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The mechanism of Kondo screening in strongly correlated molecules with several unpaired electrons on a metal surface is still under debate. Here, we provide a theoretical framework that rationalizes the emergence of Kondo screening involving several extended molecular orbitals with unpaired electrons. We introduce a perturbative model, which provides simple rules to identify the presence of antiferromagnetic spin-flip channels involving charged molecular multiplets responsible for Kondo screening. The Kondo regime is confirmed by numerical renormalization group calculations. In addition, we introduce the concept of Kondo orbitals as molecular orbitals associated with the Kondo screening process, which provide a direct interpretation of experimental $dI/dV$ maps of Kondo resonances. We demonstrate that this theoretical framework can be applied to different strongly correlated open-shell molecules on metal surfaces, obtaining good agreement with previously published experimental data., Comment: 13 pages, 12 figures

Magnetic anisotropy and magnetic exchange interactions are crucial parameters that characterize the hybrid metal-organic interface, key component of an organic spintronic device. We show that the incorporation of 4$f$ RE atoms to hybrid metal-organic interfaces of CuPc/REAu$_2$ type (RE= Gd, Ho) constitutes a feasible approach towards on-demand magnetic properties and functionalities. The GdAu$_2$ and HoAu$_2$ substrates differ in their magnetic anisotropy behavior. Remarkably, the HoAu$_2$ surface boosts the inherent out-of-plane anisotropy of CuPc, owing to the match between the anisotropy axis of substrate and molecule. Furthermore, the presence of RE atoms leads to a spontaneous antiferromagnetic (AFM) exchange coupling at the interface, induced by the 3$d$-4$f$ superexchange interaction between the unpaired 3$d$ electron of CuPc and the 4$f$ electrons of the RE atoms. We show that 4$f$ RE atoms with unquenched quantum orbital momentum ($L$), as it is the case of Ho, induce an anisotropic interfacial exchange coupling., Comment: Main paper: 10 pages and 3 figures; Supplementary Material: 13 pages, 5 figures

We discuss coexistence of Kondo and spin excitation signals in tunneling spectroscopy in strongly correlated polyradical $\pi$-magnetic nanographenes on a metal surface. The Kondo signal is rationalized by a multi-orbital Kondo screening of the unpaired electrons. The fundamental processes are spin-flips of antiferromagnetic (AFM) order involving charged molecular multiplets. We introduce a~perturbative model, which provides simple rules to identify the presence of AFM channels responsible for Kondo screening. The Kondo regime is confirmed by numerical renormalization group calculations. This framework can be applied to similar strongly correlated open-shell systems., Comment: 43 pages (14 in main, 29 in SM), 20 figures (3 in main, 17 in SM)

The numerical renormalization group (NRG) has been widely used as a magnetic impurity solver since the pioneering works by Wilson. Over the past decades, a significant attention has been focused on the application of symmetries in order to reduce the computational cost of the calculations and to improve their accuracy. In particular, a notable progress has been made in implementing continuous symmetries such as $SO(3)$, useful for studying impurities in an isotropic medium, or $SU(N)$, which is applicable to a wide range of systems. In this work, we focus on the application of discrete point group symmetries, which are particularly relevant for impurity systems in metals where crystal field effects are important. With this aim, we have developed an original NRG code written in the Julia language, PointGroupNRG, where we have implemented crystal point-group symmetries for the Anderson impurity model, as well as the continuous spin and charge symmetries. Among other results, we demonstrate the advantage of our procedure by performing thermodynamic calculations for an impurity system with two orbitals of $E_g$ symmetry and two channels. We compare the results with those obtained for an approximate equivalent model with continuous orbital symmetry., Comment: 17 pages, 1 figure

Climate change has been shown to affect fitness-related traits in a wide range of taxa; for instance, warming leads to phenological advancements in many plant and animal species. The influence of climate change on social and secondary sexual traits, that are associated with fitness due to their role as quality signals, is however unknown. Here, we use more than 5800 observations collected on two Mediterranean blue tit subspecies (Cyanistes caeruleus caeruleus and C.c. ogliastrae) to explore whether blue crown and yellow breast patch colourations have changed over the past 15 years. Our data suggests that colouration has become duller and less chromatic in both sexes. In addition, in the Corsican C.c. ogliastrae, but not in the mainland C.c. caeruleus, the decrease is associated with an increase in temperature at moult. Quantitative genetic analyses do not reveal any microevolutionary change in the colour traits along the study period, strongly suggesting that the observed change over time was caused by a plastic response to the environmental conditions. Overall, this study suggests that ornamental colourations could become less conspicuous due to warming, revealing climate change effects on sexual and social ornaments and calling for further research on the proximate mechanisms behind these effects.

