Noncollinear Spin Order Research Articles

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.

Dielectric, magnetic, and magnetodielectric change mechanisms in Y-type BaSrZn2Fe12O22 ceramics regulated by doping Al3+ and Ga3+ ions

We systematically investigated the dielectric, magnetic, and magnetodielectric (MD) properties of Y-type hexaferrite doped with Al3+ and Ga3+ ions. Al3+ ions preferentially enter the spin-up octahedral lattice sites while Ga3+ ions occupy the spin-down octahedral lattice sites first and then, enter the spin- octahedral sites with the increase in doping amount. The initial magnetization reaches saturation from outside of the hysteresis loops, exhibiting a non-collinear spin order. The step-like increase in magnetization with magnetic field indicates the ferroelectric changes in longitudinal conical spin order. The positive MD effect at low temperatures and the negative MD effect after warming for the doped samples are controlled by non-collinear spin ordering and electron hopping, respectively. The Al-doped and Ga-doped samples exhibit different ferroelectric behaviors driven by magnetic fields. Their ferroelectric phase diagrams were proposed on the basis of magnetic and MD properties. The results associate the physical properties with the doped ions in Y-type hexaferrite.

Observation of stacking engineered magnetic phase transitions within moiré supercells of twisted van der Waals magnets

Recent demonstrations of moiré magnetism, featuring exotic phases with noncollinear spin order in the twisted van der Waals (vdW) magnet chromium triiodide CrI3, have highlighted the potential of twist engineering of magnetic (vdW) materials. However, the local magnetic interactions, spin dynamics, and magnetic phase transitions within and across individual moiré supercells remain elusive. Taking advantage of a scanning single-spin magnetometry platform, here we report observation of two distinct magnetic phase transitions with separate critical temperatures within a moiré supercell of small-angle twisted double trilayer CrI3. By measuring temperature-dependent spin fluctuations at the coexisting ferromagnetic and antiferromagnetic regions in twisted CrI3, we explicitly show that the Curie temperature of the ferromagnetic state is higher than the Néel temperature of the antiferromagnetic one by ~10 K. Our mean-field calculations attribute such a spatial and thermodynamic phase separation to the stacking order modulated interlayer exchange coupling at the twisted interface of moiré superlattices.

Hidden non-collinear spin-order induced topological surface states

Rare-earth monopnictides are a family of materials simultaneously displaying complex magnetism, strong electronic correlation, and topological band structure. The recently discovered emergent arc-like surface states in these materials have been attributed to the multi-wave-vector antiferromagnetic order, yet the direct experimental evidence has been elusive. Here we report observation of non-collinear antiferromagnetic order with multiple modulations using spin-polarized scanning tunneling microscopy. Moreover, we discover a hidden spin-rotation transition of single-to-multiple modulations 2 K below the Néel temperature. The hidden transition coincides with the onset of the surface states splitting observed by our angle-resolved photoemission spectroscopy measurements. Single modulation gives rise to a band inversion with induced topological surface states in a local momentum region while the full Brillouin zone carries trivial topological indices, and multiple modulation further splits the surface bands via non-collinear spin tilting, as revealed by our calculations. The direct evidence of the non-collinear spin order in NdSb not only clarifies the mechanism of the emergent topological surface states, but also opens up a new paradigm of control and manipulation of band topology with magnetism.

Magnetic structure of the S = ½ staircase kagome lattice PbCu3TeO7

The crystal and magnetic structure characterization of geometrically distorted PbCu3TeO7 with S=1/2 Cu2+ spins forming a staircase kagome lattice was investigated using x-ray and neutron diffraction on a powder sample. The distorted kagome lattice of antiferromagnet PbCu3TeO7 exhibits a quasi-two-dimensional spin network. The x-ray diffraction data show that PbCu3TeO7 crystallizes in the orthorhombic system in the space group Pnma (No. 62). The lattice parameters a = 10.488(1) Å, b = 6.353(1) Å, and c = 8.814(2) Å. Our temperature-dependent x-ray diffraction data show that there is no structure phase transition between 12 and 298 K. From our powder neutron diffraction data at 2 K, we observed two distinct magnetic Bragg peaks at low angles, confirming the magnetic transition to the ordered state at low temperatures. In previous work, the ordering vector for the magnetic structure was determined using simulations to be (0,1/3,0). However, in this work, we found that based on the neutron diffraction data the ordering vector is in fact (0,1/3,1/3). The magnetic structure of PbCu3TeO7 exhibiting an antiferromagnet with noncollinear spin order is proposed.

