Noncollinear Magnetism Research Articles

Nonreciprocity of surface acoustic waves coupled to spin waves in a ferromagnetic bilayer with noncollinear layer magnetizations

Nonreciprocity of propagation of surface acoustic waves (SAWs) in the microwave frequency band can be achieved using the magnetoelastic interaction of SAWs with spin waves (SWs) propagating in magnetic heterostructures. Recent works have shown that the ultimate isolation of a counterpropagating hybridized SAW/SW is achieved in heterostructures consisting of a synthetic antiferromagnet—a ferromagnetic (FM) bilayer with antiferromagnetic Ruderman-Kittel-Kasuya-Yosida interlayer coupling—placed on top of a piezoelectric acoustic waveguide. In this work, we study in detail a more practical and technologically simpler system based on an FM bilayer, where layers are coupled by only dipole-dipole interaction, and having noncollinear magnetizations of the FM layers. A weak in-plane anisotropy with noncollinear easy axes in the layers is shown to be the only essential factor for the realization of strongly nonreciprocal propagation of a hybridized SAW/SW. We formulate requirements for the relative orientation of the layer’s magnetizations and wave propagation direction necessary to realize an efficient SAW isolator, and demonstrate examples of SAW transmission characteristics which prove the possibility of achieving an isolation exceeding 50 dB for a submillimeter-long FM bilayer with insertion losses of just a few decibels more than those of a pure SAW device. In addition to relative fabrication simplicity, the proposed magnetoelastic heterostructure exhibits a reasonable robustness in respect to deviations in the anisotropy axes and/or bias field directions—an important benefit for device mass production. Published by the American Physical Society 2024

Multiple Valley Modulations in Noncollinear Antiferromagnets.

Two-dimensional valleys and magnetism are rising areas with intriguing properties and practical uses in advanced information technology. By coupling valleys to collinear magnetism, valley degeneracy is lifted in a large number of magnetic valley materials to exploit the valley degree of freedom. Beyond collinear magnetism, new coupling modes between valley and magnetism are few but highly desirable. By tight-binding calculations of a breathing Kagome lattice, we demonstrate a tunable valley structure and valley-contrasting physical properties in noncollinear antiferromagnets. Distinct from collinear magnetism, noncollinear antiferromagnetic order enables valley splittings even without spin-orbit coupling. Both the canting and azimuthal angles of magnetic moments can be used as experimentally accessible knobs to tune valley splittings. Our first-principles calculations of the Fe3C6O6-silicene-Fe3C6O6 heterostructure also exhibit tunable valley splittings in noncollinear antiferromagnetism, agreeing with our tight-binding results. Our work paves avenues for designing novel magnetic valley materials and energy-efficient valleytronic devices based on noncollinear magnetism.

Non-relativistic torque and Edelstein effect in non-collinear magnets

The Edelstein effect is the origin of the spin-orbit torque: a current-induced torque that is used for the electrical control of ferromagnetic and antiferromagnetic materials. This effect originates from the relativistic spin-orbit coupling, which necessitates utilizing materials with heavy elements. Here, we show that in magnetic materials with non-collinear magnetic order, the Edelstein effect and, consequently, a current-induced torque can exist even in the absence of the spin-orbit coupling. Using group symmetry analysis, model calculations, and realistic simulations on selected compounds, we identify large classes of non-collinear magnet candidates and demonstrate that the current-driven torque is of similar magnitude as the celebrated spin-orbit torque in conventional transition metal structures. We also show that this torque can exist in an insulating material, which could allow for highly efficient electrical control of magnetic order.

Триплетные сверхпроводящие корреляции гибридной меза-структуры с двухслойной ферромагнитной прослойкой

We present results on electron transport in hybrid Josephson mesa-structure Sd/F1F2/S, consisting of epitaxial films of cuprate superconductor YBa2Cu3O7-δ (Sd), bi-layer ferromagnetic interlayer (F1F2), thin film of metallic Nb was deposited on the top of a thin protective Au film layer used as the upper superconducting electrode (S). The long-range triplet component of superconducting correlations arises when strontium ruthenate SrRuO3 F1 and manganiteLa0.7Sr0.3MnO3 with non-collinear magnetizations are used as ferromagnetic material F2. Superconducting current took place up to the thickness d = 52 nm of the F1F2 interlayer. Superconducting current disappeared in the case of a single ferromagnetic interlayer of manganite (La0.7Sr0.3MnO3 or La0.7Ca0.3MnO3) and SrRuO3 with minimized thicknesses, limited by the occurrence of pinholes. The magnetic field properties of mesa-structure are discussed as well, along with the impact of the second harmonic in the superconducting current-phase relation.

