--- title: 'Co1/3TaS2: Cobalt-Intercalated Dichalcogenide' url: https://www.emergentmind.com/topics/co1-3tas2 type: topic --- # Co1/3TaS2: Cobalt-Intercalated Dichalcogenide Searching arXiv for recent papers on Co1/3TaS2 to ground the article in the latest literature. Co$_{1/3}$TaS$_2$ is a cobalt-intercalated van der Waals transition-metal dichalcogenide derived from 2H-TaS$_2$, in which Co ions occupy the van der Waals gap and form a triangular magnetic sublattice. Across work on nominally stoichiometric and near-stoichiometric samples, it has been studied as a metallic antiferromagnet whose magnetic ground state is exceptionally sensitive to cobalt occupancy near $x \approx 1/3$. Reported phases include single-$Q$ collinear or commensurate order, noncoplanar tetrahedral triple-$Q$ order, an anisotropic $(2+1)Q$ state, and a coplanar helical state, with corresponding transport and optical signatures such as spontaneous Hall conductivity, topological Hall response, Kerr rotation, anomalous magneto-birefringence, and electrically driven chirality switching [2303.03760; 2401.10421; 2507.12588; 2409.02710; 2511.14241]. ## 1. Crystal framework and electronic setting Co intercalation into 2H-TaS$_2$ produces a layered metallic crystal in which Co ions occupy octahedral sites between TaS$_2$ layers and form a triangular lattice within each intercalant plane. At $x=1/3$, the intercalants order into a $\sqrt{3}\times\sqrt{3}$ superstructure in the van der Waals gap. Several studies describe the structure as hexagonal space group P$6_3$22, with a non-symmorphic $6_3$ screw axis and broken inversion symmetry; one device study writes the overall symmetry as P6$_{222}$, while a symmetry analysis of the parent crystal uses space group No. 182 [2303.03760; 2401.10421; 2511.14241; 2409.02710; 2507.12588]. The Co sublattice is magnetically active, whereas the low-energy itinerant states are dominated by Ta $5d$ orbitals. In the tetrahedral low-temperature phase, the ordered moment refined from neutron powder diffraction is $1.27(1)\,\mu_B$/Co at $3$ K, smaller than the high-spin Co$^{2+}$ value expected from $S=3/2$, consistent with partial itinerancy or screening and frustration-enhanced quantum fluctuations. The nearest Co-Co distance is reported as $5.74$ Å, and successive Co layers follow AB or hcp-like stacking along $c$, with antiferromagnetic interlayer coupling emphasized in neutron and spin-dynamics analyses [2303.03760; 2410.02180]. ARPES and model analyses place the Fermi surface close to the $3/4$-filling regime, with nearly hexagonal geometry and nesting at the $M$ points. This nesting is central to itinerant-electron descriptions of the magnetic instability, and later electrical-control studies explicitly treat carrier density as a tuning parameter for the balance among single-$Q$, triple-$Q$, and helical phases [2303.03760; 2409.02710]. ## 2. Composition-sensitive phase behavior near one-third intercalation The most reproducible conclusion across composition-controlled bulk studies is that small changes in $x$ around $1/3$ qualitatively alter the magnetic ground state. For $0.299 < x \le 0.325$, Co$_x$TaS$_2$ shows two antiferromagnetic transitions, with $T_{N1} \approx 38$ K and $T_{N2} \approx 26.5$ K over $0.31 < x \le 0.325$. In this regime, neutron diffraction identifies a collinear single-$Q$ state with $q_{m2}=(1/2,0,0)$ between $T_{N2}$ and $T_{N1}$, followed below $T_{N2}$ by a noncoplanar tetrahedral triple-$Q$ state carrying