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We study the Berry curvature and Chern number of a non-collinear spin state on a honeycomb lattice that evolves from coplanar to ferromagnetic with a magnetic field applied along the $z$ axis. The coplanar state is stabilized by nearest-neighbor ferromagnetic interactions, single-ion anisotropy along $z$, and Dzyalloshinskii-Moriya interactions between next-nearest neighbor sites. Below the critical field $H_c$ that aligns the spins, the magnetic unit cell contains $M=6$ sites and the spin dynamics contains six magnon subbands. Although the classical energy is degenerate wrt the twist angle $\phi $ between nearest-neighbor spins, the dependence of the free energy on $\phi $ at low temperatures is dominated by the magnon zero-point energy, which contains extremum at $\phi =\pi l/3$ for integer $l$. The only unique ground states GS($\phi )$ have $l=0$ or 1. For $H < H_c'$, the zero-point energy has minima at even $l$ and the ground state is GS(0). For $H_c' < H < H_c$, the zero-point energy has minima at odd $l$ and the ground state is GS($\pi/3$). In GS(0), the magnon density-of-states exhibits five distinct phases with increasing field associated with the opening and closing of energy gaps between the two or three magnonic bands, each containing between 1 and 4 four magnon subbands. While the Berry curvature vanishes for the coplanar $\phi=0$ phase in zero field, the Berry curvature and Chern numbers exhibit signatures of the five phases at nonzero fields below $H_c'$. If $\phi \ne \pi l/3$, the Chern numbers of the two or three magnonic bands are non-integer. We also evaluate the inelastic neutron-scattering spectrum $S(\vk ,\omega )$ produced by the six magnon subbands in all five phases of GS(0) and in GS($\pi/3$)., Comment: 13 pages, 12 figures

Unlike the Berry phase, the orbital angular momentum (OAM) of magnons with two-dimensional wavevector k in band n is not gauge invariant for arbitrary phase lambda_n(k). However, by integrating the OAM over the orientation $\phi $ of wavevector k, we construct a gauge-invariant function F_n(k). Like F_n(k), the average OAM for magnon band n in a circle of radius k is also gauge invariant. We demonstrate these results for a ferromagnet on a honeycomb lattice with Dzyalloshinskii-Moriya interactions between next-nearest neighbor spins. With wavevectors k restricted to the first Brillouin zone, the angular averaged OAM F_n(k) then has opposite signs for lower and upper bands n=1 and 2 for all k., Comment: 6 figures

Motivated by the potential to suppress the antiferromagnetic long-range order in favor of the long-sought-after Kitaev quantum spin liquid state, we study the effect of spin vacancies in the extended Kitaev-Heisenberg model. In particular, we focus on a realistic model obtained from fitting inelastic neutron scattering on $\alpha$-RuCl$_3$. We observe that the long-range zigzag magnetic ordered state only survives when the doping concentration is smaller than 5\%. Upon further increasing the spin vacancy concentration, the ground state becomes a short-range ordered state at low temperatures. Compared with experiments, our classical solution over-stabilizes the zigzag correlation in the presence of spin vacancies. Our theoretical results provide guidance toward interpreting inelastic neutron scattering experiments on magnetically diluted Kitaev candidate materials., Comment: 9 figures

Identifying and characterizing new magnetic systems with Co2+ ions can enhance our understanding of quantum behavior since Co2+ can host a pseudospin-1/2 magnetic ground state. Understanding the magnetic ground state and the phase diagrams of such systems are central to the development of new theoretical models to described emergent quantum properties of complex magnetic systems. The sawtooth chain compound, CsCo2MoO4_2OH, is one such complex magnetic system and here, we present a comprehensive series of magnetic and neutron scattering measurements to determine its magnetic phase diagram. The magnetic properties of CsCo2MoO4_2OH exhibit a strong coupling to the crystal lattice and its magnetic ground state can be easily manipulated by applied magnetic fields. There are two unique Co2+ ions, base and vertex, with Jbb and Jbv magnetic exchange. The magnetism is highly anisotropic with the b-axis (chain) along the easy axis and the material orders antiferromagnetically at TN = 5 K. The zero field antiferromagnetic phase contains vertex magnetic vectors Co1 aligned parallel to the b-axis, while the base vectors Co2 are canted by 34 and aligned in an opposite direction to the vertex vectors. The spins in parallel adjacent chains align in opposite directions, creating an overall antiferromagnetic structure. At a 3 kOe applied magnetic field, adjacent chains flip by 180{\deg} to generate a ferrimagnetic phase. An increase in field gradually induces the Co(1) moment to rotate along the b-axis and align in the same direction with Co2 generating a ferromagnetic structure. Our results demonstrate that the CsCo2MoO4_2OH is a promising candidate to study new physics associated with sawtooth chain magnetism.

