Electronic structure and spin dynamics of $A\mathrm{C}{\mathrm{o}}_2\mathrm{A}{\mathrm{s}}_2\left(A=\mathrm{Ba},\mathrm{Sr},\mathrm{Ca}\right)$

The electronic structures, charge, and spin dynamics of the cobalt pnictide compounds $A\mathrm{C}{\mathrm{o}}_2\mathrm{A}{\mathrm{s}}_2\left(A=\mathrm{Ba},\mathrm{Sr},\mathrm{Ca}\right)$ in the paramagnetic state are investigated by using density functional theory combined with dynamical mean-field theory. In contrast to their iron counterparts, these cobalt pnictide compounds have three-dimensional electronic structures and strong ferromagnetic low-energy spin excitations. The $\mathrm{Co}3d{e}_g$ orbitals dominate the electronic states around the Fermi level and have stronger electronic correlation strength than the $\mathrm{Co}3d{t}_{2g}$ orbitals. The overall electronic correlation strength is much weaker than that in the iron arsenides; however, the most strongly correlated $\mathrm{Co}3d{x}^2-y^2$ orbital, especially in ${\mathrm{CaCo}}_2{\mathrm{As}}_2$, has electronic correlation strength comparable to $\mathrm{Fe}3d{t}_{2g}$ orbitals in iron arsenides. $A\mathrm{C}{\mathrm{o}}_2\mathrm{A}{\mathrm{s}}_2\left(A=\mathrm{Ba},\mathrm{Sr},\mathrm{Ca}\right)$ shows similar electronic structures where a conduction band of primarily $\mathrm{Co}3d{x}^2-y^2$ orbital character is close to a Van Hove singularity around the Brillouin-zone corner, which promotes ferromagnetic low-energy spin excitations. Originated from its increased nearest-neighbor Co-Co distance and significantly reduced As height from the Co plane, the strong electronic correlation strength and close proximity to the Van Hove singularity of the $\mathrm{Co}3d{x}^2-y^2$ orbital in ${\mathrm{CaCo}}_2{\mathrm{As}}_2$ is responsible for its unique A-type antiferromagnetic order observed in experiments. In comparison, despite substantial ferromagnetic low-energy spin excitations, ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ and ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ remain paramagnetic down to very low temperature because the $\mathrm{Co}3d{x}^2-y^2$ orbital has weaker electronic correlation strength and is further away from the Van Hove singularity.

Figure 1

The electronic band structure (a)–(f) and $\mathrm{Co}3d$ partial density of states (g)–(i) of ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ (a), (d), (g), ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ (b), (e), (h), and ${\mathrm{CaCo}}_2{\mathrm{As}}_2$ (c), (f), (i) obtained by $\mathrm{DFT}+\mathrm{DMFT}$ calculations (a)–(c), (g)–(i) and standard DFT calculations (d)–(f) in the paramagnetic state.

Figure 2

Three-dimensional Fermi surfaces for (a) ${\mathrm{BaCo}}_2{\mathrm{As}}_2$, (b) ${\mathrm{SrCo}}_2{\mathrm{As}}_2$, and (c) ${\mathrm{CaCo}}_2{\mathrm{As}}_2$ plotted in the PM tetragonal Brillouin zone obtained by $\mathrm{DFT}+\mathrm{DMFT}$ calculations. The corresponding two-dimensional FS cuts in ${k_z}_{}=0$ and $2\pi /\mathrm{c}$ plane of ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ (d), (e), ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ (f), (g), and ${\mathrm{CaCo}}_2{\mathrm{As}}_2$ (i), (j) in the first Brillouin zone of the one-Co unit cell. The black, red, green, and blue colors denote the $\mathrm{Co}3d{z}^2$, $x^2-y^2$, $xz/yz$, and $xy$ orbital characters, respectively. In panels (d)–(i), the units of the reciprocal-lattice vector $k_x$ and $k_y$ are $\sqrt{2}\pi /a$.

Figure 3

Dynamic spin structure factor $S\left(q,\omega \right)$ for ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ (left column) and ${\mathrm{CaCo}}_2{\mathrm{As}}_2$ (right column). From top to bottom are the total $S\left(q,\omega \right)$ (a), (e) and the diagonal component $S_{\alpha ,\alpha }\left(q,\omega \right)$ ($\alpha$ is the orbital index) of the $\mathrm{Co}3d{x}^2-y^2$ orbital (b), (f) and $z^2$ orbital (c), (g) along the high-symmetry path $\left(0,0\right)\to \left(1,0\right)\to \left(1,1\right)\to \left(0,0\right)$, and (d), (h) the 2D plot in the $L=0$ plane with constant energy $\omega =5\mathrm{meV}$. The $S\left(q,\omega \right)$ of ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ is very similar to that of ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ and thus is not shown. The wave vector is defined in terms of the reciprocal lattice of the one-Co unit cell.

Figure 4

The (a) in-plane and (b) out-of-plane optical conductivity of $A\mathrm{C}{\mathrm{o}}_2\mathrm{A}{\mathrm{s}}_2\left(A=\mathrm{Ba},\mathrm{Sr},\mathrm{Ca}\right)$ in the PM state obtained by $\mathrm{DFT}+\mathrm{DMFT}$ calculations.