Magnetic phases of electron-doped infinite-layer ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{\mathrm{CuO}}_2$ from first-principles density functional calculations

The magnetic phases of electron-doped infinite-layer ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{\mathrm{CuO}}_2$ are elucidated by first-principles density functional calculations. The antiferromagnetic parent state, metallic transition, as well as lattice evolution with doping and pressure are found to be consistent with experiments. The specific heat coefficient $\gamma$, magnetic exchange coupling $J$, as well as the density of states at Fermi level $N\left(0\right)$ of low-energy states with multiple magnetic configurations are investigated. We highlight a subset of such states in which we note an increase in $N\left(0\right)$ to suggest the interesting effects of magnetic fluctuations and La substitution on the electronic structure of this material.

Figure 1

The unit cell of ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{\mathrm{CuO}}_2$ (SLCO) with the atoms occupying Sr/La, O, and Cu sites represented by green, red, and blue spheres, respectively.

Figure 2

Schematics of the (a) “G” and (b) “C” AFM configurations in a $\sqrt{2}\times \sqrt{2}\times 2$ supercell. The AF moments are drawn to align normal to the ${\mathrm{CuO}}_2$ plane for simplicity. Blue and red spheres represent Cu and O atoms. Sr atoms have been omitted for clarity.

Figure 3

A schematic energy diagram of our search. The AFM G, C, and nonmagnetic states are robust. Most of our calculations from various starting conditions converge into these single-phase states, which we illustrate with deep arcs (large curvature). The ground state is drawn with solid curves to indicate its position as the most stable state. The multiphase states are low-energy states that our calculations may end up converging into, given suitable initial parameters. These are drawn in shallow arcs (small curvature). We search for such local minima with increased DOS at Fermi level, $N\left(0\right)$.

Figure 4

The plotted band structure for SLCO with $x=0$ (blue) and $x=0.25$ (orange) [35]. Only the spin-up bands are shown. The Fermi level is set to zero. A metallic phase transition with electron doping character is achieved.

Figure 5

The lattice parameters versus $\mathrm{La}$ concentration $x$. The open (closed) symbols denote DFT values without (with) magnetic order. Experimental values are from Ref. [34].

Figure 6

The top view of AFM supercells for the magnetic anisotropy energy study. Blue and red spheres represent Cu and O atoms. Black vectors represent the sign of magnetic moment at Cu sites. Dashed lines indicate the direction along the Cu-O-Cu bond. Structures with AFM order aligned within the ${\mathrm{CuO}}_2$ plane along the (a) Cu-Cu and (b) Cu-O-Cu directions are shown.

Figure 7

(a) The top view of a $4\times 4\times 2$ supercell in the $\mathrm{G}+\mathrm{E}$ state for SLCO with $x=0.0625$. Yellow, red, and blue spheres represent La, O, and Cu atoms. Sr atoms have been omitted for clarity. The magnetic moments are drawn along the ${\mathrm{CuO}}_2$ plane for simplicity. The orange vectors illustrate the magnetic moments at corner sites, for which an E-type magnetic order [30] can be observed. Dotted lines mark the Cu-O bonds. (b) The DOS normalized per Cu atom of $\text{G}$ and $\text{G}+\text{E}$ states. The Fermi level is set to zero. Only the spin-up DOS is shown. Inset: The DOS from single Cu atom located at the corner sites in the $\mathrm{G}+\mathrm{E}$ state. Upper and lower halves of the inset illustrate the spin-up and spin-down DOS, respectively. The orange (blue) curve marks the DOS from sites with positive (negative) magnetic moment $m$.

Figure 8

An illustration of the $2\times 2\times 5$ supercell in the $\mathrm{G}+\mathrm{C}+\mathrm{N}$ state for SLCO with $x=0.1$, viewed along the ${\mathrm{CuO}}_2$ plane. Yellow, red, and blue (white) spheres represent La, O, and magnetic (nonmagnetic) Cu atoms. Sr atoms are omitted for clarity. The magnetic moments are drawn normal to the ${\mathrm{CuO}}_2$ planes for simplicity.

Figure 9

The $\sqrt{2}\times \sqrt{2}\times 4$ supercell in the $\mathrm{G}+\mathrm{N}$ state for SLCO with $x=0.125$ with the nonmagnetic sites being closer (a) and further (b) from the dopant site. The Sr atoms are omitted for clarity. Yellow, red, and blue (white) spheres represent La, O, and magnetic (nonmagnetic) Cu atoms. The magnetic moments are drawn normal to the ${\mathrm{CuO}}_2$ planes for simplicity. (c) The total DOS (in black) for $\text{G}+\text{N}$ state from (b). The Fermi level is set to zero. Projected DOS to the Cu $d$ and O $p$ orbitals from magnetic and nonmagnetic planes are shown in blue and red traces, respectively.

Figure 10

The density of states at Fermi level $N\left(0\right)$ and the estimated specific heat coefficient ${\gamma }_n^0$ for ${\mathrm{Sr}}_{0.875}{\mathrm{La}}_{0.125}{\mathrm{CuO}}_2$ in the G (closed symbols) and $\mathrm{G}+\mathrm{N}$ (open symbols) states under hydrostatic ($P_{\mathrm{all}}$), in-plane ($P_{ab}$), and uniaxial $c$-axis ($P_c$) compressions.