Theoretical study of the magnetic order in $\alpha$-CoV${}_2$O${}_6$

The electronic structure and magnetic properties of $\alpha$-CoV${}_2$O${}_6$ are investigated using density functional theory calculations including spin-orbit coupling and orbital polarization effects. These calculations reveal a strong magnetocrystalline anisotropy with a magnetization easy axis close to the $c$ axis. The evaluation of magnetic couplings on the basis of broken-symmetry formalism suggests the occurrence of an antiferromagnetic ground-state order where ferromagnetic chains running along $b$ are coupled antiferromagnetically to their nearest neighbors along $a$ and $c$. Monte Carlo simulations are finally employed to explore the origins of the $1/3$ plateau observed in the magnetization curves of this compound and to propose a structure for the corresponding state.

Figure 1

(a) Atomic structure of $\alpha$-CoV${}_2$O${}_6$: Red balls denote oxygen ions, CoO${}_6$ octahedra are shown in blue, and VO${}_5$ square pyramids in green. (b) Magnetic couplings in $\alpha$-CoV${}_2$O${}_6$. Intrachain couplings ($J_1$ and $J_6$) are shown in red and interchain couplings ($J_2$, $J_3$, $J_4$, $J_5$, and $J_7$) are shown in blue. (c) Splitting of the Co $3d$ levels illustrating successively the effects of the tetragonal and orthorhombic distortions of the Co coordination octahedron.

Figure 2

(a) Co, V, and O projected densities of states calculated in the GGA with the experimental crystal structure and a ferromagnetic arrangement of the Co magnetic moments in $\alpha$-CoV${}_2$O${}_6$; (b) Co $3d$ projected density of states calculated with the $\text{GGA}+\text{SO}+\text{OP}$ decomposed on complex $d_m$ orbitals. For symmetry reasons, a nonconventional orientation of the local system of coordinates has been chosen.

Figure 3

Graphical representation of the results obtained using the least-squares fit procedure: for each configuration, the DFT relative energy is represented as a function of the optimized Ising energy. The best-fit values are shown in the inset. According to the convention used in Eq. (2), positive couplings correspond to AF interactions. (a) Magnetization along the easy axis. (b) Magnetization perpendicular to the easy axis.

Figure 4

(a) Magnetic couplings computed in $\alpha$-CoV${}_2$O${}_6$ up to the seventh-nearest neighbor for a direction of the magnetization along or perpendicular to the magnetic easy axis.

Figure 5

Magnetization curve obtained by Metropolis Monte Carlo calculations. The schematic structures corresponding to antiferromagnetic ($M/M_s=0$ for $h<h_{c1}$), intermediate ($M/M_s=1/3$ for $h_{c1}<h<h_{c2}$), and ferromagnetic ($M/M_s=1$ for $h>h_{c2}$) orders are shown in the insets. The crystal is observed along the chain direction and red (blue) octahedra represent spin-up (spin-down) magnetic moments.