Atomic- and Nanoscale Magnetism

We review the magnetism of tailored bottom-up nanostructures which have been assembled of 3d-transition metal atoms on nonmagnetic metallic substrates. We introduce the newly developed methodology of single atom magnetometry which combines spin-resolved scanning tunneling spectroscopy (SPSTS) and inelastic STS (ISTS) pushed to the limit of an individual atom. We describe how it can be used to measure the magnetic moment, magnetic anisotropy, and g-factor of individual atoms, as well as their pair-wise Ruderman-Kittel-Kasuya-Yosida (RKKY)-interaction. Finally, we will show that, using these measured quantities in combination with STM-tip induced manipulation of the atoms, nanostructures ranging from antiferromagnetic chains and two-dimensional arrays over all-spin based logic gates to magnetic memories composed of only few atoms can be realized and their magnetic properties characterized.

The Kondo effect of adatoms on surfaces may to some extent be controlled by manipulating their electronic and geometric environment. Results are presented from artificial structures like quantum well systems, from arrangements of single atoms made with a scanning tunneling microscope, and from custom-made molecules. Spin-orbit coupling at single adatoms is probed via measurements of the anisotropic magnetoresistance, in particular in single atom contacts. Such junctions are also investigated with respect to the current shot noise, which is influenced by the electron spin.

Advanced atomic force microscopy based techniques were developed to investigate local properties of individual well-separated adsorbed molecules, which can be applied to all kinds of supporting substrates independent of their conductivity. First, we find that due to the Smoluchowski effect a localized electrostatic dipole moment is present at the end of metallic tips. Since its positive pole points towards the surface, we are able to identify the chemical species in atomically resolved images on polar surfaces. We employed such tips to determine the exact adsorption geometry of single molecules on ionic bulk insulators. Moreover, we were able to detect magnitude and direction of the electrostatic dipole moment of adsorbed molecules. Secondly, if the tip is magnetic, we are even able to probe the short-range electron-mediated magnetic exchange interaction between the foremost tip apex atom and the sample atom directly below and thus established magnetic exchange force microscopy as a novel method to study magnetic sample systems with atomic resolution. By applying this new kind of magnetically sensitive force microscopy to a paramagnetic organo-metallic complex adsorbed on an antiferromagnetic bulk insulator, we find indications for a superexchange-mediated coupling between molecule and substrate.

Cooperative effects such as ferro- or antiferromagnetic interactions are accessible through tailor-made molecular structures of linearly arranged paramagnetic complexes. Since it is well-known that subtle changes in the molecular structure can cause distinct changes in the magnetic interaction, the inter-metal distances were varied as well as the number of stacked complexes. In addition the metal centers were changed in order to vary the numbers of interacting unpaired electrons. The final target was an investigation of the properties of stacked magnetic molecules on a substrate.

Designing and understanding spin coupling within and between molecules is important for, e.g., nanoscale spintronics, magnetic materials, catalysis, and biochemistry. We review a recently developed approach to analyzing spin coupling in terms of local pathways, which allows to evaluate how much each part of a structure contributes to coupling, and present examples of how first-principles electronic structure theory can help to understand spin coupling in molecular systems which show the potential for photo- or redoxswitching, or where the ground state is stabilized with respect to spin flips by adding unpaired spins on a bridge connecting two spin centers. Finally, we make a connection between spin coupling and conductance through molecular bridges.

Clusters are structures in the nano- or sub-nanometer regime ranging from a few atoms up to several thousand atoms per cluster. Supported metal clusters and adatoms are interesting systems for magnetic studies as their magnetic properties can strongly depend on the size, composition and the substrate due to quantum size effects. This offers rich possibilities to tailor systems to specific applications by choosing the proper size and composition of the cluster. In this article the magnetic properties of small 3d metal and alloy clusters in the few atom limit measured by X-ray magnetic circular dichroism and how their spin and orbital moments depend on size and composition are discussed. Special emphasis is put on the non-collinear magnetic coupling in the clusters resulting in complex spin structures and the influence of oxidation on the magnetic properties of the clusters.

