Noncollinear Magnetic Structure Research Articles

Structural order and disorder within novel antiferromagnetic RCrxGa3-yGey and R4Cr1-xGa12-yGey intermetallic compounds (R = Tb, Dy)

Single crystals of intermetallic phases RCrxGa3−yGey (R = Tb, Dy; x = 0.19–0.23, y = 0–0.4) and R4Cr1−xGa12−yGey (R = Tb, Dy; x = 0–0.13, y = 3–4) were grown from Ga flux ensuring the absence of magnetic impurities. The X-ray diffraction experiments revealed that the compounds belong to the family of filled AuCu3-type gallides. The compounds are formed upon the insertion of Cr atoms into E6 octahedral voids (E = Ga/Ge), which can occur in either disordered (RCrxGa3-yGey) or ordered (R4Cr1-xGa12-yGey) fashion. The unique feature of the obtained compounds is the strong correlation between the level of Ge doping and the Cr concentration in the phases, which allows one to control both the structural and magnetic ordering. At low Ge concentration, the cubic RCrxGa3-yGey phases form, which then experience tetragonal distortion upon the increase in the Ge content, and the cubic R4Cr1-xGa12-yGey 2×2×2 superstructures are formed at even higher Ge concentrations. The X-ray diffraction analysis also showed a presence of structural defects in the phases, which are caused by different size of empty E6 and filled CrE6 octahedra. Magnetic measurements of the single crystals of the cubic phases reveal antiferromagnetic ordering of the rare earth sublattice with the Neel temperatures decreasing upon Ge doping from 22 K for RCrxGa3 to 10 K for R4Cr1−xGa12−yGey. The Ge doping causes gradual decrease in the strength of antiferromagnetic R-R interactions ultimately leading to noncollinear magnetic structure in the superstructure R4Cr1−xGa12−yGey phases.

Anomalous Nernst effect in the noncollinear antiferromagnet Mn5Si3

Investigating the off-diagonal components of the conductivity and thermoelectric tensor of materials hosting complex antiferromagnetic structures has become a viable method to reveal the effects of topology and chirality on the electronic transport in these systems. In this respect, Mn5Si3 is an interesting metallic compound that exhibits several antiferromagnetic phases below 100 K with different collinear and noncollinear arrangements of Mn magnetic moments determined from neutron scattering. Previous electronic transport measurements have shown that the transitions between the various phases give rise to large changes of the anomalous Hall effect. Here, we report measurements of the anomalous Nernst effect of Mn5Si3 single crystals that also show clear transitions between the different magnetic phases. In the noncollinear phase, we observe an unusual sign change of the zero-field Nernst signal with a concomitant decrease of the Hall signal and a gradual reduction of the remanent magnetization. Furthermore, a symmetry analysis of the proposed magnetic structures shows that both effects should actually vanish. These results indicate a symmetry-breaking modification of the magnetic state with a rearrangement of the magnetic moments at low temperatures, thus questioning the previously reported models for the noncollinear magnetic structure obtained from neutron scattering.

Magnetic Structure-Dependent Spin Texture Lattice in Hexagonal MnFeCoGe Magnets.

Topological spin textures are of great significance in magnetic information storage and spintronics due to their high storage density and low drive current. In this work, the transformation of magnetic configuration from chaotic labyrinth domains to uniform stripe domains was observed in MnFe1-xCoxGe magnets. This change occurs due to the noncollinear magnetic structure switching to a uniaxial ferromagnetic structure with increasing Co content, as identified by neutron diffraction results and Lorentz transmission electron microscopy (L-TEM). Of utmost importance, a hexagonal lattice of high-density robust type-II magnetic bubble lattice was established for x = 0.8 through out-of-plane magnetic field stimulation and field-cooling. The dimensions of the type-II magnetic bubbles were found to be tuned by the sample thickness. Therefore, the stabilization of complex magnetic spin textures, associated with enhanced uniaxial ferromagnetic interaction and magnetic dipole-dipole interaction in MnFe1-xCoxGe through magnetic structure manipulation, as further confirmed by the micromagnetic simulations, will provide a convenient and efficient strategy for designing topological spin textures with potential applications in spintronic devices.

