Single-Ion Anisotropy-Stabilized Short-Period Helimagnetism in Frustrated Chiral Co<sub>5</sub>TeO<sub>8</sub>

Single-Ion Anisotropy-Stabilized Short-Period Helimagnetism in Frustrated Chiral Co₅TeO₈

PDF

Priya R. Baral¹^,²^,³^,^*, Ravi Yadav³, Victor Ukleev²^,⁴, Thomas LaGrange³, Ivica Živković³, Wen H. Bi³, Marek Bartkowiak², Robert Cubitt⁵, Nina-Juliane Steinke⁵, Vladimir Pomjakushin², Yurii Skourski⁶, Henrik M. Rønnow³, Oleg V. Yazyev³, Arnaud Magrez³, Jonathan S. White²^,^*

Research. Vol 9 Article ID 1334

Less

Research. Vol 9 Article ID 1334

• RESEARCH ARTICLE •

Single-Ion Anisotropy-Stabilized Short-Period Helimagnetism in Frustrated Chiral Co₅TeO₈

Full

Affiliations

¹Department of Applied Physics and Quantum-Phase Electronics Center, The University of Tokyo, Tokyo 113-8656, Japan.

²PSI Center for Neutron and Muon Sciences, 5232 Villigen PSI, Switzerland.

³Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

⁴Helmholtz-Zentrum Berlin für Materialien und Energie, D-12489 Berlin, Germany.

⁵Institut Laue–Langevin, Grenoble 38000, France.

⁶Dresden High Magnetic Field Laboratory (HLD-EMFL), 01328 Dresden, Germany.

Published: 2026-06-20 doi: 10.34133/research.1334

Outline

Abstract

Less

Chiral spin textures in magnetic insulators promise magneto-electric (ME) spintronics with orders-of-magnitude lower power consumption than metallic systems. However, realizing the short magnetic periods required for high-density device integration remains difficult, as conventional Dzyaloshinskii–Moriya interaction (DMI)-based mechanisms typically constrain spiral periods to tens of nanometers. While theory predicts that strong single-ion anisotropy (SIA) on frustrated lattices can stabilize complex non-coplanar textures, the potential for using this mechanism to engineer such compact textures remains largely unexplored. Here, we report that a cubic chiral insulator Co₅TeO₈ provides an experimental example of this paradigm. Comprehensive neutron scattering and magnetometry reveal helimagnetic spirals with continuously tunable pitch of 5.7 to 10 nm embedded in a complex phase diagram spanning 8 distinct phases. Capacitance anomalies throughout the phase diagram indicate ME coupling, pointing to the possibility of future E-field control of these textures. The temperature and field dependence of the helical wavevector strongly support a scenario in which site-dependent SIA provides the leading contribution to the selection of the helical period from a frustration-induced degenerate manifold. Consistent with this interpretation, ab initio calculations place SIA approximately an order of magnitude above DMI, distinct from conventional helimagnets. Co₅TeO₈ thus offers an experimental realization of sub-10-nm helimagnetism and motivates a design principle for anisotropy-engineered correlated insulators.

Cite this Article

Priya R. Baral, Ravi Yadav, Victor Ukleev, Thomas LaGrange, Ivica Živković, Wen H. Bi, Marek Bartkowiak, Robert Cubitt, Nina-Juliane Steinke, Vladimir Pomjakushin, Yurii Skourski, Henrik M. Rønnow, Oleg V. Yazyev, Arnaud Magrez, Jonathan S. White. Single-Ion Anisotropy-Stabilized Short-Period Helimagnetism in Frustrated Chiral Co₅TeO₈[J]. Research, 2026 , 9 (6) : 1334 - . DOI: 10.34133/research.1334

Full Text

Less

Introduction

Less

Non-coplanar magnetic states—ranging from topological skyrmions to chiral vortex lattices—are central to modern spintronics owing to their emergent electrodynamics and robust stability against weak perturbations [1–4]. Yet, these intricate multi-Q architectures typically nucleate from a more fundamental parent phase: the single-Q spiral state [5,6]. As the elementary building block of non-coplanar magnetic states, the single-Q spiral emerges when competing interactions preclude collinear spin alignment [7,8], making a microscopic understanding of its stability essential for engineering complex topological phases [9,10]. Conventionally, this stability is attributed to specific exchange pathways governed by crystal symmetry and electronic structure of the material: the anti-symmetric Dzyaloshinskii–Moriya interaction (DMI) in chiral noncentrosymmetric hosts [11–13], geometric frustration [14,15] or Fermi-surface-nested Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions in centrosymmetric systems [16,17], and, in itinerant magnets, higher-order terms such as the biquadratic exchange interaction [18,19]. Crucially, while these diverse mechanisms successfully predict a wide array of noncollinear magnetic phases, they share a common paradigm in which spatial modulation is driven primarily by intersite exchange, with local energy scales typically treated as subleading.

Conversely, magnetic anisotropy—traditionally treated as a weak perturbative correction—can fundamentally restructure the magnetic energy landscape when its magnitude rivals the exchange energy scales [20–22]. In isotropic Heisenberg models, single-Q helices are generically favored as a simple harmonic modulation preserves the fixed-moment constraint, whereas multi-Q superpositions tend to generate amplitude modulations that require higher harmonics to restore normalization. However, this exchange cost can be offset by strong easy-axis single-ion anisotropy (SIA), which, aided by thermal softening of the longitudinal spin stiffness [20], promotes multi-Q formation. On frustrated lattices, this mechanism stabilizes a hierarchy of exotic phases, including the skyrmion lattice [23]. Moreover, in multi-sublattice magnets, inequivalent SIA tensors can compete with the leading exchange to promote noncollinearity [24], yet experimental realizations of anisotropy-dominated helimagnets remain elusive.

Here, we combine comprehensive experimental characterization with first-principles calculations to investigate helimagnetism in chiral Co₅TeO₈. Our density functional theory (DFT) calculation predicted a 127-meV charge-transfer gap, motivating the synthesis and investigation of its magnetic properties. Using magnetic and thermodynamic probes, we constructed a high-resolution multi-phase diagram consisting of 8 different phases. In addition, we employ neutron scattering, high-field magnetometry, and capacitance measurements to map this magnetic landscape and characterize compact field-tunable helical textures. These experiments indicate that site-dependent SIA, rather than DMI, is the leading interaction governing the stabilization of the helical state—a scenario further supported by ab initio many-body wavefunction calculations. Together with the experimental observations, these results suggest a framework for engineering compact magnetic textures in correlated oxides, with potential implications for magneto-electric (ME) spintronics.

Results

Less

Strong electronic correlations in Co₅TeO₈

To search for magnets with enhanced SIA, we turned our attention to Co-based systems, targeting spinel-type Co₅TeO₈. Although its magnetic ground state depends on structural polymorphism [25], we focused on the chiral cubic phase (P4₁32/P4₃32), where geometric frustration and broken inversion symmetry enable complex magnetic textures. The combination of these structural features with Co₅TeO₈’s partially filled d-orbitals, likely involving strong electronic correlations, motivated us to investigate its electronic structure.

To assess the metallic versus insulating character of its electronic structure, we performed DFT calculations within the local density approximation (LDA) + U framework, using the experimental crystal structure (see Fig. 1A). The LDA + U approach, incorporating on-site Coulomb repulsion via a Hubbard U parameter, has successfully reproduced band gaps in Mott insulators such as Na₂IrO₃ [26]. For Co₅TeO₈, while standard LDA predicts metallic behavior, introducing U = 3 eV opens a charge-transfer gap of 127 meV at the Γ-point (Fig. S1), a result robust to the choice of U. The predominant d-character of the bands near the Fermi energy indicates strong electronic correlations, implying sensitivity to external fields and potential ME coupling.

To explore magnetism of Co₅TeO₈, we synthesized a high-quality microcrystalline sample and performed comprehensive structural characterization. Structural analysis confirms that Co₅TeO₈ crystallizes in the chiral space group P4₃32 (or its enantiomorph P4₁32), with both inequivalent magnetic Co sites adopting a 2+ oxidation state as confirmed from electron energy loss spectroscopy (EELS) measurements (Section S2). Further structural details are provided in Section S1. The Co1 sublattice (12d sites) forms corner-sharing triangular motifs that interconnect with Co2 ions (8c sites) to complete a 3-dimensional framework of corner-sharing tetrahedra. This geometry generates strong magnetic frustration where competing exchange interactions between the 2 sublattices may suppress conventional magnetic order [27]. The combination of strong electronic correlations on the chiral frustrated lattice establishes Co₅TeO₈ as a platform for hosting nontrivial magnetic textures. As we demonstrate in the following sections, localized 3d electrons in Co₅TeO₈ enable tunable magnetic phenomena with a rich phase diagram.

Complex field-tunable magnetic phase diagram

High-resolution magnetometry reveals a complex magnetic energy landscape in Co₅TeO₈ with multiple phase transitions, as shown in Fig. 1C. The real component of ac susceptibility (

χ ac ′

) exhibits a sharp peak at 44.9 K (T_HM), indicating onset of long-range magnetic order in phase I (see Fig. 2A). This transition displays clear dissipative character, as evidenced by a corresponding peak in imaginary susceptibility (

χ ac ′ ′

). Below T_HM, 2 additional hysteretic regions emerge at

T hys 1

and

T hys 2

, consistently observed in both ac susceptibility and dc magnetization. Applied magnetic fields cause these transitions to converge and shift toward T_HM (Fig. 2C and Section S3), suggesting renormalization effects similar to skyrmion lattice hosts [28–30].