Non-collinear magnetic states in nanostructures and ultra thin films have moved into the focus of research upon the experimental discovery that the interface -induced Dzyaloshinskii–Moriya interaction (DMI) can play a crucial role for the magnetic ground state. In particular, DMI-induced magnetic skyrmions, which are particle-like knots in the magnetization of two-dimensional systems, have attracted significant attention due to their potential use in future spintronic devices. Since then, research has focused both on tailoring thin-films and multilayers hosting magnetic skyrmions, and investigating specific processes such as controlled lateral movement, detection, as well as writing and deleting of single magnetic skyrmions. This chapter reviews the fundamental interactions and mechanisms for the formation of non-collinear spin textures and then introduces how scanning tunneling microscopy (STM) can be exploited to investigate such magnetic states. Next, examples of (one-dimensional) spin spirals will be discussed before the emergence of two-dimensional non-collinear spin textures is studied and characterized in detail. Finally, different mechanisms for the controlled writing and deleting of magnetic skyrmions with the STM tip are explored.

Complex spin structures feature a periodic variation of the local alignment of non-collinear magnetic moments. The number of systems showing non-trivial magnetic structuring steadily increases. Particularly, several uniaxial as well as two-dimensionally modulated magnetic states were found with unique rotational sense due to the spin-orbit based Dzyaloshinskii-Moriya-interaction. Another source for the modulated magnetic configurations is given by the frustration and competing higher-order exchange interactions arising due to the itinerant nature of electrons. One of the most exciting recent developments with respect to these non-trivial configurations is the emergence of magnetic quasiparticles, which are characterized by their enhanced temporal and thermal stability. In this review several aspects of the static and dynamic properties of the quasiparticles and other interfacial non-collinear magnetic structures will be addressed.

Various novel effects in nanostructures of magnetic atoms exchange-coupled to a metallic system of conduction electrons are reviewed. To this end we discuss analytical results and numerical data obtained by the density-matrix renormalization group and the real-space dynamical mean-field theory for the multi-impurity Kondo model. This model hosts complex physics resulting from the competition or cooperation of different mechanisms, such as the Kondo effect, the RKKY indirect magnetic exchange, finite-size gaps and symmetry-induced degeneracies in the electronic structure of finite metallic systems, quantum confinement in the strong-coupling limit, and geometrical frustration .

Spin-polarized scanning tunneling microscopy is used to study the magnetization reversal of individual quasiclassical and quantum atomic-scale magnets. Modifications of the dynamics arising from the presence of the biased magnetic probe tip are identified in terms of spin-transfer torque, Joule heating, Oersted field, magneto-electric coupling and spin-polarized field emission. Observing the switching behavior over a wide temperature range allows for a detailed study of nucleation, propagation and annihilation of domain walls in quasi-classical nanomagnets. Quantum magnets are found to be intrinsically stable at ultra-low temperature, and magnetization dynamics can be controlled by the spin-polarized tunnel current injection from the magnetic tip.

A method is introduced that allows for the investigation of the magnetic behavior of single nanostructures in a wide range of temperatures and external magnetic fields. The technique is based on the anomalous Hall Effect utilizing nano-scaled Hall crosses. The nano-devices as well as the nanostructures are created out of sandwich films made from Pt/Co/Pt via ion milling. For the single nanostructures we identify a much too large attempt frequency which is shown to be partially caused by a temperature dependence of the magnetic anisotropy. It is shown that the magnetic behavior of and the mutual interaction in small numbers of nanostructures can be resolved. The interactions cause a strong change of the magnetic behavior of the individual particle particularly in case the system is affected by thermal energy. The latter happens even on a reasonable large scale of particle separation.

The stability of magnetic moments in a nanostructure against thermal and quantum fluctuations and the real-time dynamics of strongly excited nanosystems on metallic surfaces are studied theoretically on the basis of microscopic models addressing the degrees of freedom on the atomic level. To this end, different theoretical approaches and computational tools are employed and developed, such as classical Monte-Carlo simulations, quantum-classical hybrid dynamics and time-dependent density-matrix renormalization group.