Photo-induced non-collinear interlayer RKKY coupling in bulk Rashba semiconductors

The interplay between light-matter, spin-orbit, and magnetic interactions allows the investigation of light-induced magnetic phenomena that are otherwise absent without irradiation. We present our analysis of light-driven effects on the interlayer exchange coupling mediated by a bulk Rashba semiconductor in a magnetic multilayer. The collinear magnetic exchange coupling mediated by the photon-dressed spin-orbit coupled electrons of BiTeI develops light-induced oscillation periods and displays new decay power laws, both of which are enhanced with an increasing light-matter coupling. For magnetic layers with non-collinear magnetization, we find a non-collinear magnetic exchange coupling uniquely generated by light-driving of the multilayer. As the non-collinear magnetic exchange coupling mediated by the photon-dressed electrons of BiTeI is unique to the irradiated system and it is enhanced with increasing light-matter coupling, this effect offers a promising platform of investigation of light-driven effects on magnetic phenomena in spin-orbit coupled systems. In this platform, light properties, such as its intensity, can serve as external knobs for inducing non-collinear couplings of the interlayer exchange and for modulating the collinear couplings. Both of these effects signify the photo-generated modification in the spin textures of spin-orbit coupled electrons in BiTeI.

Quantum Transport through a Quantum Dot Coupled to Majorana Nanowire and Two Ferromagnets with Noncollinear Magnetizations.

We study the electron tunneling (ET) and local Andreev reflection (AR) processes in a quantum dot (QD) coupled to the left and right ferromagnetic leads with noncollinear ferromagnetisms. In particular, we consider that the QD is also side-coupled to a nanowire hosting Majorana bound states (MBSs) at its ends. Our results show that when one mode of the MBSs is coupled simultaneously to both spin-up and spin-down electrons on the QD, the height of the central peak is different from that if the MBS is coupled to only one spin component electrons. The ET and AR conductances, which are mediated by the dot-MBS hybridization, strongly depend on the angle between the left and right magnetic moments in the leads. Interaction between the QD and the MBSs will result in sign change of the angle-dependent tunnel magnetoresistance. This is very different from the case when the QD is coupled to regular fermonic mode, and can be used for detecting the existence of MBSs, a current challenge in condensed matter physics under extensive investigations.

Controlling Noncollinear Ferromagnetism in van der Waals Metal-Organic Magnets.

Van der Waals (vdW) magnets both allow exploration of fundamental 2D physics and offer a route toward exploiting magnetism in next generation information technology, but vdW magnets with complex, noncollinear spin textures are currently rare. We report here the syntheses, crystal structures, magnetic properties and magnetic ground states of four bulk vdW metal-organic magnets (MOMs): FeCl2(pym), FeCl2(btd), NiCl2(pym), and NiCl2(btd), pym = pyrimidine and btd = 2,1,3-benzothiadiazole. Using a combination of neutron diffraction and bulk magnetometry we show that these materials are noncollinear magnets. Although only NiCl2(btd) has a ferromagnetic ground state, we demonstrate that low-field hysteretic metamagnetic transitions produce states with net magnetization in zero-field and high coercivities for FeCl2(pym) and NiCl2(pym). By combining our bulk magnetic data with diffuse scattering analysis and broken-symmetry density-functional calculations, we probe the magnetic superexchange interactions, which when combined with symmetry analysis allow us to suggest design principles for future noncollinear vdW MOMs. These materials, if delaminated, would prove an interesting new family of 2D magnets.

Ab initio study of the adsorption of O, O2, H2O and H2O2 on UO2 surfaces using DFT+U and non-collinear magnetism

