The emergence of classical behaviour in magnetic adatoms

A wide class of nanomagnets shows striking quantum behaviour, known as quantum spin tunnelling (QST): instead of two degenerate ground states with opposite magnetizations, a bonding-antibonding pair forms, resulting in a splitting of the ground-state doublet with wave functions linear combination of two classically opposite magnetic states, leading to the quenching of their magnetic moment. Here we study how QST is destroyed and classical behaviour emerges in the case of magnetic adatoms, where, contrary to larger nanomagnets, the QST splitting is in some instances bigger than temperature and broadening. We analyze two different mechanisms for the renormalization of the QST splitting: Heisenberg exchange between different atoms, and Kondo exchange interaction with the substrate electrons. Sufficiently strong spin-substrate and spin-spin coupling renormalize the QST splitting to zero allowing the environmental decoherence to eliminate superpositions between classical states, leading to the emergence of spontaneous magnetization. Importantly, we extract the strength of the Kondo exchange for various experiments on individual adatoms and construct a phase diagram for the classical to quantum transition.

Cotunneling theory of atomic spin inelastic electron tunneling spectroscopy

We propose cotunneling as the microscopic mechanism that makes possible inelastic electron tunneling spectroscopy of magnetic atoms in surfaces for a wide range of systems, including single magnetic adatoms, molecules, and molecular stacks. We describe electronic transport between the scanning tip and the conducting surface through the magnetic system (MS) with a generalized Anderson model, without making use of effective spin models. Transport and spin dynamics are described with an effective cotunneling Hamiltonian in which the correlations in the magnetic system are calculated exactly and the coupling to the electrodes is included up to second order in the tip MS and MS substrate. In the adequate limit our approach is equivalent to the phenomenological Kondo exchange model that successfully describes the experiments. We apply our method to study in detail inelastic transport in two systems, stacks of cobalt phthalocyanines and a single Mn atom on Cu2N. Our method accounts for both the large contribution of the inelastic spin exchange events to the conductance and the observed conductance asymmetry.

Electronic properties of transition metal atoms on Cu2N/Cu(100)

We study the nature of spin excitations of individual transition metal atoms (Ti, V, Cr, Mn, Fe, Co, and Ni) deposited on a Cu2N/Cu(100) surface using both spin-polarized density functional theory (DFT) and exact diagonalization of an Anderson model derived from DFT. We use DFT to compare the structural, electronic, and magnetic properties of different transition metal adatoms on the surface. We find that the average occupation of the transition metal d shell, main contributor to the magnetic moment, is not quantized, in contrast with the quantized spin in the model Hamiltonians that successfully describe spin excitations in this system. In order to reconcile these two pictures, we build a zero bandwidth multi-orbital Anderson Hamiltonian for the d shell of the transition metal hybridized with the p orbitals of the adjacent nitrogen atoms, by means of maximally localized Wannier function representation of the DFT Hamiltonian. The exact solutions of this model have quantized total spin, without quantized charge at the d shell. We propose that the quantized spin of the models actually belongs to many-body states with two different charge configurations in the d shell, hybridized with the p orbital of the adjacent nitrogen atoms. This scenario implies that the measured spin excitations are not fully localized at the transition metal.

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.

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.

Storage of classical information in quantum spins

Digital magnetic recording is based on the storage of a bit of information in the orientation of a magnetic system with two stable ground states. Here we address two fundamental problems that arise when this is done on a quantized spin: quantum spin tunneling and backaction of the readout process. We show that fundamental differences exist between integer and semi-integer spins when it comes to both reading and recording classical information in a quantized spin. Our findings imply fundamental limits to the miniaturization of magnetic bits and are relevant to recent experiments where a spin-polarized scanning tunneling microscope reads and records a classical bit in the spin orientation of a single magnetic atom.

A highly resistive layer within the crust of X-ray pulsars limits their spin periods

The lack of isolated X-ray pulsars with spin periods longer than 12 s raises the question of where the population of evolved high-magnetic-field neutron stars has gone. Unlike canonical radiopulsars, X-ray pulsars are not subject to physical limits to the emission mechanism nor observational biases against the detection of sources with longer periods. Here we show that a highly resistive layer in the innermost part of the crust of neutron stars naturally limits the spin period to a maximum value of about 10–20 s. This highly resistive layer is expected if the inner crust is amorphous and heterogeneous in nuclear charge, possibly owing to the existence of a nuclear ‘pasta’ phase. Our findings suggest that the maximum period of isolated X-ray pulsars may be the first observational evidence for an amorphous inner crust, whose properties can be further constrained by future X-ray timing missions combined with more detailed models.