Negative charge-transfer energy in SrFeO3 revisited with hard x-ray photoemission spectroscopy

We report hard x-ray photoelectron spectroscopy on SrFeO3 which is one of the classical conducting transition-metal oxides with a noncollinear magnetic structure. The obtained spectra show a detailed charge-transfer (CT) satellite structure, the Fe 2p3/2 main peak exhibits multiplet splitting, and the deterioration signs present in previous reports are absent here, allowing for a better determination of its intrinsic electronic structure. The results are well described by a FeO6 cluster model with a charge-transfer energy of about −1.0 eV, confirming the values obtained in the previous works. The negative CT energy indicates that the electronic configuration of the tetravalent Fe is d5L rather than d4 where L represents an O 2p hole. The small spectral weight observed at the Fermi level indicates the correlated metallic state with localized Fe 3d electrons and mobile O 2p holes which are governed by a large d−d Coulomb interaction and negative CT energy. Published by the American Physical Society 2024

Magnetic structure of Tb[formula omitted]NbO[formula omitted] determined using neutron diffraction experiments and magnetic anisotropy calculations

We determined the magnetic structure of Tb3NbO7 based on powder neutron diffraction experiments and magnetic anisotropy calculations. We calculated the energy levels split by crystalline electric fields, and the magnetic moments using McPhase. The c axis is the easy axis for Tb1 moments, and magnetic anisotropy is small for Tb2 moments. Magnetic reflections were observed at low temperatures. The propagation vector is k1=(0,0,0) at 1.8 K and k2=(1/2,1/2,0) at 2.5 K between transition temperatures TN1=2.0 K and TN2=3.2 K. We selected candidates for an irreducible representation (IR) of the magnetic structures using magnetic anisotropy. From Rietveld refinements, we determined the following: The IRs are mΓ4 and mS2 at 1.8 K and 2.5 K, respectively. The main component of Tb1 ordered moments is w at 1.8 K. The order of the main components in each chain along the c axis is antiferromagnetic. Tb1 moments are disordered at 2.5 K. Tb2 moments form noncollinear magnetic structures in the ab plane perpendicular to Tb1 chains with a small w component at both the 1.8 K and 2.5 K. The magnetic structure at 1.8 K is consistent with the magnetic anisotropies obtained using McPhase calculations. Only Tb2 moments are ordered at 2.5 K, indicating the appearance of a partially disordered state. We also considered the origin of the two magnetic transitions.

Magnetism in the axion insulator candidate Eu5In2Sb6

Eu5In2Sb6 is a member of a family of orthorhombic nonsymmorphic rare-earth intermetallics that combines large localized magnetic moments and itinerant exchange with a low carrier density and perpendicular glide planes. This may result in special topological crystalline (wallpaper fermion) or axion insulating phases. Recent studies of Eu5In2Sb6 single crystals have revealed colossal negative magnetoresistance and multiple magnetic phase transitions. Here, we clarify this ordering process using neutron scattering, resonant elastic x-ray scattering, muon spin-rotation, and magnetometry. The nonsymmorphic and multisite character of Eu5In2Sb6 results in coplanar noncollinear magnetic structures with an Ising-like net magnetization along the a axis. A reordering transition, attributable to competing ferro- and antiferromagnetic couplings, manifests as the onset of a second commensurate Fourier component. In the absence of spatially resolved probes, the experimental evidence for this low-temperature state can be interpreted either as an unusual double-q structure or in a phase separation scenario. The net magnetization produces variable anisotropic hysteretic effects which also couple to charge transport. The implied potential for functional domain physics and topological transport suggests that this structural family may be a promising platform to implement concepts of topological antiferromagnetic spintronics. Published by the American Physical Society 2024

