Collinear Spin Research Articles

Double-Q Checkerboard Bubble Crystal in Centrosymmetric Tetragonal Magnets

We report our numerical studies on the emergence of a double-Q checkerboard bubble crystal in centrosymmetric tetragonal magnets. The double-Q checkerboard bubble crystal is characterized by a fourfold-symmetric collinear spin configuration consisting of a superposition of two sinusoidal waves with the out-of-plane spin modulations along the [110] and [1¯10] directions. The numerical calculations based on the simulated annealing for an effective spin model with the momentum-resolved easy-axis exchange interactions reveal that the double-Q checkerboard bubble crystal is energetically degenerate with the single-Q collinear state when the ordering wave vector lies on the quarter of the reciprocal lattice vector along the ⟨110⟩ direction. We show that such a degeneracy is lifted by considering the biquadratic interaction. We also find that the double-Q checkerboard bubble crystal turns into another double-Q state characterized by the in-plane spin modulations by increasing an external magnetic field.

Stability of spin-spiral magnetic structures in Mn2PtSn

The stability of a long-periodic homogeneous spin-spiral configuration in an inverse tetragonal Heusler compound, Mn2PtSn, is studied with the help of density functional theory calculations. The energetically most stable collinear magnetic state in this system is the ferrimagnetic one. However, the existence of negative phonon frequency makes this configuration dynamically unstable. The energy dispersion plots reveal that an energy minimum exists at q=0.1 along [100] and [110] propagating directions, which correspond to a stable non-collinear configuration compared to the collinear spin states. The inclusion of spin–orbit coupling further reduces the ground-state energy without changing the q-vector of the energy minima. The cycloidal spiral configuration, where the spins rotate at an angle of 36° along the propagating direction, is found to be more stable than the screw spiral configuration. The calculated density of state plots further supports the stability of the non-collinear cycloidal spin order. This stable, non-collinear spin-spiral configuration of Mn2PtSn makes this compound a prospective material for spintronics device applications.

Noncollinear spin texture-driven torque in deterministic spin–orbit torque-induced magnetization switching

To reveal the role of chirality on field-free spin–orbit torque (SOT) induced magnetization switching, we propose an existence of z-torque through the formation of noncollinear spin texture during SOT-induced magnetization switching in a laterally two-level perpendicular magnetic anisotropy (PMA) system. For the investigation of torque, we simulate magnetization dynamics in the two-level PMA system with SOT, which generates the noncollinear spin texture. From the spatial distribution of magnetic energy, we reveal the additional z-directional torque contribution in the noncollinear spin texture, which is unexpected in the conventional SOT-induced magnetization switching in collinear spin texture. The z-directional torque originates from the interaction between the chirality of the noncollinear spin texture and the interfacial Dzyaloshinskii-Moriya interaction of the system. Furthermore, the experimental observation of the asymmetric magnetization switching to the direction of the current flow in the two-level PMA system supports our theoretical expectation.

Magnetic relaxation between ferromagnetic and helix spin configurations in holmium films

Multiple noncollinear spin structures and transitions between them initiated by field and temperature have attracted attention due to the extraordinary coexistence of complicated spin phases in Ho. We explore the magnetic relaxation dynamics within thin films undergoing transitions between ferromagnetic (FM) and helix states. When measuring susceptibility in a relatively high frequency range (∼100–1500 Hz) and magnetic viscosity at lower frequency (∼0.01 Hz), we focus on 400 nm thick Ho film. Notably, sharp variations in the real and imaginary components of magnetic susceptibility are discerned during the FM – Helix transition, occurring at temperatures between 15 and 30 K. Hysteresis effects in the magnetic susceptibility components are identified during cyclic variations in the external field, indicating a relatively rapid process with a timescale of approximately 10 ms accompanying the FM – Helix transition. The slow relaxation process is also found to exhibit sensitivity to this transition. Furthermore, the field dependence of magnetic viscosity displays a marked decline at the FM – Helix transition. The research methodologies proposed for the investigation of relaxation processes in materials with multiphase spin structures are deemed universally applicable and offer insights into transitions between spin states in materials manifesting non collinear spin structures.