Heat capacity measurements reveal contrasting thermodynamic signatures. While magnetometry shows pronounced features at all 3 transitions, heat capacity exhibits only weak anomalies at T_HM and

T hys 2

, with no discernible signature at

T hys 1

(see Fig. 2B). This suppressed response despite clear magnetic signatures suggests minimal entropy changes governed by persistent short-range correlations, previously identified in Ref. [25]. Field-dependent magnetometry data reveal pronounced metamagnetic transitions below T_HM, becoming increasingly steeper at lower temperatures with broadened hysteresis, as shown in Fig. 2D. These field-driven responses coincide with sharp anomalies in electrical capacitance (Fig. 2E, inset, and Section S3), confirming ME coupling in Co₅TeO₈, which is crucial for functional control. Remarkably, magnetic saturation is absent even at 60-T pulsed fields (Fig. 2E), presumably reflecting frustration in the strongly-coupled tetrahedral framework where competing exchanges prevent forced ferromagnetic alignment [31]. This intricate behavior necessitates comprehensive neutron scattering to resolve the underlying magnetic structure.

Compact spiral order revealed by neutron scattering

To uncover the magnetic structure in Co₅TeO₈, we performed powder neutron diffraction (PND) measurements. Just below T_HM, magnetic satellites emerge around (h,h,h) and (h,h,0) nuclear reflections (see Fig. 3A), characterized by incommensurate propagation vectors

Q IC 1 a

= G₁₁₁ ± q⁽¹⁾ = G₁₁₀ ± q⁽¹⁾, consistent with a previous report [25]. Notably, no magnetic satellites appear around G_h00 reflections within instrumental resolution. The systematic absences of (h,0,0) reflections (h ≠ 4n) confirm that the 4₁ (or 4₃) screw symmetry of the parent space group is retained, although overall cubic magnetic symmetry is broken by incommensurate modulation.

Small-angle neutron scattering (SANS) measurements provide complementary information about the magnetic order. Due to powder averaging, the discrete incommensurate Q-vectors manifest as ring-like scattering patterns on the 2-dimensional multidetector. Figure 3B and C show data at 44 and 2 K, respectively. The ring-like scattering centered at the Γ-point corresponds to

Q IC 1

with |Q| = 0.903(2) nm⁻¹ at T_HM and

Q IC 2

with |Q| = 1.1(1) nm⁻¹ below

T hys 2

(Fig. 3D). The corresponding pitch length at 2 K is λ_h = 5.71 ± 0.51 nm, increasing with temperature from λ_h (T_HM) = 6.96 ± 0.02 nm to λ_h (

T hys 1

) = 9.66 ± 0.15 nm. These compact magnetic periodicities are among the shortest reported in chiral insulator magnets. See Table 1 for a thorough comparative list of most-relevant noncentrosymmetric magnets. However, the unpolarized neutron scattering measurements alone cannot distinguish between different spiral helicities. To determine whether these ultracompact spirals adopt proper-screw or cycloidal character, we performed polarization-analyzed SANS measurements as described in the following section.

Bloch-type modulation deduced from polarized SANS

Having established the compact spiral order, we performed uniaxial polarization-analyzed SANS to determine the helical spin texture. A schematic of the experimental setup is shown in Fig. 3E. The incoming neutron polarization vector is aligned (or anti-aligned) with the neutron beam. Non-spin-flip (NSF) and spin-flip (SF) scattering cross-sections are probed using a spin state analyzer placed between sample and detector. This configuration enables the decomposition of the magnetic interaction vector m_⊥(Q) into components defined by the polarization axis. The NSF cross-section isolates the projection of m_⊥(Q) parallel to the initial polarization P_i (as indicated in Fig. 3E), whereas the SF channel is sensitive to the component simultaneously orthogonal to both P_i and Q. Consequently, for a helimagnetic spiral characterized by moments distributed isotropically in the plane normal to Q, the scattering intensity is expected to be equally distributed between the NSF and SF channels. In contrast, for an easy-plane cycloidal structure with moments confined to the Q–x (or Q–z) plane, the magnetic scattering is expected to appear exclusively in the NSF (or SF) channel, respectively. See Ref. [32, 33] for more details. Since the ring-like scattering pattern (Fig. 3F) represents a superposition of multiple magnetic domains, each angular segment provides equivalent information about NSF and SF cross-sections, enabling systematic analysis across different Q-vector orientations.

Analysis of polarized SANS data at 40 K shows nearly equivalent intensities in both NSF and SF channels for phase I (Fig. 3G). This balanced contribution indicates that magnetic Fourier components lie predominantly in the plane perpendicular to Q with comparable amplitudes in both horizontal and vertical directions, consistent with helimagnetic spiral arrangement (schematic shown in inset of Fig. 3G). The helicity is retained down to

T hys 2

as deduced from equal NSF-SF intensities (Fig. 3H). More detailed analysis using narrower sector boxes reproduces the same result (Section S4). While helical modulation is expected due to the chiral crystal structure, the unusually short magnetic period sharply differentiates Co₅TeO₈ from archetypal DM-stabilized helimagnets [34–36]. Having confirmed the Bloch-type helical character, we next investigate how applied magnetic fields modify the helical pitch and induce phase transitions, as revealed by field-dependent SANS measurements.

Field-driven transformation of the helimagnetic spiral

To investigate the magnetic field response of the incommensurate phases, we systematically tracked the evolution of

Q IC 1

under applied transverse magnetic fields (μ₀H ⊥ k_i) using SANS. Starting from zero-field ring-like scattering at 36 K in phase I (Fig. 4A), applied magnetic field gradually transforms the ring into an intermediate phase characterized by arcs of scattering (Fig. 4B) before entering a well-defined conical phase at higher fields (Fig. 4C). The conical phase is clearly identified by a pair of spots with propagation vectors aligned parallel and antiparallel to the applied field, consistent with other cubic helimagnets [34,35]. Further field increase suppresses incommensurate satellites above 2.5 T, leading to field-polarized magnetic order. Notably, the absence of scattering intensity in sectors perpendicular to the applied field (around Ψ = 0° or 180° in Fig. 4D and teal sector box in Fig. 4E) definitively excludes formation of the conventional multi-Q skyrmion lattice observed in other chiral cubic magnets.

The intermediate phase (phase II) exhibits distinctive characteristics revealing complexity of underlying magnetic interactions. Unlike the conical phase with monotonic peak-width decay, the intermediate phase maintains nearly constant azimuthal intensity distribution across its stability range (Fig. 4E, inset). This behavior suggests stabilization of a multi-domain incommensurate structure with Q-vectors distributed between 〈110〉 and 〈111〉 directions, with the field only partially selecting preferred orientations. Remarkably, the incommensurate wavevector magnitude |Q⁽¹⁾| increases systematically with applied field (see Fig. 4F), indicating that the spiral shortens under field rather than collapsing into ferromagnetic-type alignment. This field-driven reduction of helical pitch is rare among DMI-stabilized helimagnets, necessitating ab initio wavefunction-based calculations to understand microscopic magnetic interactions.

SIA-dominated magnetic energy landscape

The Co–O coordination geometries in Co₅TeO₈ deviate significantly from ideal octahedral and tetrahedral environments with ∠Co1–O–Co1 and ∠Co2–O–Co2 bond angles of 94.51(1)° and 116.77(1)°, respectively. These distortions make prediction of exchange interactions via Goodenough–Kanamori–Anderson rules challenging, thus requiring explicit quantum chemistry calculations. Hence, we employed electrostatically embedded finite-size clusters extracted from the experimental crystal structure (see Fig. 1A), an approach well-suited for strongly correlated d-electron systems with highly localized electronic states [37–42]. We used the following spin Hamiltonian encompassing both on-site and intersite magnetic interactions:

H = ∑ i j = 1, 2 J ij S i · S j + K i j S i · S j 2 + D ij · S i × S j + ∑ i A i S i · e ̂ i 2

(1)

The summation 〈i, j〉 runs over all nearest-neighbor bonds. The exchange parameters: bilinear (

J

_ij), biquadratic (

K

_ij), and antisymmetric DM interaction vectors (

D

_ij (11, 12)) are bond-type-dependent, taking 3 distinct sets of values corresponding to Co1–Co1 (

J

₁₁,

K

₁₁,

D

₁₁), Co2–Co2 (

J

₂₂,

K

₂₂,

D

₂₂), and Co1–Co2 (

J

₁₂,

K

₁₂,

D

₁₂) bonds, as shown in Fig. 1A.

A

_i is the SIA coefficient for site i, where

e ̂

_i represents the site-dependent anisotropy axis. Further details about our quantum chemistry calculations can be found in the Methods section and Section S5.

