Spiral Magnetic Order Research Articles

Canted spiral magnetic order in Hubbard model

Canted spiral magnetic order in Hubbard model

Orbitally driven spin reorientation in Mn-doped YBaCuFeO5

The oxygen-deficient layered perovskite YBaCuFeO5 (YBCFO) is a rare type-II multiferroic material where ferroelectricity, driven by incommensurate spiral magnetic order, is believed to be achievable up to temperatures higher than room temperature. A cycloidal spiral order rather than a helical spiral order is an essential ingredient for the existence of ferroelectricity in this material. Motivated by a recent experimental study on Mn-doped YBCFO where the spiral plane was observed to cant more towards the crystallographic c-axis upon Mn doping at Fe sites than in the parent compound, we performed a detailed theoretical investigation using density functional theory calculations to understand the mechanism behind such spin reorientation. Our total energy calculations, within the generalized gradient approximation plus U plus spin–orbit coupling approach, reveal that Fe/Cu spin moments indeed align more towards the c-axis in Mn-doped YBCFO than in the parent compound. The largest exchange interaction (Cu–Cu in the a−b plane) is observed to decrease systematically with Mn doping concentration, reflecting the lowering of the transition temperature seen in experiments. Further, the inter-bilayer Cu–Mn exchange interaction becomes ferromagnetic in Mn-doped YBCFO, whereas the corresponding Cu–Fe exchange is antiferromagnetic in the parent compound, giving rise to frustration in the commensurate magnetic order. Most importantly, our electronic structure calculations reveal that in Mn-doped YBCFO because of hybridization with the Mn dz2 orbital, the highest occupied Cu orbital becomes the dz2 orbital as opposed to the dx2−y2 orbital in the parent compound. Therefore, we believe that the occupancy of the out-of-plane-oriented Cu dz2 orbital in place of the planar dx2−y2 orbital along with the frustrating exchange interaction drives the spins to align along the c-axis in Mn-doped YBCFO.

Commensurate and spiral magnetic order in the doped two-dimensional Hubbard model: Dynamical mean-field theory analysis

We develop a dynamical mean-field theory approach for the spiral magnetic order, changing to a local coordinate frame with preferable spin alignment along the $z$-axis, which can be considered with the impurity solvers treating the spin diagonal local Green's function. We furthermore solve the Bethe-Salpeter equations for nonuniform dynamic magnetic susceptibilities in the local coordinate frame. We apply this approach to describe the evolution of magnetic order with doping in the $t-t'$ Hubbard model with $t'=0.15$, which is appropriate for the description of the doped La$_2$CuO$_4$ high-temperature superconductor. We find that with doping the antiferromagnetic order changes to the $(Q,\pi)$ incommensurate one, and then to the paramagnetic phase. The spectral weight at the Fermi level is suppressed near half filling and continuously increases with doping. The dispersion of holes in the antiferromagnetic phase shows qualitative agreement with the results of the $t$-$J$ model consideration. In the incommensurate phase we find two branches of hole dispersions, one of which crosses the Fermi level. The resulting Fermi surface forms hole pockets. We also consider the dispersion of the magnetic excitations, obtained from the non-local dynamic magnetic susceptibilities. The transverse spin excitations are gapless, fulfilling the Goldstone theorem; in contrast to the mean-field approach the obtained magnetic state is found to be stable. The longitudinal excitations are characterized by a small gap, showing the rigidity of the spin excitations. For realistic hopping and interaction parameters we reproduce the experimentally measured spin-wave dispersion of La$_2$CuO$_4$.

Large Topological Hall Effect and Spiral Magnetic Order in the Weyl Semimetal SmAlSi

Weyl electrons are intensely studied due to novel charge transport phenomena such as chiral anomaly, Fermi arcs, and photogalvanic effect. Recent theoretical works suggest that Weyl electrons can also participate in magnetic interactions, and the Weyl-mediated indirect exchange coupling between local moments is proposed as a new mechanism of spiral magnetism that involves chiral electrons. Despite reports of incommensurate and non-collinear magnetic ordering in Weyl semimetals, an actual spiral order has remained hitherto undetected. Here, we present evidence of Weyl-mediated spiral magnetism in SmAlSi from neutron diffraction, transport, and thermodynamic data. We show that the spiral order in SmAlSi results from the nesting between topologically non-trivial Fermi pockets and weak magnetocrystalline anisotropy, unlike related materials (Ce,Pr,Nd)AlSi, where a strong anisotropy prevents the spins from freely rotating. We map the magnetic phase diagram of SmAlSi and reveal an A-phase where topological magnetic excitations may exist. This is corroborated by the observation of a topological Hall effect within the A-phase.