We obtain exact results for the orbital angular momentum (OAM) of magnons at the high symmetry points of ferromagnetic (FM) and antiferromagnetic (AF) honeycomb lattices in the presence of Dzyallonshinskii-Moriya (DM) interactions. For the FM honeycomb lattice in the absence of DM interactions, the values of the OAM at the corners of the Brillouin zone (BZ) (${\bf k}_1^*=(0,2\sqrt{3}/9)2\pi/a $, ${\bf k}_2^*=(1/3,\sqrt{3}/9)2\pi/a ,\ldots $) are alternately $\pm 3\hbar /16$ for both magnon bands. The presence of DM interactions dramatically changes those values by breaking the degeneracy of the two magnon bands. The OAM values are alternately $3\hbar /8$ and 0 for the lower magnon band and $-3\hbar /8$ and 0 for the upper magnon band. For the AF honeycomb lattice, the values of the OAM at the corners of the BZ are $\mp (3\hbar /16)\kappa $ on one of the degenerate magnon bands and $\pm (3\hbar /8) (1+\kappa /2)$ on the other, where $\kappa $ measures the anisotropy and the result is independent of the DM interaction., Comment: 8 pages and 6 figures

While certain magnetic sublattices have long been known theoretically to give rise to emergent physics via competing magnetic interactions and quantum effects, finding such configurations in real materials is often deeply challenging. Here we report the synthesis and characterization of a new such material, NaCo2(SeO3)2(OH) which crystallizes with a highly frustrated sublattice of sawtooth Co2+ chains. Single crystals of NaCo2(SeO3)2(OH) were synthesized using a low-temperature hydrothermal method. X-ray single crystal structure analysis reveals that the material crystallizes in orthorhombic space group of Pnma (no. 62). Its crystal structure exhibits one-dimensional chains of corner-sharing isosceles triangles that are made of two crystallographically distinct 3d7 Co2+ sites (Co(1) and Co(2)). The chains run along the b-axis and are interconnected via [SeO3] groups to form a three-dimensional structure mediating super-exchange interactions. The temperature dependent magnetization data show a ferromagnetic-like (FM) transition at 11 K (T1) followed by an antiferromagnetic (AFM) transition at about 6 K (T2). Neutron-powder diffraction measurements reveal that at T1 = 11 K only Co(2) site orders magnetically, forming ferromagnetic zigzag chains along the b-axis. Below T2 = 6 K, both Co(1) and Co(2) sites order in an nearly orthogonal configuration, with Co(1) moments lying inside the plane of the sawtooth chain while Co(2) moments cant out of the plane. The canting of the magnetic moments leads to a net ferromagnetic component along b-axis, parallel to the chain direction. The ordered moments are fully compensated in the ac-plane., Comment: N/A

We study the orbital angular momentum of magnons for collinear ferromagnet (FM) and antiferromagnetic (AF) systems with nontrivial networks of exchange interactions. The orbital angular momentum of magnons for AF and FM zig-zag and honeycomb lattices becomes nonzero when the lattice contains two inequivalent sites and is largest at the avoided-crossing points or extremum of the frequency bands. Hence, the arrangement of exchange interactions may play a more important role at producing the orbital angular momentum of magnons than the spin-orbit coupling energy and the resulting non-collinear arrangement of spins., Comment: Main text 7 pages with 4 figures, and supplementary material 6 pages with 3 figures

