Effective One-Dimensional Coupling in the Highly Frustrated Square-Lattice Itinerant Magnet ${\mathrm{CaCo}}_{2-y}{\mathrm{As}}_2$

Inelastic neutron scattering measurements on the itinerant antiferromagnet ${\mathrm{CaCo}}_{2-y}{\mathrm{As}}_2$ at a temperature of 8 K reveal two orthogonal planes of scattering perpendicular to the Co square lattice in reciprocal space, demonstrating the presence of effective one-dimensional spin interactions. These results are shown to arise from near-perfect bond frustration within the $J_1\text{−}{J}_2$ Heisenberg model on a square lattice with ferromagnetic $J_1$ and hence indicate that the extensive previous experimental and theoretical study of the $J_1\text{−}{J}_2$ Heisenberg model on local-moment square spin lattices should be expanded to include itinerant spin systems.

Figure 1

Spin fluctuations in ${\mathrm{CaCo}}_{2-y}{\mathrm{As}}_2$: Experimental INS data ($E_{\mathrm{i}}=75\mathrm{meV}$) vs diffusive model. (a)–(c) Constant-energy slices of the background-subtracted data (the isotropic background is estimated similar to Ref. [22]) averaged over the energy ranges of 50–60, 40–50, and 10–20 meV, respectively. (d)–(f) Corresponding constant-energy slices calculated using the diffusive model and parameters obtained from fitting the data shown in Fig. 2. In (d), the black dashed arrows show the LO directions and the maroon arrow shows the TR direction. (g),(h) Transverse slices of the background-subtracted data along the [$-K$, $K$] direction through (0.25, 0.25) and (0.45, 0.45) (r.l.u.), respectively, obtained after averaging over the LO direction by $\pm 0.1\mathrm{r}.\mathrm{l}.\mathrm{u}.$ (i),(j) Corresponding energy dependence of the scattering obtained using the diffusive model and parameters of fits to the data in Fig. 2. The energy-dependent figures are averaged over all four symmetry-related quadrants. The color scale represents the intensity in each panel. The maximum/minimum intensities in the panels are (a) $0.34/-0.5$, (b) $0.42/-0.3$, (c) $0.65/-0.15$, (d)–(f) $0.43/0$, (g) $0.52/-0.45$, (h) $0.65/-0.35$, and (i),(j) $0.52/0$ in arbitrary units.

Figure 2

Constant-energy cuts and dynamical susceptibility of the data fitted with the diffusive model. (a),(c) LO and (b),(d) TR cuts of data through (0.55, 0.55) at (a),(b) 52.5–57.5 and (c),(d) 42.5–47.5 meV. TR cuts were averaged from 0.3–0.8 r.l.u. in the LO direction and LO cuts $\pm 0.1\mathrm{r}.\mathrm{l}.\mathrm{u}.$ in the TR directions. Both data are corrected for the ${\mathrm{Co}}^{+1}$ magnetic form factor after subtracting a background contribution estimated from Gaussian fits to the TR cuts. The single peaked TR cuts are an outcome of the unresolvable broader dispersion branches due to the diffusive nature of the spin fluctuations. The green lines in the TR cuts are fits to a Gaussian line shape and blue solid lines are fits to the diffusive model. (e) Energy dependence of the imaginary part of the dynamical susceptibility centered at (0.55, 0.55) and averaged along the LO direction from 0.3–0.8 r.l.u. Each data point is obtained after fitting the TR cuts with a Gaussian line shape. The closed symbols are data measured with $E_i=75\mathrm{meV}$ and open symbols with $E_i=250\mathrm{meV}$.

Figure 3

(a),(b) Coupling of spins on a square lattice corresponding to stripe-type AFM and $\mathrm{FM}/\text{A}$-type spin dynamics, respectively, for an extreme degree of frustration showing effective zero coupling along the LO directions. Red and blue circles represent transition metals on different magnetic sublattices. Magnetic NN ($J_1$) and NNN ($J_2$) interactions are shown where $J_1$ is FM and $J_2$ is AFM. Stable (frustrated) bonds are denoted by a solid (dashed) lines. (c),(d) Spin fluctuations corresponding to highly frustrated spin interactions in (a) and (b), respectively. The empty rods shown in (c) are due to the twin domain of (a), that has alternating chains of blue and red circles along the perpendicular directions. Both occur with equal populations.