Magnetic Ordering under Strain and Spin-Peierls Dimerization in ${\mathrm{GeCuO}}_3$

Studying from first principles the competition between ferromagnetic (FM) and antiferromagnetic (AF) interactions in the charge-transfer-insulator ${\mathrm{GeCuO}}_3$, we predict that a small external pressure should switch the uniform AF ground state to FM, and estimate (using exchange parameters computed as a function of strain) the competing AF couplings and the transition temperature to the dimerized spin-Peierls state. Although idealized as a one-dimensional Heisenberg antiferromagnet, ${\mathrm{GeCuO}}_3$ is found to be influenced by nonideal geometry and side groups.

Figure 1

Structure of $Pmma$ AF ${\mathrm{GeCuO}}_3$. Dashed line: nonmagnetic unit cell (2 f.u.); AF cell is doubled along $c$. Internal parameters [10]: $x_1(\mathrm{Ge})=0.0743$, $x_1(\mathrm{O}2)=0.87$, $x_1(\mathrm{O}1)=0.2813$, $x_2(\mathrm{O}1)=0.0838$.

Figure 2

Band energies of AF ${\mathrm{GeCuO}}_3$. $K$ points: $X=[1/2,0,0]$, $M=[1/2,1/2,0]$, $R=[1/2,1/2,1/2]$, $M^{\prime }=[0,1/2,1/2]$, $M^{\prime \prime }=[1/2,0,1/2]$ in units of $2\pi /a$, $2\pi /b$, $2\pi /c$. Energy zero is the valence band top.

Figure 3

Orbital-resolved DOS of AF ${\mathrm{GeCuO}}_3$. For clarity, only $d$ $t_{2g}$ orbitals are shown for Cu (the $e_g$’s are localized and lie 4 to 6 eV interval below $E_F$).

Figure 4

Hole magnetization in ${\mathrm{GeCuO}}_3$ in a 4 eV energy interval above $E_F$. Cyan (light) and red (dark) isosurfaces: magnetization density $\pm 0.027/{\mathrm{Bohr}}^3$, respectively.

Figure 5

Panel (a) (upper): AF-FM energy difference per cell $\delta E=2\times J_c$, magnetic stress ${\sigma }_M$, and raw FM and AF energies vs Cu-O1-Cu angle. Vertical lines: FM-AF crossover (solid) and theoretical equilibrium (dashed). Panel (b) (lower): same, vs $b/a$ ratio. See text for discussion.

Figure 6

Panel (a) (upper): orbital occupations of O1 $p_x$,$p_y$,$p_z$, minority Cu $d_{xz}$ vs Cu-O1-Cu angle. Panel (b) (lower): same, plus Ge s, vs $b/a$ ratio. See text for discussion.