In order to model correctly the corrosion of spent nuclear fuel under disposal conditions, it is important to understand its behavior in the presence of oxidants. To advance in this direction, we consider the oxidation of UO2. We investigate computationally the adsorption of various species on its three most stable surfaces: (111), (110), and (100), with emphasis on incorporating a full non-collinear PBE+U approach. Various species, namely O, O2, H2O and H2O2 are considered due to their relevance for the oxidation of UO2. The dissociation energy and an estimate for the dissociation barrier for O2 were obtained, using the preferred adsorption configurations of O and O2. The adsorption configurations for H2O in our study compare well with previous studies that used collinear approximations, both in terms of relative stability of configurations and bond lengths. Differences in adsorption energies were found, which may be important for reaction kinetics. Dissociative reactions in which the water molecule splits in hydrogen and hydroxyl occur only on one of the three surfaces. The hydrogen further reacts with a surface oxygen to also form a hydroxyl group. Not surprisingly, we find that H2O2 binds more strongly to the three surfaces than water (lower formation energy), and similar to H2O adsorption, dissociative reactions may occur. The dissociated hydrogen reacts with a surface oxygen to form a hydroxyl group and the hydroperoxyl molecule binds with a surface uranium. Our study, which includes a detailed study of electron transfer, magnetic structure and the preferred adsorption configurations, gives insight into the uranium oxidation states and the influence of surface geometry on adsorption. The findings contribute to a more comprehensive understanding of the early stages of UO2 oxidation.

Machine learning inspired models for Hall effects in non-collinear magnets

The anomalous Hall effect has been front and center in solid state research and material science for over a century now, and the complex transport phenomena in nontrivial magnetic textures have gained an increasing amount of attention, both in theoretical and experimental studies. However, a clear path forward to capturing the influence of magnetization dynamics on anomalous Hall effect even in smallest frustrated magnets or spatially extended magnetic textures is still intensively sought after. In this work, we present an expansion of the anomalous Hall tensor into symmetrically invariant objects, encoding the magnetic configuration up to arbitrary power of spin. We show that these symmetric invariants can be utilized in conjunction with advanced regularization techniques in order to build models for the electric transport in magnetic textures which are, on one hand, complete with respect to the point group symmetry of the underlying lattice, and on the other hand, depend on a minimal number of order parameters only. Here, using a four-band tight-binding model on a honeycomb lattice, we demonstrate that the developed method can be used to address the importance and properties of higher-order contributions to transverse transport. The efficiency and breadth enabled by this method provides an ideal systematic approach to tackle the inherent complexity of response properties of noncollinear magnets, paving the way to the exploration of electric transport in intrinsically frustrated magnets as well as large-scale magnetic textures.

The role of non-uniform magnetization texture for magnon–magnon coupling in an antidot lattice

We numerically study the spin-wave dynamics in an antidot lattice based on a Co/Pd multilayer structure with reduced perpendicular magnetic anisotropy at the edges of the antidots. This structure forms a magnonic crystal with a periodic antidot pattern and a periodic magnetization configuration consisting of out-of-plane magnetized bulk and in-plane magnetized rims. Our results show a different behavior of spin waves in the bulk and in the rims under varying out-of-plane external magnetic field strength, revealing complex spin-wave spectra and hybridizations between the modes of these two subsystems. A particularly strong magnon–magnon coupling, due to exchange interactions, is found between the fundamental bulk spin-wave mode and the second-order radial rim modes. However, the dynamical coupling between the spin-wave modes at low frequencies, involving the first-order radial rim modes, is masked by the changes in the static magnetization at the bulk–rim interface with magnetic field changes. The study expands the horizons of magnonic-crystal research by combining periodic structural patterning and non-collinear magnetization texture to achieve strong magnon–magnon coupling, highlighting the significant role of exchange interactions in the hybridization.

Magneto-optical detection of non-collinear magnetization states in ferromagnetic multilayers

We have experimentally studied the relationship in between non-collinear magnetization states in ferromagnetic (FM) multilayers and their resulting magneto-optical (MO) properties. Hereby, we observe that the phase of the complex-valued MO parameters are especially sensitive towards non-collinear magnetization states and enable their unambiguous detection. For the purpose of our experimental study, we designed, fabricated and characterized a set of epitaxial FM/NM/FM multilayers with in-plane uniaxial anisotropy, in which the non-magnetic (NM) interlayer thickness t was varied, so that tunable FM interlayer exchange coupling strength in between the two FM layers could be achieved. Furthermore, the two FM layers were made from different alloys, so that they exhibit different levels of magnetocrystalline anisotropy, which enables a collinear to non-collinear magnetization state transition upon applying a magnetic field H away from the in-plane easy axis for samples with sufficiently large t . Utilizing generalized MO ellipsometry, we determined the full reflection matrix R as a function of H and we observed that the phases of the complex-valued MO coefficients in R change with H in multilayers that have sufficiently weak interlayer coupling strength, i.e. large t, which can only happen if non-collinear magnetization states of varying non-collinearity occur in those samples. For samples with small t, corresponding to strongly exchange coupled FM layers, this effect is absent, consistent with the existence of collinear magnetization states in those multilayers for all H values.