Anomalous behavior of magnetic linear dichroism in HoFe3(BO3)4 crystal with spiral magnetic ordering

Spectra of magnetic linear dichroism of the optical transition 5I8 → 5F3 were studied in the HoFe3(BO3)4 single crystal as a function of magnetic field directed along the trigonal c axis at the temperature 2 K. It has been found that dichroism in the basal plane appears even in low magnetic field in the easy-axis state of the crystal. This indicates a violation of the axial symmetry of spiral structure of Ho magnetic moments. Moreover, the sign of dichroism is changed with the change of the magnetic field sign both below and above the field of spin-reorientation transition. This could mean that the average magnetic moment of three Ho3+ ions forming the spiral rotates in magnetic field both relative to the c axis and in the ab plane.

Mitigating the fermion sign problem by automatic differentiation

As an intrinsically unbiased method, the quantum Monte Carlo (QMC) method is of unique importance in simulating interacting quantum systems. Although the QMC method often suffers from the notorious sign problem, the sign problem of quantum models may be mitigated by finding better choices of the simulation scheme. However, a general framework for identifying optimal QMC schemes has been lacking. Here, we propose a general framework using automatic differentiation to automatically search for the best QMC scheme within a given ansatz of the Hubbard-Stratonovich transformation, which we call ``automatic differentiable sign optimization'' (ADSO). We apply the ADSO framework to the honeycomb lattice Hubbard model with Rashba spin-orbit coupling and demonstrate that ADSO is remarkably effective in mitigating and even solving its sign problem. Specifically, ADSO finds a sign-free point in the model which was previously thought to be sign-problematic. For the sign-free model discovered by ADSO, its ground state is shown by sign-free QMC simulations to possess spiral magnetic ordering; we also obtained the critical exponents characterizing the magnetic quantum phase transition.

Helimagnets by disorder: Its role on the high-temperature magnetic spiral in the YBaCuFeO5 perovskite

Most of the spiral magnetoelectric multiferroics investigated in recent years are geometrically or exchange-frustrated magnets, where the presence of triangular or other frustrated spin networks produce low magnetic transition temperatures. This critically limits their potential uses. The exceptional stability of the spiral magnetic order (at ${T}_{S}$) in the layered structure of the ${\mathrm{YBaCuFeO}}_{5}$ double perovskite involves a nonconventional mechanism: spiral order by disorder. The model has been theoretically developed by Scaramucci et al. [Phys. Rev. Res. 2, 013273 (2020)] after the discovery of a huge impact of cation disorder on ${T}_{S}$ [M. Morin et al., Nat. Commun. 7, 13758 (2016)]. In this work the influence of disorder (and only disorder) on the magnetic phase diagram is studied on a quantitative basis extending the range of previous studies. We thoroughly investigate the impact of frustration due to $B$-site disorder (${n}_{d}$) on the magnetic spirals in the reference composition ${\mathrm{YBaCuFeO}}_{5}$. The interplay between disorder, stability, and the detailed features of the incommensurate spiral magnetic orders were systematic, quantitative, and methodically investigated in samples of identical composition, spanning a wide range of ${n}_{d}$ values. Three different regimes are distinguished in the ${\mathrm{YBaCuFeO}}_{5}$ phase diagram versus disorder. A triple point is found in ${\mathrm{YBaCuFeO}}_{5}$ driven by Fe/Cu disorder that sets limits to ${T}_{S}$ and the cycloidal component of the helicoidal order. These layered materials appear as a very efficient realization of the avenue ``spiral order by disorder'' to supply functional helimagnets at normal working temperatures.

SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model

We present a SU(2) gauge theory of fluctuating magnetic order in the two-dimensional Hubbard model. The theory is based on a fractionalization of electrons in fermionic chargons and bosonic spinons. The chargons undergo N\'eel or spiral magnetic order below a density-dependent transition temperature ${T}^{*}$. Fluctuations of the spin orientation are described by a nonlinear sigma model obtained from a gradient expansion of the spinon action. The spin stiffnesses are computed from a renormalization group improved random phase approximation. Our approximations are designed for moderate, not for strong, Hubbard interactions. The stiffnesses are strongly doping dependent with discontinuities at half-filling and a pronounced electron-hole asymmetry. The spinon fluctuations prevent magnetic long-range order of the electrons at any finite temperature. The phase with magnetic chargon order shares characteristic features with the pseudogap regime in high-${T}_{c}$ cuprates: a strong reduction of charge carrier density, a spin gap, and Fermi arcs. A substantial fraction of the pseudogap regime exhibits electronic nematicity.

