Noncollinear Magnetism Research Articles

Parametrization of LSDA+U for noncollinear magnetic configurations: Multipolar magnetism in UO2

To explore the formation of noncollinear magnetic configurations in materials with strongly correlated electrons, we derive a noncollinear LSDA+$U$ model involving only one parameter $U$, as opposed to the difference between the Hubbard and Stoner parameters $U-J$. Computing $U$ in the constrained random phase approximation, we investigate noncollinear magnetism of uranium dioxide UO$_2$ and find that the spin-orbit coupling (SOC) stabilizes the 3$\textbf{k}$ ordered magnetic ground state. The estimated SOC strength in UO$_2$ is as large as 0.73 eV per uranium atom, making spin and orbital degrees of freedom virtually inseparable. Using a multipolar pseudospin Hamiltonian, we show how octupolar and dipole-dipole exchange coupling help establish the 3$\textbf{k}$ magnetic ground state with canted ordering of uranium $f$-orbitals. The cooperative Jahn-Teller effect does not appear to play a significant part in stabilizing the noncollinear 3$\textbf{k}$ state, which has the lowest energy even in an undistorted lattice. The choice of parameter $U$ in the LSDA+$U$ model has a notable quantitative effect on the predicted properties of UO$_2$, in particular on the magnetic exchange interaction and, perhaps trivially, on the band gap: The value of $U=3.46$ eV computed fully $ab$ $initio$ delivers the band gap of 2.11~eV in good agreement with experiment, and a balanced account of other pertinent energy scales.

Spin-orbit coupling from a two-component self-consistent approach. I. Generalized Hartree-Fock theory.

Formal and computational aspects are discussed for a self-consistent treatment of spin-orbit coupling within the two-component generalization of the Hartree-Fock theory. A molecular implementation into the CRYSTAL program is illustrated, where the standard one-component code (typical of Hartree-Fock and Kohn-Sham spin-unrestricted methodologies) is extended to work in terms of two-component spinors. When passing from a one- to a two-component description, the Fock and density matrices become complex. Furthermore, apart from the αα and ββ diagonal spin blocks, one has also to deal with the αβ and βα off-diagonal spin blocks. These latter blocks require special care as, for open-shell electronic configurations, certain constraints of the one-component code have to be relaxed. This formalism intrinsically allows us to treat local magnetic torque as well as noncollinear magnetization and orbital current-density. An original scheme to impose a specified noncollinear magnetization on each atomic center as a starting guess to the self-consistent procedure is presented. This approach turns out to be essential to surpass local minima in the rugged energy landscape and allows possible convergence to the ground-state solution in all of the discussed test cases.

Spin-orbit coupling from a two-component self-consistent approach. II. Non-collinear density functional theories.

We revise formal and numerical aspects of collinear and noncollinear density functional theory (DFT) in the context of a two-component self-consistent treatment of spin-orbit coupling (SOC). While the extension of the standard one-component theory to a noncollinear magnetization is formally well-defined within the local density approximation, and therefore results in a numerically stable theory, this is not the case within the generalized gradient approximation (GGA). Previously reported formulations of noncollinear DFT based on GGA exchange-correlation potentials have several limitations: (i) they fail at reducing (either formally or numerically) to the proper collinear limit (i.e., when the magnetization is parallel or antiparallel to the z axis everywhere in space); (ii) they fail at ensuring a quantitative rotational invariance of the total energy and even a qualitative rotational invariance of the spatial distribution of the magnetization when a SOC operator is included in the Hamiltonian; (iii) they are numerically very unstable in regions of small magnetization. All of the above-mentioned problems are here shown (both formally and through test examples) to be solved by using instead a new formulation of noncollinear DFT for GGA functionals, which we call the "signed canonical" theory, as combined with an effective screening algorithm for unstable terms of the exchange-correlation potential in regions of small magnetization. All methods are implemented in the CRYSTAL program and tests are performed on simple molecules to compare the different formulations of noncollinear DFT.