Spin-resolved counting statistics as a sensitive probe of spin correlation in transport through a quantum dot spin valve

We investigate the noise in spin transport through a single quantum dot (QD) tunnel coupled to ferromagnetic (FM) electrodes with noncollinear magnetizations. Based on a spin-resolved quantum master equation, auto- and cross-correlations of spin-resolved currents are analyzed to reveal the underlying spin transport dynamics and characteristics for various polarizations. We find the currents of majority and minority spins could be strongly autocorrelated despite uncorrelated charge transfer. The interplay between tunnel coupling and the Coulomb interaction gives rise to an exchange magnetic field, leading to the precession of the accumulated spin in the QD. It strongly suppresses the bunching of spin tunneling events and results in a unique double-peak structure in the noise of the net spin current. The spin autocorrelation is found to be susceptible to magnetization alignments, which may serve as a sensitive tool to measure the magnetization directions between the FM electrodes.

Topological superconductivity by engineering noncollinear magnetism in magnet/superconductor heterostructures: A realistic prescription for the two-dimensional Kitaev model

Topological superconductivity by engineering noncollinear magnetism in magnet/superconductor heterostructures: A realistic prescription for the two-dimensional Kitaev model

GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Non-collinear magnetism driven by a hidden multipolar order in PrO2

Standard microscopic approach to magnetic orders is based on assuming a Heisenberg form for inter-atomic exchange interactions. These interactions are considered as the driving force for the ordering transition with magnetic moments serving as the primary order parameter. Any higher-rank multipoles appearing simultaneously with such magnetic order are typically treated as auxiliary order parameters rather than a principal cause of the transition. In this study, we show that these traditional assumptions are violated in the case of PrO2. Evaluating a full set of Pr-Pr superexchange interactions from a first-principles many-body technique we find that its unusual non-collinear 2k magnetic structure stems from high-rank multipolar interactions, and that the corresponding contribution of the Heisenberg interactions is negligible. The observed magnetic order in PrO2 is thus auxiliary to high-rank “hidden” multipoles. Within this picture we consistently account for previously unexplained experimental observations like the magnitude of exchange splitting and the evolution of magnetic structure in external field. Our findings challenge the standard paradigm of observable magnetic moments being the driving force for magnetic transitions.

Self-interaction correction schemes for non-collinear spin-density-functional theory

We extend some of the well-established self-interaction correction (SIC) schemes of density-functional theory—the Perdew–Zunger SIC and the average-density SIC—to the case of systems with noncollinear magnetism. Our proposed SIC schemes are tested on a set of molecules and metallic clusters in combination with the widely used local spin-density approximation. As expected from the collinear SIC, we show that the averaged-density SIC works well for improving ionization energies but fails to improve more subtle quantities like the dipole moments of polar molecules. We investigate the exchange-correlation magnetic field produced by our extension of the Perdew–Zunger SIC, showing that it is not aligned with the local total magnetization, thus producing an exchange-correlation torque.

Observation of the Anomalous Hall Effect in a Layered Polar Semiconductor

AbstractProgress in magnetoelectric materials is hindered by apparently contradictory requirements for time‐reversal symmetry broken and polar ferroelectric electronic structure in common ferromagnets and antiferromagnets. Alternative routes can be provided by recent discoveries of a time‐reversal symmetry breaking anomalous Hall effect (AHE) in noncollinear magnets and altermagnets, but hitherto reported bulk materials are not polar. Here, the authors report the observation of a spontaneous AHE in doped AgCrSe2, a layered polar semiconductor with an antiferromagnetic coupling between Cr spins in adjacent layers. The anomalous Hall resistivity 3 is comparable to the largest observed in compensated magnetic systems to date, and is rapidly switched off when the angle of an applied magnetic field is rotated to ≈80° from the crystalline c‐axis. The ionic gating experiments show that the anomalous Hall conductivity magnitude can be enhanced by modulating the p‐type carrier density. They also present theoretical results that suggest the AHE is driven by Berry curvature due to noncollinear antiferromagnetic correlations among Cr spins, which are consistent with the previously suggested magnetic ordering in AgCrSe2. The results open the possibility to study the interplay of magnetic and ferroelectric‐like responses in this fascinating class of materials.

