Sub-10 nm helices stabilized by single-ion anisotropy in the chiral Mott insulator Co$_5$TeO$_8$

Abstract

Narrow-gap Mott insulators promise exceptional opportunities for voltage-controlled magnetic textures in low-dissipation spintronics, although their prediction remains challenging. Here we employ a density functional theory-guided approach to predict a narrow charge-transfer gap (127 meV) in the chiral cubic frustrated oxide Co$_5$TeO$_8$. Comprehensive neutron scattering and magnetometry reveal proper-screw Bloch-type helices with field- and temperature-tunable pitch of 5.7-10 nm embedded in a complex phase diagram with eight distinct phases. Ab initio wavefunction calculations demonstrate site-dependent single-ion anisotropy exceeding Dzyaloshinskii-Moriya (DM) interactions by an order of magnitude, establishing the anisotropy-frustration interplay as the stabilization mechanism, contrasting starkly with DM-dominated cubic helimagnets. Sharp capacitance anomalies at phase boundaries confirm intrinsic magnetoelectric coupling throughout the phase diagram. Co$_5$TeO$_8$ thus provides a platform for voltage-tunable sub-10 nm magnetic textures, demonstrating effective theory-guided discovery of functional magnetic materials in correlated oxides.

Figures (5)

• Figure 1: Phase diagram of chiral cubic Co5TeO8 encompassing frustration and narrow Mott gap.(a) Crystal structure of Co5TeO8 viewed slightly away from [111] axis, comprising of two inequivalent Co ions: Co1 in blue and Co2 in teal. For simplicity, Te and O atoms are omitted. The dashed double arrows represent the Co1 ions arranged along $\left< \text{110}\right>$, which form triangular plaquettes (shaded yellow). Two corner-sharing plaquettes are mutually rotated by 110$^{\circ}$ 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-neighbour (NN) and next-nearest-neighbour (NNN) superexchange pathways represented by dashed lines. Crystal electric field (CEF) splitting diagrams of Co$^{2+}$ ions in tetrahedral and octahedral environments are depicted. (b) Electronic band structure of Co5TeO8 determined using LDA+$U$ approach. See Methods for more information. (c) Magnetic phase diagram of Co5TeO8 constructed from high-resolution M(H) and $\chi_{\text{ac}}$(T) data. We identify up to 8 distinct phases in the explored parameter space. Filled circles and rectangles represent phase boundaries extracted from $\chi_{\text{ac}}$(T) and M(H) data, respectively. For magnetic field dependent phase boundaries, we only consider data obtained while the field is ramped up.
• Figure 2: Magnetic and thermodynamic response across the multi-phase diagram of magnetoelectric Co5TeO8.(a) Shows the result of ac susceptibility measurement on Co5TeO8 polycrystalline powder in zero field. A constant factor of 10 has been multiplied with the imaginary part of the total susceptibility ($\chi^{\prime\prime}_{\text{ac}}$) for better visualization. (b) Specific heat data collected in zero field shows a weak anomaly at $\text{\it T}_{\text{HM}}$. Inset shows the pressed pellet ($\phi\sim$3.2 mm) used for these measurements. (c) Ac susceptibility data as a function of temperature measured at four different magnetic fields, scanning across various transitions. (d) Shows magnetization evolution as a function of magnetic field at seven different temperatures selected according to the phase diagram shown in Fig. \ref{['Fig1']}e. (e) High pulsed magnetic field data of Co5TeO8 collected at two 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.
• Figure 3: Compact proper-screw helical order revealed by neutron scattering.(a) Wide angle neutron diffractograms of Co5TeO8 obtained at two temperatures above and below $\text{\it T}_{\text{HM}}$, focused on two reflections of the principal cubic directions show appearance of magnetic satellites around them. The nuclear reflections (from low- to high-$\mathbf{Q}$: (100), (110) and (111)) are marked by dashed vertical lines. We do not observe any incommensurate (IC) satellites around forbidden (001) reflection. (b), (c) Show the SANS 2D detector image obtained just below $\text{\it T}_{\text{HM}}$ 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 $\mathbf{Q}$ within randomly oriented grains of the polycrstalline sample. (d) Shows the length of incommensurate magnetic wavevectors (and the corresponding pitch length of the spiral in real space, $\lambda_{\text{h}}$) as a function of temperature. Phase boundaries, as obtained from our $\chi_{\text{ac}}$ 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 analyser removed. (f) Shows a representative detector image obtained at T = 40 K. Polarization analysis is only performed on the scattered neutrons forming the the upper arc on the detector (inside the white sector box). Due to the analyser's finite size, only scattering within the top portion of the detector could be analyzed. (g) Integrated intensity of non spin-flip and spin-flip polarized SANS signals observed in Phase-I at 40 K. An equal distribution of NSF scattering intensity combined with SF scattering is consistent with a Bloch-type modulation. Inset shows a real-space sketch of the proper helix magnetic structure realized in Co5TeO8. The real-space pitch length of this incommensurate structure is the one obtained at 44 K, just below T$_{\text{HM}}$. (h) Shows evolution of NSF-SF scattering intensity between T$_\text{HM}$ and T$^\text{(1)}_\text{hys}$.
• Figure 4: Evolution of the proper-screw spiral in transverse magnetic field. Panels- (a), (b), and (c) show the respective detector image in a transverse magnetic field for 0 T, 0.39 T, and 2.5 T at T = 36 K, respectively. (d) Shows the respective azimuthal scans at the three magnetic field values, mentioned previously. Compared with zero field, a constant offset of 250 counts/mon has been applied to both curves obtained for 0.39 T and 2.5 T for clarity. (e) Shows the width in azimuthal angle of the intensity arcs observed on the detector as a function of magnetic field. (f) Shows the magnetic field dependence of the scattering intensities extracted from the orange and cyan sector boxes shown in Panel- b. (g) Shows the field evolution of the incommensurate component of the magnetic order ($\mathbf{q}$), together with its corresponding pitch length in real-space. The data obtained above 1.5 T are fitted with a linear function, highlighting the linearity observed in $|\mathbf{q}^\text{(1)}\text{(H)}|$ (and their corresponding $\lambda_{\text{h}}$).
• Figure 5: Electronic band gap comparison for Mott insulators. A quantitative comparison of band gap values for some of the well-studied Mott insulators, including non-magnetic insulators as well as magnetic insulators with and without long-range ordering. The error bar for some of the systems shows the range of band gaps reported in literature. The detailed list is provided in the Supplementary Information Table S3.