Spin waves in antiferromagnetically coupled bilayers of transition-metal dichalcogenides with Dzyaloshinskii–Moriya interaction

In this paper we analyse quantized spin waves (also referred to as magnons) in bilayers of two-dimensional van der Waals materials, like Vanadium-based dichalcogenides, VX2 (X = S, Se, Te) and other materials of similar symmetry. We assume that the materials exhibit Dzyaloshinskii–Moriya interaction and in-plane easy-axis magnetic anisotropy due to symmetry breaking induced externally (e.g. by strain, gate voltage, proximity effects to an appropriate substrate/oberlayer, etc.). The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong in-plane magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Holstein–Primakoff–Bogoliubov transformation. Accordingly, the description takes into account quantum antiferromagnetic fluctuations. However, it is limited to linear spinwave modes. The Dzyaloshinskii–Moriya interaction is shown to modify the spin wave spectrum of the bilayers, making its low energy part qualitatively similar to the electronic spectrum of the Rashba spin–orbit model.

Two-dimensional chiral perovskites with large spin Hall angle and collinear spin Hall conductivity.

Two-dimensional hybrid organic-inorganic perovskites with chiral spin texture are emergent spin-optoelectronic materials. Despite the wealth of chiro-optical studies on these materials, their charge-to-spin conversion efficiency is unknown. We demonstrate highly efficient electrically driven charge-to-spin conversion in enantiopure chiral perovskites (R/S-MB)2(MA)3Pb4I13 (〈n〉 = 4), where MB is 2-methylbutylamine, MA is methylamine, Pb is lead, and I is iodine. Using scanning photovoltage microscopy, we measured a spin Hall angle θsh of 5% and a spin lifetime of ~75 picoseconds at room temperature in 〈n〉 = 4 chiral perovskites, which is much larger than its racemic counterpart as well as the lower 〈n〉 homologs. In addition to current-induced transverse spin current, the presence of a coexisting out-of-plane spin current confirms that both conventional and collinear spin Hall conductivities exist in these low-dimensional crystals.

Highly efficient field-free switching of perpendicular yttrium iron garnet with collinear spin current

Yttrium iron garnet, a material possessing ultralow magnetic damping and extraordinarily long magnon diffusion length, is the most widely studied magnetic insulator in spintronics and magnonics. Field-free electrical control of perpendicular yttrium iron garnet magnetization with considerable efficiency is highly desired for excellent device performance. Here, we demonstrate such an accomplishment with a collinear spin current, whose spin polarization and propagation direction are both perpendicular to the interface. Remarkably, the field-free magnetization switching is achieved not only with a heavy-metal-free material, Permalloy, but also with a higher efficiency as compared with a typical heavy metal, Pt. Combined with the direct and inverse effect measurements, we ascribe the collinear spin current to the anomalous spin Hall effect in Permalloy. Our findings provide a new insight into spin current generation in Permalloy and open an avenue in spintronic devices.

Spontaneous Vortex-Antivortex Pairs and Their Topological Transitions in a Chiral-Lattice Magnet.

The spontaneous formation and topological transitions of vortex-antivortex pairs have implications for a broad range of emergent phenomena, for example, from superconductivity to quantum computing. Unlike magnets exhibiting collinear spin textures, helimagnets with noncollinear spin textures provide unique opportunities to manipulate topological forms such as (anti)merons and (anti)skyrmions. However, it is challenging to achieve multiple topological states and their interconversion in a single helimagnet due to the topological protection for each state. Here, the on-demand creation of multiple topological states in a helimagnet Fe0.5 Co0.5 Ge, including a spontaneous vortex pair of meron with topological charge N=-1/2 and antimeron with N=1/2, and a vortex-antivortex bundle, that is, a bimeron (meron pair) with N=-1 is reported. The mutual transformation between skyrmions and bimerons with respect to the competitive effects of magnetic field and magnetic shape anisotropy is demonstrated. It is shown that electric currents drive the individual bimerons to form their connecting assembly and then into a skyrmion lattice. These findings signify the feasibility of designing topological states and offer new insights into the manipulation of noncollinear spin textures for potential applications in various fields.