We find that all 3 bilinear exchange pathways are antiferromagnetic with

J

₁₁ = 0.116 meV,

J

₂₂ = 0.088 meV, and

J

₁₂ = 0.208 meV (see Table S2), at least 20 times weaker than the thermal energy scale (k_BT_HM ∼ 3.9 meV) associated with T_HM, suggesting that the bilinear exchanges alone underestimate the long-range ordering temperature. The biquadratic interactions, in turn, are ferromagnetic-type with

K

₁₁ = −8.4 μeV,

K

₂₂ = −1.11 μeV, and

K

₁₂ = −3.2 μeV, representing 5% to 8% of the corresponding bilinear strengths. Remarkably, the Co1–Co1 bonds exhibit exceptionally large DMI, with |

D

| = 0.099 meV yielding |

D

J

| ≃ 0.84, atypical for insulating chiral oxides, while Co2–Co2 bonds show negligible DMI (|

D

J

| ≃ 0.03) and Co1–Co2 bonds display intermediate values (|

D

J

| ≃ 0.102). As schematically shown in Fig. 1B, the calculated SIA constants are site-dependent, with

A

₁ = −2.1 meV (easy-axis along [111] for Co1 at 12d sites) and

A

₂ = 3.1 meV (xy-easy-plane for Co2 at 8c sites), representing the dominant energy scale, approximately 10 to 15 times larger than exchange interactions. In the absence of strong anisotropy in a single sublattice system without interaction, the canonical DMI helimagnet relation λ_h = 4π

J

D

predicts λ_h ≃ 5.3 nm for Co1–Co1, coincidentally close to the observed range of 5.7 to 9.6 nm across the temperature-dependent phases. The same relation predicts λ_Co1–Co2 ≃ 45 nm and λ_Co2–Co2 ≃ 109 nm, both incompatible with experimental observations. The calculated energy hierarchy

A

≫

J

D

≫

K

, combined with competing antiferromagnetic exchanges on the 2-sublattice spinel-like structure, identifies Co₅TeO₈ as a frustrated magnetic system in which the SIA exceeds the exchange and DMI. In this regime, frustration and DMI drive the underlying finite-Q instability and chirality, while the dominant site-dependent SIA is proposed to lift the directional degeneracy and to favor a propagation vector selected from the otherwise nearly degenerate manifold.

This counterintuitive strong SIA can be traced to the electronic structure of high-spin Co²⁺ (d⁷, S = 3/2) in distinct local environments. For the octahedral Co1 sites (12d,

t 2 g 5 e g 2

), the incompletely filled t_2g manifold is expected to retain unquenched orbital angular momentum, in contrast to either fully filled or half-filled configurations. The Co1 octahedron exhibits a local ⟨111⟩-oriented distortion where the 6 Co–O coordinations comprise 2 short (2.01 Å), 2 intermediate (2.14 Å), and 2 long (2.17 Å) bond lengths, with the 2 short bonds subtending an expanded angle of 97.3° and the 2 long bonds subtending a contracted angle of 86.3°, consistent with compression along the pseudo-3-fold axis. This distortion splits the parent ⁴T_1g term into ⁴A_2g and ⁴E_g components in D_3d symmetry. Mixed with spin-orbit coupling, this split manifold produces zero-field splitting of the S = 3/2 states with easy-axis character along the compression direction, yielding in our calculation

A

₁ = −2.1 meV [43,44]. In contrast, the tetrahedrally coordinated Co2 (8c sites,

e g 4 t 2 g 3

) presents a distinct scenario. The ⁴A₂ ground term of tetrahedral Co²⁺ is an orbital singlet with no first-order orbital angular momentum. Nevertheless, Co2 occupies a trigonally compressed tetrahedron (C_3v symmetry) with one short Co–O bond (1.91 Å) along the 3-fold axis and 3 longer bonds (2.02 Å), yielding O–Co–O angles of 106.6° and 112.2°. This distortion modifies both the energies and symmetries of the excited-state manifold (primarily ⁴T₂) that couples to the ground state via spin-orbit interaction. Our ab initio calculations indicate that this second-order mechanism produces easy-plane anisotropy (

A

₂ = 3.1 meV), whose magnitude appears to be enhanced by covalent mixing with heavy tellurium ligands. This overlap is expected to increase the effective spin-orbit coupling at Co2 sites and amplifies these second-order contributions despite the absence of first-order orbital effects. The insulating state with persistent correlations in Co₅TeO₈ is likely essential for preserving this strong SIA. In itinerant systems, electron delocalization into broad conduction bands quenches orbital angular momentum and averages over local distortions, substantially reducing magnetic anisotropy. This suppression is evidenced by the 4-fold reduction in near-metallic CoV₂O₄ compared to the wider-gap isostructural Mott insulator MnV₂O₄, where electron localization preserves the orbital physics [45–47]. The combination of Te-induced distortions at both Co sites, unquenched orbital moments at Co1, heavy-ligand spin-orbit enhancement at Co2, and Mott localization preserving the local electronic structure is proposed to produce the dominant site-dependent SIA.

Discussion

Less

The microscopic origin of sub-10-nm helimagnetism in Co₅TeO₈ presents a compelling materials physics puzzle: In the absence of strong anisotropy, canonical DMI helimagnets achieve λ_h ∼ 18 to 130 nm, yet Co₅TeO₈ realizes λ_h ∼ 5.7 to 9.6 nm despite only moderately enhanced |

D

J

| compared to archetypal chiral magnets (e.g., MnSi ∼ 0.12 [48]; Cu₂OSeO₃ ∼ 0.04 to 0.58 [31]). Our ab initio calculations point to a different mechanism in which site-dependent SIA, an order of magnitude larger than all exchange interactions, provides the leading energy scale. Three competing antiferromagnetic exchanges on the 2-sublattice structure create geometric frustration, producing a nearly flat E(Q) landscape over 0.8 to 1.3 nm⁻¹. Within this degenerate manifold, dominant SIA is proposed to select the helical wavevector through Q-dependent orientational averaging, where shorter wavelengths reduce anisotropy penalties by allowing larger intersite spin canting that better accommodates the conflicting easy-axis (Co1) and easy-plane (Co2) local environments. While the canonical λ_h = 4π

J

D

relationship using Co1–Co1 parameters coincidentally predicts λ_h ∼ 5.2 nm, this numerical agreement may mask distinct physics: Large DMI creates the helical instability and establishes chirality, but we argue that SIA provides the leading contribution to wavelength selection within the frustrated landscape. This SIA-selection mechanism is supported by T- and H-dependent neutron scattering data, detailed below. Additionally, weak ferromagnetic-type biquadratic interactions (5% to 8% of bilinear strength) lift residual degeneracies within the frustrated Q-space manifold and provide energy barriers between competing helical variants, enabling sharp phase transitions and hysteretic behavior. Although individual exchange bonds are modest, the experimentally observed T_HM is driven by collective stabilization from the full frustrated lattice and strong anisotropy, as captured by mean-field analysis (Section S5). This mechanism is intrinsically tied to the predicted insulating ground state with strong electronic correlations, which favors the localized orbital physics underlying the enhanced SIA while maintaining sufficient correlation strength to generate competing exchange pathways. In summary, Co₅TeO₈ thus appears to realize a DMI-initiated, SIA-enhanced, frustration-enabled compact helimagnet and may serve as a prototype for a class of anisotropy-dominated helimagnets in strongly correlated insulators.

Another indication of SIA dominance emerges from the field dependence of the helical wavevector. Co₅TeO₈ exhibits field-driven compression (dQ/dH > 0 as shown in Fig. 4F), not what is expected from canonical DMI helimagnets for which the modulation period is typically field independent to first approximation. In Co₅TeO₈, the field reorients the spin configuration, and on the frustrated 2-sublattice landscape, this favors shorter helical pitches that better accommodate the conflicting easy-axis (Co1) and easy-plane (Co2) environments. This distinctive field response is difficult to reconcile with a purely DMI-controlled wavelength selection and is most naturally explained if SIA provides the leading contribution. The synergy between frustration and SIA manifests dramatically in high-field magnetization, which fails to saturate even at 60 T (E_Zeeman ∼ 10.4 meV), as shown in Fig. 2E. This nonsaturation arises from geometric frustration creating competing exchange fields that reduce the effective molecular field, while calculated SIA barriers (∼24 T for Co1, ∼36 T for Co2) must be overcome to fully polarize spins. The contrasting anisotropy character of the 2 sublattices, combined with competing interactions, underlies the rich 8-phase magnetic diagram, where phase boundaries reflect competition between helical wavevector selection, rotation plane orientation, and Co1–Co2 sublattice coupling. Further experiments on Co₅TeO₈ single crystals combined with theoretical modeling are required to validate these points.

The SIA-dominated mechanism is further supported by 2 distinct temperature-induced features. First, at T_HM, long-range helical order emerges with a temperature-dependent wavevector |Q(T)| that evolves as thermal fluctuations partially quench the effective anisotropy. Second, upon cooling through a first-order lock-in transition at T_lock (=

T hys 2

∼ 25 K) exhibiting substantial thermal hysteresis (Fig. 2A), the helical period becomes temperature independent and rigidly fixed at λ_h = 5.7 nm. The energy scale k_BT_lock ∼ 2.15 meV is comparable to the calculated Co1 single-ion barrier

A

₁ (also naturally lower than

A

₂), suggesting that reduction of thermal energy below this scale may trigger the transition and pins the system in the SIA-optimized configuration. This 2-transition phenomenology bears striking similarity to the archetypal Ising chain material CoNb₂O₆, which also exhibits an incommensurate–commensurate lock-in [49], but with a fundamental mechanistic difference. In CoNb₂O₆, ultra-strong crystal-field splitting (∼30 meV) quenches the spin to S_eff = 1/2 and rigidly locks spin directions along a single axis, permitting only amplitude modulation of collinear ferromagnetic chains in the intermediate phase; lock-in is then driven by weak interchain coupling, occurring at an energy scale much smaller than the crystal-field splitting. In contrast, Co₅TeO₈’s moderate SIA preserves S = 3/2 and permits continuous spin rotation, resulting in helimagnetic spiral, with lock-in occurring at T_lock ∼

A

₁/k_B via anisotropy saturation rather than interchain coupling. The hysteretic first-order character in Co₅TeO₈ points to an energy landscape with multiple metastable Q-states separated by nucleation barriers, consistent with the frustrated E(Q) manifold. Above T_lock, the system occupies a thermally accessible “soft” Q-state with broader distribution, while below T_lock, it nucleates into a “locked” Q-state with narrow, rigid distribution. This comparison supports the picture of SIA-dominated helical behavior with sufficient DMI and frustration in Co₅TeO₈, fundamentally distinct from DMI-controlled systems with monotonic changes in helical period [50].