Torque equilibrium spin wave theory study of anisotropy and Dzyaloshinskii-Moriya interaction effects on the indirect K -edge RIXS spectrum of a triangular lattice antiferromagnet

We apply the recently formulated torque equilibrium spin wave theory (TESWT) to compute the $1/S$-order interacting $K$ -edge bimagnon resonant inelastic x-ray scattering (RIXS) spectra of an anisotropic triangular lattice antiferromagnet with Dzyaloshinskii-Moriya (DM) interaction. We extend the interacting torque equilibrium formalism, incorporating the effects of DM interaction, to appropriately account for the zero-point quantum fluctuation that manifests as the emergence of spin Casimir effect in a noncollinear spin spiral state. Using inelastic neutron scattering data from Cs$_2$CuCl$_4$ we fit the 1/S corrected TESWT dispersion to extract exchange and DM interaction parameters. We use these new fit coefficients alongside other relevant model parameters to investigate, compare, and contrast the effects of spatial anisotropy and DM interaction on the RIXS spectra at various points across the magnetic Brillouin zone. We highlight the key features of the bi- and trimagnon RIXS spectrum at the two inequivalent rotonlike points, $M(0,2 \pi/\sqrt{3})$ and $M^{\prime}(\pi,\pi/\sqrt{3})$, whose behavior is quite different from an isotropic triangular lattice system. While the roton RIXS spectrum at the $M$ point undergoes a spectral downshift with increasing anisotropy, the peak at the $M^\prime$ location loses its spectral strength without any shift. With the inclusion of DM interaction the spiral phase is more stable and the peak at both $M$ and $M^\prime$ point exhibits a spectral upshift. Our calculation offers a practical example of how to calculate interacting RIXS spectra in a non-collinear quantum magnet using TESWT. Our findings provide an opportunity to experimentally test the predictions of interacting TESWT formalism using RIXS, a spectroscopic method currently in vogue.

Frustrated Dipole Order Induces Noncollinear Proper Ferrielectricity in Two Dimensions.

Within Landau theory, magnetism and polarity are homotopic, displaying a one-to-one correspondence between most physical characteristics. However, despite widely reported noncollinear magnetism, spontaneous noncollinear electric dipole order as a ground state is rare. Here, a dioxydihalides family is predicted to display noncollinear ferrielectricity, induced by competing ferroelectric and antiferroelectric soft modes. This intrinsic of dipoles generates unique physical properties, such as Z_{2}×Z_{2} topological domains, atomic-scale dipole vortices, and negative piezoelectricity.

Interlayer RKKY coupling in bulk Rashba semiconductors under topological phase transition

The bulk Rashba semiconductors BiTeX (X=I, Cl and Br) with intrinsically enhanced Rashba spin-orbit coupling provide a new platform for investigation of spintronic and magnetic phenomena in materials. We theoretically investigate the interlayer exchange interaction between two ferromagnets deposited on opposite surfaces of a bulk Rashba semiconductor BiTeI in its trivial and topological insulator phases. In the trivial phase BiTeI, we find that for ferromagnets with a magnetization orthogonal to the interface, the exchange coupling is reminiscent of that of a conventional three-dimensional metal. Remarkably, ferromagnets with a magnetization parallel to the interface display a magnetic exchange qualitatively different from that of conventional three-dimensional metal due to the spin-orbit coupling. In this case, the interlayer exchange interaction acquires two periods of oscillations and decays as the inverse of the thickness of the BiTeI layer. For topological BiTeI, the magnetic exchange interaction becomes mediated only by the helical surface states and acts between the one-dimensional spin chains at the edges of the sample. The surface state-mediated interlayer exchange interaction allows for the coupling of ferromagnets with non-collinear magnetization and displays a decay power different from that of trivial BiTeI, allowing the detection of the topological phase transition in this material. Our work provides insights into the magnetic properties of these newly discovered materials and their possible functionalization.

Electrically driven spin torque and dynamical Dzyaloshinskii-Moriya interaction in magnetic bilayer systems

Efficient control of magnetism with electric means is a central issue of current spintronics research, which opens an opportunity to design integrated spintronic devices. However, recent well-studied methods are mostly based on electric-current injection, and they are inevitably accompanied by considerable energy losses through Joule heating. Here we theoretically propose a way to exert spin torques into magnetic bilayer systems by application of electric voltages through taking advantage of the Rashba spin-orbit interaction. The torques resemble the well-known electric-current-induced torques, providing similar controllability of magnetism but without Joule-heating energy losses. The torques also turn out to work as an interfacial Dzyaloshinskii-Moriya interaction which enables us to activate and create noncollinear magnetism like skyrmions by electric-voltage application. Our proposal offers an efficient technique to manipulate magnetizations in spintronics devices without Joule-heating energy losses.

Fundamental Role of Fock Exchange in Relativistic Density Functional Theory.

We perform a formal analysis of relativistic density functional theory for the treatment of spin-orbit coupling (SOC), noncollinear magnetization (NCM), and orbital current density (OCD). We identify specific components of the spinors (namely, those mapped onto imaginary diagonal spin-blocks of the density matrix) that arise from the SOC operator and define the OCD. We show that these pieces of the spinors only enter in the bielectronic part of the potential through the exact Fock exchange (FE) operator. The lack of FE therefore leads to a correspondingly incorrect physical description of SOC, NCM, and OCD. This analysis is complemented with an illustrative example, where we show that, while in the absence of FE, the theory fails even at reproducing the expected right-hand relationship between the NCM and OCD, its inclusion provides results that match those from a reference SOC configuration-interaction calculation.