Spin waves in monolayers of transition-metal dichalcogenides with Dzyaloshinskii–Moriya interaction

Dzyaloshinski–Moriya interaction, known also as the antisymmetric exchange coupling, leads to a variety of interesting spin phenomena, like spin canting, skyrmion formation, nonreciprocal spin wave propagation, and others. In this paper we analyze spin waves in monolayers of two-dimensional van–der–Waals materials, such as Vanadium–based dichalcogenides, VX2 (X=S, Se, Te) and other materials of similar symmetry. The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Holstein–Primakoff–Bogoliubov transformation.

Systematic determination of coupling constants in spin clusters from broken-symmetry mean-field solutions.

Quantum-chemical calculations aimed at deriving magnetic coupling constants in exchange-coupled spin clusters commonly utilize a broken-symmetry (BS) approach. This involves calculating several distinct collinear spin configurations, predominantly by density-functional theory. The energies of these configurations are interpreted in terms of the Heisenberg model, H̃=∑i<jJijs̃i⋅s̃j, to determine coupling constants Jij for spin pairs. However, this energy-based procedure has inherent limitations, primarily in its inability to provide information on isotropic spin interactions beyond those included in the Heisenberg model. Biquadratic exchange or multi-center terms, for example, are usually inaccessible and hence assumed to be negligible. The present work introduces a novel approach employing BS mean-field solutions, specifically Hartree-Fock wave functions, for the construction of effective spin Hamiltonians. This expanded method facilitates the extraction of a broader range of coupling parameters by considering not only the energies, but also Hamiltonian and overlap elements between different BS states. We demonstrate how comprehensive s=12 Hamiltonians, including multi-center terms, can be straightforwardly constructed from a complete set of BS solutions. The approach is exemplified for small clusters within the context of the half-filled single-band Hubbard model. This allows to contrast the current strategy against exact results, thereby offering an enriched understanding of the spin-Hamiltonian construction from BS solutions.

Exchange and Dzyaloshinskii-Moriya interaction in Rh/Co/Fe/Ir multilayers: Towards skyrmions in exchange-frustrated multilayers

We study the magnetic interactions in transition-metal multilayers composed of Co layers and Co/Fe bilayers sandwiched between Ir and Rh layers based on density functional theory (DFT). By mapping our total energy DFT calculations of collinear and noncollinear spin states including spin-orbit coupling to an atomistic spin model we extract the intra- and interlayer exchange constants, the intra- and interlayer Dzyaloshinskii-Moriya interaction constants and the magnetocrystalline anisotropy energies of several multilayers. We demonstrate that the exchange frustration, which stabilizes zero-field sub-10 nm magnetic skyrmions in Rh/Co films on the Ir(111) surface [S. Meyer et al., Nat. Commun. 10, 3823 (2019)], can be transferred to multilayers formed by a repetition of Rh/Co/Ir trilayers. Increasing the number of Co layers reduces the exchange frustration whereas with adding Fe, a sufficient exchange frustration and strength of the Dzyaloshinskii-Moriya interaction can be obtained to stabilize topological spin structures such as skyrmions in Rh/Co/Fe/Ir multilayers. We show that the exchange interaction in Rh/Co/Fe/Ir multilayers results from the interplay of strong frustration of intralayer exchange in the Fe layer, weak ferromagnetic intralayer exchange in the Co layer, and ferromagnetic interlayer Fe-Co exchange. We analyze the Dzyaloshinskii-Moriya interaction in terms of inter- and intralayer contributions as well as its sign based on the electronic structure of Co/Fe based multilayers with different stacking sequences.