One-dimensional metal-organic chains often possess a complex magnetic structure susceptible to be modified by a alteration of their chemical composition. The possibility to tune their magnetic properties provides an interesting playground to explore quasiparticle interactions in low-dimensional systems. Despite the great effort invested so far, a detailed understanding of the interactions governing the electronic and magnetic properties of the low-dimensional systems is still incomplete. One of the reasons is the limited ability to characterize their magnetic properties at the atomic scale. Here, we provide a comprehensive study of the magnetic properties of metal-organic one-dimensional (1D) coordination polymers consisting of 2,5-diamino-1,4-benzoquinonediimine ligands coordinated with Co or Cr atoms synthesized in ultra-high vacuum conditions on a Au(111) surface. A combination of an integral X-ray spectroscopy with local-probe inelastic electron tunneling spectroscopy corroborated by multiplet analysis, density functional theory, and inelastic electron tunneling simulations enable us to obtain essential information about their magnetic structure, including the spin magnitude and orientation at the magnetic atoms, as well as the magnetic anisotropy., Comment: 35 pages, 8 Figures, 3 tables

Using density functional theory and Monte Carlo calculations, we study the thickness dependence of the magnetic and electronic properties of a van der Waals interlayer antiferromagnet in the two-dimensional limit. Considering $\mathrm{MnBi_2Te_4}$ as a model material, we find it to demonstrate a remarkable set of thickness-dependent magnetic and topological transitions. While a single septuple layer block of $\mathrm{MnBi_2Te_4}$ is a topologically trivial ferromagnet, the thicker films made of an odd (even) number of blocks are uncompensated (compensated) interlayer antiferromagnets, which show wide bandgap quantum anomalous Hall (zero plateau quantum anomalous Hall) states. Thus, $\mathrm{MnBi_2Te_4}$ is the first stoichiometric material predicted to realize the zero plateau quantum anomalous Hall state intrinsically. This state has been theoretically shown to host the exotic axion insulator phase.

Despite immense advances in the field of topological materials, the antiferromagnetic topological insulator (AFMTI) state, predicted in 2010, has been resisting experimental observation up to now. Here, using density functional theory and Monte Carlo method we predict and by means of structural, transport, magnetic, and angle-resolved photoemission spectroscopy measurements confirm for the first time realization of the AFMTI phase, that is hosted by the van der Waals layered compound MnBi$_2$Te$_4$. An interlayer AFM ordering makes MnBi$_2$Te$_4$ invariant with respect to the combination of the time-reversal ($\Theta$) and primitive-lattice translation ($T_{1/2}$) symmetries, $S=\Theta T_{1/2}$, which gives rise to the $Z_2$ topological classification of AFM insulators, $Z_2$ being equal to 1 for this material. The $S$-breaking (0001) surface of MnBi$_2$Te$_4$ features a giant bandgap in the topological surface state thus representing an ideal platform for the observation of such long-sought phenomena as the quantized magnetoelectric coupling and intrinsic axion insulator state.

The magnetic anisotropy and exchange coupling between spins localized at the positions of 3d transition metal atoms forming two-dimensional metal-organic coordination networks (MOCNs) grown on the Au(111) metal surface are studied. In particular, we consider MOCNs made of Ni or Mn metal centers linked by TCNQ (7,7,8,8-tetracyanoquinodimethane) organic ligands, which form rectangular networks with 1:1 stoichiometry. Based on the analysis of X-ray magnetic circular dichroism (XMCD) data taken at T= 2.5 K, we find that Ni atoms in the Ni-TCNQ MOCNs are coupled ferromagnetically and do not show any significant magnetic anisotropy, while Mn atoms in the Mn-TCNQ MOCNs are coupled antiferromagnetically and do show a weak magnetic anisotropy with in-planemagnetization. We explain these observations using both amodelHamiltonian based on mean-fieldWeiss theory and density functional theory calculations that include spin-orbit coupling. Our main conclusion is that the antiferromagnetic coupling between Mn spins and the in-plane magnetization of the Mn spins can be explained neglecting effects due to the presence of the Au(111) surface, while for Ni-TCNQ the metal surface plays a role in determining the absence of magnetic anisotropy in the system., Comment: 17 pages, 7 figures, submitted to Molecules (MDPI) on February 21st 2018, Supplementary Material in submit/2172866