The most direct way of accessing and understanding fast dynamical processes in nature is by capturing the motion in real space with a high temporal and spatial resolution. This chapter details time-resolved imaging techniques for probing the transient evolution of the magnetization in small magnetic systems in the visible and soft X-ray spectral range. Optical methods using femtosecond laser pulses can follow ultrafast processes with an extreme temporal resolution. The spatial resolution, however, is limited by diffraction to a few hundred nanometers at visible wavelengths. The dynamics of smaller structures can be investigated using X-ray microscopy at synchrotron radiation sources. A resolution of a few ten nanometers can be achieved, however, the time-resolution is limited to a few hundred picoseconds due to the pulse duration of the synchrotron bunches. Spin-wave packets are captured by optical methods using a time-resolved confocal Kerr microscope where backward volume spin-wave packets with counterpropagating group- and phase velocity are observed directly. Time-resolved X-ray microscopy is used to monitor the destruction and emergence of equilibrium domain patterns out of uniformly magnetized states.

We investigate the dynamics of magnetic antivortices by time-resolved magnetic X-ray microscopy and high-frequency absorption spectroscopy. A method for the reliable generation of isolated magnetic antivortices is devised using specifically formed microstructures and two-dimensional sequences of magnetic fields. For antivortices the measured resonance frequency is lower than for comparable vortices. The deflection of antivortices by external fields reveals strong deviations from a harmonic potential as well as rather low annihilation fields. Spectroscopy yields a characteristic absorption signal for antivortices for strong excitation that indicates a continuous switching of the antivortex core.

Magnetic textures in solid-state nanostructures can be manipulated by an applied electrical current and are thus promising candidates for new classes of electronic devices. The manipulation of a magnetization texture occurs via a spin torque exerted by the spin-polarized current on the local magnetic moments. We present different approaches how to calculate this spin torque under nonequilibrium conditions. In particular, we generalize the conventional approach to calculate the spin torque to treat magnetic structures which have a large spatial gradient (steep structures). We discuss this for the case of ferromagnetic domain walls and show how their chirality can be switched by an external spin-orbit torque. Besides domain walls, we also investigate the dynamics of two-dimensional ferromagnetic skyrmions and derive an equation of motion for the skyrmion’s topological charge density. By this equation we are able to explain the current-induced creation of neutral skyrmion-antiskyrmion pairs which can be used for the production of stable skyrmions after the antiskyrmion partner has disappeared due to dissipation.

About a decade ago, the understanding of the interaction mechanisms between electrical currents and magnetic objects like domain walls or vortices was still in its infancy. Both, theory and experiments were moving on uncharted grounds, with new and many times contradicting results being published from different groups at increasing pace. Previously, only the Oersted field from a current was available to manipulate the magnetic state of a system. The latter was extensively used in magnetic storage devices, starting from the early core memory up to the write heads of the latest hard drive technologies based on perpendicular recording and tunnel-magnetoresistive (TMR) readout sensors, to alter the state of the magnetic bits. Even early prototypes of magnetic random-access memory (MRAM) used the Oersted field for writing.

The proposal of logic- and memory devices based on magnetic domain-wall motion in nanostructures created a great demand on the understanding of the dynamics of domain walls. We describe the controlled creation and annihilation of domain walls by Oersted-field pulses as well as their internal dynamics during motion. Electric measurements of the magnetoresistance are utilized to identify permanent- or temporal creation and continuous motion of domain walls initiated by nanosecond short field pulses in external magnetic fields. The injection of domain walls into nanowires with control of their magnetic pattern (transverse or vortex), their type (head-to-head or tail-to-tail magnetization orientation) and their sense of magnetization rotation (clockwise or counter clockwise chirality) is reliably achieved. Influencing the creation process of consecutively created domain walls to obtain multiple walls inside one wire or to mutually annihilate the walls is found to be possible by changes of magnetic field parameters. The time structure of the creation process is analysed by time-resolved transmission X-ray microscopy. After complete formation wall transformations are observed above a critical driving field known as the Walker breakdown. Internal excitations of vortex domain walls are also found in low field motion. A strong interplay between internal dynamics and the macroscopic motion is identified.