Atomically thin dilute magnetism in Co-doped phosphorene

Two-dimensional dilute magnetic semiconductors can provide fundamental insights into the very nature of magnetic order and their manipulation through electron and hole doping. Besides the fundamental interest, due to the possibility of control of charge density, they can be extremely important in spintronics applications such as spin valve and spin-based transistors. In this paper, we studied a two-dimensional dilute magnetic semiconductor consisting of a phosphorene monolayer doped with cobalt atoms in substitutional and interstitial defects. We show that these defects can be stabilized and are electrically active. Furthermore, by including holes or electrons by a potential gate, the exchange interaction and magnetic order can be engineered, and may even induce a ferromagnetic-to-antiferromagnetic phase transition in $p$-doped phosphorene. At a Co concentration of 2.7%, we estimate a Curie temperature of $T_{\text{C}}^{MFA}=466$ K in the mean-field approximation.

Figure 1

Ball-and-stick representation of phosphorene with (a) substitutional Co (${\mathrm{Co}}_{\mathrm{P}}$) defect and (b) interstitial (or adsorbed) Co (${\mathrm{Co}}_{\mathrm{i}}$) defect. Electronic band structures for (c) pristine phosphorene, (d) ${\mathrm{Co}}_{\mathrm{P}}$-doped phosphorene, (e),(f) ${\mathrm{Co}}_{\mathrm{i}}$-doped phosphorene for spin up and down, respectively. The Fermi level is set at zero.

Figure 2

(a)–(e) Density of states (DOS) shown as light blue and light red areas, and projected density of states (PDOS) on cobalt atoms shown as dark blue and dark red areas. The PDOS are decomposed on atomic orbitals: (a) $d_{z^2}$, (b) $d_{xy}$, (c) $d_{x^2-y^2}$, (d) $d_{xz}$, and (e) $d_{yz}$. The DOS scale is ten times larger than the PDOS scale. (f) Schematic representation of $3d$ level splitting in crystal field with $C_s$ point symmetry and exchange interaction.

Figure 3

Formation energy vs Fermi level for charged and neutral states of ${\mathrm{Co}}_{\mathrm{P}}$ (light green) and ${\mathrm{Co}}_{\mathrm{i}}$ (dark violet) defects.

Figure 4

(a) Schematic representation of Co impurity sites along zigzag and armchair directions. (b) Energy differences between parallel ($E_{\uparrow \uparrow }$) and antiparallel spins ($E_{\uparrow \downarrow }$) as a function of distance and direction.

Figure 5

Spin density isosurfaces of $\pm 2\times {10}^{-3}{\mathrm{bohrs}}^{-3}$ for (a) antiferromagnetic (AFM) order, and (b) ferromagnetic (FM) order. Positive and negative values of isosurfaces are shown in different colors. (c) Energy difference between FM and AFM orders as function of carrier densities (electrons and holes) for $n$-doped ${\mathrm{Co}}_{\mathrm{i}}$ (blue), $p$-doped ${\mathrm{Co}}_{\mathrm{i}}$ (red), $n$-doped ${\mathrm{Co}}_{\mathrm{P}}$ (green) defects.