uniform scalar spin chirality. A weak ferromagnetic moment $M_z(H=0)\approx 0.01\,\mu_B$ per Co appears only below $T_{N2}$, together with a spontaneous Hall conductivity $\sigma_{xy}(H=0)\approx 70\ \Omega^{-1}\,\mathrm{cm}^{-1}$ [2401.10421]. For $x \ge 0.330$, the reported ground state changes to a coplanar helical antiferromagnet with $q_{m1}=(1/3,0,0)$, moments in the $b^\ast$-$c$ plane, and an interlayer angle of $150^\circ$. In this over-doped regime, there is a single magnetic transition, $T_N \approx 35$ K for $x=0.330(4)$ and $T_N \approx 41$ K for $x=0.340(4)$, with no weak ferromagnetic moment along $c$ and no spontaneous Hall conductivity. Refined ordered moments are $1.37(3)\,\mu_B$ for $x=0.330(4)$ and $1.79(4)\,\mu_B$ for $x=0.340(4)$ [2401.10421]. A later symmetry-based optical and neutron study sharpens the distinction between exact stoichiometry and slight Co deficiency. It states that the stoichiometric compound Co$_{1/3}$TaS$_2$ undergoes a single transition into a commensurate single-$Q$ antiferromagnetic phase at $Q=(1/3,0,0)$, with no zero-field anomalous Hall effect and no Kerr signal, whereas samples with $x \le 0.325$ exhibit two transitions and an anomalous Hall effect only in the lower-temperature phase. For a representative $x=0.32$, magnetization gives $T_{N1}=36$ K and $T_{N2}=26$ K, while thermal-modulation optics tracks the same split as $T'_{N1}\approx 30$ K and $T'_{N2}\approx 20$ K because of cryostat thermalization [2507.12588]. This phase sensitivity is attributed to vacancy-driven changes in higher-order and long-range interactions. In particular, Co vacancies for $x<1/3$ are argued to stabilize multi-$Q$ order by promoting higher-order, multi-spin couplings, whereas the exact $x=1/3$ state is presented as commensurate and AHE-inactive [2507.12588]. ## 3. Noncoplanar multi-\(Q\) order, scalar spin chirality, and Hall transport In the noncoplanar regime, the central order parameter is scalar spin chirality, \[ \chi_{ijk}=\mathbf{S}_i\cdot(\mathbf{S}_j\times\mathbf{S}_k), \] defined on a triangular plaquette. In the tetrahedral triple-$Q$ description, the magnetic Bragg peaks lie at the three symmetry-related $M$-point vectors \[ Q_1=(1/2,0,0),\quad Q_2=(0,1/2,0),\quad Q_3=(1/2,1/2,0), \] and the spin texture can be written as \[ S(r)=\sum_{n=1}^{3} m_n\cos(Q_n\cdot r+\phi_n), \] with mutually orthogonal $m_n$ and equal amplitudes. This produces a four-sublattice all-in/all-out tetrahedral state in which every elementary triangle has the same-sign chirality, yielding a three-dimensional ferro-chiral texture once adjacent layers are locked by antiferromagnetic interlayer exchange [2303.03760]. Transport analyses interpret the zero-field Hall signal as a real-space Berry-curvature effect of this noncoplanar texture. One common decomposition is \[ \rho_{xy}(H)=R_0H+R_sM(H)+\rho^T_{xy}, \] with $\rho^T_{xy}$ assigned to the chirality-driven Hall contribution. In this regime, the low-temperature spontaneous response reaches $\rho_{xy}\approx 4\ \mu\Omega\,\mathrm{cm}$ and $\sigma_{xy}\approx 70\ \Omega^{-1}\,\mathrm{cm}^{-1}$ at $H=0$, while the Hall loop is hysteretic and vanishes near $25$ K [2410.02180; 2401.10421]. A later study proposes a more specific low-temperature symmetry assignment for sub-stoichiometric crystals. For $x\le 0.325$, the higher-temperature phase is identified as a single-$Q$ $mM2$ state with order parameter $(a;0;0)$ and magnetic space group 19.29. Below $T_{N2}$, an in-plane $mM4$ component condenses at the same $M$-star wave vectors, and the resulting order is determined as the coherent anisotropic $(2+1)Q$ superposition \[ (a;0;0\ |\ 0;b;c), \] with magnetic space group 4.7 and $b\neq c$. In this construction, one $Q$ vector carries the out-of-plane $mM2$ modulation and the other two carry in-plane $mM4$ modulation; the inequality $b\neq c$ breaks threefold rotational symmetry and distinguishes the state from a rotationally symmetric $3Q$ texture. The same work derives a scalar-chirality-induced fictitious field from coupled $mM2$ and $mM4$ order parameters and shows that the anisotropic $(2+1)Q$ state inherently has nonzero scalar spin chirality and therefore a natural AHE mechanism [2507.12588]. Electrical-control studies continue to describe the chiral low-temperature state as a tetrahedral $3Q$ phase. In that literature, the Hall response is frequently called an anomalous Hall effect even though the origin is assigned to scalar spin chirality and a topological Hall mechanism without reliance on spin-orbit coupling. A single-carrier estimate is written as \[ \rho_{xy}^{\mathrm{THE}}\approx P\,R_0\,B_{\mathrm{eff}},\qquad R_0=\frac{1}{ne}, \] where the emergent field is generated by the dense real-space Berry curvature of the $3Q$ texture [2409.02710]. ## 4. Microscopic models and dynamical signatures An itinerant-electron description begins from a triangular-lattice Kondo-lattice model, \[ H=-t\sum_{\langle ij\rangle,\alpha} c^\dagger_{i\alpha}c_{j\alpha} -J\sum_i \mathbf{s}_i\cdot\mathbf{S}_i, \] with Ta-derived itinerant electrons coupled to localized Co moments. In the weak-coupling regime, integrating out the electrons yields RKKY-type bilinear exchanges that leave single-$Q$ stripe and triple-$Q$ tetrahedral states classically degenerate, while higher-order terms generate effective multispin interactions. A positive biquadratic term, \[ H_{\mathrm{bq}}=K_{\mathrm{bq}}\sum_{\langle ij\rangle}(\mathbf{S}_i\cdot\mathbf{S}_j)^2,\qquad K_{\mathrm{bq}}>0, \] selects the noncoplanar tetrahedral state, and a minimal stacked-triangular $J_1$-$J_2$-$J_c$-$K_{\mathrm{bq}}$ model reproduces the experimentally observed two-step sequence from collinear single-$Q$ to tetrahedral triple-$Q$ order [2303.03760]. Two complementary neutron-based parameterizations have been reported. A low-temperature fit to inelastic neutron scattering in the tetrahedral phase gives $J_1S=3.92$ meV, $J_cS=2.95$ meV, $J_2/J_1=0.19$, and a small positive $K_{\mathrm{bq}}$; the linear magnon branches show a gap of about $0.5$ meV, and a weaker quadratic mode appears above about $1.5$ meV [2303.03760]. A later study instead fitted the paramagnetic-phase spectrum first, using Langevin/Landau-Lifshitz dynamics and Bayesian optimization, and obtained \[ J_1=1.212\pm0.104\ \mathrm{meV},\quad J_2=0.320\pm0.061\ \mathrm{meV},\quad J_3=0.022\pm0.036\ \mathrm{meV}, \] \[ J_{c1}=1.406\pm0.097\ \mathrm{meV},\quad J_{c2}=-0.260\pm0.036\ \mathrm{meV}, \] with $S=3/2$ and a small positive four-spin coupling $K\approx0.06J_1$. After the $1/S$ renormalization \[ \tilde K=\left(1-\frac{1}{S}+\frac{1}{4S^2}\right)K, \] one has $\tilde K=(4/9)K$ for $S=3/2$, and $\tilde K\approx0.027J_1$ reproduces $T_{N2}/T_{N1}\approx0.7$ [2410.02180]. The same later work proposes a general INS diagnostic for triangular-lattice multi-$Q$ order. Near an $M$ point, single-$Q$ order has a linear Goldstone mode \[ \omega_{L,s}(k)=\sqrt{v_{\parallel,s}^2k_\parallel^2+v_{\perp,s}^2k_\perp^2}, \] with