The calculated anisotropy in Co₅TeO₈ places it in an intermediate regime within the broader landscape of chiral magnetism. At one extreme, archetypal cubic chiral magnets with weak magnetocrystalline anisotropy preserve near-degeneracy among multi-Q propagation vectors, enabling continuous Q(T) evolution and field-stabilized skyrmion lattices; metallic MnSi, Fe_1-xCo_xSi, and the insulating Cu₂OSeO₃ exemplify this regime. At the opposite extreme, CoNb₂O₆’s ultra-strong anisotropy restricts magnetic modulation to amplitude fluctuations of collinear order, suppressing all noncollinear textures and enforcing rigid uniaxial Ising behavior. Co₅TeO₈ lies between these limits where site-dependent SIA dominates exchange by at least an order of magnitude, yet remains small enough in absolute terms to preserve unquenched S = 3/2 and permit continuous spin rotation. Unlike weak-anisotropy systems where higher-harmonic coupling enables multi-Q states [23], the dominant SIA in Co₅TeO₈ strongly penalizes spin textures that deviate from locally optimized easy axes defined by the chiral crystal structure. A multi-Q superposition, which inherently requires spins to point in nearly isotropic directions to satisfy multiple wavevectors, incurs higher anisotropy cost compared to a single-Q helix that can coherently adapt its phase to the local anisotropy axes [21]. Consequently, the system is driven toward a single-Q harmonic state, effectively “locking” the magnetic texture to the structural chirality and suppressing complex multi-Q topologies. The lock-in transition and field-driven helix compression described above are absent in weaker-anisotropy systems, consistent with SIA playing the leading role. The β-Mn-type Co₈Zn₈Mn₄, with comparable DMI but weaker anisotropy, provides direct comparison, as it exhibits a longer λ_h (Table 1) while retaining skyrmion phases, supporting the role of SIA in suppressing multi-Q skyrmion phases [51]. These findings suggest a transferable design principle: Systematically weakening SIA through selective dilution or enhancing DMI via heavier 4d/5d element substitution at Co²⁺ sites could generate skyrmion derivatives in isostructural compounds. More broadly, Co₅TeO₈ exemplifies how strong single-ion terms in frustrated geometries expand the accessible magnetic texture space beyond DMI paradigms, motivating exploration of anisotropy-engineered noncollinear states in other frustrated pyrochlore and spinel oxides with heavy transition metals. We note, however, that the present polycrystalline measurements do not permit a direct experimental determination of the full anisotropy tensor; accordingly, the microscopic interaction values should be viewed as semiquantitative estimates whose main importance lies in the inferred energy-scale hierarchy.

Our work establishes Co₅TeO₈ as a magnetic insulator hosting a short-period helical ground state, with calculations indicating the presence of strong electronic correlations. The stabilization mechanism is proposed to arise from a distinctive competition between site-dependent SIA, DMI and frustration, unlike that seen in archetypal cubic helimagnets. Our results suggest a design principle that links the local coordination geometry to the nanoscale spin texture. The interplay between SIA and DMI proposed here broadens the search for short-period helimagnets beyond compounds stabilized by DMI alone, extending it to material classes with weak to moderate anisotropy. Mixed coordination structures, such as Co-based chalcogenide spinels and β-Mn-type compounds, are therefore natural candidates for systematic exploration of this mechanism. The short-period helical texture itself may find practical use in 3 areas: first, in high-frequency nano-oscillators, where the insulating ground state avoids eddy-current losses and the antiferromagnetic background cancels the Magnus force, both favoring dynamical stability [52]; second, in reservoir computing, where the 2 crystallographically distinct Co sites could provide additional nonlinear degrees of freedom compared with single-sublattice magnetic domains [53]; third, in ME switching, where the insulating ground state allows electric field rather than current-driven control—an advantage for device miniaturization, contingent on sufficiently large ME tensor elements in Co₅TeO₈ [54]. Quantitative measurement of the Mott gap and the ME coefficients will therefore be needed to assess the practical viability of voltage-controlled manipulation of the helices. Further experiments to resolve the magnon band structure of these compact helices [55], to probe nonreciprocal thermal transport arising from broken inversion symmetry [56], and to measure electric field-driven phase transitions [57] would clarify the functional potential of Co₅TeO₈ and related materials for low-dissipation spintronics. More broadly, this work suggests that competing anisotropies between inequivalent magnetic sites, usually regarded as detrimental to magnetic order, can instead serve as a design principle for engineering compact spin textures in correlated insulators.

Materials and Methods

Less

Density functional theory calculations

Density functional theory calculations were performed using the Vienna Ab-initio Simulation Package (VASP) [58]. Electron-core interactions are described using the projector-augmented wave method [59], while the Kohn–Sham wavefunctions for the valence electrons were expanded in a plane wave basis with a cutoff on the kinetic energy of 400 eV. LDA + U calculations were performed within the local density approximation framework with a Coulomb on-site repulsion U = 3 eV acting on the d shell of Co atoms following the rotationally invariant scheme proposed by Dudarev et al. [60]. The calculations included spin-orbit coupling and noncollinear magnetism to capture the essential magnetism of Co₅TeO₈. The cubic cell (a = 8.535 Å) had 56 atoms, and the Brillouin zone sampling used 100 k-points with the Methfessel–Paxton smearing (width 0.01 eV). The intrinsic C₃ symmetry of the system was utilized, and static single-point energy calculations were performed without ionic relaxation. It should be noted that residual self-interaction errors inherent to LDA often result in slight underestimation of band gaps in systems with localized 3d electronic states. Thus, we may expect a slightly larger band gap in reality.

Microcrystalline sample preparation

The pure phase microcrystalline Co₅TeO₈ sample was synthesized using conventional solid-state reactions. Stoichiometric amounts of CoCO₃ (Aldrich, 99.999%) and TeO₂ (Aldrich, 99.999%) were thoroughly mixed using a mortar. The resultant mixture was transferred to a platinum crucible and placed inside a high-temperature muffle furnace. The temperature of the furnace was slowly raised to 1000 °C at a rate of 100 °C per hour. The furnace was then dwelled for an hour at that temperature, followed by increasing the temperature to 1100 °C at a slower rate of 50 °C per hour. The powder was then sintered at this temperature for 72 h, followed by quenching to room temperature. The quenching process was necessary to avoid co-crystallization of Co₃O₄ spinel. Results presented throughout this article were obtained on the same batch of microcrystalline sample.

Single-crystal x-ray diffraction

Microcrystalline Co₅TeO₈ grains with suitable size were mounted onto the goniometer head with cryo-loop obtained from MiTeGen, followed by installing on an Agilent SuperNOVA single-crystal diffractometer, equipped with Cu/Mo sealed tube x-ray source and an Atlas charge-coupled device detector. The temperature of the setup was controlled by an Oxford Cryostream 800 Plus system.

Electron backscatter diffraction and energy-dispersive x-ray spectroscopy measurements

We performed 2 electron backscatter diffraction (EBSD) and energy-dispersive x-ray spectroscopy (EDX) experiments. For the first experiment, Co₅TeO₈ particles were distributed over a silver-pasted stub, and EBSD spectra were collected using a field emission gun (FEG) scanning electron microscope (SEM) Zeiss Gemini 450 equipped with Oxford Instruments UltimMax EDX detector and CMOS EBSD Symmetry camera. Data acquisition was performed with the AZtec system, and subsequent processing utilized the AZtecCrystal software suite. In the second experiment, Co₅TeO₈ particles were embedded in resin and cured at 180 °C for 5 min. Prior to EBSD and EDX analysis on the same specimen, a thin carbon layer was deposited in order to reduce the electron irradiation-induced charging effects.

Magnetometry, heat capacity, and capacitance measurements

DC magnetization as well as AC susceptibility measurements were performed using the VSM and ACMS-II option of a commercial Quantum Design (QD) 14 T Physical Property Measurement System (PPMS), as well as a Magnetic Property Measurement System (MPMS), MPMS3 from QD. The polycrystalline sample was enclosed in a standard polypropylene holder provided by QD. High-field magnetization experiments were performed in pulsed magnetic fields up to μ₀H = 60 T at the Dresden High Magnetic Field Laboratory, which were normalized to laboratory measurements up to μ₀H = 14 T.