Magnetic structures are known to possess magnon excitations confined to their surfaces and interfaces, but these spatially localized modes are often not resolved in spectroscopy experiments. We develop a theory to calculate the confined magnon spectra and its associated spin scattering function, which is the physical observable in neutron and electron scattering, and a proxy for photon spectroscopy based on X-ray, Raman and THz sources. We show that extra anisotropy at the surface or interface plays a key role in magnon confinement. We obtain analytical expressions for the confinement length scale, and show that it is qualitatively similar for ferromagnets and antiferromagnets in dimension d>=2. For d=1 we find remarkable differences between ferromagnetic and antiferromagnetic models. The theory indicates the presence of several confined magnon resonances in addition to the usual magnons thought to explain the excitations of magnetic nanostructures. Detecting these modes may elucidate the impact of the interface on spin anisotropy and magnetic order., Comment: Revised version with many clarifications, submitted to Phys. Rev. B

Due to the strong coupling between magnetism and ferroelectricity, $(\mathrm{ND}_4)_2\mathrm{FeCl}_5\cdot\mathrm{D}_2\mathrm{O}$ exhibits several intriguing magnetic and electric phases. In this letter, we include high-order onsite spin anisotropic interactions in a spin model that successfully captures the ferroelectric phase transitions of $(\mathrm{ND}_4)_2\mathrm{FeCl}_5\cdot\mathrm{D}_2\mathrm{O}$ under a magnetic field and produces 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. Our results emphasize the importance of the high-order spin anisotropic interactions and provide a guideline to understand multiferroic materials with rich phase diagrams., Comment: 6 pages, 5 figures

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)

The entropy stabilized oxide Mg$_{0.2}$Co$_{0.2}$Ni$_{0.2}$Cu$_{0.2}$Zn$_{0.2}$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 report a comprehensive inelastic neutron scattering study of the hybrid molecule-based multiferroic compound (ND4)2FeCl5D2O in the zero-field incommensurate cycloidal phase and the high-field quasi-collinear 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 change of polarization direction, the underlying multiferroic mechanism was proposed to switch from the spin-current model induced via the inverse Dzyalloshinskii-Moriya interaction to the p-d hybridization model. We perform a detailed analysis of the inelastic neutron data of (ND4)2FeCl5D2O using linear spin-wave theory to quantify magnetic interaction strengths and investigate 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 an 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 (ND4)2FeCl5D2O are much more robust than the electric polarization in response to delicate reorganizations of the electronic degrees of freedom in an applied magnetic field., Comment: 18 pages, 4 main figures, 1 Table

Rare earth triangular lattice materials have been proposed as a good platform for the investigation of frustrated magnetic ground states. KErSe$_2$ with the delafossite structure, contains perfect two-dimensional Er$^{3+}$ triangular layers separated by potassium ions, realizing this ideal configuration and inviting study. Here we investigate the magnetism of KErSe$_2$ at miliKelvin temperatures by heat capacity and neutron powder diffraction. Heat capacity results reveal a magnetic transition at 0.2 K in zero applied field. This long-range order is suppressed by an applied magnetic field of 0.5 T below 0.08 K. Neutron powder diffraction suggests that the zero-field magnetic structure orders with $k=(\frac{1}{2},0,\frac{1}{2})$ in a stripe spin structure. Unexpectedly, Er is found to have a reduced moment of 3.06(1) $\mu_B$/Er in the ordered state and diffuse magnetic scattering, which originates at higher temperatures, is found to persist in the ordered state potentially indicating magnetic fluctuations. Neutron diffraction collected under an applied field shows a metamagnetic transition at $\sim$ 0.5 T to ferromagnetic order with $k$=(0,0,0) and two possible structures, which are likely dependent on the applied field direction. First principle calculations show that the zero field stripe spin structure can be explained by the first, second and third neighbor couplings in the antiferromagnetic triangular lattice., Comment: 9 pages, 6 figures

