Local probe of fractional edge states of S=1 Heisenberg spin chains

Spin chains are among the simplest physical systems in which electron-electron interactions induce novel states of matter. Here we propose to combine atomic scale engineering and spectroscopic capabilities of state of the art scanning tunnel microscopy to probe the fractionalized edge states of individual atomic scale S=1 spin chains. These edge states arise from the topological order of the ground state in the Haldane phase. We also show that the Haldane gap and the spin-spin correlation length can be measured with the same technique.

Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the noncollinear nature of the classical ground state, there is a significant zero-point reduction of the ground-state magnetization of the spin spiral. Second, there is a critical external field from which the ground state changes from chiral spin ground state to collinear ferromagnetic order. The character of the two lowest-energy spin waves changes from edge modes to confined bulk modes over this critical field. Third, in the spin-spiral state, the spin-wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Imaging of spin waves in atomically designed nanomagnets

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 neutron1 and photon scattering2 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 Cu2N 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 states3, 4, 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-states5, 6, in engineered spin chains.

Emergence of half-metallicity in suspended NiO chains: Ab initio electronic structure and quantum transport calculations

Contrary to the antiferromagnetic and insulating character of bulk NiO, one-dimensional chains of this material can become half metallic due to the lower coordination of their atoms. Here we present ab initio electronic structure and quantum transport calculations of ideal infinitely long NiO chains and of more realistic short ones suspended between Ni electrodes. While infinite chains are insulating, short suspended chains are half-metallic minority-spin conductors that displays very large magnetoresistance and a spin-valve behavior controlled by a single atom.

Theory of single-spin inelastic tunneling spectroscopy

I show that recent experiments of inelastic scanning tunneling spectroscopy of single and a few magnetic atoms are modeled with a phenomenological spin-assisted tunneling Hamiltonian so that the inelastic dI/dV line shape is related to the spin spectral weight of the magnetic atom. This accounts for the spin selection rules and dI/dV spectra observed experimentally for single Fe and Mn atoms deposited on Cu2N. In the case of chains of Mn atoms it is found necessary to include both first and second-neighbor exchange interactions as well as single-ion anisotropy.

Evidence for non-conservative current-induced forces in the breaking of Au and Pt atomic chains

This experimental work aims at probing current-induced forces at the atomic scale. Specifically it addresses predictions in recent work regarding the appearance of run-away modes as a result of a combined effect of the non-conservative wind force and a ‘Berry force’. The systems we consider here are atomic chains of Au and Pt atoms, for which we investigate the distribution of break down voltage values. We observe two distinct modes of breaking for Au atomic chains. The breaking at high voltage appears to behave as expected for regular break down by thermal excitation due to Joule heating. However, there is a low-voltage breaking mode that has characteristics expected for the mechanism of current-induced forces. Although a full comparison would require more detailed information on the individual atomic configurations, the systems we consider are very similar to those considered in recent model calculations and the comparison between experiment and theory is very encouraging for the interpretation we propose.

Derivation of the spin Hamiltonians for Fe in MgO

A method to calculate the effective spin Hamiltonian for a transition metal impurity in a non-magnetic insulating host is presented and applied to the paradigmatic case of Fe in MgO. In the first step we calculate the electronic structure employing standard density functional theory (DFT), based on generalized gradient approximation (GGA), using plane waves as a basis set. The corresponding basis of atomic-like maximally localized Wannier functions is derived and used to represent the DFT Hamiltonian, resulting in a tight-binding model for the atomic orbitals of the magnetic impurity. The third step is to solve, by exact numerical diagonalization, the N electron problem in the open shell of the magnetic atom, including both effects of spin–orbit and Coulomb repulsion. Finally, the low energy sector of this multi-electron Hamiltonian is mapped into effective spin models that, in addition to the spin matrices S, can also include the orbital angular momentum L when appropriate. We successfully apply the method to Fe in MgO, considering both the undistorted and Jahn–Teller (JT) distorted cases. Implications for the influence of Fe impurities on the performance of magnetic tunnel junctions based on MgO are discussed.

Controlled Complete Suppression of Single-Atom Inelastic Spin and Orbital Cotunneling

The inelastic portion of the tunnel current through an individual magnetic atom grants unique access to read out and change the atom’s spin state, but it also provides a path for spontaneous relaxation and decoherence. Controlled closure of the inelastic channel would allow for the latter to be switched off at will, paving the way to coherent spin manipulation in single atoms. Here, we demonstrate complete closure of the inelastic channels for both spin and orbital transitions due to a controlled geometric modification of the atom’s environment, using scanning tunneling microscopy (STM). The observed suppression of the excitation signal, which occurs for Co atoms assembled into chains on a Cu2N substrate, indicates a structural transition affecting the dz2 orbital, effectively cutting off the STM tip from the spin-flip cotunneling path.