Specific heat measurements were performed on a pelletized sample. In order to produce a pellet with higher structural stability, microcrystalline sample was first crushed in a mortar for about 5 min. The diameter and height of the disc-shaped pellet were made to be 3 and 0.5 mm, respectively. Measurements were performed using the Heat Capacity option of the 14 T PPMS, in the typical relaxation method. The pellet was mounted on the 3 × 3 mm² sapphire plate provided by QD. Apiezon-N grease was used to ensure good thermal contact between the sample and the platform. Later, the long-pulse technique was also used to measure the sample heat capacity.

Capacitance measurements were performed on a pressed Co₅TeO₈ pellet of size 5 × 5 × 0.5 mm³, using an AH2700A ultraprecision capacitance bridge in zero dc field, and with a 1-kHz excitation and a voltage of 15 V. The sample mount was installed onto 9-T PPMS. Capacitance measurements were performed as a function of magnetic field at fixed temperatures in a sweep mode.

EELS experiment

The experimental determination of the cation oxidation state in Co₅TeO₈ was carried out on a thin lamella prepared from a microcrystalline specimen using focused ion beam (FIB). We used the double aberration corrected, monochromated Titan Themis at the Interdisciplinary Centre for Electron Microscopy (CIME) of École Polytechnique Fédérale de Lausanne (EPFL). We acquired spectrum images (see the Supplementary Materials) in the dual EELS mode, which allowed for calibrating the absolute edge energy position and determining chemical shifts in the edge energies associated with changes in valence. We chose to acquire spectra at dispersions of 0.1 eV/channel and dwell time of 50 ms, which provided high energy resolution and produced well-defined L-edges above background in a single pixel spectrum but limited the electron beam interactions and radiation damage.

Neutron diffraction experiments

Wide-angle neutron powder diffraction measurements were carried out on a polycrystalline Co₅TeO₈ sample using the high-resolution powder diffractometer (HRPT) of the SINQ instrumental suite at Paul Scherrer Institute (PSI). Data were collected in both medium resolution and high-resolution modes, employing neutrons with a fixed wavelength of 2.45 Å. Each measurement was preceded by a 10-min thermal stabilization period to ensure equilibrium, followed by a 2-h acquisition of high-statistics data.

SANS experiments

SANS experiments, without polarization analysis, were carried out using the SANS-I instrument of Swiss Spallation Neutron Source (SINQ) located at the Paul Scherrer Institute (PSI). About 200 mg of microcrystalline sample was mixed thoroughly with a 1:1 mixture of hydrogen-free FC-77 and FC-75 Fluorinert liquid and enclosed in a vanadium can. The Fluorinert freezes upon cooling to cryogenic temperatures, providing a quasi-strain-free matrix that maintains the random zero-field orientations of the sample grains in finite magnetic field. The can was then installed inside a 6.8-T horizontal field magnet. For all of our experiments, neutrons with wavelength 5 Å with a full width at half maximum (FWHM) spread Δλ/λ = 10% were used. The incoming neutron beam was collimated by a distance of 8 m before the sample, whereas the scattered neutrons were collected by a 2-dimensional ³He multidetector placed 3.5 m behind the sample.

Uniaxial polarization analysis was performed using the D33 SANS instrument at the Institut Laue-Langevin (ILL), Grenoble. The polycrystalline Co₅TeO₈ sample was embedded in hydrogen-free glue and encapsulated within a vanadium can. Measurements utilized longitudinal polarization geometry with the incident neutron beam collinear to the applied magnetic field. A weak longitudinal magnetic field of 50 mT was applied to the sample, while a 10-mT guide field maintained the neutron spin quantization axis parallel to the incident beam. Scattered neutrons were analyzed using a spin-polarized ³He cell with maximum polarization of 98.6%. Four neutron spin states (↓↓, ↑↓, ↑↑, and ↓↑) were systematically measured as a function of temperature during cooling. Neutron beam depolarization was monitored at 2-h intervals in the paramagnetic regime (T = 65 K). Data analysis was conducted using GRA_SANSP software [61].

Cluster-based quantum chemistry calculations

We performed many-body wavefunction calculations on electrostatically embedded finite-size cluster models extracted from the experimental crystal structure. The crystallographic unit cell contains 2 distinct Co²⁺ sites: Co1 atoms in distorted octahedral coordination and Co2 atoms in tetrahedral coordination with oxygen ligands, as shown in Fig. 1A. Our computational models feature a central cluster containing 1 or 2 coordination polyhedra, with the active Co²⁺ centers treated using multireference wavefunctions. Adjacent Co polyhedra representing nearest-neighbor environments were included at the Hartree–Fock level to account for local charge distribution effects. Long-range electrostatic interactions were incorporated through an array of point charges fitted to reproduce the crystalline Madelung potential [62]. Electron correlation effects in the central clusters were described using complete-active-space self-consistent-field (CASSCF) and subsequent multi-reference configuration interaction (MRCI) calculations. The MRCI treatment incorporated single and double excitations from the Co²⁺ 3d valence orbitals and the bridging oxygen 2p orbitals. Co²⁺ oxidation states were confirmed through EELS measurements (see Section S2), providing the electronic configuration basis for all quantum chemical calculations. The multiplet structure obtained then entered into spin-orbit calculations to obtain spin-orbit coupled eigenstates and wavefunctions [63].

The generalized spin Hamiltonian considered to determine the local magnetic interactions in Co₅TeO₈ can be expressed as

H = H I + H II,

(2)

where

H

^I denotes the coupling between the ith and jth nearest-neighbor sites bearing spin S_i and S_j, respectively, while

H II

contains the contribution of the interactions within sites of spin S_i. The intersite contribution,

H

^I, reads as

H I = ∑ i j = 1, 2 J ij S i · S j + K i j S i · S j 2 + D ij · S i × S j

(3)

where

J

_ij and

K

_ij are the bilinear and biquadratic isotropic exchange couplings, respectively, and

D

_ij is the antisymmetric DMI vector (11, 12). The intra-site contribution

H

^II takes the following form:

H II = ∑ i A i S i · e ̂ i 2

(4)

Here,

A

_i is the SIA. Further details about our quantum chemistry calculations can be found in Section S5.

References

Less

Fert

, Reyren

, Cros

.Magnetic skyrmions: Advances in physics and potential applications. Nat Rev Mater. 2017;2(7):Article 17031.

Matsui

, Nomoto

, Arita

.Skyrmion-size dependence of the topological Hall effect: A real-space calculation. Phys Rev B. 2021;104(17):Article 174432.

Hamamoto

, Ezawa

, Nagaosa

.Quantized topological Hall effect in skyrmion crystal. Phys Rev B. 2015;92(11):Article 115417.

Kurumaji

, Nakajima

, Hirschberger

, Kikkawa

, Yamasaki

, Sagayama

, Nakao

, Taguchi

, Arima

, Tokura

.Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet. Science. 2019;365(6456):914–918.

Ghimire

, Dally

, Poudel

, Jones

, Michel

, Magar

, Bleuel

, MA

, Jiang

, Mitchell

, et al.Competing magnetic phases and fluctuation-driven scalar spin chirality in the kagome metal YMn₆Sn₆. Sci Adv. 2020;6(51):Article eabe2680.

Baral

, Ukleev

, Živković

, Lee

, Orlandi

, Manuel

, Skourski

, Keller

, Stunault

, Rodríguez-Velamazán

, et al.Fluctuation-driven topological Hall effect in room-temperature itinerant helimagnet Fe₃Ga₄. Nat Commun. 2025;16(1):3898.

Tokura

, Seki

.Multiferroics with spiral spin orders. Adv Mater. 2010;22(14):1554–1565.

Tokura

, Seki

, Nagaosa

.Multiferroics of spin origin. Rep Prog Phys. 2014;77(7):Article 076501.

Nagaosa

, Tokura

.Topological properties and dynamics of magnetic skyrmions. Nat Nanotechnol. 2013;8(12):899–911.

10.

Tokura

, Kanazawa

.Magnetic skyrmion materials. Chem Rev. 2020;121(5):2857–2897.

11.

Dzyaloshinsky

.A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J Phys Chem Solids. 1958;4(4):241–255.

12.

Moriya

.Anisotropic superexchange interaction and weak ferromagnetism. Phys Rev. 1960;120(1):91.

13.

Bak

, Jensen

.Theory of helical magnetic structures and phase transitions in MnSi and FeGe. J Phys C Solid State Phys. 1980;13(31):L881.

14.

Richter

, Darradi

, Schulenburg

, Farnell

, Rosner

.Frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice studied via exact diagonalization and coupled-cluster method. Phys Rev B. 2010;81(17):Article 174429.

15.

Okubo

, Chung

, Kawamura

.Multiple-qstates and the skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields. Phys Rev Lett. 2012;108(1):Article 017206.

16.

Bouaziz

, Mendive-Tapia

, Blügel

, Staunton

.Fermi-surface origin of skyrmion lattices in centrosymmetric rare-earth intermetallics. Phys Rev Lett. 2022;128(15):Article 157206.

17.

Nomoto

, Koretsune

, Arita

.Formation mechanism of the helical Q structure in Gd-based skyrmion materials. Phys Rev Lett. 2020;125:Article 117204.

18.

Hayami

, Ozawa

, Motome

.Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets. Phys Rev B. 2017;95(22):Article 224424.

19.

Batista

, Lin

S-Z

, Hayami

, Kamiya

.Frustration and chiral orderings in correlated electron systems. Rep Prog Phys. 2016;79(8):Article 084504.