We present a comprehensive neutron scattering study of the breathing pyrochlore magnet LiGaCr4S8. 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 parameterize 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 [Ghoshet al.,npj Quantum Mater.4, 63 (2019)]. We explain the origin of geometrical frustration in LiGaCr4S8 interms of net antiferromagnetic coupling between emergent tetrahedral spin clusters that occupy a face-centered 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., Comment: Supplemental information available upon request

Single crystals of a honeycomb lattice antiferromagnet, Tb$_2$Ir$_3$Ga$_9$ were synthesized, and the physical properties have been studied. From magnetometry, a long-range antiferromagnetic ordering at $\approx$12.5 K with highly anisotropic magnetic behavior was found. Neutron powder diffraction confirms that the Tb spins lie along the $\va $-axis, parallel to the shortest Tb-Tb contact. Two field-induced spin-flip transitions are observed when the field is applied parallel to this axis, separated by a plateau corresponding roughly to M$\approx$M$_{\rm{s}}$/2. Transport measurements show the resistivity to be metallic with a discontinuity at the onset of N\'eel order. Heat capacity shows a $\lambda$-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 Tb$^{3+}$ ion in a site of \textit{C$_s$} symmetry and expressing a significant bond dependent anisotropy., Comment: 11 pages, 9 figures

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

Earlier models for the room-temperature multiferroic BiFeO3 implicitly assumed that a very strong anisotropy restricts the domain wavevectors q to the three-fold symmetric axis normal to the static polarization P. However, recent measurements demonstrate that the domain wavevectors rotate so that q rotates within the hexagonal plane normal to P away from the field orientation m. We show that the previously neglected three-fold anisotropy K3 restricts the wavevectors to lie along the three-fold axis in zero field. For m along a three-fold axis, the domain with q parallel to m remains metastable below Bc1 = 7 T. Due to the pinning of domains by non-magnetic impurities, the wavevectors of the other two domains start to rotate away from m above 5.6 T, when the component of the torque t = M x B along P exceeds a threshold value tpin. Since t =0 when m is perpendicular to q, the wavevectors of those domains never become completely perpendicular to the magnetic field. Our results explain recent measurements of the critical field as a function of field orientation, small-angle neutron scattering measurements of the wavevectors, as well as spectroscopic measurements with m along a three-fold axis.

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 axis 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 show that the anisotropy energy $-K_3 S^6 \sin^6 \theta \cos 6 \phi $ confines the wavevectors q to the three-fold axis $\phi =0$ and $+-2 \pi/3$ within the hexagonal plane with $\theta = \pi /2$.

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.

A compound with very weakly interacting chains, 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., Comment: 4 figures

We report a neutron diffraction study of the multiferroic mechanism in (ND4)2FeCl5D2O, 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 TN=7.3 K, followed by a second transition to an IC cycloidal spin state at TFE=6.8 K, the later 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 appearance of the 2nd-order harmonic coincides with the onset of the electric polarization, thereby providing unambiguous evidence that the induced electric polarization is mediated by the spin-lattice interaction. Our results for this system, in which the orbital angular momentum is expected to be quenched, are remarkably similar to those of the prototypical TbMnO3, in which the magnetoelectric effect is attributed to spin-orbit coupling., Comment: 5 pages, 4 figures

Despite its great technological importance, the magnetoelectric (ME) couplings in \BF are barely understood. By using a first-principles approach, we uncover the {\it dynamic} ME couplings of the long-range spin-cycloid in BiFeO$_3$. Based on a microscopic Hamiltonian, our first-principles approach disentangles the hidden ME couplings due to spin-current and exchange-striction. Beyond the spin-current polarization governed by the inverse Dzyaloshinskii-Moriya interaction \cite{iDM}, various spin-current polarizations derived from both ferroelectric and antiferrodistortive distortions cooperatively produce the strong non-reciprocal directional dichroism or the asymmetry in the absorption of counter-propagating light in BiFeO$_3$. Our systematic approach can be generally applied to any multiferroic material, laying the foundation for revealing hidden ME couplings on an atomic scale and for exploiting optical ME effects in the next generation of technological devices such as optical diodes., Comment: 11 pages, 4 figures, 1 table

