Strain-Induced Spin-Nematic State and Nematic Susceptibility Arising from $2\times 2$ Fe Clusters in ${\mathrm{KFe}}_{0.8}{\mathrm{Ag}}_{1.2}{\mathrm{Te}}_2$

Spin nematics break spin-rotational symmetry while maintaining time-reversal symmetry, analogous to liquid crystal nematics that break spatial rotational symmetry while maintaining translational symmetry. Although several candidate spin nematics have been proposed, the identification and characterization of such a state remain challenging because the spin-nematic order parameter does not couple directly to experimental probes. ${\mathrm{KFe}}_{0.8}{\mathrm{Ag}}_{1.2}{\mathrm{Te}}_2$ (${\mathrm{K}}_5{\mathrm{Fe}}_4{\mathrm{Ag}}_6{\mathrm{Te}}_{10}$, KFAT) is a local-moment magnet consisting of well-separated $2\times 2$ Fe clusters, and in its ground state the clusters order magnetically, breaking both spin-rotational and time-reversal symmetries. Using uniform magnetic susceptibility and neutron scattering measurements, we find a small strain induces sizable spin anisotropy in the paramagnetic state of KFAT, manifestly breaking spin-rotational symmetry while retaining time-reversal symmetry, resulting in a strain-induced spin-nematic state in which the $2\times 2$ clusters act as the spin analog of molecules in a liquid crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe its nematic susceptibility, revealing a divergentlike increase upon cooling, indicating the ordered ground state is driven by a spin-orbital entangled nematic order parameter.

Figure 1

(a) The magnetic structure of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, a prototypical PCIBS. (b) The crystal and magnetic structures of KFAT. The shaded circles represent the magnetic easy plane. (c) The magnetic structure of KFAT projected into the $ab$ plane. The solid box is the $I4/mmm$ unit cell used in this work. (d) The magnetic susceptibility of freestanding KFAT measured along three high-symmetry directions. ${\chi }_{110}$ and ${\chi }_{100}$ almost overlap.

Figure 2

(a) Schematic of our experimental setup with the sample glued onto a GFRP substrate. Upon cooling, the direction parallel (perpendicular) to the glass fibers become relatively longer (shorter), applying strain to the sample (arrows). This setup is used for magnetization measurements parallel and perpendicular to the fibers for (b) $(100)/(010)$ strain and (c) $(110)/(1\overline{1}0)$ strain. (d) Magnetic susceptibilities parallel (${\chi }_{\mathrm{para}}$) and perpendicular (${\chi }_{\mathrm{perp}}$) to the fibers. (e) ${\chi }_{\mathrm{para}}-{\chi }_{\mathrm{perp}}$. (f) $\eta =({\chi }_{\mathrm{para}}-{\chi }_{\mathrm{perp}})/({\chi }_{\mathrm{para}}+{\chi }_{\mathrm{perp}})$.

Figure 3

Pseudocolor plots of longitudinal scans for (a) (220) and (b) $(2\overline{2}0)$ Bragg peaks as a function of temperature. Representative scans are compared for (c) $T=5\mathrm{K}$, (d) $T=50\mathrm{K}$, and (e) $T=300\mathrm{K}$. (f) Scattering angles $2\theta$ for longitudinal scans in (a) and (b), obtained from fits to Gaussian peaks. (g) The lattice anisotropy $\epsilon$ (strain), for a sample under strain and a freestanding sample. The solid lines in (c)–(e) are the results of fits to Gaussian peaks.

Figure 4

(a) Allowed structural and magnetic peaks in the [$H$, $K$, 0] scattering plane of KFAT. Superstructure peaks occur due to the $\sqrt{5}\times \sqrt{5}$ ordering between Fe and Ag, and incommensurate magnetic peaks straddle allowed structural Bragg peaks. ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$ are two magnetic Bragg peaks related by a 90° rotation, corresponding to magnetic domains with AFM spins along (110) and $(1\overline{1}0)$, respectively. Only peaks associated with one of two $\sqrt{5}\times \sqrt{5}$ superstructures are shown [35]. (b) Temperature dependence of ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$ magnetic Bragg peaks measured with (110) parallel to fibers. (c) Temperature dependence of the ${\mathbf{Q}}_1$ magnetic peak in a freestanding and a strained sample compared, after normalizing by the intensity at low temperatures. (d) Uniform magnetic susceptibilities of a freestanding and a strained sample compared near $T_{S,N}$.

Figure 5

(a) $\eta /\epsilon$. The red line is a Curie-Weiss fit for $T\ge 50\mathrm{K}$, with the Weiss temperature $T^{*}=29(3)\mathrm{K}$. We note $T^{*}$ also has a dependence on the temperature range used in fitting. (b) Two stripe-type configurations of $2\times 2$ Fe clusters with corresponding local spin anisotropies (easy axis along shaded slabs). The local spin anisotropy is present in the ordered state, as well as in the paramagnetic state when the clusters fluctuate between the two configurations. In the strained paramagnetic state, the clusters fluctuate in one of the configurations more than the other, resulting in a spin-nematic state with macroscopic spin anisotropy.