Elastoresistivity Signatures of Nematic Fluctuations in Layered Antiferromagnet CoTa3S6

Abstract

Nematic phases that break rotational symmetry are widely observed in quantum materials, and clarifying their origin and relationship with other symmetry-breaking phases remains an important but challenging task. In this work, we investigate nematic fluctuations in CoTa$_3$S$_6$ using elastoresistivity experiments to resolve the nature of the proposed nematic phase intertwined with collinear and non-coplanar antiferromagnetic orders. We observe a divergence-like antisymmetric elastoresistivity that rapidly develops below the stripe antiferromagnetic transition, consistent with a distinct nematic degree of freedom coupled to the magnetic order. While nematic fluctuations are strongly modulated by an external out-of-plane magnetic field and the onset temperature of resistivity anisotropy shows pronounced strain dependence, the antiferromagnetic transition temperatures remain nearly unchanged under either magnetic field or strain. Additionally, complementary magnetoresistance measurements reveal characteristic signatures of three-state nematicity in a hexagonal system. Our findings demonstrate CoTa$_3$S$_6$ as a unique case of intertwined nematic and AFM orders with distinct origins.

Figures (4)

• Figure 1: Schematics of probing nematic order in CoTa3S6 with external strain. (a) Schematic of the modified Montgomery technique for elastoresistivity measurement. A near square sample with four contacts on the corner is glued onto a titanium platform to apply uniaxial strain along the $x$-direction, with resistances $R_{xx}$ and $R_{yy}$ measured at the same time, which are converted to resistivities $\rho_{xx}$ and $\rho_{yy}$ (see Methods). (b) Schematic of strain deformations classified by the $A_{1}$ (left) and $E_{2}$ (right) irreducible representations in the $D_{6}$ point group; throughout the work we adopt a Cartesian coordinate system ($x$, $y$, $z$). (c) Landau-theory-based schematic temperature dependence of nematic susceptibility ($d[\Delta\rho/\rho]/d\epsilon$) for a primary nematicity scenario, where nematicity exists as an independent order parameter. The inset shows the nematic order on the triangular lattice, where the long axis of the red shaded ellipse correspond to the direction along which $\Delta \rho >0$. (d) Schematic temperature dependence of nematic susceptibility ($d[\Delta\rho/\rho]/d\epsilon$) for a secondary nematicity scenario induced by single-$\boldsymbol{q}$ (e.g. AFM) order, in which nematicity arises as a "by product" associated with magnetic symmetry breaking. $T_N$ corresponds to the single-$\boldsymbol{q}$ (e.g. AFM) transition temperature (see text). The inset shows a typical single-$\boldsymbol{q}$ AFM order on the triangular lattice. (e) Corresponding schematic for a primary nematicity scenario coupled to single-$\boldsymbol{q}$ (e.g. AFM) order, where $p=1,2$ demonstrates the results from different nemato-magnetic coupling strength (see Methods). In this model, we adopt the case where AFM transition temperature $T_N$ is above $T^*$. Below $T^*$, hatched area indicates the hysteretic region with multiple nematic domains. (f-g) Temperature dependence of the longitudinal resistivity $\rho_{xx}$ and $\rho_{yy}$ showing strain-cooling–induced selection of nematic domains in CoTa3S6 under tensile (red curve) and compressive strain (blue curve), corresponding to the domain configurations illustrated schematically.
• Figure 2: Elastoresistivity and nematic susceptibility. (a-b) Relative changes of resistivity $\rho_{ii}$ ($i=x,y$) as a function of strain (defined as $\Delta \rho_{ii}=\rho_{ii}-\bar{\rho}$) at representative temperatures measured by the modified Montgomery method. $\bar{\rho} = (\rho_{xx,0}+\rho_{yy,0})/2$ is the average in-plane resistivity, where $\rho_{xx,0}$ and $\rho_{yy,0}$ are the resistivity value at $\varepsilon_{xx}=0$ for the increasing strain scan. The black arrows denote the strain scan direction for the hysteresis loop. (c-d) Representative data of resistivity decomposed to the isotropic $A_{1}$ and anisotropic $E_{2}$ channels at different temperatures. The gray arrow in (d) defines the size of hysteresis at $\varepsilon = 0$. (e) Temperature dependence of elastoresistivity coefficients (see Methods). Transition temperatures $T_{\mathrm{N1}}$, $T^*$ , $T_{\mathrm{N2}}$ are indicated with dashed lines. Inset shows the temperature dependence of hysteresis size of $E_{2}$ channel defined in (d) in the resistivity-strain scan. $T^*$ is defined as the onset temperature of hysteresis: intercept of the dashed line with the temperature axis.
• Figure 3: Nematic fluctuations controlled by out-of-plane magnetic fields. (a) Temperature dependence of the elastoresistivity coefficient in the $E_{2}$ channel ($m_{E_2}$), measured under different out-of-plane magnetic fields. (b) Colormap of $m_{E_2}$ in log scale, overlaying with magnetic transition temperatures, illustrating the $H$--$T$ phase diagram. The phase boundaries $T^*$ (blue triangles), $H_c$ (blue squares), $T_{N1}$ (yellow dots) and $T_{N2}$ (green dots) are indicated by symbols extracted from anomalies in $M(T)$ (circles), $\rho_{xx}(H)$ (squares), and $\rho_{xx}(T)$ (triangles), compiled from previous work fengNonvolatileNematic2025.
• Figure 4: Strain dependence of transition temperatures and features of three-state nematicity. (a,c) Resistivity anisotropy $\Delta \rho_{xx}$ obtained by subtracting a zero strain background from strained states (see Methods), from which $T^*$ under different bias strains is determined. (b,d) Representative $d\rho_{xx}/dT$ curves under bias strains where $T_{N1}$ and $T_{N2}$ are determined from kinks. (e) Summarized strain dependence of the transition temperatures $T_{N1}$, $T_{N2}$ and $T^*$. $T_{N1}$ ($T_{N2}$) under different bias strains fall on the line of $T=38\mathrm{~K}$ (blue) ($T=26.5\mathrm{~K}$ (red)). Two shaded regions divided by the dashed line indicate the nematic phases with illustrated domains favored by compressive (left) and tensile (right) strains respectively. (f) Out-of-plane magnetic field ($H\parallel z$) dependence of $\rho_{xx}$ measured at 10 K under various magnitudes of strain along the $x$ axis ($\epsilon_{xx}$). (g) Strain dependence of nematic order parameter at each bias strain projected on the $x$-axis extracted from $(\rho_{xx}(3\mathrm{T})-\rho_{xx}(4\mathrm{T}))/\rho_{xx}(4\mathrm{T})$ (see text). The red line is a fit to domain population formula modified for the three-state nematicity (see SI).