A microscopic model for the room-temperature multiferroic BiFeO$_3$ 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 non-reciprocal directional dichroism: the spin current, magnetostriction, and single-ion anisotropy. We conclude that the non-reciprocal directional dichroism in \BF 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 non-reciprocal 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, BiFeO$_3$ can be used as a room-temperature optical diode at certain frequencies in the GHz to THz range. Our work demonstrates that an analysis of the non-reciprocal 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., Comment: 15 pages, 7 figures

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 BiFeO3. 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 octahedra rotation. Comparison with recent neutron scatterings reveals that first polarization reaches 3.0 $\mu$C/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., Comment: 5pages, 3figures

We theoretically investigate the ground state magnetic properties of the brownmillerite phase of SrCoO2.5. Strong correlations within Co d electrons are treated within the local spin density approximations of Density Functional theory (DFT) with Hubbard U corrections (LSDAU) and results are compared with the Heyd Scuzeria 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 s 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 becomes dominant at different momenta. These predictions can be tested by experimentally.

Multiferroic BiFeO3 undergoes a transition from a distorted spiral phase to a G-type antiferromagnet above a critical field H_c that depends on the orientation m of the field. We show that H_c(m) has a maximum when oriented along a cubic diagonal parallel to the electric polarization P and a minimum in the equatorial plane normal to P when two magnetic domains with the highest critical fields are degenerate. The measured critical field along a cubic axis is about 19 T but H_c is predicted to vary by as much as 2.5 T above and below this value. The orientational dependence of H_c(m) is more complex than indicated by earlier work, which did not consider the competition between magnetic domains., Comment: 4 pages, 3 figures

The spectroscopic modes of multiferroic BiFeO$_3$ provide detailed information about the very small anisotropy and Dzyaloshinskii-Moriya (DM) interactions responsible for the long-wavelength, distorted cycloid below $\TN = 640$ K. A microscopic model that includes two DM interactions and easy-axis anisotropy predicts both the zero-field spectroscopic modes as well as their splitting and evolution in a magnetic field applied along a cubic axis. While only six modes are optically active in zero field, all modes at the cycloidal wavevector are activated by a magnetic field. The three magnetic domains of the cycloid are degenerate in zero field but one domain has lower energy than the other two in nonzero field. Measurements imply that the higher-energy domains are depopulated above about 6 T and have a maximum critical field of 16 T, below the critical field of 19 T for the lowest-energy domain. Despite the excellent agreement with the measured spectroscopic frequencies, some discrepancies with the measured spectroscopic intensities suggest that other weak interactions may be missing from the model.

Spectroscopic modes provide the most sensitive probe of the very weak interactions responsible for the properties of the long-wavelength cycloid in the multiferroic phase of \BF below $\TN \approx 640$ K. Three of the four modes measured by THz and Raman spectroscopies were recently identified using a simple microscopic model. While a Dzyaloshinskii-Moriya (DM) interaction $D$ along $[-1,2,-1]$ induces the cycloid with wavevector $(2\pi /a)(0.5+\delta, 0.5, 0.5-\delta)$ ($\delta \approx 0.0045$), easy-axis anisotropy $K$ along the $[1,1,1]$ direction of the electric polarization ${\bf P}$ induces higher harmonics of the cycloid, which split the $\Psi_1$ modes at 2.49 and 2.67 meV and activate the $\Phi_2$ mode at 3.38 meV. However, that model could not explain the observed low-frequency mode at about 2.17 meV. We now demonstrate that an additional DM interaction $D'$ along $[1,1,1]$ not only produces the observed weak ferromagnetic moment of the high-field phase above 18 T but also activates the spectroscopic matrix elements of the nearly-degenerate, low-frequency $\Psi_0$ and $\Phi_1$ modes, although their scattering intensities remain extremely weak. Even in the absence of easy-axis anisotropy, $D'$ produces cycloidal harmonics that split $\Psi_1 $ and activate $\Phi_2$. However, the observed mode frequencies and selection rules require that both $D'$ and $K$ are nonzero. This work also resolves an earlier disagreement between spectroscopic and inelastic neutron-scattering measurements., Comment: 11 pages, 6 Figures, Submitted to Physical Review B

