# Single-Electron Tunneling Spectroscopy in Magnetic Nanoparticles and Molecular Magnets

Sammanfattning: This thesis deals with single-electron tunneling in transistor-like devices in which the central electrode is either a metal nanoparticle (possibly ferromagnetic) or a molecular magnet. The investigated systems split into two different categories, depending on the size of the central island. The smaller islands, such as ultrasmall magnetic metal nanoparticles and Mn12 molecular magnets, are studied in the first part of the thesis (Papers I-III). The larger metal islands, both ferromagnetic and nonmagnetic, are studied in the second part (Papers IV-V). Different size regimes result in different types of energy spectra (discrete for the small and continuous for the large islands), and thus in different ways of calculating the electric current through the system. All the systems are investigated within the regime of weak coupling to the external leads. In this regime, quantum transport is characterized by the physics of Coulomb blockade and can be described theoretically by sequential-tunneling rate equations. Papers I-III are purely theoretical, while Papers IV-V consist both of experimental and theoretical parts, the theoretical ones belonging explicitly to this thesis. In Paper I we present a theory of quantum transport through a small ferromagnetic nanoparticle in which particle-hole excitations are coupled to spin collective modes. For strong electron-magnon coupling, we find that the tunneling conductance as a function of bias voltage is characterized by a large and dense set of resonances. Their magnetic field dependence in the large-field regime is linear, with slopes of the same sign. Both features are in agreement with tunneling experiments on similar nanoparticles. Papers II and III deal with transport through a Mn12 molecule. The many-body energy spectrum (composed of spin multiplets) and spin-dependent inter-level transition matrix elements used in transport calculations are determined by means of spin density-functional theory (SDFT). This theory provides several other properties of the molecular magnet, such as the magnetic moment and magnetic anisotropy energy of its charged states, anion and cation. In transport calculations, we compare the results obtained by the SDFT with those based on a phenomenological giant-spin model. The tunneling conductance at finite bias is characterized by peaks representing transitions between spin multiplets, separated by an energy on the order of the magnetic anisotropy. We find that the orbital degrees of freedom, included in SDFT and absent in the spin model, play an important role in transport and can lead to negative differential conductance. In Paper IV we investigate spin accumulation in a Ni/Au/Ni single-electron transistor assembled by atomic force microscopy. Transport measurements in magnetic field at 1.7 K reveal no clear spin accumulation in the device (that is, no tunneling-magnetoresistance (TMR) signal is observed), which can be attributed to fast spin relaxation in the Au disk caused by strong spin-orbit interaction. From numerical simulations using the rate-equation approach of orthodox Coulomb-blockade theory, we can put an upper bound of a few nanoseconds on the spin-relaxation time for electrons in the Au disk. The focus of Paper V is on magnetic-field dependent transport in nanoscaled ferromagnetic Co/Ni/Co single-electron transistors. Magnetotransport measurements carried out at 1.8 K reveal TMR traces with negative coercive fields, which we interpret in terms of a switching mechanism driven by the shape anisotropy of the central wire-like Ni island. A large TMR of about 18% is observed within a finite source-drain bias regime. A numerical simulation within the Coulomb-blockade theory gives a TMR which is on the order of magnitude of the experimental signal. The TMR decreases rapidly with increasing bias. The vanishing of the TMR with bias is tentatively ascribed to excitations of magnons in the central island, which cause a fast decrease of the island spin polarization.

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