}$ a gap of 6.8 meV develops. The RIXS data reveals splitting of the T$_{2g}$ multiplet consistent with that seen in other 5d$^3$ osmium based double perovskites. Together these results suggest that spin-orbit coupling is important for ground state selection in 3d-5d$^3$ double perovskite materials., 5 figures, supplementary material available on request

In order to model a spiral spin state in a thin film, we study a classical Heisenberg model with open boundary conditions. With magnetic field applied in the plane of the film, the spin state becomes ferromagnetic above a critical field that increases with thickness $N$. For a given $N$, the spiral passes through states with $n={n}_{0}$ up to 0 complete periods in steps of 1. These numerical results agree with earlier analytic results in the continuum limit and help explain the susceptibility jumps observed in thin films.

Competing exchange interactions can produce complex magnetic states together with spin-induced electric polarizations. With competing interactions on alternating triangular and kagome layers, the swedenborgite ${\mathrm{CaBaCo}}_{4}{\mathrm{O}}_{7}$ may have one of the largest measured spin-induced polarizations of $\ensuremath{\sim}1700$ nC/${\mathrm{cm}}^{2}$ below its ferrimagnetic transition temperature at 70 K. Upon rotating our sample about $\mathbf{c}=[0,0,1]$ while the magnetic field is fixed along $[1,0,0]$, the threefold splitting of the spin-wave frequencies indicates that our sample is hexagonally twinned. Magnetization measurements then suggest that roughly 20% of the sample is in a domain with the $a$ axis along $[1,0,0]$ and that 80% of the sample is in one of two other domains with the $a$ axis along either $[\ensuremath{-}1/2,\sqrt{3}/2,0]$ or $[\ensuremath{-}1/2,\ensuremath{-}\sqrt{3}/2,0]$. Powder neutron-diffraction data, magnetization measurements, and terahertz (THz) absorption spectroscopy reveal that the complex spin order in each domain can be described as a triangular array of bitetrahedral $c$-axis chains ferrimagnetically coupled to each other in the $ab$ plane. The electric-field dependence of bonds coupling those chains produces the large spin-induced polarization of ${\mathrm{CaBaCo}}_{4}{\mathrm{O}}_{7}$.

Many years and great effort have been spent constructing the microscopic model for the room temperature multiferroic BiFeO3. However, earlier models implicitly assumed that the cycloidal wavevector q was confined to one of the three-fold symmetric axes in the hexagonal plane normal to the electric polarization. Because recent measurements indicate that q can be rotated by a magnetic field, it is essential to properly treat the anisotropy that confines q at low fields. We propose that the anisotropy energy − K 3 S 6 sin 6 θ cos 6 ϕ confines the wavevectors q to the three-fold axis ϕ = 0 and ± 2 π / 3 within the hexagonal plane with θ = π / 2 .

We report a neutron diffraction study of the multiferroic mechanism in ${({\mathrm{ND}}_{4})}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$, a molecular compound that exhibits magnetically induced ferroelectricity. This material exhibits two successive magnetic transitions on cooling: a long-range order transition to an incommensurate (IC) collinear sinusoidal spin state at ${T}_{N}=7.3$ K, followed by a second transition to an IC cycloidal spin state at ${T}_{FE}=6.8$ K, the latter of which is accompanied by spontaneous ferroelectric polarization. The cycloid structure is strongly distorted by spin-lattice coupling, as evidenced by the observations of both odd and even higher-order harmonics associated with the cycloid wave vector, and a weak commensurate phase that coexists with the IC phase. The second-order harmonic appears at ${T}_{FE}$, thereby providing unambiguous evidence that the onset of the electric polarization is accompanied by a lattice modulation due to spin-lattice interaction. The neutron results, in conjunction with the negative thermal expansion and large magnetostriction observed in Ref. [19], indicate that spin-lattice coupling plays a critical role in the ferroelectric mechanism of ${({\mathrm{ND}}_{4})}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$.

Mean field expressions based on the simple Heisenberg model were derived to correlate the intra- and interlayer exchange couplings to the critical temperatures, Tc, for three metallocyanide-based magnets with extended 2- and 3-D structure types. These expressions were used to estimate the exchange coupling, J, for 2-D ferrimagnetic [NEt4]2MnII3(CN)8, 3-D antiferromagnetic [NEt4]MnII3(CN)7, and 3-D antiferromagnetic interpenetrating 3-D MnII(CN)2. The type and magnitude of the exchange coupling are in accord with the previously reported magnetic data.