We have studied the magnetic field dependence of far-infrared active magnetic modes in a single ferroelectric domain \BFO/ crystal at low temperature. The modes soften close to the critical field of 18.8\,T along the [001] (pseudocubic) axis, where the cycloidal structure changes to the homogeneous canted antiferromagnetic state and a new strong mode with linear field dependence appears that persists at least up to 31\,T. A microscopic model that includes two \DM/ interactions and easy-axis anisotropy describes closely both the zero-field spectroscopic modes as well as their splitting and evolution in a magnetic field. The good agreement of theory with experiment suggests that the proposed model provides the foundation for future technological applications of this multiferroic material., Comment: Added Randy S. Fishman to the author list, he contributed the theory

We have identified three of the four magnetoelectric modes of multiferroic BiFeO$_3$ measured using THz spectroscopy. Excellent agreement with the observed peaks is obtained by including the effects of easy-axis anisotropy along the direction of the electric polarization. By distorting the cycloidal spin state, anisotropy splits the $\Psi_{\pm 1}$ mode into peaks at 20 and 21.5 cm$^{-1}$ and activates the lower $\Phi_{\pm 2}$ mode at 27 cm$^{-1}$ (T=200 K). An electromagnon is identified with the upper $\Psi_{\pm 1}$ mode at 21.5 cm$^{-1}$. Our results also explain recent Raman and inelastic neutron-scattering measurements., Comment: 5 pages, 4 Figures, Submitted to Physical Review Letters

The spin-wave excitations of the multiferroic $\rm MnWO_4$ have been measured in its low-temperature collinear commensurate phase using high-resolution inelastic neutron scattering. These excitations can be well described by a Heisenberg model with competing long-range exchange interactions and a single-ion anisotropy term. The magnetic interactions are strongly frustrated within the zigzag spin chain along c axis and between chains along the a axis, while the coupling between spin along the b axis is much weaker. The balance of these interactions results in the noncollinear incommensurate spin structure associated with the magnetoelectric effect, and the perturbation of the magnetic interactions leads to the observed rich phase diagrams of the chemically-doped materials. This delicate balance can also be tuned by the application of external electric or magnetic fields to achieve magnetoelectric control of this type of materials., Comment: 4 pages, 4 figures

We obtain the non-collinear ground states of a triangular-lattice antiferromagnet with exchange interactions up to third nearest neighbors as a function of the single-ion anisotropy $D$. At a critical value of $D$, the collinear $\uudd $ phase transforms into a complex non-collinear phase with odd-order harmonics of the fundamental ordering wavevector $\vQ $. The observed elastic peaks at $2\pi \vx -\vQ $ in both Al- and Ga- doped CuFeO$_2$ are explained by a "scalene" distortion of the triangular lattice produced by the repulsion of neighboring oxygen atoms., Comment: 4 pages 3 figures, accepted for publication by Phys. Rev. B Rapid communications

The molecule-based magnet [Ru$_2$(O$_2$CMe)$_4$]$_3$[Cr(CN)$_6$] contains two weakly-coupled, interpenetrating sublattices in a body-centered cubic structure. Although the field-dependent magnetization indicates a metamagnetic transition from an antiferromagnet to a paramagnet, the hysteresis loop also exhibits a substantial magnetic remanance and coercive field uncharacteristic of a typical metamagnet. We demonstrate that this material behaves like two giant moments with a weak antiferromagnetic coupling and a large energy barrier between the orientations of each moment. Because the sublattice moments only weakly depend on field in the transition region, the magnetic correlation length can be directly estimated from the magnetization., Comment: 3 figures