Temperature-dependent evolution of micromagnetic structure of B20-type Fe1-xCoxGe studied by Mössbauer spectroscopy

The non-collinear magnetic structures hosted in magnets with broken central inversion symmetry, some of which are topologically non-trivial, have unique physical properties and application prospects. This paper presents a detailed study of the temperature evolution of the micromagnetic structures of B20-type Fe1-xCoxGe (x = 0, 0.05, 0.10) polycrystalline samples using 57Fe Mössbauer spectroscopy. We take the relatively weak electric quadrupole interaction as a perturbation of the hyperfine magnetic interaction to obtain the distribution of the hyperfine magnetic field Hhf (φ) in the plane perpendicular to the magnetic propagation vector ks. It is found that the geometric features of Hhf (φ) are sensitive to the relative orientation of ks regarding the electric field gradient at the iron nucleus, as well as to the spin texture. The temperature dependence of Hhf (φ) provides a distinct signal of first-order phase transition when ks shifts from [100] to [111]. The doping of cobalt atoms leads to out-of-plane component and in-plane component aggregation of the neighboring iron magnetic moments. These results are instructive for understanding the dynamical behavior of spiral magnets with long-periods.

Effects of Ni2+ doping on magnetic and magnetoelectric properties of Y-type hexaferrite BaSrCo2Fe11AlO22

Magnetoelectric hexaferrites are the promising candidate materials for low-consumption magnetic memory device application, due to the existence of room-temperature magnetoelectric effect and the tunable magnetic structure. In this work, we studied the Ni doping effect on a rare room-temperature multiferroic BaSrCo2Fe11AlO22. With the comprehensive study of magnetism, magnetoelectricity, and ferroelectric properties, magnetoelectric phase diagrams of BaSrCo2-xNixFe11AlO22 were established. Generally, Ni doping has two important effects on magnetic and magnetoelectric properties. One is to strengthen superexchange interactions, greatly enhancing magnetic order temperature. Another effect is to destabilize the noncollinear magnetic structure at high temperature, causing the absence of ME effect at room temperature. In addition, the converse ME effects have been studied, revealing that converse ME coupling strength become weakened with the increase in Ni concentration. Our systematic studies provide important clues for synthesizing high performance magnetoelectric hexaferrites.

Spontaneous Topological (Anti)meron Chains in the Domain Walls of Centrosymmetric Rare‐Earth Magnet

AbstractExploration and manipulation of topological protected magnetic swirls, such as skyrmion, antiskyrmion, meron, and vortex, holds significance for fundamental research and practical applications in high‐density magnetic information storage and spintronics because of their high storage density and low driven current. This study unveils the existence of field‐free spontaneous (anti)meron chains with a topological charge of ±1/2 in the centrosymmetric rare‐earth magnet Tb6Co2.17Si2.5 via in situ real‐space observation. The spin reorientation transition from in‐plane to uniaxial anisotropy contributes to the spontaneous transformation from straight domain walls to topological (anti)meron chains and to stripe domains along the [110] zone axis during in situ cooling. The study further confirms the critical role of the noncollinear magnetic structure of Tb atoms in the formation of topological (anti)meron chains via real‐space observations, first‐principles calculations, and micromagnetic simulations. The spontaneous topological magnetic texture is strongly correlated with the 4f electrons of rare‐earth atoms, enriching and stimulating alternative generation mechanisms of topological spin textures from emerging rare‐earth magnets, and further applications in spintronics.