Investigation of Charge-Ordered Barium Iron Fluorides with One-Dimensional Structural Diversity and Complex Magnetic Interactions.

Three mixed-valence barium iron fluorides, Ba7Fe7F34, Ba2Fe2F9, and BaFe2F7, were prepared through hydrothermal redox reactions. The characteristic structures of these compounds feature diverse distributions of FeIIF6 octahedra and FeIIIF6 groups. Ba7Fe7F34 contained one-dimensional infinite ∞[FeIIFeIII6F34]14- double chains, comprising cis corner-sharing octahedra along the b direction; Ba2Fe2F9 contained one-dimensional ∞[Fe2F9]4- double chains, consisting of cis corner-sharing octahedra along the chain (a-axis direction) and trans corner-sharing octahedra vertical to the chain, while BaFe2F7 revealed three-dimensional (3D) frameworks that consist of isolated edge-sharing dinuclear FeII2F10 units linked via corners by FeIIIF6 octahedra. Magnetization and Mössbauer spectroscopy measurements revealed that Ba7Fe7F34 exhibits an antiferromagnetic phase transition at ∼11 K, where ferrimagnetic ∞[FeIIFeIII6F34]14- double chains are arranged in a paralleling manner, while Ba2Fe2F9 shows canted antiferromagnetic ordering at ∼32.5 K, leading to noncollinear spin ordering.

Majorana vortex modes in spin-singlet chiral superconductors with noncollinear spin ordering: Local density of states study

In the present study topologically nontrivial edge and vortex bound states are described in the coexistence phase of chiral spin-singlet superconductivity and noncollinear spin ordering on a triangular lattice in the presence of few (up to four) vortices. We consider the topological phase transition induced by the magnetic order between the phase hosting Majorana modes and the initial phase of the chiral d-wave superconductivity supporting non-Majorana modes which is also topologically nontrivial. The change of the excitation spectrum at the critical point is obtained in both cases of open and periodic boundary conditions in the presence of vortices. It is proved that zero energy Majorana modes localized at vortex cores are caused by noncollinear long-range magnetic ordering. Even though nearby excitation energies of subgap states including the edge-localized and vortex-localized states are very close to each other, the energy difference between different vortex bound states is an order of magnitude higher. This difference determines the energy gap for Majorana vortex modes separating them from other vortex bound states. It is found that even in the presence of noncollinear spin ordering its value can be estimated from the excitation energy of vortex bound states in the pure chiral d-wave state for the nonmagnetic case. By studying local density of states near the vortex cores the possibility to experimentally detect the described Majorana vortex modes by scanning tunneling microscopy is discussed. It is demonstrated that Majorana vortex modes and Majorana antivortex modes induced by noncollinear magnetism have different features in energy and spatially resolved density of states due to the chiral symmetry on the superconducting order parameter.

Thickness-Dependent Topological Hall Effect in 2D Cr5 Si3 Nanosheets with Noncollinear Magnetic Phase.

Antiferromagnets with noncollinear spin order are expected to exhibit unconventional electromagnetic response, such as spin Hall effects, chiral abnormal, quantum Hall effect, and topological Hall effect. Here, 2D thickness-controlled and high-quality Cr5 Si3 nanosheets that are compatible with the complementary metal-oxide-semiconductor technology are synthesized by chemical vapor deposition method. The angular dependence of electromagnetic transport properties of Cr5 Si3 nanosheets is investigated using a physical property measurement system, and an obvious topological Hall effect (THE) appears at a large tilted magnetic field, which results from the noncollinear magnetic structure of the Cr5 Si3 nanosheet. The Cr5 Si3 nanosheets exhibit distinct thickness-dependent perpendicular magnetic anisotropy (PMA), and the THE only emerges in the specific thickness range with moderate PMA. This work provides opportunities for exploring fundamental spin-related physical mechanisms of noncollinear antiferromagnet in ultrathin limit.