A compound with very weakly interacting chains, ${\mathrm{MnCl}}_{3}$(bpy), has attracted a great deal of attention as a possible $S=2$ Haldane chain. However, long-range magnetic order of the chains prevents the Haldane gap from developing below 11.5 K. Based on a four-sublattice model, a description of the antiferromagnetic resonance (AFMR) spectrum up to frequencies of 1.5 THz and magnetic fields up to 50 T indicates that the interchain coupling is indeed quite small but that the Dzaloshinskii-Moriya interaction produced by broken inversion symmetry is substantial (0.12 meV). In addition, the antiferromagnetic, nearest-neighbor interaction within each chain (3.3 meV) is significantly stronger than previously reported. The excitation spectrum of this $S=2$ compound is well described by a $1/S$ expansion about the classical limit.

The role of spin-orbit coupling (SOC) in 4$d$ and 5$d$ transition metal oxides is relatively poorly understood outside of the LS or JJ coupling limits. In this work, the importance of the intermediate regime is demonstrated through the identification of SOC as an essential feature of the collective properties in nominally orbitally quenched 5${d}^{3}$ systems. The authors probe the magnetic excitations in model system Sr${}_{2}$ScOsO${}_{6}$ via inelastic neutron scattering and model the results including the effects of SOC-induced anisotropy. Experimentally determining the strengths of nearest and next-nearest neighbor interactions leads to the important discovery that the magnetic ground state is controlled by anisotropy, which would not be possible in the LS coupling limit. This indicates that SOC plays a key role in relieving frustration and promoting heightened transition temperatures in 5${d}^{3}$ double perovskites.

Mean field expressions based on the simple Heisenberg model were derived to correlate the inter- and intralayer exchange couplings to the critical temperatures, Tc, for several tetracyanoethylene (TCNE)-based magnets with extended two- and three-dimensional (2-D and 3-D) structure types. These expressions were used to estimate the exchange coupling, J, for 2-D ferrimagnetic [MII(TCNE)(NCMe)2]+ (M = Mn, Fe), 3-D antiferromagnetic MnII(TCNE)[C4(CN)8]1/2, and 3-D ferrimagnetic MnII(TCNE)3/2(I3)1/2. The type and magnitude of the exchange coupling are in accord with the previously reported magnetic data.

The spin-driven polarizations of type-I multiferroics are veiled by the preexisting ferroelectric (FE) polarization. Using first-principles calculations combined with a spin model, we uncover two hidden but huge spin-driven polarizations in the room-temperature multiferroic BiFeO(3). One is associated with the global inversion symmetry broken by a FE distortion, and the other is associated with the local inversion symmetry broken by an antiferrodistortive octahedral rotation. Comparison with recent neutron scatterings reveals tha first polarization reaches ∼3.0 μC/cm(2), which is larger than in any other multiferroic material. Our exhaustive study paves a way to uncover the various magnetoelectric couplings that generate hidden spin-driven polarizations in other type-I multiferroics.

Due to the lack of suitable single crystals, the average g-factor of anisotropic polycrystalline samples are commonly estimated from either the Curie−Weiss susceptibility or the saturation magnetization. We show that the average g-factor obtained from the Curie constant is always greater than or equal to the average g-factor obtained from the saturation magnetization. The average g-factors are equal only for a single crystal or an isotropic polycrystal. We review experimental results for several compounds containing the anisotropic cation [Fe(C5Me5)2]+ and propose an experiment to test this inequality using a compound with a spinless anion.

The C3-symmetric crystal-field potential in the Fe(II)Fe(III) bimetallic oxalates splits the L = 2 Fe(II) multiplet into two doublets and one singlet. In compounds that exhibit magnetic compensation, one of the doublets lies lowest in energy and carries an average orbital angular momentum Lcf z that exceeds a threshold value of roughly 0.25. In a range of Lcf z , a Jahn-Teller (JT) distortion increases the energy splitting of the low-lying doublet and breaks the C3 symmetry of the bimetallic planes around the ferrimagnetic transition temperature. Due to the competition with the spin-orbit coupling, the JT distortion disappears at low temperatures in compounds that display magnetic compensation. A comparison with recent measurements provides strong evidence for this inverse, low-temperature JT transition. The size of the JT distortion is estimated using first-principles calculations, which suggest that the long-range ordering of smaller, non-C3-symmetric organic cations can eliminate magnetic compensation. Keywords: Jahn-Teller distortion; Spin-orbit interaction; Crystal fields; Bimetallic oxalates