Stoichiometry driven tuning of physical properties in epitaxial Fe3-xCrxO4 thin films

Tuning magnetic and electronic transport properties in spinel oxides requires a faithful description between chemical composition and cation site-occupation. Here this challenge is addressed using Fe3-xCrxO4 thin films grown by oxygen-assisted molecular-beam epitaxy within a wide range of composition (0.0 ≤ x ≤ 1.2). Spectroscopic measurements (e.g., X-ray magnetic circular dichroism), refined by theoretical simulations (e.g., crystal field multiplet), are performed to establish a quantitative link between chromium content, Fe2+/Fe3+ site-occupation and macroscopic physical properties of the layers. It is found that Fe3-xCrxO4 thin films (i) delay the transition from inverse to normal spinel configuration with increasing chromium content and (ii) promote collinear spin structure, at odds with bulk material. As a result, strong antiferromagnetic interactions are preserved between spins in tetrahedral and octahedral spinel sublattices, so that chromium-rich thin films exhibit Curie temperatures above room temperature and higher magnetization. Electron hopping is also favored by this singular cation distribution and electronic band gap is smaller than expected for these thin films. The cation site-occupation is therefore a key feature to consider for applications of Fe3-xCrxO4 thin films in spintronics and photocatalysis, as it enables manipulation of magnetic properties (Curie temperature and magnetization) and band gap engineering.

Field-Free-Switching State Diagram of Perpendicular Magnetization Subjected to Conventional and Unconventional Spin-Orbit Torques

The lack of certain crystalline symmetries in strong spin-orbit-coupled nonmagnetic materials allows for the existence of unconventional spin Hall responses, with electrically generated transverse spin currents possessing collinear flow and spin directions. The injection of such spin currents into an adjacent ferromagnetic layer can excite magnetization dynamics via unconventional spin-orbit torques, leading to deterministic switching in ferromagnets with perpendicular magnetic anisotropy. We study the interplay between conventional and unconventional spin-orbit torques on the magnetization dynamics of a perpendicular ferromagnet in the small intrinsic damping limit, and identify a rich set of dynamical regimes that includes deterministic and probabilistic switching, precessional and pinning states. Contrary to common belief, we find that there exists a critical conventional spin Hall angle, beyond which deterministic magnetization switching transitions to a precessional or pinned state. Conversely, we show that larger unconventional spin Hall angle is generally beneficial for deterministic switching. We derive an approximate expression that qualitatively describes the state-diagram boundary between the full deterministic switching and precessional states and discuss a criterion for searching symmetry-broken spin Hall materials in order to maximize switching efficiency. Our work offers a roadmap towards energy-efficient spintronic devices, which might open the door for applications in advanced in-memory computing technologies.

Spin-charge coupling and decoupling in perovskite-type iron oxides (Sr1−xBax)2/3La1/3FeO3

The perovskite-type iron oxide Sr$_{2/3}$La$_{1/3}$FeO$_3$ is known to show characteristic spin-charge ordering (SCO), where sixfold collinear spin ordering and threefold charge ordering are coupled with each other. Here, we report the discovery of a spin-charge decoupling and an antiferromagnetic (AFM) state competing with the SCO phase in perovskites (Sr$_{1-x}$Ba$_x$)$_{2/3}$La$_{1/3}$FeO$_3$. By comprehensive measurements including neutron diffraction, M$\"{o}$ssbauer spectroscopy, and x-ray absorption spectroscopy, we found that the isovalent Ba$^{2+}$ substitution systematically reduces the critical temperature of the SCO phase and additionally yields the spin-charge decoupling in $x$ > 0.75. Whereas the ground state remains in the SCO phase in the whole $x$ region, an unexpected G-type AFM phase with incoherent charge ordering or charge fluctuation appears as the high-temperature phase in the range of $x$ > 0.75. Reflecting the competing nature between them, the G-type AFM phase partially exists as a metastable state in the SCO phase at low temperatures. We discuss the origin of the spin-charge decoupling and the emergence of the G-type AFM phase with charge fluctuation in terms of the bandwidth reduction by the Ba substitution.