Nonsinusoidal current-phase relations in semiconductor–superconductor– ferromagnetic insulator devices

Coherent tunneling processes of multiple Cooper pairs across a Josephson junction give rise to high harmonics in the current phase relation. In this work, we propose and study Josephson junctions based on semiconductor--superconductor--ferromagnetic insulator heterostructures to engineer nonsinusoidal current-phase relations. The gate-tunability of the charge carriers' density in the semiconductor, together with the adjustable magnetization of the ferromagnetic insulator, provides control over the content of the supercurrent harmonics. At finite exchange field, hybrid junctions can undergo a $0 -- \ensuremath{\pi}$ phase transition, resulting in a supercurrent reversal. Close to the transition, single-pair tunneling is suppressed and the current-phase relation is dominated by the second-harmonic, indicating transport primarily by pairs of Cooper pairs. Finally, we demonstrate that noncollinear magnetization or spin-orbit coupling in the leads and the junction can lead to a gate-tunable Josephson diode effect with efficiencies of up to $\ensuremath{\sim}30%$.

Quantum classical approach to spin and charge pumping and the ensuing radiation in terahertz spintronics: Example of the ultrafast light-driven Weyl antiferromagnet Mn3Sn

The interaction of a femtosecond laser pulse with magnetic materials has been intensely studied for more than two decades in order to understand ultrafast demagnetization in single magnetic layers or terahertz emission from their bilayers with nonmagnetic spin-orbit (SO) materials. However, in contrast to well-understood spin and charge pumping by dynamical magnetization in spintronic systems driven by microwaves or current injection, analogous processes in light-driven magnets and radiation emitted by them remain largely unexplained due to the multiscale nature of the problem. Here we develop a multiscale quantum-classical formalism---where conduction electrons are described by quantum master equation (QME) of the Lindblad type, classical dynamics of local magnetization is described by the Landau-Lifshitz-Gilbert (LLG) equation, and incoming light is described by classical vector potential, while outgoing electromagnetic radiation is computed using the Jefimenko equations for retarded electric and magnetic fields---and apply it to a bilayer of antiferromagnetic Weyl semimetal ${\mathrm{Mn}}_{3}\mathrm{Sn}$, hosting noncollinear local magnetization, and SO-coupled nonmagnetic material. Our $\mathrm{QME}+\mathrm{LLG}+$Jefimenko scheme makes it possible to understand how a femtosecond laser pulse directly generates spin and charge pumping and electromagnetic radiation by the ${\mathrm{Mn}}_{3}\mathrm{Sn}$ layer, including both odd and even high harmonics (of the pulse center frequency) up to order $n\ensuremath{\le}7$. The directly pumped spin current then exerts spin torque on local magnetization whose dynamics, in turn, pumps additional spin and charge currents radiating in the terahertz range. By switching on and off LLG dynamics and SO couplings, we unravel which microscopic mechanism contributes the most to emitted terahertz radiation---charge pumping by local magnetization of ${\mathrm{Mn}}_{3}\mathrm{Sn}$ in the presence of its own SO coupling is far more important than standardly assumed (for other types of magnetic layers) spin pumping and subsequent spin-to-charge conversion within the adjacent nonmagnetic SO-coupled material.

Theory of superdiffusive spin transport in noncollinear magnetic multilayers

Ultrafast demagnetization induced by femtosecond laser pulses in thin metallic layers is caused by the outflow of spin-polarized hot-electron currents describable by the superdiffusive transport model. These laser-generated spin currents can cross the interface into another magnetic layer and give rise to magnetization dynamics in magnetic spin valves with noncollinear magnetizations. To describe ultrafast transport and spin dynamics in such nanostructures, we develop here the superdiffusive theory for general noncollinear magnetic multilayers. Specifically, we introduce an Al/Ni/Ru/Fe/Ru multilayer system with noncollinear Ni and Fe magnetic moments and analyze how the ultrafast demagnetization and spin-transfer torque depend on the noncollinearity. We employ ab initio calculations to compute the spin- and energy-dependent transmissions of hot electrons at the interfaces of the multilayer. Taking into account multiple electron scattering at interfaces and spin mixing in the spacer layer, we find that the laser-induced demagnetization of the Ni layer and the magnetization change of the Fe layer strongly depend on the angle between their magnetizations. Similarly, the spin-transfer torques on the Ni and Fe layers and the total spin momentum absorbed in the Ni and Fe layer are found to vary markedly with the amount of noncollinearity. These results suggest that by changing the amount of noncollinearity in magnetic multilayers, one can efficiently control the hot-electron spin transport, which may open a way toward achieving fast, laser-driven spintronic devices.