20.

Hayami

, Lin

S-Z

, Batista

.Bubble and skyrmion crystals in frustrated magnets with easy-axis anisotropy. Phys Rev B. 2016;93(18):Article 184413.

21.

Hayami

, Motome

.Noncoplanar multiple-Q spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy. Phys Rev B. 2021;103(5):Article 054422.

22.

Lin

S-Z

, Saxena

, Batista

.Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy. Phys Rev B. 2015;91(22):Article 224407.

23.

Leonov

, Mostovoy

.Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet. Nat Commun. 2015;6(1):8275.

24.

Rinaldi

, Pareti

.A model for a two sublattice system with high competing single ion anisotropies. J Appl Phys. 1979;50(B11):7719–7721.

25.

Podchezertsev

, Barrier

, Pautrat

, Suard

, Retuerto

, Alonso

, Fernandez-Diaz

, Rodriguez-Carvajal

.Influence of polymorphism on the magnetic properties of Co₅TeO₈ spinel. Inorg Chem. 2021;60(18):13990–14001.

26.

Comin

, Levy

, Ludbrook

, Zhu

, Veenstra

, Rosen

, Singh

, Gegenwart

, Stricker

, Hancock

, et al.Na₂IrO₃ as a novel relativistic Mott insulator with a 340-meV gap. Phys Rev Lett. 2012;109(26):Article 266406.

27.

Ukleev

, Karube

, Derlet

, Wang

, Luetkens

, Morikawa

, Kikkawa

, Mangin-Thro

, Wildes

, Yamasaki

, et al.Frustration-driven magnetic fluctuations as the origin of the low-temperature skyrmion phase in Co₇Zn₇Mn₆. npj Quantum Mater. 2021;6(1):Article 40.

28.

Živković

, White

, Rønnow

, Prša

, Berger

.Critical scaling in the cubic helimagnet Cu₂OSeO₃. Phys Rev B. 2014;89(6):Article 060401.

29.

Janoschek

, Garst

, Bauer

, Krautscheid

, Georgii

, Boeni

, Pfleiderer

.Fluctuation-induced first-order phase transition in Dzyaloshinskii-Moriya helimagnets. Phys Rev B. 2013;87(13):Article 134407.

30.

Kindervater

, Stasinopoulos

, Bauer

, Haslbeck

, Rucker

, Chacon

, Mühlbauer

, Franz

, Garst

, Grundler

, et al.Weak crystallization of fluctuating skyrmion textures in MnSi. Phys Rev X. 2019;9(4):Article 041059.

31.

Janson

, Rousochatzakis

, Tsirlin

, Belesi

, Leonov

, Rößler

, Van Den Brink

, Rosner

.The quantum nature of skyrmions and half-skyrmions in Cu₂OSeO₃. Nat Commun. 2014;5(1):5376.

32.

Kurumaji

, Nakajima

, Feoktystov

, Babcock

, Salhi

, Ukleev

, Arima

, Kakurai

, Tokura

.Direct observation of cycloidal spin modulation and field-induced transition in Néel-type skyrmion-hosting VOSe₂O₅. J Phys Soc Jpn. 2021;90(2):Article 024705.

33.

Takagi

, Matsuyama

, Ukleev

, Yu

, White

, Francoual

, Mardegan

, Hayami

, Saito

, Kaneko

, et al.Square and rhombic lattices of magnetic skyrmions in a centrosymmetric binary compound. Nat Commun. 2022;13(1):1472.

34.

Adams

, Mühlbauer

, Pfleiderer

, Jonietz

, Bauer

, Neubauer

, Georgii

, Böni

, Keiderling

, Everschor

, et al.Long-range crystalline nature of the skyrmion lattice in MnSi. Phys Rev Lett. 2011;107(21):Article 217206.

35.

Adams

, Chacon

, Wagner

, Bauer

, Brandl

, Pedersen

, Berger

, Lemmens

, Pfleiderer

.Long-wavelength helimagnetic order and skyrmion lattice phase in Cu₂OSeO₃. Phys Rev Lett. 2012;108(23):Article 237204.

36.

Seki

, Yu

, Ishiwata

, Tokura

.Observation of skyrmions in a multiferroic material. Science. 2012;336(6078):198–201.

37.

de PR Moreira

, Illas

, Calzado

, Sanz

, Malrieu

, Amor

, Maynau

.Local character of magnetic coupling in ionic solids. Phys Rev B. 1999;59(10):R6593.

38.

Bogdanov

, van den Brink

, Hozoi

.Ab initio computation of d-d excitation energies in low-dimensional Ti and V oxychlorides. Phys Rev B. 2011;84(23):Article 235146.

39.

Katukuri

, Stoll

, van den Brink

, Hozoi

.Ab initio determination of excitation energies and magnetic couplings in correlated quasi-two-dimensional iridates. Phys Rev B. 2012;85(22):Article 220402.

40.

Bogdanov

, Maurice

, Rousochatzakis

, van den Brink

, Hozoi

.Magnetic state of pyrochlore Cd₂Os₂O₇ emerging from strong competition of ligand distortions and longer-range crystalline anisotropy. Phys Rev Lett. 2013;110(12):Article 127206.

41.

de PR Moreira

, Illas

.A unified view of the theoretical description of magnetic coupling in molecular chemistry and solid state physics. Phys Chem Chem Phys. 2006;8(14):1645–1659.

42.

Malrieu

, Caballol

, Calzado

, De Graaf

, Guihery

.Magnetic interactions in molecules and highly correlated materials: Physical content, analytical derivation, and rigorous extraction of magnetic Hamiltonians. Chem Rev. 2014;114(1):429–492.

43.

Gransbury

, Boulon

, Mole

, Gable

, Moubaraki

, Murray

, Sorace

, Soncini

, Boskovic

.Single-ion anisotropy and exchange coupling in cobalt (II)-radical complexes: Insights from magnetic and ab initio studies. Chem Sci. 2019;10(38):8855–8871.

44.

Tripathi

, Vaidya

, Ahmed

, Klahn

, Cao

, Spillecke

, Koo

, Spachmann

, Klingeler

, Rajaraman

, et al.Structure-property correlation in stabilizing axial magnetic anisotropy in octahedral Co (II) complexes. Cell Rep Phys Sci. 2021;2(4):Article 100404.

45.

Lee

, Ma

, Hahn

, Cao

, Lee

, Hong

, Lee

, Yeom

, Okamoto

, Zhou

, et al.Magnetic frustration driven by itinerancy in spinel CoV₂O₄. Sci Rep. 2017;7(1):17129.

46.

Kismarahardja

, Brooks

, Kiswandhi

, Matsubayashi

, Yamanaka

, Uwatoko

, Whalen

, Siegrist

, Zhou

.Co[V₂]O₄: A spinel approaching the itinerant electron limit. Phys Rev Lett. 2011;106(5):Article 056602.

47.

Katsufuji

, Ikeda

, Ashizawa

, Oike

, Kajita

.Nonlinear behavior in the electrical resistance of strongly correlated insulators. J Phys Soc Jpn. 2020;89(4):Article 044702.

48.

Shanavas

, Satpathy

.Electronic structure and the origin of the Dzyaloshinskii-Moriya interaction in MnSi. Phys Rev B. 2016;93(19):Article 195101.

49.

Heid

, Weitzel

, Burlet

, Bonnet

, Gonschorek

, Vogt

, Norwig

, Fuess

.Magnetic phase diagram of CoNb₂O₆: A neutron diffraction study. J Magn Magn Mater. 1995;151(1–2):123–131.

50.

Baral

, Utesov

, Luo

, Radu

, Magrez

, White

, Ukleev

.Direct observation of exchange anisotropy in the helimagnetic insulator Cu₂OSeO₃. Phys Rev Res. 2023;5(3):L032019.

51.

Tokunaga

, Yu

, White

, Rønnow

, Morikawa

, Taguchi

, Tokura

.A new class of chiral materials hosting magnetic skyrmions beyond room temperature. Nat Commun. 2015;6(1):7638.

52.

Gupta S, Sharma A, Das D, Tulapurkar AA, Muralidharan B. Ultrahigh frequency and multichannel output skyrmion-based nano-oscillator. IEEE Trans Electron Devices. 2025:2618–2624.

53.

Lee

, Wei

, Stenning

, Gartside

, Prestwood

, Seki

, Aqeel

, Karube

, Kanazawa

, Taguchi

, et al.Task-adaptive physical reservoir computing. Nat Mater. 2024;23(1):79–87.

54.

Mostovoy

.Multiferroics: Different routes to magnetoelectric coupling. npj Spintron. 2024;2(1):18.

55.

Che

, Ciola

, Garst

, Kravchuk

, Baral

, Magrez

, Berger

, Schönenberger

, Rønnow

, Grundler

.Short-wave magnons with multipole spin precession detected in the topological bands of a skyrmion lattice. Commun Mater. 2025;6(1):139.

56.

Ding

, Zhang

, Wang

, Cookmeyer

, Moritz

, Kim

, Devereaux

.Intrinsic thermal Hall effect in Mott insulators. Phys Rev Lett. 2025;134(25):Article 256501.

57.

Stoliar

, Cario

, Janod

, Corraze

, Guillot-Deudon

, Salmon-Bourmand

, Guiot

, Tranchant

, Rozenberg

.Universal electric-field-driven resistive transition in narrow-gap Mott insulators. Adv Mater. 2013;25(23):3222–3226.

