Mixed configuration ground state in iron(II) phthalocyanine

We calculate the angular dependence of the x-ray linear and circular dichroism at the $L_{2,3}$ edges of $\alpha$-Fe(II) Phthalocyanine (FePc) thin films using a ligand-field model with full configuration interaction. We find the best agreement with the experimental spectra for a mixed ground state of ${}^3{E}_g\left(a_{1g}^2{e}_g^3{b}_{2g}^1\right)$ and ${}^3{B}_{2g}\left(a_{1g}^1{e}_g^4{b}_{2g}^1\right)$ with the two configurations coupled by the spin-orbit interaction. The ${}^3{E}_g\left(b\right)$ and ${}^3{B}_{2g}$ states have easy-axis and easy-plane anisotropies, respectively. Our model accounts for an easy-plane magnetic anisotropy and the measured magnitudes of the in-plane orbital and spin moments. The proximity in energy of the two configurations allows a switching of the magnetic anisotropy from easy plane to easy axis with a small change in the crystal field, as recently observed for FePc adsorbed on an oxidized Cu surface. We also discuss the possibility of a quintet ground state (${}^5{A}_{1g}$ is 250 meV above the ground state) with planar anisotropy by manipulation of the Fe-C bond length by depositing the complex on a substrate that is subjected to a mechanical strain.

Figure 1

(a) Crystal-field levels of the $d$ orbitals in FePc obtained from the fitting of the experimental spectra [26] and (b) energy-level diagram showing the ground state and lowest-lying $dd$ excitations obtained from exact diagonalization of the many-body Hamiltonian.

Figure 2

Best fit to the experimental x ray linearly polarized absorption (XLPA) (a) and XMCD (b) at the Fe $L_{2,3}$ edges. We show the calculated spectra for different x-ray incidence angles $\theta =0,45,{75}^{\mathrm{o}}$ with respect to the FePc $C_4$ axis. The XLPA plot (a) includes the classification of the absorption peaks in terms of transitions to valence orbitals belonging to different representations of $D_{4h}$. The spectra correspond to a mixed ${}^3{E}_g\left(b\right)$ and ${}^3{B}_{2g}$ ground state. We also show in panel (c) the expectation values of the spin ${\langle m_S\rangle }_{\theta }$ and orbital ${\langle m_L\rangle }_{\theta }$ magnetic moments along the direction of the applied magnetic field ($H=5$ T) as a function of $\theta$. We also include the effective spin moment ${\langle m_S^{\mathrm{eff}}\rangle }_{\theta }$ that results from applying the spin sum rule to the calculated spectra.

Figure 3

Dependence with the x-ray incidence angle $\theta$ of the x-ray linearly polarized absorption (XLPA) and XMCD for single-configuration ${}^3{\mathrm{E}}_g\left(b\right)$ (a, b) and ${}^3{\mathrm{B}}_{2g}$ (d, e) ground states. (c, f) Angular dependence of the expectation values of the spin ${\langle m_S\rangle }_{\theta }$ and orbital ${\langle m_L\rangle }_{\theta }$ magnetic moments along the magnetic field together with the spin magnetic moment determined from the XMCD sum rule ${\langle m_S^{\mathrm{eff}}\rangle }_{\theta }$.

Figure 4

Changes in the ground state and magnetic anisotropy as a function of the change in the crystal-field energies: (a–d) varying the energy of the $a_{1g}\left(d_{z^2}\right)$ orbital and (e–h) changing the $b_{1g}\left(d_{x^2-y^2}\right)$ energy. $\mathrm{\Delta }\varepsilon \left(a_{1g}\right)$ and $\mathrm{\Delta }\varepsilon \left(b_{1g}\right)$ correspond to the difference in the single-particle orbital energies from the fitted values. The plots show the orbital and spin magnetic moments generated for axial and in-plane applied fields, the changes in the orbital occupations, and the energies relative to the ground state for the three configurations ${}^3{B}_{2g},{}^3{E}_g\left(b\right)$, and ${}^5{A}_{1g}$. The splitting of the configurations produced by spin-orbit coupling are not shown in (d) and (h).

Figure 5

Spin magnetic moment ${\langle m_S\rangle }_{\theta }$ along the direction of the applied magnetic field ($H=5$ T) as a function of the rotation angle $\theta$ of the ligand environment for different ground states in tetragonal $\left(D_{4h}\right)$, octahedral $\left(O_h\right)$, and trigonal $\left(D_{3h}\right)$ symmetries. The spin-moment values are plotted together with the effective spin ${\langle m_{\text{SE}}\rangle }_{\theta }$ that includes the magnetic dipole contribution $\left({\text{SE}}_z=S_z+\frac{7}{2}{T}_z\right)$ and the spin value ${\langle m_{\text{SR}}\rangle }_{\theta }$ determined from the application of the spin sum rule to the calculated XMCD spectra.