Skyrmions in magnetic materials offer attractive perspectives for future spintronic applications since they are topologically stabilized spin structures on the nanometre scale, which can be manipulated with electric current densities that are by orders of magnitude lower than those required for moving domain walls. So far, they were restricted to bulk magnets with a particular chiral crystal symmetry greatly limiting the number of available systems and the adjustability of their properties. Recently, it has been experimentally discovered that magnetic skyrmion phases can also occur in ultra-thin transition metal films at surfaces. Here we present an understanding of skyrmions in such systems based on first-principles electronic structure theory. We demonstrate that the properties of magnetic skyrmions at transition metal interfaces such as their diameter and their stability can be tuned by the structure and composition of the interface and that a description beyond a micromagnetic model is required in such systems.

Linear π-conjugated oligomers have been widely investigated, but the behavior of the corresponding cyclic oligomers is poorly understood, despite the recent synthesis of π-conjugated macrocycles such as [n]cycloparaphenylenes and cyclo[n]thiophenes. Here we present an efficient template-directed synthesis of a π-conjugated butadiyne-linked cyclic porphyrin hexamer directly from the monomer. Small-angle X-ray scattering data show that this nanoring is shape-persistent in solution, even without its template, whereas the linear porphyrin hexamer is relatively flexible. The crystal structure of the nanoring-template complex shows that most of the strain is localized in the acetylenes; the porphyrin units are slightly curved, but the zinc coordination sphere is undistorted. The electrochemistry, absorption, and fluorescence spectra indicate that the HOMO-LUMO gap of the nanoring is less than that of the linear hexamer and less than that of the corresponding polymer. The nanoring exhibits six one-electron reductions and six one-electron oxidations, most of which are well resolved. Ultrafast fluorescence anisotropy measurements show that absorption of light generates an excited state that is delocalized over the whole π-system within a time of less than 0.5 ps. The fluorescence spectrum is amazingly structured and red-shifted. A similar, but less dramatic, red-shift has been reported in the fluorescence spectra of cycloparaphenylenes and was attributed to a high exciton binding energy; however the exciton binding energy of the porphyrin nanoring is similar to those of linear oligomers. Quantum-chemical excited state calculations show that the fluorescence spectrum of the nanoring can be fully explained in terms of vibronic Herzberg-Teller (HT) intensity borrowing.

A series of thioacetate-terminated butadiyne-linked porphyrin oligomers have been synthesized with one to three porphyrin repeat units. Single molecule electrical scanning tunneling microscopy measurements using the I(s) and I(t) methods were used to determine the molecule conductances for this series of oligomers. The molecular conductance shows an exponential falloff with sulfur-sulfur distance with a remarkably low attenuation factor of beta = (0.04 +/- 0.006) A-1.

Chiral magnets are an emerging class of topological matter harboring localized and topologically protected vortex-like magnetic textures called skyrmions, which are currently under intense scrutiny as an entity for information storage and processing. Here, on the level of micromagnetics we rigorously show that chiral magnets can not only host skyrmions but also antiskyrmions as least energy configurations over all non-trivial homotopy classes. We derive practical criteria for their occurrence and coexistence with skyrmions that can be fulfilled by (110)-oriented interfaces depending on the electronic structure. Relating the electronic structure to an atomistic spin-lattice model by means of density functional calculations and minimizing the energy on a mesoscopic scale by applying spin-relaxation methods, we propose a double layer of Fe grown on a W(110) substrate as a practical example. We conjecture that ultra-thin magnetic films grown on semiconductor or heavy metal substrates with C 2v symmetry are prototype classes of materials hosting magnetic antiskyrmions.

We have investigated the influence of nuclear geometric relaxation on the extent of the excited-state electronic delocalization in conjugated zinc porphyrin oligomers using ultrafast transient photoluminescence spectroscopy. By use of metal-coordinating templates that force the oligomers into specific geometries in solution we are able to distinguish clearly between relaxation effects arising from the two vibrational modes that preferentially couple to the electronic transitions in such materials, i.e., carbon-carbon bond stretches and inter-ring torsions. We find that light absorption generates an excited state that is initially strongly delocalized along the oligomer but contracts rapidly following vibrational relaxation of the nuclei along C-C stretch coordinates on the subpicosecond time scale. We are able to monitor such excitonic self-trapping effects by observing the extent to which the concomitant ultrafast rotation of the transition dipole moment is found to correlate with the degree of bending induced in the molecular backbone. We further demonstrate that interporphyrin torsional relaxation leads to a subsequent increase in the excited-state electronic delocalization on a longer time scale (approximately 100 ps). Such dynamic planarization of the molecular backbone is evident from the time-dependent increase in the overall emission intensity and red-shift in the peak emission energy that can be observed for wormlike flexible porphyrin octamers but not for torsionally rigidified cyclic or double-strand octamer complexes. These results therefore indicate that, following excitation, the initially highly delocalized excited-state wave function first contracts and then expands again along the conjugated backbone in accordance with the time periods for the vibrational modes coupled to the electronic transition.