Non-collinear magnetic atomic cluster expansion for iron

The Atomic Cluster Expansion (ACE) provides a formally complete basis for the local atomic environment. ACE is not limited to representing energies as a function of atomic positions and chemical species, but can be generalized to vectorial or tensorial properties and to incorporate further degrees of freedom (DOF). This is crucial for magnetic materials with potential energy surfaces that depend on atomic positions and atomic magnetic moments simultaneously. In this work, we employ the ACE formalism to develop a non-collinear magnetic ACE parametrization for the prototypical magnetic element Fe. The model is trained on a broad range of collinear and non-collinear magnetic structures calculated using spin density functional theory. We demonstrate that the non-collinear magnetic ACE is able to reproduce not only ground state properties of various magnetic phases of Fe but also the magnetic and lattice excitations that are essential for a correct description of finite temperature behavior and properties of crystal defects.

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.

Microstructure parameter-dependent non-collinear magnetic structures in scandium-doped M-type hexaferrite nanocrystals.

The quest for materials with non-collinear magnetic structures has been driven by their unique properties and potential applications in advanced spintronics and data storage technologies. In this study, we investigate the induction of a non-collinear conical state in BaFe12O19 (M-type) nanocrystal fibers through the substitution of Fe3+ ions with diamagnetic Sc3+ ions. This substitution introduces an additional parameter for tuning the magnetic structure and allows precise control over the substitution amount. We demonstrate that the non-collinear conical state remains stable within a temperature range of 125 K to 325 K and can be finely adjusted by varying the Sc3+ substitution amount. The selective occupancy of Sc3+ ions at the 2a, 4f2, and 2b sites within the M-type ferrite lattice weakens the super-exchange interaction between Fe1, Fe2, and Fe5 ions. This weakening disrupts interactions between different blocks S/R (R*/S*) and stabilizes the conical state. These findings highlight a significant approach to modulating non-collinear magnetic structures in hexagonal ferrites, with implications for both fundamental research and practical applications in the development of novel magnetic materials.

Dependence of electronic properties on Coulomb repulsion and electric field in single layer FeI2

The Coulomb repulsion was applied in the framework of LDA+U approach and electric field to find out the electronic properties of a single layer 1T-FeI2. This calculation relies on the density functional theory of non-collinear magnetic structure. From the curve of energy dispersion, increasing the Coulomb parameter and electric field yields an electronic transition from a metallic state to an insulating state. This only holds in case the spin-orbit coupling is incorporated. While the magnetism still holds as the Coulomb parameter is tuned, the magnetism vanishes as the electric field is included. However, as the magnetism disappears, the spin splitting appears when increasing the electric field. This indicates that the Coulomb repulsion and electric field give a prominent impact on the electronic properties in the single layer FeI2 as the spin-orbit coupling is included.

Stability of the atomic arrangement in Laves phases Be2Fe1–xOsx (0 ≤ x ≤ 0.75) and Be2Fe1–xRux (x[formula omitted] 0.5)

The binary Be2Fe, which crystallizes in the C14-structure type hexagonal Laves phase, can dissolve a large amount of Os as a third element, without changing the crystal structure (about ¾ of Fe can be replaced by Os). A study of the homogeneity range for the Be2Fe1–xOsx Laves phase, shows an increase of the lattice parameters with an increase of the Os content. When Ru substitutes Fe in Be2Fe, a temperature- and composition-dependent transformation from the C14 to the cubic C15 Laves phase is observed, with a narrow homogeneity range. Formation energy calculations revealed that the C14-structure type is energetically favored when Os substitutes Fe in Be2Fe, while a structural phase transition is observed between Be2Fe (C14) and Be2Fe0.5Ru0.5 (C15), all in good agreement with the experimental results. A strong charge transfer from Be to Os or Ru is observed from the analysis of electron density within the Quantum Theory of Atoms in Molecules (QTAIM) framework. A formation of multiatomic bonds is found from the electron localizability approach. Be2Fe1–xOsx undergoes a transition to a disordered ferromagnetic state at TC= 350 K and behaves like a ferromagnet with a non-collinear magnetic structure (not all domains polarized along field). Be2Fe1–xRux orders ferromagnetically below TC= 340 K and the very narrow hysteresis curves show that Be2Fe1–xRux is a soft ferromagnet.

