The spin dynamics of all ferromagnetic materials are governed by two types of collective phenomenon: spin waves and domain walls. The fundamental processes underlying these collective modes, such as exchange interactions and magnetic anisotropy, all originate at the atomic scale. However, conventional probing techniques based on neutron and photon scattering provide high resolution in reciprocal space, and thereby poor spatial resolution. Here we present direct imaging of standing spin waves in individual chains of ferromagnetically coupled S = 2 Fe atoms, assembled one by one on a Cu(2)N surface using a scanning tunnelling microscope. We are able to map the spin dynamics of these designer nanomagnets with atomic resolution in two complementary ways. First, atom-to-atom variations of the amplitude of the quantized spin-wave excitations are probed using inelastic electron tunnelling spectroscopy. Second, we observe slow stochastic switching between two opposite magnetization states, whose rate varies strongly depending on the location of the tip along the chain. Our observations, combined with model calculations, reveal that switches of the chain are initiated by a spin-wave excited state that has its antinodes at the edges of the chain, followed by a domain wall shifting through the chain from one end to the other. This approach opens the way towards atomic-scale imaging of other types of spin excitation, such as spinon pairs and fractional end-states, in engineered spin chains.

The ability to manipulate single atoms has opened up the door to constructing interesting and useful quantum structures from the ground up 1 . On the one hand, nanoscale arrangements of magnetic atoms are at the heart of future quantum computing and spintronic devices 2,3 ; on the other hand, they can be used as fundamental building blocks for the realization of textbook many-body quantum models 4 , illustrating key concepts such as quantum phase transitions, topological order or frustration as a function of system size. Here, we use low-temperature scanning tunnelling microscopy to construct arrays of magnetic atoms on a surface, designed to behave like spin-1/2 XXZ Heisenberg chains in a transverse field, for which a quantum phase transition from an antiferromagnetic to a paramagnetic phase is predicted in the thermodynamic limit 5. Site-resolved measurements on these finite-size realizations reveal a number of sudden ground state changes when the field approaches the critical value, each corresponding to a new domain wall entering the chains. We observe that these state crossings become closer for longer chains, suggesting the onset of critical behaviour. Our results present opportunities for further studies on quantum behaviour of many-body systems, as a function of their size and structural complexity.Since the birth of quantum mechanics, lattice spin systems 6 have represented a natural starting point for understanding collective quantum dynamics. Today, scanning tunnelling microscopy (STM) techniques allow one to experimentally build and probe realizations of exchange-coupled lattice spins in different geometries [7][8][9] . In linear arrangements, quantum effects are strongest 10 and notions such as quantum phase transitions 11 are most easily understood, the simplest illustration being the Ising model in a transverse field 12,13 . In this work, using STM, we construct finite-size versions of a model in the same universality class, namely the spin-1/2 XXZ chain in a transverse field 5 , which has previously been realized in the bulk material Cs 2 CoCl 4 (refs 14,15). Our set-up allows us to probe the chains with single-spin resolution while tuning an externally applied transverse field through the critical regime.The chains are created by manipulating Co atoms evaporated onto a Cu 2 N/Cu(100) surface (see Methods), which provides efficient decoupling for the magnetic d-shell electrons from the underlying bulk electrons 7 . Employing inelastic electron tunnelling spectroscopy (IETS) 16,17 at sufficiently low temperature (330 mK) allows us to determine the magnetic anisotropy vector of each atom 18 as well as the strength of the exchange coupling between neighbouring atoms 19 . It was previously demonstrated that Co atoms on this surface behave as spin S = 3/2 objects experiencing a strong uniaxial hard-axis anisotropy pointing inplane, perpendicular to the bond with the neighbouring N atoms 20 . As a result, the m z = ±3/2 states split off approximately 5.5 meV above the m z = ±1/2 doublet (see Fig. 1a)...

Individual Fe atoms on a Cu(2)N/Cu(100) surface exhibit strong magnetic anisotropy due to the crystal field. We show that we can controllably enhance or reduce this anisotropy by adjusting the relative position of a second nearby Fe atom, with atomic precision, in a low-temperature scanning tunneling microscope. Local inelastic electron tunneling spectroscopy, combined with a qualitative first-principles model, reveal that the change in uniaxial anisotropy is driven by local strain due to the presence of the second Fe atom.

A system of two exchange-coupled Kondo impurities in a magnetic field gives rise to a rich phase space hosting a multitude of correlated phenomena. Magnetic atoms on surfaces probed through scanning tunnelling microscopy provide an excellent platform to investigate coupled impurities, but typical high Kondo temperatures prevent field-dependent studies from being performed, rendering large parts of the phase space inaccessible. We present a study of pairs of Co atoms on insulating Cu2N/Cu(100), which each have a Kondo temperature of only 2.6 K. The pairs are designed to have interaction strengths similar to the Kondo temperature. By applying a sufficiently strong magnetic field, we are able to access a new phase in which the two coupled impurities are simultaneously screened. Comparison of differential conductance spectra taken on the atoms to simulated curves, calculated using a third-order transport model, allows us to independently determine the degree of Kondo screening in each phase.

manganites are technologically important materials, used widely as solid oxide fuel cell cathodes; they have also been shown to exhibit electroresistance. oxygen bulk diffusion and surface exchange processes are critical for catalytic action, and numerous studies of manganites have linked electroresistance to electrochemical oxygen migration. Direct imaging of individual oxygen defects is needed to underpin understanding of these important processes. Currently, it is not possible to collect the required images in bulk, but scanning tunnelling microscopy (sTm) could provide such data for surfaces. Here, we report the first atomic resolution images of oxygen defects at a manganite surface. our experiments also reveal defect dynamics, including oxygen adatom migration, vacancy-adatom recombination and adatom bistability. Beyond providing an experimental basis for testing models describing the microscopics of oxygen migration at transition-metal oxide interfaces, our work resolves the long-standing puzzle of why sTm is more challenging for layered manganites than for cuprates.