Although the exchange coupling and local crystal-field environment are almost identical in the two-dimensional (2D) and three-dimensional (3D) series of bimetallic oxalates, those two classes of materials exhibit quite different magnetic properties. Using mean-field theory to treat the exchange interaction, we evaluate the transition temperatures and magnetizations of the 3D Fe(II)Fe(III) and Mn(II)Cr(III) bimetallic oxalates. Because of the tetrahedral coordination of the chiral anisotropy axis, the 3D bimetallic oxalates have lower transition temperatures than their 2D counterparts, and much stronger anisotropy is required to produce magnetic compensation in the 3D Fe(II)Fe(III) compounds. The spin-orbit coupling with the non-collinear orbital moments causes the spins to cant in both 3D compounds.

Unlike the coercive field H c of a bulk ferrimagnet, which diverges at the compensation temperature T comp , the coercive field of a polycrystalline ferrimagnet with uni-axial anisotropy is shown to have a minimum at T comp . Despite this behavior, the field required for domain-wall motion still diverges at the compensation temperature. These ideas are used to treat a ferrimagnetic class of molecule-based magnets, the bimetallic oxalates, that exhibit a minimum coercivity at T comp .

We report elastic and inelastic neutron-scattering measurements of the high-${T}_{\mathrm{C}}$ ferromagnet ${\mathrm{Mn}}_{1+\ensuremath{\delta}}\mathrm{Sb}$. Measurements were performed on a large, ${T}_{\mathrm{C}}=434$ K, single crystal with an interstitial Mn content of $\ensuremath{\delta}\ensuremath{\approx}0.13$. The neutron-diffraction results reveal that the interstitial Mn has a magnetic moment, and that it is aligned antiparallel to the main Mn moment. We perform density functional theory calculations including the interstitial Mn and find the interstitial to be magnetic, in agreement with the diffraction data. The inelastic neutron-scattering measurements reveal two features in the magnetic dynamics: (i) a spin-wave-like dispersion emanating from ferromagnetic Bragg positions $(\mathrm{H}\phantom{\rule{4pt}{0ex}}\mathrm{K}\phantom{\rule{0.16em}{0ex}}2n)$, and (ii) a broad, nondispersive signal centered at forbidden Bragg positions $(\mathrm{H}\phantom{\rule{4pt}{0ex}}\mathrm{K}\phantom{\rule{0.16em}{0ex}}2n+1)$. The inelastic spectrum cannot be modeled by simple linear spin-wave-theory calculations and appears to be significantly altered by the presence of the interstitial Mn ions. The results show that the influence of the interstitial Mn on the magnetic state in this system is more important than previously understood.

Using dc and ac magnetometry, the pressure dependence of the magnetization of the three-dimensional antiferromagnetic coordination polymer $\text{Mn}{(\text{N}{(\text{CN})}_{2})}_{2}$ was studied up to 12 kbar and down to 8 K. The antiferromagnetic transition temperature, ${T}_{\mathrm{N}}$, increases dramatically with applied pressure $(P)$, where a change from ${T}_{\mathrm{N}}(P=\text{ambient})=16.0\phantom{\rule{4pt}{0ex}}\mathrm{K}$ to ${T}_{\mathrm{N}}(P=12.1\phantom{\rule{4pt}{0ex}}\text{kbar})=23.5\phantom{\rule{4pt}{0ex}}\mathrm{K}$ was observed. In addition, a marked difference in the magnetic behavior is observed above and below 7.1 kbar. Specifically, for $Pl7.1$ kbar, the differences between the field-cooled and zero-field-cooled magnetizations, the coercive field, and the remanent magnetization decrease with increasing pressure. However, for $Pg7.1$ kbar, the behavior is inverted. Additionally, for $Pg8.6$ kbar, minor hysteresis loops are observed. All of these effects are evidence of the increase of the superexchange interaction and the appearance of an enhanced exchange anisotropy with applied pressure.

