Long-range ferrimagnetic order in a two-dimensional supramolecular Kondo lattice

Abstract

Realization of long-range magnetic order in surface-supported two-dimensional systems has been challenging, mainly due to the competition between fundamental magnetic interactions as the short-range Kondo effect and spin-stabilizing magnetic exchange interactions. Spin-bearing molecules on conducting substrates represent a rich platform to investigate the interplay of these fundamental magnetic interactions. Here we demonstrate the direct observation of long-range ferrimagnetic order emerging in a two-dimensional supramolecular Kondo lattice. The lattice consists of paramagnetic hexadeca-fluorinated iron phthalocyanine (FeFPc) and manganese phthalocyanine (MnPc) molecules co-assembled into a checkerboard pattern on single-crystalline Au(111) substrates. Remarkably, the remanent magnetic moments are oriented in the out-of-plane direction with significant contribution from orbital moments. First-principles calculations reveal that the FeFPc-MnPc antiferromagnetic nearest-neighbour coupling is mediated by the Ruderman-Kittel-Kasuya-Yosida exchange interaction via the Au substrate electronic states. Our findings suggest the use of molecular frameworks to engineer novel low-dimensional magnetically ordered materials and their application in molecular quantum devices.

Figure 1. Assessing competing fundamental magnetic interactions.

(a) Scheme of the FeFPc and (b) scheme of the MnPc molecules. The former has all hydrogen atoms on the periphery of the molecule replaced with fluorine. The pictograms shown next to the molecular sketches are used to distinguish the molecules. (c) STM image (Bias=−2.2 V, I_t=5 pA) acquired on an extended domain of FeFPc and MnPc molecules on a Au(111) substrate co-assembled in a checkerboard pattern. Scale bar, 10 nm. The inset shows a zoom of the STM image providing details of the checkerboard pattern with one MnPc species surrounded by four FeFPc molecules and vice versa (scale bar, 1 nm). (d) Sketch of the two occurring magnetic interactions in the remanent state, the short-range many-body Kondo screening and the long-range RKKY exchange interaction of the magnetic molecular centres mediated by the conduction electrons of the Au(111) substrate. (e) The magnetic moments of the two molecular species are antiferromagnetically coupled and align their moments in the out-of-plane direction.

Figure 2. Observation of long-range ferrimagnetic order in a 2D supramolecular layer.

(a) Sketch of the experimental set-up, in which the XMCD and XAS measurements are performed in normal incidence geometry, with the external magnetic field B and the k-vector of the X-rays parallel to the surface normal, that is, [111] direction. Illustration of the ferrimagnetically ordered molecular spins in the ground state (B=0 T) and the ferromagnetically aligned spins at B=6.8 T. (b,c) XAS/XMCD spectra measured at the Fe L_3,2 edge and B=0 T demonstrate remanent magnetic moments of FeFPc molecules, which are aligned antiparallel to the remanent magnetic moments observed for the MnPc molecules. (d,e) In the applied external magnetic field of B=6.8 T, both molecular spins are aligned parallel to the applied field. (f) The measured individual XMCD peak height versus B curves of FeFPc and MnPc molecules show long-range order with antiferromagnetic coupling between the two sublattices. For the FeFPc molecules, the magnetic moment becomes aligned with the applied field for B≥2 T, as is evidenced by the zero crossing, which appears when the Zeeman energy wins over the FeFPc-MnPc antiferromagnetic exchange coupling. Open down triangles depict the data points at B∼0 T that possess higher noise level due to the measurement protocol (see Methods). All measurements were performed at T=2.5 K. Full lines show the fit of the XMCD data to a Brillouin function, adopting a mean field approximation without anisotropy terms (m(Mn)=2.3 μ_B, m(Fe)=−1.2 μ_B and J_Fe−Mn=0.12 meV).

Figure 3. STS measurements of FeFPc and MnPc.

(a) The temperature-dependent differential conductance dI/dV spectra acquired above the centre of the FeFPc molecules show Kondo features around zero bias voltage. The dip-like feature measured on the centre of the FeFPc molecules broadens and becomes shallower with increasing temperature. (b) Spectra acquired above the centre of the MnPc species show a step-like shape, which is a signature of the Kondo resonance that broadens and vanishes with increasing temperature. Red full curves are fits to the temperature dependent dI/dV spectra with a modified Frota function to determine the Kondo temperatures. The inset shows the area where the spectra where acquired, with a scale bar of 2 nm.

Figure 4. Results of density-functional theory-based calculations.

(a) Top-view of the DFT+U computed spin densities of the 2D supramolecular layer on the Au(111) substrate. The red iso-surfaces depict the positive spin density on the Mn atoms of the MnPc molecules and the green iso-surfaces the negative spin density on the Fe atoms of the FeFPc molecules. It is noteworthy that the spin densities on the ligand atoms are opposite to those on the metal centres. (b) Side view of the spin density plot at an enlarged iso-density value (5 × 10⁻³ eÅ⁻³), which shows the interaction of the spin magnetization on the metallo-phthalocyanines with the Au substrate atoms. At this iso-density value, the dominant spin polarization is clearly visible. The direction of the side view is given by the arrow in a. Colour code: yellow atoms depict the Au(111) substrate atoms, brown the carbon atoms, blue the nitrogen atoms, white the hydrogen atoms and orange the fluorine atoms.