Superconducting Spin Valves Based on a Single Spiral Magnetic Layer

A detailed investigation of a superconducting spin-triplet valve is presented. This spin valve consists of a superconducting film covering a metal with an intrinsic spiral magnetic order, which could result from competing isotropic exchanges or, if the crystal lattice breaks central symmetry, from asymmetric Dzyaloshinskii-Moriya exchange. Depending on the anisotropy, such a metal may change its magnetization either from a spiral to uniform order, as seen in $\mathrm{Ho}$ and $\mathrm{Er}$, or in the direction of the spiral itself, as in crystals of the B20-type structure [such as $\mathrm{Mn}\mathrm{Si}$, ($\mathrm{Fe}$,$\mathrm{Co}$)$\mathrm{Si}$, $\mathrm{Fe}\mathrm{Ge}$, etc.]. The nonuniform magnetic order controls the appearance of long-range triplet superconducting correlations at strong exchange fields, affecting the detailed character of the proximity effect. We show that the magnetic control of the spin-valve behavior can also be obtained from moderately low exchange fields (typically associated to negligible long-range triplet correlations), thanks to an orientation-dependent averaging mechanism of the magnetic inhomogeneity on the scale of the Cooper pairs. Our numerical calculations reveal that the spin-valve effect is in fact magnified at moderately low exchange fields, when the exchange splitting in the spiral magnet is comparable to the superconducting gap, and the spiral period is less than or equal to the superconducting coherence length in the magnet multiplied by $2\ensuremath{\pi}$.

Magnetic domains in two distinct antiferromagnetic phases of CuO

Multiferroic CuO showing two distinct antiferromagnetic (AFM) phases: incommensurate (ICM) spiral and commensurate (CM) collinear AFM phases, is investigated by resonant x-ray diffraction (RXD) at the Cu ${L}_{3}$ edge. In the ICM phase where spin-spiral-induced ferroelectricity develops, circular dichroism ascribed to the handedness of the spiral magnetic order is observed at the magnetic Bragg (0.506, 0, \ensuremath{-}0.483) reflection. By measuring two-dimensional maps of the reflection intensity, the spatial distribution of the ferroelectric domains is clarified and is found to be strongly influenced by crystallographic twin structures. In the CM phase, weaker but substantial circular dichroic signals are observed at the magnetic Bragg (0.5, 0, \ensuremath{-}0.5) reflection. It is found that the spatial distributions of the circular dichroic signals resemble those in the ICM phase, suggesting some relation between the ICM and CM phases. The origin of the circular dichroic RXD observed in CuO is discussed based on the experimental observations.

Spin stiffness, spectral weight, and Landau damping of magnons in metallic spiral magnets

We analyze the properties of magnons in metallic electron systems with spiral magnetic order. Our analysis is based on the random phase approximation for the susceptibilities of tight binding electrons with a local Hubbard interaction in two or three dimensions. We identify three magnon branches from poles in the susceptibilities, one associated with in-plane, the other two associated with out-of-plane fluctuations of the spiral order parameter. We derive general expressions for the spin stiffnesses and the spectral weights of the magnon modes, from which also the magnon velocities can be obtained. Moreover, we determine the size of the decay rates of the magnons due to Landau damping. While the decay rate of the in-plane mode is of the order of its excitation energy, the decay rate of the out-of-plane mode is smaller so that these modes are asymptotically stable excitations even in the presence of Landau damping.