Frustration model and spin excitations in the helimagnet FeP

The metallic compound FeP belongs to the class of materials that feature a complex noncollinear spin order driven by magnetic frustration. While its double-helix magnetic structure with a period $\lambda_{\text{s}} \approx 5c$, where $c$ is the lattice constant, was previously well determined, the relevant spin-spin interactions that lead to that ground state remain unknown. By performing extensive inelastic neutron scattering measurements, we obtained the spin-excitation spectra in a large part of the momentum-energy space. The spectra show that the magnons are gapped with a gap energy of $\sim$5 meV. Despite the 3D crystal structure, the magnon modes display strongly anisotropic dispersions, revealing a quasi-one-dimensional character of the magnetic interactions in FeP. The physics of the material, however, is not determined by the dominating exchange, which is ferromagnetic. Instead, the weaker two-dimensional antiferromagnetic interactions between the rigid ferromagnetic spin chains drive the magnetic frustration. Using linear spin-wave theory, we were able to construct an effective Heisenberg Hamiltonian with an anisotropy term capable of reproducing the observed spectra. This enabled us to quantify the exchange interactions in FeP and determine the mechanism of its magnetic frustration.

Exploration of trivial and nontrivial electronic phases and of collinear and noncollinear magnetic phases in low-spin d5 perovskites

The $4d$ and $5d$ transition metal oxides have become important members of the emerging quantum materials family due to competition between onsite Coulomb repulsion ($U$) and spin-orbit coupling (SOC). Specifically, the systems with $d^5$ electronic configuration in an octahedral environment are found to be capable of posessing invariant semimetallic state and perturbations can lead to diverse magnetic phases. In this work, by formulating a multi-band Hubbard model and performing SOC tunable DFT+$U$ calculations on a prototype SrIrO$_3$ and extending the analysis to other iso-structural and isovalent compounds, we present eight possible electronic and magnetic configurations in the $U$-SOC phase diagram that can be observed in the family of low-spin $d^5$ perovskites. They include the protected Dirac semimetal state, metal and insulator regimes, collinear and noncollinear spin ordering. The latter is explained through connecting hopping interactions to the rotation and tilting of the octahedra as observed in GdFeO$_3$. Presence of several soft phase boundaries makes the family of $d^5$ perovskites an ideal platform to study electronic and magnetic phase transitions under external stimuli.

Giant Effective Damping of Octupole Oscillation in an Antiferromagnetic Weyl Semimetal

A magnetic Weyl semimetal is a recent focus of extensive research as it may exhibit large and robust transport phenomena associated with topologically protected Weyl points in momentum space. Since a magnetic texture provides a handle for the configuration of the Weyl points and its transport response, understanding of magnetic dynamics forms the basis for future control of a topological magnet. Mn3Sn is an example of an antiferromagnetic Weyl semimetal that exhibits a large response comparable to the one observed in ferromagnets despite a vanishingly small magnetization. The noncollinear spin order in Mn3Sn can be viewed as a ferroic order of cluster magnetic octupole and breaks the time‐reversal symmetry, stabilizing Weyl points and the significantly enhanced Berry curvature near the Fermi energy. Herein, the first observation of time‐resolved octupole oscillation in Mn3Sn is reported. In particular, the giant effective damping of the octupole dynamics is found, and it is feasible to conduct an ultrafast switching at <10 ps, a hundred times faster than the case of spin‐magnetization in a ferromagnet. Moreover, high domain wall velocity over 10 km s−1 is theoretically predicted. This work paves the path toward realizing ultrafast electronic devices using the topological antiferromagnet.

