Magnetic Phases of Sputter Deposited Thin-Film Erbium.

We present a detailed structural and magnetic characterization of sputter deposited thin film erbium, determined by x-ray diffraction, transport measurements, magnetometry and neutron diffraction. This provides information on the onset and change of the magnetic state as a function of temperature and applied magnetic field. Many of the features of bulk material are reproduced. Also of interest is the identification of a conical magnetic state which repeats with a wavevector parallel to the c axis τc = 4/17 in units of the reciprocal lattice parameter c*, which is a state not observed in any other thin film or bulk measurements. The data from the various techniques are combined to construct magnetic field, temperature (H, T)-phase diagrams for the 200 nm-thick Er sample that serves as a foundation for future exploitation of this complex magnetic thin film system.

Thermodynamic phase transitions in a frustrated magnetic metamaterial.

Materials with interacting magnetic degrees of freedom display a rich variety of magnetic behaviour that can lead to novel collective equilibrium and out-of-equilibrium phenomena. In equilibrium, thermodynamic phases appear with the associated phase transitions providing a characteristic signature of the underlying collective behaviour. Here we create a thermally active artificial kagome spin ice that is made up of a large array of dipolar interacting nanomagnets and undergoes phase transitions predicted by microscopic theory. We use low energy muon spectroscopy to probe the dynamic behaviour of the interacting nanomagnets and observe peaks in the muon relaxation rate that can be identified with the critical temperatures of the predicted phase transitions. This provides experimental evidence that a frustrated magnetic metamaterial can be engineered to admit thermodynamic phases.

Direct observation of thermal relaxation in artificial spin ice.

We study the thermal relaxation of artificial spin ice with photoemission electron microscopy, and are able to directly observe how such a system finds its way from an energetically excited state to the ground state. On plotting vertex-type populations as a function of time, we can characterize the relaxation, which occurs in two stages, namely a string and a domain regime. Kinetic Monte Carlo simulations agree well with the temporal evolution of the magnetic state when including disorder, and the experimental results can be explained by considering the effective interaction energy associated with the separation of pairs of vertex excitations.

Artificial ferroic systems: novel functionality from structure, interactions and dynamics.

Lithographic processing and film growth technologies are continuing to advance, so that it is now possible to create patterned ferroic materials consisting of arrays of sub-1 µm elements with high definition. Some of the most fascinating behaviour of these arrays can be realised by exploiting interactions between the individual elements to create new functionality. The properties of these artificial ferroic systems differ strikingly from those of their constituent components, with novel emergent behaviour arising from the collective dynamics of the interacting elements, which are arranged in specific designs and can be activated by applying magnetic or electric fields. We first focus on artificial spin systems consisting of arrays of dipolar-coupled nanomagnets and, in particular, review the field of artificial spin ice, which demonstrates a wide range of fascinating phenomena arising from the frustration inherent in particular arrangements of nanomagnets, including emergent magnetic monopoles, domains of ordered macrospins, and novel avalanche behaviour. We outline how demagnetisation protocols have been employed as an effective thermal anneal in an attempt to reach the ground state, comment on phenomena that arise in thermally activated systems and discuss strategies for selectively generating specific configurations using applied magnetic fields. We then move on from slow field and temperature driven dynamics to high frequency phenomena, discussing spinwave excitations in the context of magnonic crystals constructed from arrays of patterned magnetic elements. At high frequencies, these arrays are studied in terms of potential applications including magnetic logic, linear and non-linear microwave optics, and fast, efficient switching, and we consider the possibility to create tunable magnonic crystals with artificial spin ice. Finally, we discuss how functional ferroic composites can be incorporated to realise magnetoelectric effects. Specifically, we discuss artificial multiferroics (or multiferroic composites), which hold promise for new applications that involve electric field control of magnetism, or electric and magnetic field responsive devices for high frequency integrated circuit design in microwave and terahertz signal processing. We close with comments on how enhanced functionality can be realised through engineering of nanostructures with interacting ferroic components, creating opportunities for novel spin electronic devices that, for example, make use of the transport of magnetic charges, thermally activated elements, and reprogrammable nanomagnet systems.

Single domain spin manipulation by electric fields in strain coupled artificial multiferroic nanostructures.