Role of disorder in electronic and magnetic properties of Ag3LiIr2O6

The nature of magnetism in the intercalated honeycomb iridate Ag$_3$LiIr$_2$O$_6$ has been a subject of recent intensive debate, where the absence or presence of antiferromagnetic order has been reported to be related to possible structural disorder effects and, an enhanced Ir-O hybridization and itinerancy with respect to the parent Li$_2$IrO$_3$ has been suggested as the origin of distinct x-ray spectroscopy features. In the present work we investigate the microscopic nature of the electronic and magnetic properties of Ag$_3$LiIr$_2$O$_6$ via a combination of density functional theory combined with exact diagonalization of ab initio-derived models for various experimental and theoretical structures. We evaluate two possible scenarios, the itinerant quasimolecular framework (QMO) on the one hand, and the localized relativistic $j_{\rm eff} = 1/2$ and $j_{\rm eff} = 3/2$ picture on the other hand, and find that the latter description is still viable for this system. We further calculate resonant inelastic x-ray scattering spectra and show that agreement with experimental observations can be obtained if the presence of Ag vacancies leading to changes in Ir filling and structural disorder is assumed. Finally, we show that the experimentally observed antiferromagnetic spiral magnetic order is reproduced by our ab-initio derived magnetic models.

Spiral magnetism and chiral superconductivity in a Kondo-Hubbard triangular lattice model

Building on the results of Ref. \cite{faye2018phase}, which identified an antiferromagnetic and Kondo singlet phases on the Kondo-Hubbard square lattice, we use the variational cluster approximation (VCA) to investigate the competition between these phases on a two-dimensional triangular lattice with $120^{o}$ spin orientation. In addition to the antiferromagnetic exchange interaction $J_{\perp}$ between the localized (impurity) and conduction (itinerant) electrons, our model includes the local repulsion $U$ of the conduction electrons and the Heisenberg interaction $J_H$ between the impurities. At half-filling, we obtain the quantum phase diagrams in both planes $(J_{\perp}, U J_{\perp})$ and $(J_{\perp}, J_{H})$. We identify a long-range, three-sublattice, spiral magnetic order which dominates the phase diagrams for small $J_{\perp}$ and moderate $U$, while a Kondo singlet phase becomes more stable at large $J_{\perp}$. The transition from the spiral magnetic order to the Kondo singlet phase is a second-order phase transition. In the $(J_{\perp}, J_{H})$ plane, we observe that the effect of $J_H$ is to reduce the Kondo singlet phase, giving more room to the spiral magnetic order phase. It also introduces some small magnetic oscillations of the spiral magnetic order parameter. At finite doping and when spiral magnetism is ignored, we find superconductivity with symmetry order parameter $d+id$, which breaks time reversal symmetry. The superconducting order parameter has a dome centered at around $5\%$ hole doping, and its amplitude decreases with increasing $J_{\perp}$. We show that spiral magnetism can coexist with $d+id$ state and that superconductivity is suppressed, indicating that these two phases are in competition.

Spiral magnetic order and metal-insulator transition in the Hubbard model on a triangular lattice

The magnetic phase diagrams of the two-dimensional Hubbard model for isotropic and anisotropic triangular lattices are constructed within the Hartree--Fock and slave boson approximations. The triangular lattice specific non-collinear and spiral magnetic states, as well as phase separation between them, are shown to be realized in a wide range of model parameters along with collinear magnetic states (stripe antiferromagnetic and ferromagnetic). Phase transitions of the first and second order are found, and the boundaries of the phase separation regions are determined. A comparison of the two approximations, Hartree--Fock and slave boson, shows that electronic correlations suppress magnetic states, the region of paramagnetism being expand, for values U/t>~=5. At the same time, when the Fermi level is near the van Hove singularity, electron correlations do not change the diagrams qualitatively, which is consistent with the previously obtained result for square and cubic lattices. The results are compared with the data available in the literature for other methods and approaches. Keywords: Hubbard model, phase separation, spiral magnetic order, triangular lattice, metal-insulator transition

Importance of intersite Hubbard interactions in β−MnO2 : A first-principles DFT+U+V study

We present a first-principles investigation of the structural, electronic, and magnetic properties of pyrolusite ($\beta$-MnO$_2$) using conventional and extended Hubbard-corrected density-functional theory (DFT+$U$ and DFT+$U$+$V$). The onsite $U$ and intersite $V$ Hubbard parameters are computed using linear-response theory in the framework of density-functional perturbation theory. We show that while the inclusion of the onsite $U$ is crucial to describe the localized nature of the Mn($3d$) states, the intersite $V$ is key to capture accurately the strong hybridization between neighboring Mn($3d$) and O($2p$) states. In this framework, we stabilize the simplified collinear antiferromagnetic (AFM) ordering (suggested by the Goodenough-Kanamori rule) that is commonly used as an approximation to the experimentally-observed noncollinear screw-type spiral magnetic ordering. A detailed investigation of the ferromagnetic and of other three collinear AFM spin configurations is also presented. The findings from Hubbard-corrected DFT are discussed using two kinds of Hubbard manifolds - nonorthogonalized and orthogonalized atomic orbitals - showing that special attention must be given to the choice of the Hubbard projectors, with orthogonalized manifolds providing more accurate results than nonorthogonalized ones within DFT+$U$+$V$. This work paves the way for future studies of complex transition-metal compounds containing strongly localized electrons in the presence of pronounced covalent interactions.