Multiple magnetic transitions and complex magnetic structures in Fe2SiSe4 with the sawtooth lattice

The sawtooth lattice shares some structural similarities with the kagome lattice and may attract renewed research interest. Here we report a comprehensive study on the physical properties of ${\mathrm{Fe}}_{2}{\mathrm{SiSe}}_{4}$, an unexplored member in the olivine chalcogenides with the sawtooth lattice of Fe. Our results show that ${\mathrm{Fe}}_{2}{\mathrm{SiSe}}_{4}$ is a magnetic semiconductor with band gap of 0.66 eV. It first undergoes an antiferromagnetic transition at ${\mathrm{T}}_{m1}=110$ K, then an ferrimagneticlike one at ${\mathrm{T}}_{m2}=50$ K, and finally a magnetic transition at ${\mathrm{T}}_{m3}=25$ K, which is likely driven by the thermal populations of spin-orbit manifold on the Fe sites. Neutron diffraction analysis reveals a noncollinear antiferromagnetic structure with propagation vector ${\mathbf{q}}_{\mathbf{1}}=(0,0,0)$ at ${\mathrm{T}}_{m2}<\mathrm{T}<{\mathrm{T}}_{m1}$. Interestingly, below ${\mathrm{T}}_{m2}$, an additional antiferromagnetic structure with ${\mathbf{q}}_{\mathbf{2}}=(0,0.5,0)$ appears, and ${\mathrm{Fe}}_{2}{\mathrm{SiSe}}_{4}$ exhibits a complex double-$\mathbf{q}$ magnetic structure which has never been observed in sawtooth olivines. Density functional theory calculations suggest this complex noncollinear magnetic structure may originate from the competing antiferromagnetic interactions for both intra- and interchain in the sawtooth lattice. Furthermore, band-structural calculations show that ${\mathrm{Fe}}_{2}{\mathrm{SiSe}}_{4}$ has quasi-flat-band features near the valence and conduction band structure. Our results have shown that ${\mathrm{Fe}}_{2}{\mathrm{SiSe}}_{4}$ could serve as a new material playground for further research on magnetic devices and the flat-band effect through chemical doping.

Anisotropic spin model and multiple- Q states in cubic systems

Multiple-$Q$ states manifest themselves in a variety of noncollinear and noncoplanar magnetic structures depending on the magnetic interactions and lattice structures. In particular, cubic-lattice systems can host a plethora of multiple-$Q$ states, such as magnetic skyrmion and hedgehog lattices. We here classify momentum-dependent anisotropic exchange interactions in the cubic-lattice systems based on the magnetic representation analysis. We construct an effective spin model for centrosymmetric cubic space groups, $Pm\bar{3}m$ and $Pm\bar{3}$, and noncentrosymmetric ones, $P\bar{4}3m$, $P432$, and $P23$: The former include the symmetric anisotropic exchange interaction, while the latter additionally include the Dzyaloshinskii-Moriya interaction. We demonstrate that the anisotropic exchange interaction becomes the origin of the multiple-$Q$ states by applying the anisotropic spin model to the case under $Pm\bar{3}$. We show several multiple-$Q$ instabilities in the ground state by performing simulated annealing. Our results will be a reference for not only exploring unknown multiple-$Q$ states but also understanding the origin of the multiple-$Q$ states observed in both noncentrosymmetric and centrosymmetric magnets like EuPtSi and SrFeO$_3$.