Conical order, magnetic compensation, and sign reversible exchange bias in spinel structured AB2O4 compounds: A Monte Carlo study

$A{B}_{2}{\mathrm{O}}_{4}$ are a special class of spinel structured compounds exhibiting unique multiferroic properties. Recent experimental observation confirms switchable polarization in $A{\text{Cr}}_{2}{\text{O}}_{4}$ $(A=\text{Co}, \mathrm{Mn}, \mathrm{Fe})$, arising out of noncollinear magnetic spin order. In this paper we unfold the microscopic origin behind such magnetic spin order, hysteresis, polarization, and the so-called magnetic compensation effect in $A{\text{Cr}}_{2}{\text{O}}_{4}$ $(A=\text{Co}, \mathrm{Mn}, \mathrm{Fe}, \mathrm{Ni})$ using Monte Carlo simulation. We have carefully constructed a set of exchange interaction parameters, which help to explain various experimental findings such as magnetization vs temperature $(T)$, conical stability, magnetic ordering, and polarization in a representative compound ${\text{CoCr}}_{2}{\text{O}}_{4}$. When substituted with Fe, ${\text{CoCr}}_{2}{\text{O}}_{4}$ shows few exotic phenomena such as sign reversible exchange bias effect and magnetic compensation. ${\text{CoMn}}_{2}{\text{O}}_{4}$ and ${\text{CoFe}}_{2}{\text{O}}_{4}$ are two other compounds in the spinel family where we found no conical spin order and polarization, and thus facilitate a distinct contrast compared to others.

Exchange Bias in Antiferromagnetic Mn3Sn Monolayer Films

${\mathrm{Mn}}_{3}\mathrm{Sn}$ is an antiferromagnet with a noncollinear spin order, and the spin structures can be controlled by an external magnetic field. When a magnetic field is applied, ${\mathrm{Mn}}_{3}\mathrm{Sn}$ with the inverse triangular spin structure exhibits the coexistence of antiferromagnetism and weak ferromagnetism. Here we observe that both the magnetization hysteresis loops and anomalous Hall curves of ${\mathrm{Mn}}_{3}\mathrm{Sn}$ single-layer films present exchange bias after field cooling, which are generally observed in ferromagnet/antiferromagnet bilayers. A part of the antiferromagnetic spin structure of ${\mathrm{Mn}}_{3}\mathrm{Sn}$ with negligible net moments is frozen by the field-cooling process, while for the other part of ${\mathrm{Mn}}_{3}\mathrm{Sn}$, the switching of the inverse triangular spin structure with weak moments by external magnetic fields results in sizable anomalous Hall curves. The stable frozen antiferromagnetic part pins the weak moments and the inverse triangular spin structures can explain the exchange bias in magnetization hysteresis loops and anomalous Hall curves. The finding of exchange bias in antiferromagnetic ${\mathrm{Mn}}_{3}\mathrm{Sn}$ single-layer films with noncollinear spin order adds a different dimension to antiferromagnetic spintronics.

Magnetoelectric properties and low-energy excitations of multiferroic FeCr2S4

We report on the low-frequency optical excitations in the multiferroic ground state of polycrystalline FeCr2S4 in the frequency range 0.3-3~THz and their changes upon applying external magnetic fields up to 7~T. In the ground state below the orbital-ordering temperature T_OO=9K we observe the appearance of several new modes. By applying the external magnetic field parallel and perpendicular to the propagation direction of the THz radiation, we can identify the strongest absorptions to be of predominantly electric-dipole origin. We discuss these modes as the low-energy electronic excitations of the Fe^{2+} ions (3d^6, S=2) in an tetrahedral environment. The eigenfrequencies and relative intensities of these absorption lines are satisfactorily reproduced by our calculation assuming an effective exchange field of 12.8 cm-1 at the Fe^{2+}-ions sites. The direction of the exchange field is found to be slightly tilted out of the ab-plane. With our approach we can also describe previously reported results from M\"ossbauer studies and the order of magnitude of the electric polarisation induced by orbital and non-collinear spin ordering.

