Antiferromagnetic ground state of ${\mathrm{La}}_2{\mathrm{CuO}}_4$: A parameter-free ab initio description

We show how an accurate first-principles treatment of the antiferromagnetic ground state of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ can be obtained without invoking any free parameters such as the Hubbard $U$. The magnitude and orientation of our theoretically predicted magnetic moment of $0.495{\mu }_B$ on Cu sites along the (100) direction are in excellent accord with experimental results. The computed values of the band gap (1.00 eV) and the exchange coupling ($-138$ meV) match the corresponding experimental values. We identify interesting band splittings below the Fermi energy, including an appreciable Hund's splitting of 1.25 eV. The magnetic form factor obtained from neutron scattering experiments is also well described by our calculations. Our study thus opens up a pathway for first-principles investigations of electronic and atomic structures and phase diagrams of cuprates and other complex materials.

Figure 1

(a), (b) Electronic band dispersions of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ in the LTO crystal structure for the nonmagnetic (NM) and antiferromagnetic (AFM) phases. (c) A schematic of the NM and AFM Brillouin zones; where the path followed in the electronic dispersions in (a) and (b) is marked. (d) Crystal structure of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ in the LTO phase with copper, oxygen, and lanthanum atoms represented by blue, red, and green spheres, respectively.

Figure 2

Site-resolved partial densities of states in the nonmagnetic (NM) and antiferromagnetic (AFM) states of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ in the LTO structure. Copper and oxygen characters are plotted on the left- and right-hand sides, respectively. Shadings and lines of various colors (see legend) give contributions from various orbitals of copper, apical (${\mathrm{O}}_z$), and in-plane (O) oxygen sites.

Figure 3

Electronic band structure (blue lines) of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ in the LTO structure in the nonmagnetic (NM) and antiferromagnetic (AFM) states, overlaid with site-resolved atomic projections (red dots) for Cu $d_{x^2-y^2}$ and Cu $d_{z^2}$. The sizes of the red dots are proportional to the fractional weights of the indicated orbitals. The corresponding projected DOS for the NM and AFM states are given at the periphery of the figure on the left- and right-hand sides, respectively.

Figure 4

(a) Single copper site-resolved partial densities of states in the AFM phase of LTO ${\mathrm{La}}_2{\mathrm{CuO}}_4$. Copper $d$-orbital characters are plotted in various colors (see legend). (b) Cumulative average spin-splitting energies calculated for various $d$ orbitals for a single copper site.

Figure 5

Theoretically predicted AFM state of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ in the LTO crystal structure. Red and blue arrows represent copper and apical oxygen magnetic moments, respectively; in-plane oxygen atoms have no net magnetic moment. Octahedral faces are shaded in blue; black lines mark the unit cell.

Figure 6

Theoretical (blue line) and experimental (red dots with error bars, after Ref. [56]) magnetic form factors for the AFM ground state of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ in the LTO crystal structure. Inset: Spin-density isosurface of the Cu-O plane. Yellow (blue) colors denote positive (negative) spin density; black lines mark the unit cell.

Figure 7

The schematic molecular-bonding picture of octahedrally coordinated Cu discussed in the text.

Figure 8

Band structures (blue lines) along the high-symmetry lines in the Brillouin zone in the NM and AFM phases of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ in the LTO crystal structure. Contribution of Cu $d_{x^2-y^2}$ orbitals is highlighted with red dots. The sizes of the red dots are proportional to the fractional weights of the Cu $d_{x^2-y^2}$ orbital in the corresponding crystal wave functions. A schematic diagram of the NM and AFM Brillouin zones with the path followed in presenting the band structures is shown on the right.

Figure 9

Same as the caption to Fig. 8, except that this figure refers to O $p_x+p_y$ orbital contributions to the band structures.

Figure 10

Same as the caption to Fig. 8, except that this figure refers to Cu $d_{z^2}$ orbital contributions to the band structures.

Figure 11

Same as the caption to Fig. 8, except that this figure refers to ${\mathrm{O}}_z$ $p_z$ orbital contributions to the band structures.

Figure 12

Same as the caption to Fig. 8, except that this figure refers to Cu $s$ orbital contributions to the band structures.

Figure 13

Same as the caption to Fig. 8, except that this figure refers to Cu $t_{2g}$ orbital contributions to the band structures.

Figure 14

Same as the caption to Fig. 8, except that this figure refers to O $p_z$ orbital contributions to the band structures.

Figure 15

Same as the caption to Fig. 8, except that this figure refers to ${\mathrm{O}}_z$ $p_x+p_y$ orbital contributions to the band structures.