Anomalous Hall effect and magnetic structure of the topological semimetal ( Mn0.78Fe0.22)Ge3

Me$_{3+\delta}$Ge, being a Weyl semimetal, shows a large anomalous Hall effect (AHE), which decreases slowly with an increase in $\delta$ from 0.1 to 0.4. However, AHE in this compound remains significantly large in the whole range of $\delta$ because of the robust nature of the topology of bands. To explore the possibility of tuning the anomalous transport effects in Weyl semimetals, we have studied the single-crystal hexagonal-(Mn$_{0.78}$Fe$_{0.22}$)$_3$Ge compound. Magnetization of this compound shows two magnetic transitions at 242 K ($T_{\text{N1}}$) and 120 K ($T_{\text{N2}}$). We observed that the AHE persists between $T_{\text{N2}}$ - $T_{\text{N1}}$ and vanishes below $T_{\text{N2}}$. Further, we performed single-crystal neutron diffraction experiments (using spherical neutron polarimetry and unpolarized neutron diffraction) to determine the magnetic structures of (Mn$_{0.78}$Fe$_{0.22}$)$_3$Ge at different temperatures. Our neutron diffraction results show that the sample possesses a collinear antiferromagnetic structure below $T_{\text{N2}}$. However, the magnetic structure of the sample remains noncollinear antiferromagnetic, the same as Mn$_3$Ge, between $T_{\text{N1}}$ to $T_{\text{N2}}$. The presence of AHE, and noncollinear magnetic structure in (Mn$_{0.78}$Fe$_{0.22}$)$_3$Ge, between $T_{\text{N1}}$ and $T_{\text{N2}}$, suggest the existence of Weyl points in this temperature regime. Below $T_{\text{N2}}$, AHE is absent, and the magnetic structure also changes to a collinear antiferromagnetic structure. These observations signify a strong link between the magnetic structure of the sample and AHE.

Nontrivial spin textures induced remarkable topological Hall effect and extraordinary magnetoresistance in kagome magnet TmMn6Sn6

Kagome magnets RMn6Sn6 (R = lanthanides) manifest novel topological phases and field-induced transitions, owing to the interplay between strong correlations and geometrical frustration among the corner-sharing-triangle intralayers. Here we report the magnetometry and magnetoelectric transport properties of TmMn6Sn6 single crystal, which coexists with Tm and Mn magnetic sublattices. We reveal that this compound displays multiple magnetic structures with the increase of in-plane magnetic field. The combination of non-collinear magnetic structure and real-space Berry curvature leads to a remarkable topological Hall effect over an extensive temperature range. The in-plane magnetic transition is accompanied by a large magnetoresistance effect of -32 ∼ -17% from 10 K to 300 K at 7 T, and the magnetoresistance manifests two peaks with increasing the in-plane field. These observations suggest a robust Mn - Tm magnetic coupling, which provides a nontrivial ferrimagnetic network for the further investigation of new emergent topological magnetic structures.

Modulated non-collinear magnetic structure of (Co0.9757Fe0.03)4Nb2O9 as revealed by Mössbauer spectroscopy

In this work, we present detailed 57Fe Mössbauer spectroscopy investigations of (Co0.9757Fe0.03)4Nb2O9 compound to study its possible magnetic structure. We have shown that the previously reported magnetic structures cannot satisfactorily describe our low temperature Mössbauer spectra. Therefore, in combination with theoretical calculations, we have proposed a modulated helicoidal magnetic structure that can be used to simulate the whole series of our low temperature Mössbauer spectra. Our results suggest that the combination of previously reported different magnetic structures are only approximations of the average magnetic structure from our modulated helicoidal model. We anticipate that the proposed modulated non-collinear magnetic structure might shed light on the understanding of the complex magnetoelectric effects observed in this system.

Interplay between magnetic excitations and plasticity in body-centered cubic chromium

The effect of finite-temperature magnetic excitations on the plasticity of body-centered cubic chromium is studied. In chromium, the magnetic order is disrupted by the $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ Burgers vectors of dislocations, creating magnetic frustrations partially resolved through the generation of magnetic faults. These faults may bear consequences on plasticity, the controlling parameter being their energy. Through the inclusion of finite-temperature magnetic excitations, we show in this work that these faults vanish below the N\'eel temperature, thus leaving $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ dislocations free to move. When the faults have disappeared, complex noncollinear magnetic structures are stabilized, surrounding the region sheared by these dislocations, with a negligible excess magnetic energy.