A C$_3$-symmetric crystal-field potential in the Fe(II)Fe(III) bimetallic oxalates splits the L=2 Fe(II) multiplet into two doublets and a singlet. In compounds that exhibit magnetic compensation, one of the doublets was predicted to lie lowest in energy and carry a non-quenched orbital angular momentum $\pm \ld $, where $\ld $ exceeds a threshold value. In a range of $\ld $, a Jahn-Teller (JT) distortion increases the energy splitting of the low-lying doublet and breaks the C$_3$ symmetry of the bimetallic planes around the ferrimagnetic transition temperature. At low temperatures, the JT distortion disappears in compounds that display magnetic compensation due to the competition with the spin-orbit coupling. A comparison with recent measurements provides strong evidence for this re-entrant, low-temperature JT transition and a prediction for the normal, high-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-C$_3$-symmetric organic cations can eliminate magnetic compensation., Comment: 7 pages, 4 figures, submitted to Journal of the American Chemical Society

It is well known that the magnetic anisotropy in a compressively-strained Mn-doped GaAs film changes from perpendicular to parallel with increasing hole concentration $p$. We study this reorientation transition at T=0 in a quantum well with Mn impurities confined to a single plane. With increasing $p$, the angle $\theta $ that minimizes the energy $E$ increases continuously from 0 (perpendicular anisotropy) to $\pi /2$ (parallel anisotropy) within some range of $p$. The shape of $\Emin (p)$ suggests that the quantum well becomes phase separated with regions containing low hole concentrations and perpendicular moments interspersed with other regions containing high hole concentrations and parallel moments. However, due to the Coulomb energy cost associated with phase separation, the true magnetic state in the transition region is canted with $0 < \theta < \pi /2$., Comment: 4 figures

The magnetic susceptibility and Edwards-Anderson order parameter q of the spin-glass-like (SGL) phase of the double-exchange model are evaluated in the weak-coupling or RKKY limit. Dynamical mean-field theory is used to show that q=M(T/Tsg)^2, where M is the classical Brillouin function and Tsg is the SGL transition temperature. The correlation length of the SGL phase is determined by a correlation parameter Q that maximizes Tsg and minimizes the free energy. The magnetic susceptibility has a cusp at Tsg and reaches a nonzero value as T goes to zero., Comment: 8 pages, 2 figures

Some of the highest transition temperatures achieved for Mn-doped GaAs have been in delta-doped heterostructures with well-separated planes of Mn. But in the absence of magnetic anisotropy, the Mermin-Wagner theorem implies that a single plane of magnetic ions cannot be ferromagnetic. Using a Heisenberg model, we show that the same mechanism that produces magnetic frustration and suppresses the transition temperature in bulk Mn-doped GaAs, due to the difference between the light and heavy band masses, can stabilize ferromagnetic order for a single layer of Mn in a GaAs quantum well. This comes at the price of quantum fluctuations that suppress the ordered moment from that of a fully saturated ferromagnet. By comparing the predictions of Heisenberg and Kohn-Luttinger models, we conclude that the Heisenberg description of a Mn-doped GaAs quantum well breaks down when the Mn concentration becomes large, but works quite well in the weak-coupling limit of small Mn concentrations. This comparison allows us to estimate the size of the quantum fluctuations in the quantum well., Comment: 7 pages, 3 figures: to appear in PRB

We employ dynamical mean-field theory to identify the materials properties that optimize Tc for a generalized double-exchange (DE) model. We reach the surprising conclusion that Tc achieves a maximum when the band angular momentum j equals 3/2 and when the masses in the 1/2 and 3/2 sub-bands are equal. However, we also find that Tc is significantly reduced as the ratio of the masses decreases from one. Consequently, the search for dilute magnetic semiconductors (DMS) materials with high Tc should proceed on two fronts. In semiconductors with p bands, such as the currently studied Mn-doped Ge and GaAs semiconductors, Tc may be optimized by tuning the band masses through strain engineering or artificial nanostructures. On the other hand, semiconductors with s or d bands with nearly equal effective masses might prove to have higher Tc's than p-band materials with disparate effective masses., Comment: 5 pages, 4 figures

Although diagrammatic perturbation theory fails for the dynamical-mean field theory of the double-exchange model, the theory is nevertheless Phi-derivable and hence thermodynamically consistent, meaning that the same thermodynamic properties are obtained from either the partition function or the Green's function. We verify this consistency by evaluating the magnetic susceptibility and Curie temperature for any Hund's coupling., Comment: 9 pages, 1 figure