strong anisotropy, $v_{\parallel,s}\neq v_{\perp,s}$, whereas triple-$Q$ order yields nearly isotropic linear cones with $v_{\perp,t}/v_{\parallel,t}$ narrowly distributed around unity over broad parameter ranges. Experimentally, the $30$ K intermediate phase shows anisotropic low-energy contours around $M$, while the $5$ K phase shows nearly circular contours, supporting a single-$Q\rightarrow$triple-$Q$ transition. The triple-$Q$ phase also displays stronger linewidth broadening and energy renormalization, attributed to enhanced magnon-magnon interactions and three-magnon decay [2410.02180]. ## 5. Magneto-optical probes and symmetry diagnostics Optical probes have supplied an independent symmetry classification of the low-temperature state. In one experiment, linearly polarized light reflected from Co$_x$TaS$_2$ yields a polarization rotation \[ \Theta(\phi,T)=\theta_B(T)\sin[2(\phi+\phi_0(T))]+\theta_K(T), \] where $\theta_B$ is the birefringent contribution, $\phi_0$ the principal-axis orientation, and $\theta_K$ the Kerr offset. For $x=0.32$, birefringence onsets already at the upper transition, indicating rotational-symmetry breaking in the higher-temperature phase, whereas Kerr rotation appears only below the lower transition, indicating time-reversal breaking only in the lower-temperature phase. Most notably, below $T_{N2}$ the principal optic axes rotate spontaneously in zero field, with the sign of the rotation trained by $\pm$ field cooling. This phenomenon is termed anomalous magneto-birefringence and is used to rule out low-temperature orders that remain invariant under time reversal combined with a twofold in-plane rotation; within the reported symmetry analysis, that constraint uniquely selects the anisotropic $(2+1)Q$ state with $b\neq c$ [2507.12588]. A separate optical study reports a spontaneous Kerr effect in Co$_{1/3}$TaS$_2$ without invoking spin-orbit coupling or net spin magnetization. Using a zero-area-loop fiber Sagnac interferometer in polar geometry at $1550$ nm ($0.80$ eV), with sensitivity of about $0.01\ \mu$rad and rejection of linear birefringence at the $10^{-6}$ level, it measures spontaneous Kerr rotation up to about $250\ \mu$rad after field cooling by only $0.3$ T. In that study, the Kerr signal is absent in the single-$Q$ stripe phase and the paramagnetic phase, but finite in the noncoplanar triple-$Q$ phase below $T_{N2}\approx 16$ K, where the sample is described as spin-compensated with $M_z(0)\approx0.01\,\mu_B$/Co [2507.09493]. The optical mechanism is again written in terms of scalar spin chirality. For a three-site loop, the fictitious magnetic field is described as \[ b_f\propto t^3 \chi_{ijk}\,\hat n, \] so that left- and right-circularly polarized light accumulate different Berry phases. In this framework, the polar Kerr angle is related to the off-diagonal optical response through \[ \theta_K(\omega)+i\epsilon_K(\omega)\approx-\frac{\epsilon_{xy}(\omega)}{\epsilon_{xx}(\omega)\sqrt{\epsilon_{xx}(\omega)}}, \] or equivalently \[ \theta_K(\omega)+i\epsilon_K(\omega) = -\frac{\sigma_{xy}(\omega)} {\sigma_{xx}(\omega)\sqrt{1+i(4\pi/\omega)\sigma_{xx}(\omega)}}. \] Domain imaging with a $\sim2\ \mu$m spot resolves opposite-chirality regions near switching fields and nearly uniform chirality after training. In field sweeps, $\theta_K(B)$ shows broad plateaus and a metamagnetic change near $5$ T, while the reflectivity remains constant within $0.5\%$, supporting a magnetic