58.

Kresse

, Furthmüller

.Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B. 1996;54:11169–11186.

59.

Blöchl

.Projector augmented-wave method. Phys Rev B. 1994;50:17953.

60.

Dudarev

, Botton

, Savrasov

, Humphreys

, Sutton

.Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys Rev B. 1998;57(3):1505.

61.

Dewhurst

.Graphical reduction and analysis small-angle neutron scattering program: GRASP. J Appl Crystallogr. 2023;56(5):1595–1609.

62.

Klintenberg

, Derenzo

, Weber

.Accurate crystal fields for embedded cluster calculations. Comput Phys Commun. 2000;131(1–2):120–128.

63.

Helgaker T, Jorgensen P, Olsen J. Molecular electronic-structure theory. New York (NY): John Wiley & Sons; 2014.

64.

Singh

, Fujishiro

, Hayami

, Moody

, Nomoto

, Baral

, Ukleev

, Cubitt

, Steinke

, Gawryluk

, et al.Transition between distinct hybrid skyrmion textures through their hexagonal-to-square crystal transformation in a polar magnet. Nat Commun. 2023;14(1):8050.

65.

Kaneko

, Frontzek

, Matsuda

, Nakao

, Munakata

, Ohhara

, Kakihana

, Haga

, Hedo

, Nakama

, et al.Unique helical magnetic order and field-induced phase in trillium lattice antiferromagnet EuPtSi. J Phys Soc Jpn. 2019;88(1):Article 013702.

66.

Kanazawa

, Kim

, Inosov

, White

, Egetenmeyer

, Gavilano

, Ishiwata

, Onose

, Arima

, Keimer

, et al.Possible skyrmion-lattice ground state in the B20 chiral-lattice magnet MnGe as seen via small-angle neutron scattering. Phys Rev B. 2012;86(13):Article 134425.

67.

Matsumura

, Kita

, Kubo

, Yoshikawa

, Michimura

, Inami

, Kousaka

, Inoue

, Ohara

.Chiral soliton lattice formation in monoaxial helimagnet Yb(Ni_1-xCu_x)₃Al₉. J Phys Soc Jpn. 2017;86(12):Article 124702.

68.

Marty

, Simonet

, Ressouche

, Ballou

, Lejay

, Bordet

, Bordallo

, Hardy

, Hezaim

, Maignan

, et al.Magnetic properties of the Fe langasite Ba₃NbFe₃Si₂O₁₄: A chiral spin liquid candidate. Phys Rev Lett. 2008;101:Article 247201.

69.

Puphal

, Pomjakushin

, Kanazawa

, Ukleev

, Gawryluk

, Ma

, Naamneh

, Plumb

, Keller

, Cubitt

, et al.Topological magnetic phase in the candidate Weyl semimetal CeAlGe. Phys Rev Lett. 2020;124(1):Article 017202.

70.

Takagi

, White

, Hayami

, Arita

, Honecker

, Rønnow

, Tokura

, Seki

.Multiple-q noncollinear magnetism in an itinerant hexagonal magnet. Sci Adv. 2018;4(11):Article eaau3402.

71.

Makino

, Okuyama

, Avdeev

, Sato

.Incommensurate magnetic structure in the cubic noncentrosymmetric ternary compound Pr₅Ru₃Al₂. J Phys Soc Jpn. 2016;85(7):Article 073705.

72.

Araki

, Sato

, Fujima

, Abe

, Tokunaga

, Kimura

, Morikawa

, Ukleev

, Yamasaki

, Tabata

, et al.Metamagnetic transitions and magnetoelectric responses in the chiral polar helimagnet Ni₂InSbO₆. Phys Rev B. 2020;102(5):Article 054409.

73.

Muhlbauer

, Binz

, Jonietz

, Pfleiderer

, Rosch

, Neubauer

, Georgii

, Boni

.Skyrmion lattice in a chiral magnet. Science. 2009;323(5916):915–919.

74.

Mühlbauer

, Gvasaliya

, Ressouche

, Pomjakushina

, Zheludev

.Phase diagram of the Dzyaloshinskii-Moriya helimagnet Ba₂CuGe₂O₇ in canted magnetic fields. Phys Rev B. 2012;86(2):Article 024417.

75.

Kézsmárki

, Bordács

, Milde

, Neuber

, Eng

, White

, Rønnow

, Dewhurst

, Mochizuki

, Yanai

, et al.Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV₄S₈. Nat Mater. 2015;14(11):1116–1122.

76.

Kousaka

, Ogura

, Zhang

, Miao

, Lee

, Torii

, Kamiyama

, Campo

, Inoue

, Akimitsu

.Long periodic helimagnetic ordering in CrM₃S₆ (M= Nb and ta). J Phys Conf Ser. 2016;746:Article 012061.

77.

Grigoriev

, Chernyshov

, Dyadkin

, Dmitriev

, Maleyev

, Moskvin

, Menzel

, Schoenes

, Eckerlebe

.Crystal handedness and spin helix chirality in Fe_1-xCo_xSi. Phys Rev Lett. 2009;102(3):Article 037204.

78.

Togawa

, Koyama

, Takayanagi

, Mori

, Kousaka

, Akimitsu

, Nishihara

, Inoue

, Ovchinnikov

, Kishine

.Chiral magnetic soliton lattice on a chiral helimagnet. Phys Rev Lett. 2012;108(10):Article 107202.

79.

Sosnowska

, Neumaier

, Steichele

.Spiral magnetic ordering in bismuth ferrite. J Phys C Solid State Phys. 1982;15(23):4835–4846.

80.

, Kanazawa

, Onose

, Kimoto

, Zhang

, Ishiwata

, Matsui

, Tokura

.Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nat Mater. 2011;10(2):106–109.

81.

, Jin

, Che

, Wei

, Lin

, Zhang

, Du

, Tian

, Zang

.Emergence of skyrmions from rich parent phases in the molybdenum nitrides. Phys Rev B. 2016;93(6):Article 060409.

82.

Janoschek

, Fischer

, Schefer

, Roessli

, Pomjakushin

, Meven

, Petricek

, Petrakovskii

, Bezmaternikh

.Single magnetic chirality in the magnetoelectric NdFe₃(¹¹BO₃)₄. Phys Rev B. 2010;81(9):Article 094429.

83.

Kurumaji

, Nakajima

, Ukleev

, Feoktystov

, Arima

, Kakurai

, Tokura

.Néel-type skyrmion lattice in the tetragonal polar magnet VOSe₂O₅. Phys Rev Lett. 2017;119(23):Article 237201.

84.

Nayak

, Kumar

, Ma

, Werner

, Pippel

, Sahoo

, Damay

, Rößler

, Felser

, Parkin

.Magnetic antiskyrmions above room temperature in tetragonal Heusler materials. Nature. 2017;548(7669):561–566.

85.

Karube

, Peng

, Masell

, Yu

, Kagawa

, Tokura

, Taguchi

.Room-temperature antiskyrmions and sawtooth surface textures in a non-centrosymmetric magnet with S₄ symmetry. Nat Mater. 2021;20(3):335–340.

Appendix

Less

Year 2026 volume 9 Issue 6

PDF

Cite this Article

BibTeX

Article Info

doi: 10.34133/research.1334

Receive Date：2025-11-14
Online Date：2026-10-16
Published：2026-06-20

Article Data

Affiliations

History

Received：2025-11-14
Revised：2026-05-29
Accepted：2026-05-30

Affiliations

¹Department of Applied Physics and Quantum-Phase Electronics Center, The University of Tokyo, Tokyo 113-8656, Japan.

²PSI Center for Neutron and Muon Sciences, 5232 Villigen PSI, Switzerland.

³Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

⁴Helmholtz-Zentrum Berlin für Materialien und Energie, D-12489 Berlin, Germany.

⁵Institut Laue–Langevin, Grenoble 38000, France.

⁶Dresden High Magnetic Field Laboratory (HLD-EMFL), 01328 Dresden, Germany.

Corresponding:

^* Address correspondence to: priya.baral@epfl.ch (P.R.B.);

^* Address correspondence to: jonathan.white@psi.ch (J.S.W.)

References

Share

https://castjournals.cast.org.cn/joweb/research/EN/10.34133/research.1334

Share to

Scan QR to access full text

Cite this article

BibTeX

Citations

表12种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

关闭全屏

BibTeX
EndNote
RefWorks
TxT

Table 1. List of noncentrosymmetric magnets hosting incommensurate spin textures. Here, DMI and RKKY refer to Dzyaloshinskii–Moriya interaction and Ruderman–Kittel–Kasuya–Yosida interaction, respectively. “DMI-based” refers to where DM interaction competes with leading order exchange to stabilize the incommensurate ground state. Superscripted “c” stands for the electrically conducting members from the list of compounds. Note that some systems, such as EuNiGe₃, may possess both Bloch- and Néel-type twisting, aptly designated by “mixed” helicity.