A microscopic model for the room-temperature multiferroic BiFeO3 that includes two Dzyaloshinskii- Moriya interactions and single-ion anisotropy along the ferroelectric polarization predicts both the zero-field spectroscopic modes as well as their splitting and evolution in a magnetic field. Due to simultaneously broken time-reversal and spatial-inversion symmetries, the absorption of light changes as the magnetic field or the direction of light propagation is reversed. We discuss three physical mechanisms that may contribute to this absorption asymmetry known as nonreciprocal directional dichroism: the spin current, magnetostriction, and single-ion anisotropy. We conclude that the nonreciprocal directional dichroism in BiFeO3 is dominated by the spin-current polarization and is insensitive to the magnetostriction and easy-axis anisotropy. With three independent spin-current parameters, our model accurately describes the nonreciprocal directional dichroism observed for magnetic field along [1,−1,0]. Since some modes are almost transparent to light traveling in one direction but opaque for light traveling in the opposite direction, BiFeO3 behaves as a room-temperature optical diode at certain frequencies in the gigahertz to terahertz range. Our work demonstrates that an analysis of the nonreciprocal directional dichroism spectra based on an effective spin model supplemented by first-principles calculations can produce a quantitative microscopic theory of the magnetoelectric couplings in multiferroic materials.

Multiferroics permit the magnetic control of the electric polarization and the electric control of the magnetization. These static magnetoelectric (ME) effects are of enormous interest: The ability to read and write a magnetic state current-free by an electric voltage would provide a huge technological advantage. Dynamic or optical ME effects are equally interesting, because they give rise to unidirectional light propagation as recently observed in low-temperature multiferroics. This phenomenon, if realized at room temperature, would allow the development of optical diodes which transmit unpolarized light in one, but not in the opposite, direction. Here, we report strong unidirectional transmission in the room-temperature multiferroic BiFeO_{3} over the gigahertz-terahertz frequency range. The supporting theory attributes the observed unidirectional transmission to the spin-current-driven dynamic ME effect. These findings are an important step toward the realization of optical diodes, supplemented by the ability to switch the transmission direction with a magnetic or electric field.

To facilitate the search for new magnetic semiconductors with high transition temperatures T C , we use dynamical mean-field theory to evaluate T C for a double-exchange system with general angular momentum j = 1 / 2 , 3 / 2 , 5 / 2 , … . For simplicity, we assume that there is one local moment per site and that the Hund's coupling J c between the local moments and the charge carriers (with undoped bandwidth W ) is large. The maximum Curie temperature T C max ( m j , j ) for a given m j and j occurs when the m j sub-band is half-filled. For a fixed j, T C max ( m j , j ) is the largest in the lowest or the highest sub-band with m j = ± j , where the carriers are most optimally coupled to the local moments. When j ⪢ 1 , T C max ( ± j , j ) scales like W / 2 j + 1 , which is the bandwidth of each m j sub-band. For j = 1 / 2 , T C max ( ± 1 / 2 , 1 / 2 ) is suppressed by fluctuations of the carrier spin. Surprisingly, T C max ( ± j , j ) reaches a maximum for j = 3 / 2 , the same angular momentum as the charge carriers in p-band semiconductors like GaAs and Ge.

This work examines the magnetic order and spin dynamics of a double-exchange model with competing ferromagnetic and antiferromagnetic Heisenberg interactions between the local moments. The Heisenberg interactions are periodically arranged in a Villain configuration in two dimensions with nearest-neighbor, ferromagnetic coupling $J$ and antiferromagnetic coupling $-\eta J$. This model is solved at zero temperature by performing a $1/\sqrt{S}$ expansion in the rotated reference frame of each local moment. When $\eta $ exceeds a critical value, the ground state is a magnetically frustrated, canted antiferromagnet. With increasing hopping energy $t$ or magnetic field $B$, the local moments become aligned and the ferromagnetic phase is stabilized above critical values of $t$ or $B$. In the canted phase, a charge-density wave forms because the electrons prefer to sit on lines of sites that are coupled ferromagnetically. Due to a change in the topology of the Fermi surface from closed to open, phase separation occurs in a narrow range of parameters in the canted phase. In zero field, the long-wavelength spin waves are isotropic in the region of phase separation. Whereas the average spin-wave stiffness in the canted phase increases with $t$ or $\eta $, it exhibits a more complicated dependence on field. This work strongly suggests that the jump in the spin-wave stiffness observed in Pr$_{1-x}$Ca$_x$MnO$_3$ with $0.3 \le x \le 0.4$ at a field of 3 T is caused by the delocalization of the electrons rather than by the alignment of the antiferromagnetic regions., Comment: 28 pages, 12 figures