Excitonic transverse and amplitude fluctuations in noncollinear and charge-ordered RbFe2+Fe3+F6

RbFe$^{2+}$Fe$^{3+}$F$_{6}$ is an example of an antiferromagnet with charge ordering of the octahedrally coordinated Fe$^{2+}$ and Fe$^{3+}$ ions. As well as different spin values, Fe$^{2+}$ ($S=2$) and Fe$^{3+}$ ($S={5\over2}$) possess differing orbital ground states with Fe$^{2+}$ having an orbital degeneracy with an effective orbital angular momentum of $l=1$. The resulting low temperature magnetic structure is non collinear with the spins aligned perpendicular to nearest neighbors (S. W. Kim \textit{et al.} Chem. Sci. {\bf{3}}, 741 (2012)). The combination of an orbital degeneracy and non collinear spin arrangements introduces the possibility for unusual types of excitations such as amplitude modes of the order parameter. In this paper we investigate this by applying a multi-level analysis to model neutron spectroscopy data (M. Songvilay \textit{et al.} Phys. Rev. Lett. {\bf{121}}, 087201 (2018)). In particular, we discuss the possible origins of the momentum and energy broadened continuum scattering observed in terms of amplitude fluctuations allowed through the presence of an orbital degree of freedom on the Fe$^{2+}$ site. We extend previous spin-orbit exciton models based on a collinear spin structure to understand the measured low-energy excitations and also to predict and discuss possible amplitude mode scattering in RbFe$^{2+}$Fe$^{3+}$F$_{6}$.

Structural, Degree of Inversion, and Magneton Number Studies on Fe3+‐Substituted MAl2O4 (M = Ni, Cu, Zn) Spinel Powders: The Evidence for Local Site Exchange of Cation and Magnetization Increment

Nanocrystalline Fe‐substituted metal aluminates, MFe x Al2−x O4 powders (M = Ni2+, Cu2+, and Zn2+) with different Fe3+ ion concentrations (x = 0, 0.5, 1.0, 1.5, and 2), are successfully synthesized by the sol–gel auto combustion method. Characterization of the calcined samples is carried out using X‐ray diffraction (XRD), synchrotron Extended X‐ray Absorption Fine Structure (EXAFS), and vibrating sample magnetometer (VSM) measurements. The XRD results confirm the formation of single‐phase spinel structure with Fd‐3m space group of all samples. The EXAFS spectra illustrate the main translocation trends in the trivalent and divalent ions between the tetrahedral and octahedral sublattices. When XRD Rietveld refinement, Williamson–Hall analysis, and EXAFS curve‐fitting analysis are applied to the data, the precise structural parameters, degree of inversion, and cation site occupancy are obtained. Furthermore, the Fe‐substituted samples show intense increase in the saturation magnetization with the increasing of Fe3+ ion concentrations. This occurrence is due to the rise in the net magnetic moment of the modified aluminates which took place as the distribution of the cations within the structure underwent changes. It is possible to explain the variation observed in the magneton number in the context of Fe3+ content through the application of Néel's collinear spin ordering model.