Interfacial spin Seebeck effect in noncollinear magnetic systems

The interplay between spin and heat currents at magnetic insulator|nonmagnetic metal interfaces has been a subject of much scrutiny because of both fundamental physics and the promise for technological applications. While ferrimagnetic and, more recently, antiferromagnetic systems have been extensively investigated, a theory generalizing the heat-to-spin interconversion in noncollinear magnets is still lacking. Here, we establish a general framework for thermally-driven spin transport at the interface between a noncollinear magnet and a normal metal. Modeling the interfacial coupling between localized and itinerant magnetic moments via an exchange Hamiltonian, we derive an expression for the spin current, driven by a temperature difference, for an arbitrary noncollinear magnetic order. Our theory reproduces previously obtained results for ferromagnetic and antiferromagnet systems.

Noncollinearity-modulated Electronic Properties of Monolayer CrI3

Introducing noncollinear magnetization into a monolayer CrI$_3$ is proposed to be an effective approach to modulate the local electronic properties of the two-dimensional (2D) magnetic material. Using first-principles calculation, we illustrate that both the conduction and valence bands in the monolayer CrI$_3$ are lowered down by spin spiral states. The distinct electronic structure of the monolayer noncollinear CrI$_3$ can be applied in nanoscale functional devices. As a proof of concept, we show that a magnetic domain wall can form a one-dimensional conducting channel in the 2D semiconductor via proper gating. Other possible applications such as electron-hole separation and identical quantum dots are also discussed.

Density functional perturbation theory within noncollinear magnetism

We extend the density functional perturbation theory formalism to the case of non-collinear magnetism. The main problem comes with the exchange-correlation (XC) potential derivatives, which are the only ones that are affected by the non-collinearity of the system. Most of the present XC functionals are constructed at the collinear level, such that the off-diagonal (containing magnetization densities along $x$ and $y$ directions) derivatives cannot be calculated simply in the non-collinear framework. To solve this problem, we consider here possibilities to transform the non-collinear XC derivatives to a local collinear basis, where the $z$ axis is aligned with the local magnetization at each point. The two methods we explore are i) expanding the spin rotation matrix as a Taylor series, ii) evaluating explicitly the XC for the local density approximation through an analytical expression of the expansion terms. We compare the two methods and describe their practical implementation. We show their application for atomic displacement and electric field perturbations at the second order, within the norm-conserving pseudopotential methods.

Hydrodynamic description of long-distance spin transport through noncollinear magnetization states: Role of dispersion, nonlinearity, and damping

Nonlocal compensation of magnetic damping by spin injection has been theoretically shown to establish dynamic, noncollinear magnetization states that carry spin currents over micrometer distances. Such states can be generically referred to as dissipative exchange flows (DEFs) because spatially diffusing spin currents are established by the mutual exchange torque exerted by neighboring spins. Analytical studies to date have been limited to the weak spin injection assumption whereby the equation of motion for the magnetization is mapped to hydrodynamic equations describing spin flow and then linearized. Here, we analytically and numerically study easy-plane ferromagnetic channels subject to spin injection of arbitrary strength at one extremum under a unified hydrodynamic framework. We find that DEFs generally exhibit a nonlinear profile along the channel accompanied by a nonlinear frequency tuneability. At large injection strengths, we fully characterize a novel magnetization state we call a contact-soliton DEF (CS-DEF) composed of a stationary soliton at the injection site, which smoothly transitions into a DEF and exhibits a negative frequency tuneability. The transition between a DEF and a CS-DEF occurs at the maximum precessional frequency and coincides with the Landau criterion: a subsonic to supersonic flow transition. Leveraging the hydraulic-electrical analogy, the current-voltage characteristics of a nonlinear DEF circuit are presented. Micromagnetic simulations of nanowires that include magnetocrystalline anisotropy and non-local dipole fields are in qualitative agreement with the analytical results. The magnetization states found here along with their characteristic profile and spectral features provide quantitative guidelines to pursue an experimental demonstration of DEFs in ferromagnetic materials and establishes a unified description for long-distance spin transport.