Dispersion relation of spin wave in chiral helimagnet under stationary optical vortex radiation

We investigate a dispersion relation of a spin wave of an effectively one-dimensional chiral helimagnet CrNb3S6, which is under stationary radiation of a resonant optical vortex beam coaxial to that spiral magnetic order axis. We derive a classical magnetic structure by solving Landau–Lifshitz–Gilbert equation and calculate the collective excitation on it. We show that the optical vortex radiation makes the energy gap at k ∼ 0, and the exceptional points appear in the dispersion relation. Because such a dispersion relation implies the dynamical properties with instability, our result implies a possibility to control spin wave transport.

An optically active spiral

Multiferroics The material cupric oxide exhibits magnetoelectric coupling, meaning that its magnetic properties can be controlled by electric fields. In its spin spiral phase, cupric oxide has a spiral magnetic ordering that can be right- or left-handed. Masuda et al. used electric fields to create purely left- or right-handed samples and then studied their optical activity. The samples exhibited natural optical activity, which the researchers were then able to control with electric fields. Science , this issue p. [496][1] [1]: /lookup/doi/10.1126/science.aaz4312

Electric field control of natural optical activity in a multiferroic helimagnet

Controlling the chiral degree of freedom in matter has long been an important issue for many fields of science. The spin-spiral order, which exhibits a strong magnetoelectric coupling, gives rise to chirality irrespective of the atomic arrangement of matter. Here, we report the resonantly enhanced natural optical activity on the electrically active magnetic excitation, that is, electromagnon, in multiferroic cupric oxide. The electric field control of the natural optical activity is demonstrated through magnetically induced chirality endowed with magnetoelectric coupling. These optical properties inherent to multiferroics may lead to optical devices based on the control of chirality.

Evolution of structure and the exchange bias behavior with annealing temperature in nanoscale NiCr2O4

NiCr2O4 nanoparticles have been successfully prepared by chemical co-precipitation method. Desired crystallographic phase of NiCr2O4 is confirmed by analyzing x-ray diffractrograms. With increasing annealing temperature, crystal transition from cubic to tetragonal phase is observed. The increasing average particle size from ∼80 to ∼280 nm is studied by SEM and TEM micrographs as annealing temperature increases. Exchange bias behavior is detected at 10 K accompanied by the shift of magnetic hysteresis loops along field axis. This effect is gradually weakening as annealing temperature increases. The magnetization depending on temperature under zero-field-cooled and field-cooled conditions suggests the ferrimagnetic transition at ∼72 K and the spiral magnetic order at ∼25 K. Furthermore, the ferrimagnetic transition point shifts slightly to low temperature with increasing annealing temperature. Based on the measurement results, the appearance and evolution of exchange bias effect in NiCr2O4 nanoparticles with improving annealing temperature should be simultaneously derived from the lattice transition and the surface spin effects.

Spin-helix-driven insulating phase in two-dimensional lattice

Motivated by emergent $SU(2)$ symmetry in the spin orbit coupled system, we study the spin helix driven insulating phase in two dimensional lattice. When both Rashba and Dresselhaus spin orbit couplings are present, the perfect Fermi surface nesting occurs at a special condition depending on the lattice geometry. In this case, the energies of spin up at any wave vector $\vec{k}$ are equivalent to the ones of spin down at $\vec{k}\!+\!\vec{Q}$ with so-called the \textit{shifting wave vector} $\vec{Q}$. Thus, the system stabilizes magnetic insulator with spiral like magnetic ordering even in the presence of tiny electron-electron interaction where the magnetic ordering wave vector is proportional to $\vec{Q}$. We first show the condition for existence of the \textit{shifting wave vector} in general lattice model and emergent $SU(2)$ symmetry in the spin orbit coupled system. Then, we exemplify this in square lattice at half filling and discuss the insulating phase with (non-) coplanar spin density wave and charge order. Our study emphasizes possible new types of two dimensional magnetic materials and can be applicable to various van-der Waals materials and their heterostructures with the control of electric field, strain and pressure.