Spin diffusion within the double-exchange model is studied in the limits W<

The diruthenium compound [Ru 2 (O 2 CMe) 4 ] 3 [Cr(CN) 6 ] may be the only known material that contains two weakly-coupled, magnetically-ordered sublattices occupying the same three-dimensional volume. Due to the strong easy-plane anisotropy on each Ru 2 complex, the moment of each sublattice is constrained to one of the eight cubic diagonals. At low fields, the two sublattices are antiferromagnetically aligned by weak dipolar and deformation energies. But above a metamagnetic critical field of about 1000 Oe, the sublattice moments become ferromagnetically aligned and the net magnetization increases dramatically. We have successfully modeled this metamagnetic transition by assuming that the individual sublattice spin configurations are only weakly distorted by the magnetic field. This model suggests that the ground state of each sublattice undergoes a phase transition at a pressure of about 7 kbar. The drop in the sublattice moment and the rise in the sublattice susceptibility above 7 kbar can be explained by a high- to low-spin transition ( S = 3/2 to 1/2) on the mixed-valent diruthenium complexes.

Synchrotron-based infrared and Raman spectroscopies were brought together with diamond anvil cell techniques and an analysis of the magnetic properties to investigate the pressure-induced high $\ensuremath{\rightarrow}$ low spin transition in $[{\mathrm{Ru}}_{2}{({\mathrm{O}}_{2}\mathrm{CMe})}_{4}{]}_{3}{[\mathrm{Cr}(\mathrm{CN})}_{6}]$. The extended nature of the diruthenium wave function combined with coupling to chromium-related local lattice distortions changes the relative energies of the ${\ensuremath{\pi}}^{*}$ and ${\ensuremath{\delta}}^{*}$ orbitals and drives the high $\ensuremath{\rightarrow}$ low spin transition on the mixed-valence diruthenium complex. This is a rare example of an externally controlled metamagnetic transition in which both spin-orbit and spin-lattice interactions contribute to the mechanism.

The crossover from localized- to itinerant-electron behavior is associated with many intriguing phenomena in condensed-matter physics. In this paper, we investigate the crossover from localized to itinerant regimes in the spinel system Mn$_{1-x}$Co$_x$V$_2$O$_4$. At low Co doping, orbital order (OO) of the localized electrons on the V3+ ions suppresses magnetic frustration by triggering a tetragonal distortion. With Co doping, electronic itinerancy melts the OO and suppresses the structural phase transition while the reduced spin-lattice coupling produces magnetic frustration. Neutron scattering measurements and first-principles-guided spin models reveal that the non-collinear state at high Co doping is produced by weakened local anisotropy and enhanced Co-V spin interactions., 5 pages, 4 figures

This paper reviews the behaviour of spin-density waves (SDWs) in Fe/Cr trilayers and multilayers. After providing an overview of SDWs in bulk Cr, we discuss the predicted effects of SDWs on the exchange coupling of an Fe/Cr trilayer with perfect interfaces, which is nearly realized experimentally by a Cr wedge grown atop an Fe whisker and covered with a thin Fe film. While the observed phase slips in the exchange coupling are produced by transitions between collinear SDW phases with different numbers of nodes, the growth in the distance between phase slips with increasing temperature is attributed to a transition between incommensurate and commensurate SDWs. The theoretical consequences of Fe-Cr interdiffusion and interfacial steps at imperfect interfaces are then described. Whereas Fe-Cr interdiffusion causes the observed sign change in the exchange coupling, the effects of interfacial steps depend on which of the interfacial, magnetostatic, or bulk energies are dominant. For rough interfaces, the non-collinear coupling between the Fe moments can be explained by two competing models, one of which requires the formation of a non-collinear, helical SDW that is unstable in bulk Cr. Although both collinear and non-collinear SDWs have been directly observed in Fe/Cr multilayers with neutron scattering, the role of SDWs in the exchange coupling remains uncertain. This review focuses on the following open questions. Can a SDW be detected from the exchange coupling alone? What are the requirements for a non-collinear SDW in an Fe/Cr trilayer or multilayer? Can the proximity to a SDW instability be observed? Finally, what is the origin of the discrepancy between the observed exchange coupling and the much larger coupling predicted by phenomenological, tight-binding, and first-principles calculations?