Spin Excitations in the Noncollinear Magnetic Phase of LaMn2O5

Spin dynamics of the LaMn2O5 compound, which contains manganese ions with different charges in two crystallographically different positions, has been investigated. The description of the dynamics is based on the equations of motion for the irreducible spin operators. It has been shown that the presence of a noncollinear antiferromagnetic ordering of manganese ions in the different crystallographic positions leads to the necessity of not only the determination of the frequencies of spin excitations, but also the formulation of conditions for the stability of the magnetic state relative to which the dynamic processes are considered.

Anomalous Hall conductivity of noncollinear magnetic antiperovskites

The anomalous Hall effect (AHE) is a well-known fundamental property of ferromagnetic metals, commonly associated with the presence of a net magnetization. Recently, an AHE has been discovered in non-collinear antiferromagnetic (AFM) metals. Driven by non-vanishing Berry curvature of AFM materials with certain magnetic space group symmetry, anomalous Hall conductivity (AHC) is very sensitive to the specific type of magnetic ordering. Here, we investigate the appearance of AHC in antiperovskite GaNMn$_{3}$ as a representative of broader materials family ANMn$_{3}$ (A is a main group element), where different types of non-collinear magnetic ordering can emerge. Using symmetry analyses and first-principles density-functional theory calculations, we show that with almost identical band structure, the nearly degenerate non-collinear AFM $\Gamma_{5g}$ and $\Gamma_{4g}$ phases of GaNMn$_{3}$ have zero and finite AHC, respectively. In a non-collinear ferrimagnetic $M$-1 phase, GaNMn$_{3}$ exhibits a large AHC due to the presence of a sizable net magnetic moment. In the non-collinear antiperovskite magnets, transitions between different magnetic phases, exhibiting different AHC states, can be produced by doping, strain, or spin transfer torque, which makes these materials promising for novel spintronic applications.

Spin-current-mediated rapid magnon localisation and coalescence after ultrafast optical pumping of ferrimagnetic alloys

Sub-picosecond magnetisation manipulation via femtosecond optical pumping has attracted wide attention ever since its original discovery in 1996. However, the spatial evolution of the magnetisation is not yet well understood, in part due to the difficulty in experimentally probing such rapid dynamics. Here, we find evidence of a universal rapid magnetic order recovery in ferrimagnets with perpendicular magnetic anisotropy via nonlinear magnon processes. We identify magnon localisation and coalescence processes, whereby localised magnetic textures nucleate and subsequently interact and grow in accordance with a power law formalism. A hydrodynamic representation of the numerical simulations indicates that the appearance of noncollinear magnetisation via optical pumping establishes exchange-mediated spin currents with an equivalent 100% spin polarised charge current density of 107 A cm−2. Such large spin currents precipitate rapid recovery of magnetic order after optical pumping. The magnon processes discussed here provide new insights for the stabilization of desired meta-stable states.

Magnon-photon coupling in the noncollinear magnetic insulator Cu2OSeO3

Anticrossing behavior between magnons in a non-collinear chiral magnet Cu$_2$OSeO$_3$ and a two-mode X-band microwave resonator was studied in the temperature range 5-100K. In the field-induced ferrimagnetic phase, we observed a strong coupling regime between magnons and two microwave cavity modes with a cooperativity reaching 3600. In the conical phase, cavity modes are dispersively coupled to a fundamental helimagnon mode, and we demonstrate that the magnetic phase diagram of Cu$_2$OSeO$_3$ can be reconstructed from the measurements of the cavity resonance frequency. In the helical phase, a hybridized state of a higher-order helimagnon mode and a cavity mode - a helimagnon polariton - was found. Our results reveal a new class of magnetic systems where strong coupling of microwave photons to non-trivial spin textures can be observed.

Noncollinear magnetism in Lithium-doped zigzag graphene nanoribbons

Abstract Based on density functional theory and non-equilibrium Green’s function method, we studied noncollinear magnetism and electronic transport in zigzag graphene nanoribbon (ZGNR) doped with Li atom. Compared to pristine ZGNR, the Li-doped ZGNR presents characteristic features of magnetization distribution, which depends on the position of Li atom. When the magnetizations of two leads are parallel, i.e. θ = 0 ° , the Li atom induces an antiferromagnetic order on the edge, which is attributed to the change in exchange strength due to charge transfer. As for nonzero θ , the magnetization distribution in the case of interior adsorption shows obvious spin spiral. However, in edge adsorption, the spin spiral does not occur and a two-region feature appears. Moreover, the rotation sense of magnetization for edge adsorption becomes counter-clockwise which is different from the interior adsorption. The transmission presents distinct features for edge and interior adsorption. As θ = 180 ° , the transmission coefficient at Fermi level is about two for interior adsorption but drops to about one in edge adsorption. These results provide considerable insights into the effect of doping on noncollinear magnetism and spin transport in ZGNR.

