Beyond the Heisenberg Model: Anisotropic Exchange Interaction between a Cu-Tetraazaporphyrin Monolayer and ${\mathrm{Fe}}_3{\mathbf{O}}_4(100)$

The exchange coupling of a single spin localized at the central ion of Cu-tetraazaporphyrin on a magnetite(100) surface has been studied using x-ray magnetic circular dichroism (XMCD). Sum rule analysis of the XMCD spectra results in Cu spin and orbital magnetic moments as a function of the applied external field at low temperatures (20 K). The exchange coupling is positive for magnetization direction perpendicular to the surface (ferromagnetic) while it is negative for in-plane magnetization direction (antiferromagnetic). We attribute the anisotropy of the Heisenberg exchange coupling to an orbitally dependent exchange Hamiltonian.

Figure 1

Sketch of the anisotropic exchange coupling of the Cu spin in Cu4Dinit to the octahedral Fe spin in the ${\mathrm{Fe}}_3{\mathrm{O}}_4(100)$ surface. The ${\mathrm{Fe}}_3{\mathrm{O}}_4(100)$ surface structure is adapted from Ref. 28.

Figure 2

XAS intensity at 20 K for circular polarization at the Cu $2p\to 3d$ transition normalized to the maximum. Insets indicate (from top to bottom) Cu4Dinit powder sample, Cu4Dinit ML measured for the remanent state of the magnetite film without applied field, Cu4Dinit ML measured with external field of 4.5 T applied at an angle of 55° with respect to the normal, and Cu4Dinit ML measured with external field of 1.2 T applied perpendicular to the surface.

Figure 3

XMCD calculated from the difference of XAS data measured with parallel and antiparallel orientation of magnetic field and photon spin. Same series of measurements as in Fig. 2.

Figure 4

Cu $2p\to 3d$ XAS and XMCD spectra measured for the Cu4Dinit ML on magnetite. (a) Solid (dashed) ($I^{+(-)}$) lines show the XAS spectra measured with external field 1.2 T applied parallel (antiparallel) to the surface normal and to the spin of the incident photon beam. (b) Full ($I^{+}-I^{-}$) and dotted ($\sum _{}^{}{I}_{\mathrm{XMCD}}/\sum _{}^{}{I}^{\mathrm{ISO}}$) lines represent the XMCD and its integrated spectrum normalized to the isotropic energy-integrated x-ray absorption.

Figure 5

Cu $2p\to 3d$ XAS and XMCD spectra measured for the Cu4Dinit ML on magnetite at 55° angle of incidence of the photon beam. (a) Solid (dashed) ($I^{+(-)}$) lines show the XAS spectra measured in the parallel (antiparallel) remanent magnetization state of the magnetite film without external field. (b) Solid ($I^{+}-I^{-}$) and dotted ($\sum _{}^{}{I}_{\mathrm{XMCD}}/\sum _{}^{}{I}^{\mathrm{ISO}}$) lines represent the XMCD and its integrated spectrum normalized to the isotropic energy-integrated x-ray absorption.