Material	Space group	Pitch length	Helicity	Stabilization mechanism	Reference
EuNiGe₃^c	I4mm (107)	1.7 nm	Mixed	RKKY + DM interaction	[64]
EuPtSi^c	P2₁3 (198)	1.8 nm	Bloch	Geometric frustration + DM + RKKY + four-spin interactions	[65]
MnGe^c	P2₁3 (198)	2.8–5.5 nm	Bloch	Exchange frustration	[66]
YbNi₃Al₉^c	R32 (155)	3.4 nm	Bloch	RKKY + DMI	[67]
Ba₃NbFe₃Si₂O₁₄	P321 (150)	3.7 nm	Bloch	Exchange frustration	[68]
Co₅TeO₈	P4₃32/P4₁32 (212/213)	5.7–10 nm	Bloch	SIA + DMI + Frustration	This work
CeAlGe^c	I4₁md (109)	6 nm	Néel	RKKY + DMI	[69]
Y₃Co₈Sn₄^c	P6₃mc (186)	8–16 nm	In-plane vortex	Four-spin interaction	[70]
Pr₅Ru₃Al₂^c	I2₁3 (199)	15 nm	Bloch	DMI-based	[71]
Ni₂InSbO₆	R3 (146)	15.7 nm	Bloch	DMI-based	[72]
MnSi^c	P2₁3 (198)	17 nm	Bloch	DMI-based	[73]
Ba₂CuGe₂O₇	P $4 ¯$ 2₁m (113)	22 nm	Bloch	DMI-based	[74]
GaV₄(S/Se)₈	R3m (160)	22 nm	Néel	DMI-based	[75]
CrTa₃S₆^c	P6₃22 (182)	22.5 nm	Bloch	DMI-based	[76]
Fe_1−xCo_xSi^c	P2₁3 (198)	30–200 nm	Bloch	DMI-based	[77]
Cr_1/3NbS₂^c	P6₃22 (182)	48 nm	Bloch	DMI-based	[78]
Cu₂OSeO₃	P2₁3 (198)	62 nm	Bloch	DMI-based	[35]
BiFeO₃	R3c (161)	62 nm	Néel	DMI-based	[79]
FeGe^c	P2₁3 (198)	70 nm	Bloch	DMI-based	[80]
Co_xZn_yMn_z^c	P4₃32/P4₁32 (212/213)	70–130 nm	Bloch	DMI-based	[51]
FeCo_0.5Rh_0.5Mo₃N	P4₁32 (213)	110 nm	Bloch	DMI-based	[81]
NdFe₃(BO₃)₄	R32 (155)	114 nm	Bloch	DMI-based	[82]
VOSe₂O₅	P4cc (103)	125–180 nm	Néel	DMI-based	[83]
Mn_1.4Pt_0.9Pd_0.1Sn^c	I $4 ¯$ 2m (121)	>130 nm	Mixed	Dipolar + anisotropic DMI	[84]
Fe_1.9Ni_0.9Pd_0.2P^c	I $4 ¯$ 2m (121)	280 nm	Mixed	Dipolar + anisotropic DMI	[85]

Fig. 1. Phase diagram and local magnetic anisotropy of chiral cubic Co₅TeO₈. (A) Crystal structure of Co₅TeO₈ viewed slightly away from [111] axis, consisting of 2 inequivalent Co ions: Co1 in blue and Co2 in teal. For simplicity, Te and O atoms are omitted from the full unit cell depiction. The dashed double arrows represent the Co1 ions arranged along 〈110〉, which form triangular plaquettes (shaded yellow). Two corner-sharing plaquettes are mutually rotated by 110° with respect to each other. Ultimately, they form corner-sharing tetrahedra with Co2 ions. The connectivity of various Co–O polyhedra are shown, with nearest-neighbor (NN) and next-nearest-neighbor (NNN) superexchange pathways represented by dashed lines. Here, $J 11, J 12, and J 22$ represent bilinear exchanges between Co1–Co1, Co1–Co2, and Co2–Co2 sites, respectively. Crystal electric field splitting diagrams of Co²⁺ ions in tetrahedral and octahedral environments are depicted. (B) Ab initio calculations indicate contrasting single-ion anisotropies ( $A$ ), identifying the Co1 sublattice as having easy-axis character and the Co2 sublattice as easy-plane. Consequently, the schematic depicts Co1 spins pointed along the local 〈111〉 axes, with Co2 spins constrained within the plane orthogonal to the local z axis. (C) Magnetic phase diagram of Co₅TeO₈ constructed from high-resolution M(H) and $χ ac$ (T) data. We identify up to 8 distinct phases in the explored parameter space. Filled circles and rectangles represent phase boundaries extracted from $χ ac$ (T) and M(H) data, respectively. These data can be found in Fig. 2 and Figs. S5 and S6. For magnetic field-dependent phase boundaries, we only consider data obtained while the field is ramped up. SANS analysis indicates that the helical wavevector is locked at Q = 1.1(1) nm⁻¹ in phase IV, whereas it exhibits a monotonic change of its magnitude in phase I (“soft-Q”). In phase II, the scattering intensity is distributed along an arc with constant angular width and linearly decaying intensity, eventually evolving into the characteristic 2-spot pattern of the conical state (phase VII). See Fig. 4 and main text for further details.

Fig. 2. Magnetic and thermodynamic response across the multi-phase diagram of magnetoelectric Co₅TeO₈. (A) Result of ac susceptibility measurement on Co₅TeO₈ polycrystalline powder in zero field. A constant factor of 10 has been applied to the imaginary part ( $χ ac ′ ′$ ) of the total susceptibility for better visualization. (B) Specific heat data collected in zero field shows a weak anomaly at T_HM. Inset shows the pressed pellet ( $ϕ$ ∼ 3.2 mm) used for these measurements. (C) Ac susceptibility data as a function of temperature measured at 4 different magnetic fields, scanning across various transitions. (D) Magnetization evolution as a function of magnetic field at 7 different temperatures selected according to the phase diagram shown in Fig. 1C. (E) High pulsed magnetic field data of Co₅TeO₈ collected at 2 temperatures show no sign of saturation magnetization up to 60 T. Inset shows evolution of capacitance (C), and the corresponding dC/dH, as a function of external magnetic field at a fixed temperature of 35 K. The dashed vertical lines are the phase boundaries extracted earlier. Black arrows in all panels mark the occurrence of temperature (or magnetic field)-induced transitions.

Fig. 3. Compact helimagnetic order revealed by neutron scattering. (A) Wide-angle neutron diffractograms of Co₅TeO₈ obtained at 2 temperatures above and below T_HM, focused on 2 reflections of the principal cubic directions, show appearance of magnetic satellites around them. The nuclear reflections (from low- to high-Q: (100), (110), and (111)) are marked by dashed vertical lines. We do not observe any incommensurate (IC) satellites around the forbidden (001) reflection. (B and C) SANS 2D detector image obtained just below T_HM and at T = 2 K, respectively. The circular distribution of the magnetic scattering intensity is consistent with the expectation for magnetic scattering arising at propagation vector q within randomly oriented grains of the polycrystalline sample. (D) Length of incommensurate magnetic wavevectors (and the corresponding pitch length of the spiral in real space, λ_h) as a function of temperature. Phase boundaries, as obtained from our $χ ac$ data, have been clearly marked by vertical arrows. (E) Schematic of the uniaxial polarization analysis setup employed at D33 to investigate the IC state in Co₅TeO₈. A uniform longitudinal guide field was applied along the incoming beam direction in order to maintain the polarization of the incoming beam. Representative detector image is also sketched, with a characteristic circular magnetic scattering pattern. The setup for unpolarized SANS measurements is similar, but with polarizer, spin flipper, and analyzer removed. (F) Representative detector image obtained at T = 40 K. Polarization analysis was performed only on the scattered neutrons forming the upper arc on the detector (inside the white sector box). Due to the analyzer’s finite size, only scattering within the top portion of the detector could be analyzed. (G) Integrated intensity of NSF and SF polarized SANS signals observed in phase I at 40 K. Equal NSF and SF scattering intensities are consistent with a Bloch-type modulation. Inset shows a real-space sketch of the proper helical magnetic structure realized in Co₅TeO₈. The indicated pitch length of the helix is the one obtained at 44 K, just below T_HM. (H) Evolution of NSF-SF scattering intensity between T_HM and $T hys 2$ .

Fig. 4. Evolution of the helimagnetic spiral in transverse magnetic field. (A to C) Detector images obtained in a magnetic field of 0, 0.39, and 2.5 T at T = 36 K. The incident neutron beam is directed perpendicular to the detector plane, while the magnetic field is applied transverse to it (horizontal in the detector images). (D) Corresponding azimuthal scans at the 3 magnetic field values. For clarity, a constant offset of −250 counts/mon is applied to the data at 0 T. (E) Magnetic field dependence of the scattering intensities extracted from the orange and cyan sector boxes indicated in (B). The inset displays the full width at half maximum (FWHM) of the azimuthal intensity arcs as a function of magnetic field at T = 36 K. (F) Field evolution of the incommensurate component of the magnetic order (Q), together with its corresponding pitch length in real space. Data above 1.5 T are fitted to illustrate the linear scaling of |Q(H)| and the corresponding λ_h.

Articles: Latest Articles; Most Read; Collections

Updates: Events; News; Multimedia

About: About Us

Contact

No. 86 Xueyuan South Road, Haidian District, Beijing

100081

010-62662699(Operation and Technical Support)

qkjq@cast.org.cn

Copyright © 2025 China Association for Science and Technology. All rights reserved. For all open access content, the relevant licensing terms apply.
Sponsored by the Office of the Leading Group for Cybersecurity and Informatization of CAST, and supported by Science and Technology Review Publishing House