Prediction of room-temperature two-dimensional $π$-electron half-metallic ferrimagnets

Abstract

We propose a strategy to obtain conducting organic materials with fully spin-polarized Fermi surface, lying at a singular flat band, with antiferromagnetically coupled magnetic moments that reside in pi-orbitals of nanographenes. We consider a honeycomb crystal whose unit cell combines two different molecules with S=1/2: an Aza-3-Triangulene, a molecule with orbital degeneracy, and a 2-Triangulene. The analyzed system is half-metallic with a ferrimagnetic order, presenting a zero net total magnetic moment per unit cell. We combine density functional theory calculations with a Hubbard model Hamiltonian to compute the magnetic interactions, the bands, the intrinsic Anomalous Hall effect, and the collective spin excitations. We obtain very large intermolecular exchange couplings, in the range of 50 meV, which ensures room temperature stability. When the magnetization is off-plane, intrinsic spin orbit coupling in graphene opens up a topological gap that, despite being very small, leads to a quantized Hall conductance in the tens of mK range. Above 1 Kelvin, the system will behave like a half-metal with fully compensated magnetic moments, thereby combining two characteristics that make it ideal for spintronics applications.

Figures (7)

• Figure 1: DFT computed magnetic profiles, electronic bandstructure and DOS (eV$^{-1}$) for the [2,3]triangulene a),b),c), and for the [2,A3]triangulene d),e),f). Spin up (down) is represented in red (blue) in the bandstructures computed via MFH b),e) and for the DFT magnetic profiles, bandstructures and DOS c),f). Solid line at 0 energy represents the Fermi level (E$_F$). Horizontal dashed lines in e), located at $\pm 25 meV$, represent the values of the scanned energies used for computing LDOS.
• Figure 2: a) Gap opening at the $\Gamma$ point in the presence of intrinsic SOC. The size of the gap is proportional to the strength of SOC i.e. $\lambda_\textrm{SOC}$. b) Berry curvature, $\Omega_n (\boldsymbol{k}$), in the first Brillouin zone for the the valence band (VB) and conduction band (CB). c) Zero frequency Hall conductivity, as a function of the chemical potential detuning, $\delta\mu = \mu - E_F$, at three different temperatures. A value of $\lambda_{SOC} = 45 \mu$ eV was used in the simulations.
• Figure 3: a) Magnon energies for selected wave vectors extracted from the fermionic model, for the two magnon flavors $S^z=-1$ (blue) and $S^z=1$ (red). The red dashed line marks the lower energy boundary of the $S^z=1$ Stoner continuum. Notice the large magnon energies at the edges of the BZ, compatible with the large exchange estimated from the DFT calculation. b) Total magnon density of states for $S^z=-1$ (blue) and $S^z=1$ (red). The solid lines are guides to the eye.
• Figure 4: Detecting magnons with inelastic scanning tunneling spectroscopy. The left panel a) shows schematic depictions of the inelastic tunneling processes that can lead to a feature associated with the emission of a magnon in the differential conductance of an ISTS experiment. The right panel b) shows local electron (elastic) and magnon (inelastic) local density of states maps for two values of the tip-sample bias: at $eV=-25\textrm{ meV}$ elastic tunneling from the triangulene crystal is suppressed for both spin polarizations of the tip due to the absence of available electronic states; inelastic tunneling is possible by creating a magnon of either $S^z=\pm 1$. At $eV=25\textrm{ meV}$, elastic tunneling is suppressed for tip polarization parallel to that of the individual aza-triangulene because the electronic band close to the Fermi level is polarized in the opposite direction. Inelastic tunneling is possible for both spin polarizations of the tip, each by exciting a magnon with the same energy polarization as the tip.
• Figure 5: Crystal structure for a) the undoped [2,3]triangulene and b) the doped triangulene. Brown atoms represent C atoms, light pink represent H atoms and the doped atom at the center of the [3]trianguelne is represented in light blue. Different computed doped structures are represented, when doping with boron c),d),e), with nitrogen f),g),h) and with phosphorus i),j),k). Monomers for the different doped structures are shown c),f),i), together with their respective magnetic profiles d),g),j) and their corresponding bandstructures e),h),k). In the magnetic profiles and the bandstructures, red (blue) represents spin up (down). Fermi level is depicted with a dashed line in the bandstructure plots, and it becomes obvious that for every doped case it lies very close to a nearly flat band.