Weak First-Order Transition and Pseudoscaling Behavior in the Universality Class of the O(N) Ising Model

Using Monte Carlo and renormalization group methods, we investigate systems with critical behavior described by two order parameters: continuous (vector) and discrete (scalar). We consider two models of classical three-dimensional Heisenberg magnets with different numbers of spin components N = 1,…,4: the model on a cubic lattice with an additional competing antiferromagnetic exchange interaction in a layer and the model on a body-centered lattice with two competing antiferromagnetic interactions. In both models, we observe a first-order transition for all values of N. In the case where competing exchanges are approximately equal, the first order of a transition is close to the second order, and pseudoscaling behavior is observed with critical exponents differing from those of the O(N) model. In the case N = 2, the critical exponents are consistent with the well-known indices of the class of magnets with a noncollinear spin ordering. We also give a possible explanation of the observed pseudoscaling in the framework of the renormalization group analysis.

Expansion of the spin cycloid in multiferroic BiFeO3 thin films

Understanding and manipulating complex spin texture in multiferroics can offer new perspectives for electric field-controlled spin manipulation. In BiFeO3, a well-known room temperature multiferroic, the competition between various exchange interactions manifests itself as non-collinear spin order, i.e., an incommensurate spin cycloid with period 64 nm. We report on the stability and systematic expansion of the length of the spin cycloid in (110)-oriented epitaxial Co-doped BiFeO3 thin films. Neutron diffraction shows (i) this cycloid, despite its partly out-of-plane canted propagation vector, can be stabilized in thinnest films; (ii) the cycloid length expands significantly with decreasing film thickness; (iii) theory confirms a unique [11bar 2] cycloid propagation direction; and (iv) in the temperature dependence the cycloid length expands significantly close to TN. These observations are supported by Monte Carlo simulations based on a first-principles effective Hamiltonian method. Our results therefore offer new opportunities for nanoscale magnonic devices based on complex spin textures.

Comparing the anomalous Hall effect and the magneto-optical Kerr effect through antiferromagnetic phase transitions in Mn3Sn

In the non-collinear antiferromagnet Mn3Sn, we compare simultaneous measurements of the anomalous Hall effect (AHE) and the magneto-optical Kerr effect (MOKE) through two magnetic phase transitions: the high-temperature paramagnetic/antiferromagnetic (AF) phase transition at the Néel temperature (TN ≈ 420 K) and a lower-temperature incommensurate magnetic ordering at T1 ≈ 270 K. While both the AHE and MOKE are sensitive to the same underlying symmetries of the AF non-collinear spin order, we find that the transition temperatures measured by these two techniques unexpectedly differ by approximately 10 K. Moreover, the applied magnetic field at which the AF order reverses is significantly larger when measured by MOKE than when measured by AHE. These results point to a difference between the bulk and surface magnetic properties of Mn3Sn.

Critical and multicritical behavior in the Ising–Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang–Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.

Type-II Multiferroic Hf2VC2F2 MXene Monolayer with High Transition Temperature.

Achieving multiferroic two-dimensional (2D) materials should enable numerous functionalities in nanoscale devices. Until now, however, predicted 2D multiferroics are very few and with coexisting yet only loosely coupled (type-I) ferroelectricity and magnetism. Here, a type-II multiferroic MXene Hf2VC2F2 monolayer is identified, where ferroelectricity originates directly from its magnetism. The noncollinear 120°Y-type spin order generates a polarization perpendicular to the spin helical plane. Remarkably, the multiferroic transition is estimated to occur above room temperature. Our investigation should open the door to a new branch of 2D materials in the pursuit of intrinsically strong magnetoelectricity.

Strain effect on magnetic property of antiferromagnetic insulator SmFeO3

Thin films and heterostructures of antiferromagnetic insulator SmFeO3 were fabricated on LaAlO3 (001) substrates by magnetron sputtering, and their structural, magnetic properties were investigated. It was found that epitaxially strained thin films showed a pronounced magnetic anisotropy with the enhanced magnetization up to 65 emu/cc, which is approximately ten times larger than the bulk value. The observed enhancement of magnetization was considered to be due to the lattice distortion and the non-collinear antiferromagnetic spin ordering of SmFeO3.