Magnetic phase transition induced by electrostatic gating in two-dimensional square metal-organic frameworks

We investigate theoretically magnetism and magnetic phase transitions induced by electrostatic gating of two-dimensional square metal-organic framework compounds. We find that electrostatic gating can induce phase transitions between homogeneous ferromagnetic and various spin-textured antiferromagnetic states. Electronic structure and Wannier function analysis can reveal hybridizations between transition-metal $d$ orbitals and conjugated $\pi$ orbitals in the organic framework. Mn-containing compounds exhibit a strong $d-\pi$ hybridization that leads to partially occupied spin-minority bands, in contrast to compounds containing transition-metal ions other than Mn, for which electronic structure around the Fermi energy is only slightly spin split due to weak $d-\pi$ hybridization and the magnetic interaction is of the Ruderman-Kittel-Kasuya-Yosida type. We use a ferromagnetic Kondo lattice model to understand the phase transition in Mn-containing compounds in terms of carrier density and illuminate the complexity and the potential to control two-dimensional magnetization.

Figure 1

Unit cell of transition-metal-embedded two-dimensional square (a) poly-pythalocyanine (poly-Pc) and (b) poly-(5,10,15,20-tetra(phenyl)porphyrin) (poly-TPP) metal-organic frameworks. The lattice constant is $10.67\AA$ for TM-poly-Pc and $17.80\AA$ for TM-poly-TPP.

Figure 2

DFT total energies of the ferromagnetic (FM, circles), collinear antiferromagnetic (CAF, squares), and Néel antiferromagnetic (NAF, triangles) configurations, for (a) Fe-poly-Pc, (b) Mn-poly-Pc, and (c) Mn-poly-TPP. Magnetic phase diagrams in the $J_1-J_2$ plane are shown in (d), (e), and (f). Arrows denote the increase of net charge density from negative (electron-doped) to positive (hole-doped). Schematic magnetic configurations are shown in (g).

Figure 3

The band structure (left panel) and density of states (right panel) of (a) Fe-poly-Pc, (b) Mn-poly-Pc, and (c) Mn-poly-TPP in the ferromagnetic configuration. Spin-up and spin-down channels are denoted as different colors. The total density of states is denoted by dashed lines, and that projected onto transition metal $d$ orbitals by solid lines. The projected density of states on $d_{xz}$ and $d_{yz}$ are the same and are emphasized by the filled regions.

Figure 4

Wannier function corresponding to the Mn-$d_{yz}$ orbital in (a) Mn-poly-Pc and (b) Mn-poly-TPP.

Figure 5

Magnetic phase transitions in Mn-poly-Pc using the DFT+$U$ method with $U=5\mathrm{eV}$ and $J=1\mathrm{eV}$.

Figure 6

Band structures of ${\mathrm{H}}_2$-poly-Pc, TM-poly-Pc, ${\mathrm{H}}_2$-poly-TPP, and TM-poly-TPP, with TM=Cr, Mn, Fe, Co, and Ni. TM-poly-Pc and TM-poly-TPP are in the ferromagnetic configuration.

Figure 7

Magnetic properties of Cr-poly-Pc and Cr-poly-TPP. Total energies of Cr-poly-Pc and Cr-poly-TPP in the FM, CAF, and NAF configurations are shown in (a) and (b), and magnetic phase diagrams in the $J_1-J_2$ plane of Cr-poly-Pc and Cr-poly-TPP are shown in (c) and (d).