We theoretically investigate the ground-state magnetic properties of the brownmillerite phase of SrCoO2.5. Strong correlations between Co d electrons are treated within the local spin density approximations of density functional theory (DFT) with Hubbard U corrections (LSDA+U), and results are compared with those using the Heyd?Scuseria?Ernzerhof (HSE) functional. The parameters computed with a U value of 7.5?eV are found to match closely to those computed within the HSE functional. A G-type antiferromagnetic structure is found to be the most stable one, consistent with experimental observation. By mapping the total energies of different magnetic configurations onto a Heisenberg Hamiltonian, we compute the magnetic exchange interaction parameters, J, between the nearest-neighbor Co atoms. The J values obtained are then used to compute the spin-wave frequencies and inelastic neutron scattering intensities. Among four spin-wave branches, the lowest energy mode was found to have the largest scattering intensity at the magnetic zone center, while the other modes become dominant at different momenta. These predictions can be tested experimentally.

Using a combined numerical and analytic approach, we evaluate the spin-diffusion coefficient D for the double-exchange model in the limit t 1/2). Hence, the spin-diffusion coefficient vanishes when the electrons are unable to hop between singly-occupied sites in a half-filled (p = 1/2) band.

The process of spin diffusion within the double-exchange model is studied on a Bethe lattice in infinite dimension at $T=\ensuremath{\infty}.$ In the absence of electron hopping, the spin-current correlation function oscillates with a period inversely proportional to the Hund's coupling and the spin-diffusion coefficient D vanishes. Electron hopping causes the correlation function to decay with time and yields a value for D proportional to the electron bandwidth.

When the Ni concentration exceeds about $18%,$ Mn-Ni alloys were expected to support two different noncollinear spin-density wave (SDW) phases. A triple-$Q$ SDW with moments along the crystal diagonals was believed to appear in the fcc phase between ${T}_{N}$ and ${T}_{t}.$ Below ${T}_{t},$ the fct phase with $cga$ was believed to contain a double-$Q$ SDW with moments in the $\mathrm{ab}$ plane and at $45\ifmmode^\circ\else\textdegree\fi{}$ angles from the crystal axes. Based on resistivity, neutron-scattering, and susceptibility measurements, we show that the structural and magnetic phase transitions in a ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x}$ alloy with $x\ensuremath{\approx}0.20$ are actually distinct, with the structural phase transition at ${T}_{t}\ensuremath{\approx}250 \mathrm{K}$ lying far above the magnetic transition at ${T}_{m}\ensuremath{\approx}125 \mathrm{K}.$ A Hamiltonian which includes elastic, magnetoelastic, and noncollinearity energies is used to describe these two transitions. In the tetragonal phase between ${T}_{t}$ and ${T}_{m},$ our model predicts a new SDW phase with moments tilted away from the crystal diagonals toward the $\mathrm{ab}$ plane. The energy gap in the spin-wave spectrum is predicted to change discontinuously at ${T}_{m}.$

Organic coatings often contain sufficient pigmentation that the pigment volume concentration (PVC) and the critical PVC (CPVC) must be carefully considered. Past work has shown that the CPVC can be identified with the random densest packing of pigment particles after considerations of the adsorbed polymer layer on the particles is taken into account, and that this packing can be predicted by empirical particle packing algorithms developed for mixtures of particle sizes. Recent studies have shown that local fluctuations of pigment and polymer concentrations in a film can lead to local film volumes that can exceed the CPVC even though the average PVC for the whole film (the global PVC) is below the CPVC. These effects are consistent with observations of void formation in films below the CPVC, and can be analyzed by local film statistics. We have also recently performed simulations of particle packing by the compression of multiple hard spheres that allows further insight into local concentration fluctuations in PVC within a film.

Many experiments have verified the presence of a spin-density wave (SDW) within the Cr spacer of Fe/Cr multilayers and wedges. We review the recently proposed interlayer magnetic coupling mediated by a SDW. Unlike previously proposed mechanisms, this magnetic coupling is strongly temperature-dependent. Depending on the temperature and the number N of Cr monolayers (ML), the SDW may be either commensurate (C) or incommensurate (I) with the BCC Cr lattice.