Dedicated to Professor Jeremy Sanders on the occasion of his 60th birthdayBelt-shaped chromophores provide fascinating insights into electronic p delocalization over curved surfaces with radially oriented p orbitals.[1] Examples include the cyclic para-phenylacetylenes [2] and the [4 6 ]paracyclophanedodecayne of Tsuji and coworkers, [3] as well as fullerenes and carbon nanotubes. A variety of belt-shaped porphyrin arrays have been synthesized; [4] however, the vast majority of them lacks a complete pconjugation pathway around the whole macrocycle. Recently we reported the synthesis of a belt-shaped D 8h symmetric porphyrin[8] nanoring on an octadentate template.[5] Herein we present an efficient synthesis of an even more strained p conjugated D 6h porphyrin [6] nanoring 1, by template-directed trimerization of a porphyrin dimer 2 on a hexapyridyl template 3 (Scheme 1). This route is more direct than the synthesis of the cyclic octamer since both starting materials, 2 and 3, are readily accessible. The cyclic hexamer complex 1·3 is phenomenally stable (K f = 7 10 38 m À1 ; EM = 340 m) but the free macrocycle can be liberated from the 1·3 complex with amines such as quinuclidine. The UV/Vis/NIR absorption and emission show that there is efficient p conjugation around the porphyrin[6] nanoring 1, and that its S 0 -S 1 gap is even smaller than that of the corresponding linear porphyrin hexamer 4; this conclusion is supported by time-dependent density functional (TD-DFT) calculations.The key to the synthesis of the hexamer nanoring is the design of a complementary template (Scheme 2). The hexadentate template 3 has a calculated nitrogennitrogen distance of 20.1 , which is a good fit for the cavity of cyclic hexamer 1 with a zinc-zinc ring diameter of 24.2 (assuming a Zn À N bond length of 2.2 ). The template was synthesized by a six-fold Suzuki coupling of 4-pyridineboronic acid with hexakis(4-bromophenyl)benzene [6] in 50 % yield (Supporting Information). Two versions of cyclic hexamer 1 were synthesized-1 a·3 with tert-butyl side chains in 44 % and 1 b·3 with octyloxy side chains in 33 % yield-by oxidative

Two hundred years ago, Ampère discovered that electric loops in which currents of electrons are generated by a penetrating magnetic field can mutually interact. Here we show that Ampères observation can be transferred to the quantum realm of interactions between triangular plaquettes of spins on a lattice, where the electrical currents at the atomic scale are associated with the orbital motion of electrons in response to the non-coplanarity of neighbouring spins playing the role of a magnetic field. The resulting topological orbital moment underlies the relation of the orbital dynamics with the topology of the spin structure. We demonstrate that the interactions of the topological orbital moments with each other and with the spins form a new class of magnetic interactions − topological-chiral interactions − which can dominate over the Dzyaloshinskii-Moriya interaction, thus opening a path for realizing new classes of chiral magnetic materials with three-dimensional magnetization textures such as hopfions. Exotic magnetic textures with particle-like properties 1-6 offer great potential for innovative spintronic applications 7 and brain-inspired computing 8,9 . Magnetic skyrmions, twodimensional (2D) localized solitons, are a prominent realization of chiral spin structures, first observed in the material class of non-centrosymmetric B20 bulk compounds 1 . The potential of spintronic applications would change fundamentally if the line of thought could be continued to the emergence of three-dimensional (3D) localized magnetic solitons, e.g. hopfions 10-12 . Recently, a 3D lattice of 3D magnetic textures on the nanometer scale was observed in the B20type cubic chiral magnets MnGe 13,14 . Despite the strong interest in this magnet, a complete theoretical model for the underlying magnetic interactions is remarkably elusive until now. While, for instance, the basic magnetic properties of the 2D skyrmions are determined by an intricate competition involving the Heisenberg exchange and the chiral relativistic Dzyaloshinskii-Moriya interaction 15,16 (DMI), such models fail to explain the 3D-magnetic texture observed in MnGe 17 .The 3D magnetization textures of 2D skyrmions gives rise to a scalar spin chirality, a driving force behind a plethora of macroscopic phenomena. Examples are the topological Hall effect 18,19 or a finite topological orbital moment (TOM) 20-25 , which can both serve as experimental fingerprints of skyrmions. Texture-induced contributions to these macroscopic phenomena were also predicted in frustrated magnets 26,27 , where they originate from the non-trivial spin topology associated with the real-space configuration of magnetic moments S i as reflected by the scalar spin chirality χ ijk = S i · (S j × S k ). Although the net spin magnetization might vanish, the symmetry of these chiral systems allows for lowering the energy by preferring orbital currents of specific rotational sense 26,28 . As a consequence, the motion of the electron in the complex magnetic background manifests itself in the finite T...

Round the bend: Bending a molecular wire round an eight‐spoked template leads to the formation of a highly symmetric belt‐shaped π system (green in picture). Addition of a large excess of pyridine releases the corresponding cyclic octamer from the template.