Non-collinear magnetism in Mn monolayer on Ag(111) fcc: Density functional calculations

The magnetic properties of Mn monolayer on Ag (111) surface have been studied, using the first-principle plane-wave implementation of the density-functional theory (DFT). Several collinear and non-collinear magnetic configurations have been considered including the effects of different stacking sequences for the surface termination. We compare our results with recent experimental data of Gao et al. [C. L. Gao, W. Wulfhekel and J. Kirschner, Phys. Rev. Lett. 101, 267205 (2008)]. Our simulations reveal that the lowest energy state is antiferromagnetic, and corresponds to an out-of-plane collinear antiferromagnetic state, when we take into account the spin-orbit interactions while the 120° antiferromagnetic Néel structures has an excess energy of 56.06 meV/Mn. The magnetic anisotropy energy found between the antiferromagnetic out-of-plane and in-plane structures is of 2.65 meV. These findings are in agreement with the previous electronic structure calculations, which pointed to a collinear row-by-row antiferromagnetic ground state but in disagreement with the experimental finding. Also, our results for Mn/Ag (111) suggest that a non-collinear ground state corresponding to the clean surface can be excluded while more complex systems, including surface contamination or oxidation, should be considered to reproduce the experimental 120° Néel structure.

Non-collinear magnetism and electronic transport of boron or nitrogen doped zigzag graphene nanoribbon

Zigzag graphene nanoribbon (ZGNR) is important for novel carbon-based spintronic applications. Currently, most of ZGNR spintronic studies focus on the collinear magnetism where the up-spin and down-spin are separated clearly. But in some cases, e.g. doping and adsorption, the magnetization profile can be modulated and thus noncollinear magnetism can occur. In order to shed light on possible noncollinear magnetism in ZGNR, we study non-collinear magnetism and electronic transport of boron or nitrogen-doped zigzag graphene nanoribbon based on noncollinear density functional theory and non-equilibrium Green's function method. For pristine ZGNR, our results show that the ZGNR presents helical magnetization distribution due to noncollinear magnetization in left and right lead. As the ZGNR is doped with boron and nitrogen atoms, the ZGNR shows a characteristic two-zone feature in the magnetization distribution. Near the dopant site, the magnetic moment of carbon atom is small. However, the magnetic moments of carbon atoms in the left (right) region of dopant are close to those of the left (right) lead. Such a feature provides the possibility of constructing domain walls with various widths on the edge of ZGNR. Moreover, the transmission at the Fermi level (<i>E</i> = 0 eV) decreases with the increase of relative angle between magnetizations of left and right lead, indicating that the spin-flip scattering dominates the electronic transport. However, at <i>E</i> = ±0.65 eV, there is a transmission dip with low transmission, which implies that the dopant induces the strong backscattering. To understand the origin of this dip, we calculate the density of states (DOS) and project the DOS onto each atom of doped ZGNR. The projected DOS shows a large and broad peak at <i>E</i> = −0.65 eV for N-doped ZGNR but at <i>E</i> = +0.65 eV for B-doped ZGNR. The consistency between the position of dip in transmission and the position of peak in DOS indicates that the transmission dip mentioned above is attributed to strong backscattering from the dopant-induced bound state. Our theoretical results are expected to be useful for understanding the noncollinear magnetism and spin scattering in the doped ZGNR-based devices. Also, our work provides a considerable insight into the design of ZGNR-based nanoelectronic devices, such as the transistor based on spin transfer torque effect.

Magnonic Band Structure Established by Chiral Spin-Density Waves in Thin-Film Ferromagnets

Recent theoretical studies have demonstrated the possibility to excite and sustain noncollinear magnetization states in ferromagnetic nanowires. The resulting state is referred to as a spin-density wave (SDW). SDWs can be interpreted as hydrodynamic states with a constant fluid density and fluid velocity in systems with easy-plane anisotropy. Here, we consider the effect of the nonlocal dipole field arising from the finite thickness of magnetic thin films on the spatial profile of the SDW and on the associated magnon dispersion. Utilizing a hydrodynamic formulation of the Larmor torque equation, it is found that the nonlocal dipole field modulates the fluid velocity. Such a modulation induces a magnonic band structure unlike the typical dispersion relation for magnons on uniform magnetization. The analytical results are validated by micromagnetic simulations. Band gaps on the order of gigahertz are numerically observed to depend on the SDW fluid velocity and film thickness for realistic material parameters. The presented results suggest that SDWs can find applications as reconfigurable magnonic crystals.