Nonlinear nonreciprocal transport in antiferromagnets free from spin-orbit coupling

We theoretically propose a realization of a nonlinear nonreciprocal transport in antiferromagnets without relying on the relativistic spin-orbit coupling. Through the symmetry and microscopic model analyses, we show that a local spin scalar chirality to induce an asymmetric band modulation becomes a source of a Drude-type nonlinear transport, while an electric polarization induced by a collinear spin configuration in a triangle unit leads to a Berry-curvature-dipole-type nonlinear transport. We demonstrate that 120$^\circ$ antiferromagnetic ordering on a triangular lattice and a breathing kagome lattice in an external magnetic field are typical examples. Our results open a new direction of designing and engineering functional materials with showing rich parity-violating transport phenomena by spontaneous magnetic phase transitions.

Complex magnetic ground states and topological electronic phases of atomic spin chains on superconductors

Understanding the magnetic properties of atomic chains on superconductors is an essential cornerstone on the road towards controlling and constructing topological electronic matter. Yet, even in simple models, the magnetic ground states remain debated. Ferromagnetic (FM), antiferromagnetic (AFM), and spin spiral configurations have been suggested and experimentally detected, while non-coplanar and complex collinear phases have been additionally conjectured. Here, we resolve parts of the controversy by determining the magnetic ground states of chains of magnetic atoms in proximity to a superconductor with Monte-Carlo methods. We confirm the existence of FM, AFM and spin spiral ground states, exclude non-coplanar phases in the model and clarify the parametric region of a $\uparrow\uparrow\downarrow\downarrow$-phase. We further identify a number of novel complex collinear spin configurations, including the periodic spin configurations $\uparrow\uparrow\uparrow\downarrow$, and $\uparrow \uparrow \uparrow \downarrow \uparrow \downarrow \downarrow \downarrow \uparrow \downarrow$, which are in some cases combined with harmonic and anharmonic spirals to form the ground state. We topologically classify the electronic structures, investigate their stability against increasing the superconducting order parameter, and explain the complex collinear order by an effective Heisenberg model with dominant four-spin interactions.

Magnetic phase diagram of [formula omitted][FeCl5(H2O)] ([formula omitted] = K, Rb, NH4)

Erythrosiderites with the formula A2FeX5⋅H2O, where A = Rb, K, and (NH4) and X = Cl and Br are intriguing systems that possess various magnetic and electric phases, as well as multiferroic phases in which magnetism and ferroelectricity are coupled. In this report, we study the magnetic phase diagram of erythrosiderites as a function of superexchange interactions and magnetic anisotropies. To this end, we perform classical Monte Carlo simulations on magnetic Hamiltonians that contain five different superexchange interactions with single-ion anisotropies. Our phase diagram contains all magnetic ground states that have been experimentally observed in these materials. We argue that the ground states can be explained by varying the ratio of J4J2. For J4J2>0.95 a cycloidal spins structure is stabilized as observed in (NH4)2FeCl5⋅H2O and otherwise a collinear spin structure is stabilized as observed in (K,Rb)2FeCl5⋅H2O. We also show that the difference in the single-ion anisotropy along a- and c- axes is essential to stabilize the intermediate state observed in (NH)2FeCl5⋅H2O.

Quantitative calculations of thermal-expansion coefficient in Fe–Ni alloys: First-principles approach

The thermal expansion coefficients (α) of Fe1-xNix alloys are calculated by means of the Debye-Grüneisen model, which uses the input parameters calculated from density functional theory (DFT) with collinear spin alignments. The various atomic configurations of fcc and bcc supercells with x being 0–0.5 are calculated to conduct the composition-specific analysis. Thermodynamic analysis is employed to facilitate the evaluation of α in bulk alloys, where the calculated supercells are used as the canonical ensemble. Such calculated α exhibits very similar composition-dependency in comparison with the experimental data from literature, particularly providing the well-known Invar effect at 65 wt% of Fe. The calculations also demonstrated that the pressure-derived magnetic frustration, i.e. the magneto-volume effect, is strongly correlated with the Invar effect. The present approach combining the Debye-Grüneisen formalism and the collinear DFT calculation is shown to be a comprehensive theoretical framework for analysis on the thermal expansion properties in metal alloys.