Hidden spin liquid in an antiferromagnet: Applications to FeCrAs

The recently studied material FeCrAs exhibits a surprising combination of experimental signatures, with metallic, Fermi-liquid-like specific heat but resistivity showing strong nonmetallic character. The $\mathrm{Cr}$ sublattice posseses local magnetic moments, in the form of stacked (distorted) kagome lattices. Despite the high degree of magnetic frustration, antiferromagnetic order develops below $T_N\sim 125\text{K}$ suggesting the nonmagnetic $\mathrm{Fe}$ sublattice may play a role in stabilizing the ordering. From the material properties we propose a microscopic Hamiltonian for the low-energy degrees of freedom, including the nonmagnetic $\mathrm{Fe}$ sublattice, and study its properties using slave-rotor mean-field theory. Using this approach we find a spin-liquid phase on the $\mathrm{Fe}$ sublattice, which survives even in the presence of the magnetic $\mathrm{Cr}$ sublattice. Finally, we suggest that the features of FeCrAs can be qualitatively explained by critical fluctuations in the nonmagnetic Fe sublattice due to proximity to a metal-insulator transition.

Figure 1

FeCrAs unit cell viewed along the $c$ axis (left) and tilted away by ${70}^{\circ }$ (right). Fe atoms are indicated in green, Cr in blue, and As in yellow.

Figure 2

(a) The Fe sublattice with trimers shown explicitly. (b) The local environment of the trimer, with respect to the Cr sublattice.

Figure 3

The local environments of the $\mathrm{Fe}$ (a), $\mathrm{Cr}$ (b), and trimer (c). The Fe atom is tetrahedrally coordinated and the Cr atom is approximately octahedrally coordinated. The trimer is surrounded by three tetrahedra that share a common axis.

Figure 4

The effect of the crystal field on the Fe${}^{3+}$ ion. The local symmetry about this site is tetrahedral; that is, the group $T_d$.

Figure 5

The effect of crystal fields on the Cr${}^{2+}$ ion. The Cr ion is biased toward one direction of the octahedron. This reduces the symmetry to the group $C_{4v}$.

Figure 6

The two cases that give rise to a half-filled band, with $t_{xy,xy}\approx t_{xz,yz}$. We can either have a band with (a) $d_{xy}$ character or with (b) $d_{+}$ character.

Figure 7

The hoppings and exchanges for the model Hamiltonian in Eq. (14). The notations are discussed in the text.

Figure 8

Phase diagram as a function of $J_K/t$ and $U/t$ for the value $J_H/t=0.4$. The inset diagrams show a sample of the $\mathrm{Cr}$ spin configuration on one of the kagome triangles. $\chi$ and $B$ are the slave-rotor mean-field parameters, $\langle \phi \rangle$ is the rotor condensate, and $\psi$ is the $\mathrm{Cr}$ canting angle (see text).

Figure 9

The orbitals of the $t_2$ level, rotated along the local axes of an As tetrahedron.