rather than ordinary optical origin [2507.09493]. ## 6. Electrical control and current-driven switching Carrier-density tuning provides a direct handle on the chiral state. Nanoflake Hall devices about $20$ nm thick were fabricated with a side-gate geometry and a LiClO$_4$/PEO/methanol solid electrolyte. Gate voltages were activated at $320$-$360$ K in vacuum for at least $30$ min and then measured at low temperature with out-of-plane field. Positive $V_G$ drives Li$^+$ intercalation and electron doping, whereas negative $V_G$ accumulates ClO$_4^-$ at the surface and hole dopes the flake [2409.02710]. Three compositions near $x\approx1/3$ were studied: $x=0.299$, $0.319$, and $0.327$. For $x=0.299$, positive gating enhances the low-temperature Hall loops, while negative gating suppresses them continuously to zero; both $\rho_{\mathrm{AHE}}(V_G)$ and $H_c(V_G)$ follow this trend. For $x=0.319$, the Hall loops remain large under gating, consistent with a composition near the center of the reported $3Q$ dome. For $x=0.327$, positive gating monotonically weakens $\rho_{\mathrm{AHE}}$ and $H_c$, consistent with movement toward a competing helical phase. The authors summarize this as covering the whole $3Q$ phase with ionic gating [2409.02710]. Current-driven control has also been reported in two device geometries. In a Co$_{1/3}$TaS$_2$/Pt heterostructure, Pt supplies spin current through its spin Hall effect, and large write pulses switch the Hall resistance between two nonvolatile states corresponding to opposite chiralities. The read current is $100\ \mu$A, the assisting in-plane field is $H_x=\pm12$ T, and the write currents extend to roughly $\pm20$ mA. Reversing $H_x$ reverses the switching polarity, consistent with spin-orbit torque [2511.14241]. A second set of devices omits the heavy-metal layer and shows field-free switching in pristine Co$_{1/3}$TaS$_2$. This intrinsic self-torque is attributed qualitatively to the combination of non-centrosymmetric crystal symmetry and strong Berry curvature, which allows current-induced spin accumulation to act back on the noncoplanar $3Q$ texture. The reported threshold is \[ J_{\mathrm{th}}\approx1.8\times10^6\ \mathrm{A/cm}^2, \] and switching is observed only below $T_N\approx25$ K [2511.14241]. ## 7. Evolving interpretations, competing descriptions, and open issues The literature on Co$_{1/3}$TaS$_2$ contains a significant revision of the magnetic ground-state assignment. An earlier study interpreted nominal Co$_{1/3}$TaS$_2$ as a noncollinear antiferromagnetic Weyl semimetal with coplanar $120^\circ$ order at the zone center, a ferro-toroidal moment \[ \mathbf{t}\equiv\sum_i \mathbf{r}_i\times \mathbf{S}_i, \] and an anomalous Hall conductivity of about $70\ \Omega\,\mathrm{cm}^{-1}$ at $2$ K arising from Berry curvature associated with hourglass Weyl fermions protected by the non-symmorphic lattice. In that framework, the $\Gamma_2$ magnetic state permits both $M_z$ and $\sigma_{xy}$, and the sign of $\sigma_{xy}$ follows the sign of the toroidal moment switched by $H\parallel c$ [2203.03826]. Subsequent neutron, ARPES, and spin-dynamics studies reassigned the low-temperature state of near-$1/3$ material to an $M$-point noncoplanar tetrahedral triple-$Q$ order stabilized by nesting near $3/4$ filling and higher-order multispin interactions [2303.03760; 2410.02180]. Composition-controlled bulk work then showed that the spontaneous Hall signal is confined to the under-doped regime $0.299