Two-dimensional intrinsic ferromagnetic monolayer transition metal oxyhydroxide

Using density functional theory within the generalized gradient approximation, we predict that monolayer vanadium oxyhydroxide (VOOH) and chromium oxyhydroxide (CrOOH) are two-dimensional (2D) ferromagnetic semiconductors. These two kinds of oxyhydroxides possess excellent thermal and dynamical stability as the free-standing 2D monolayer films. Our results show that the monolayer VOOH and CrOOH remain ferromagnetic ordering with the critical temperature up to $\sim 100\mathrm{K}$, and the ferromagnetic ordering is due to a superexchange interaction in the near-${90}^{\circ }$ V(Cr)-O-V(Cr) bonds in monolayer VOOH(CrOOH). However, the different occupancy of $d$ electrons between the ${\mathrm{V}}^{3+}$ and ${\mathrm{Cr}}^{3+}$ ions gives rise to the different axes or planes of easy magnetization and the different magnetic anisotropy energies between the monolayer VOOH and CrOOH. Our study demonstrates that monolayer transition metal oxyhydroxides could be one category of testing ground for the investigation of 2D ferromagnets.

Figure 1

(a) Top and (b) side views of the monolayer TMOOH with transition metal atoms represented by blue balls, O atoms represented by red balls, and H atoms represented by pink balls. The rhombic unit cell is marked by the black dashed lines. And the FM and AFM configurations (the stripe AFM and the zigzag AFM configurations) constructed in $2\times 2\times 1$ supercells are marked by yellow and green dashed rectangular boxes, respectively. Calculated phonon spectra for the monolayer (c) VOOH and (e) CrOOH. Evolutions of total energies during FPMD simulations for monolayer (d) VOOH and (f) CrOOH at the temperature of 300 K, where insets are snapshots of monolayer VOOH and CrOOH at the end of 15 ps of FPMD simulations.

Figure 2

(a) Total density of states (TDOS) and atomic projected density of states (PDOS) of monolayer VOOH. Orbital PDOS of (b) V-$d$ and (c) O2-$p$ orbitals of monolayer VOOH. (d) TDOS and atomic PDOS of monolayer CrOOH. Orbital PDOS of (e) Cr-$d$ and (f) O2-$p$ orbitals of monolayer CrOOH. The blue and pink shadows represent the hybridization between TM-$d$ and O2-$p$ orbitals. Fermi level is set at zero energy.

Figure 3

(a) Set of $XYZ$ coordinates in the monolayer TMOOH. (b) Schematic plot of $e_1$ and $e_2$ orbitals derived from Eq. (1). Schematic plot of the hopping channel involved in the (c) AFM superexchange: $a_1\text{−}{p}_z\text{−}{a}_1$ and (d) (near-) ${90}^{\circ }$ FM superexchange: $e_{a2}\text{−}(p_x,p_y)\text{−}{e}_{b2}$. Virtual hopping between $d$ orbitals of TM cations intermediated by O2-$p$ orbitals in monolayer (e) VOOH and (f) CrOOH where red and black dashed lines represent ferromagnetic and antiferromagnetic coupling, respectively.

Figure 4

Relative energy of monolayer (a) VOOH and (b) CrOOH with the magnetization rotated in $XY$ (black line) and $YZ$ planes (red line), with reference to the global minimum of energy.