We demonstrate in situ 90° electric field-induced uniform magnetization rotation in single domain submicron ferromagnetic islands grown on a ferroelectric single crystal using x-ray photoemission electron microscopy. The experimental findings are well correlated with micromagnetic simulations, showing that the reorientation occurs by the strain-induced magnetoelectric interaction between the ferromagnetic nanostructures and the ferroelectric crystal. Specifically, the ferroelectric domain structure plays a key role in determining the response of the structure to the applied electric field, resulting in three strain-induced regimes of magnetization behavior for the single domain islands.

The effect of magnetic anisotropy on the spin configurations of patterned La(0.7)Sr(0.3)MnO3 elements.

We study the effect of magnetocrystalline anisotropy on the magnetic configurations of La0.7Sr0.3MnO3 bar and triangle elements using photoemission electron microscopy imaging. The dominant remanent state is a low energy flux-closure state for both thin (15 nm) and thick (50 nm) elements. The magnetocrystalline anisotropy, which competes with the dipolar energy, causes a strong modification of the spin configuration in the thin elements, depending on the shape, size and orientation of the structures. We investigate the magnetic switching processes and observe in triangular shaped elements a displacement of the vortex core along the easy axis for an external magnetic field applied close to the hard axis, which is well reproduced by micromagnetic simulations.

Optimal ferromagnetically-coated carbon nanotube tips for ultra-high resolution magnetic force microscopy.

Using single-walled carbon nanotubes homogeneously coated with ferromagnetic metal as ultra-high resolution magnetic force microscopy probes, we investigate the key image formation parameters and their dependence on coating thickness. The crucial step of introducing molecular beam epitaxy for deposition of the magnetic coating allows highly controlled fabrication of tips with small magnetic volume, while retaining high magnetic anisotropy and prolonged lifetime characteristics. Calculating the interaction between the tips and a magnetic sample, including hitherto neglected thermal noise effects, we show that optimal imaging is achieved for a finite, intermediate-thickness magnetic coating, in excellent agreement with experimental observations. With such optimal tips, we demonstrate outstanding resolution, revealing sub-10 nm domains in hard magnetic samples, and non-perturbative imaging of nanoscale spin structures in soft magnetic materials, all at ambient conditions with no special vacuum, temperature or humidity controls.

Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles.

Artificial spin-ice systems consisting of nanolithographic arrays of isolated nanomagnets are model systems for the study of frustration-induced phenomena. We have recently demonstrated that monopoles and Dirac strings can be directly observed via synchrotron-based photoemission electron microscopy, where the magnetic state of individual nanoislands can be imaged in real space. These experimental results of Dirac string formation are in excellent agreement with Monte Carlo simulations of the hysteresis of an array of dipoles situated on a kagome lattice with randomized switching fields. This formation of one-dimensional avalanches in a two-dimensional system is in sharp contrast to disordered thin films, where avalanches associated with magnetization reversal are two-dimensional. The self-organized restriction of avalanches to one dimension provides an example of dimensional reduction due to frustration. We give simple explanations for the origin of this dimensional reduction and discuss the disorder dependence of these avalanches. We conclude with the explicit demonstration of how these avalanches can be controlled via locally modified anisotropies. Such a controlled start and stop of avalanches will have potential applications in data storage and information processing.

Ultrafast heating as a sufficient stimulus for magnetization reversal in a ferrimagnet.

The question of how, and how fast, magnetization can be reversed is a topic of great practical interest for the manipulation and storage of magnetic information. It is generally accepted that magnetization reversal should be driven by a stimulus represented by time-non-invariant vectors such as a magnetic field, spin-polarized electric current, or cross-product of two oscillating electric fields. However, until now it has been generally assumed that heating alone, not represented as a vector at all, cannot result in a deterministic reversal of magnetization, although it may assist this process. Here we show numerically and demonstrate experimentally a novel mechanism of deterministic magnetization reversal in a ferrimagnet driven by an ultrafast heating of the medium resulting from the absorption of a sub-picosecond laser pulse without the presence of a magnetic field.

Nonadiabatic spin torque investigated using thermally activated magnetic domain wall dynamics.

Using transmission electron microscopy, we investigate the thermally activated motion of domain walls (DWs) between two positions in Permalloy (Ni80Fe20) nanowires at room temperature. We show that this purely thermal motion is well described by an Arrhenius law, allowing for a description of the DW as a quasiparticle in a one-dimensional potential landscape. By injecting small currents, the potential is modified, allowing for the determination of the nonadiabatic spin torque: ßt=0.010±0.004 for a transverse DW and ßv=0.073±0.026 for a vortex DW. The larger value is attributed to the higher magnetization gradients present.

Domain-wall depinning assisted by pure spin currents.

We study the depinning of domain walls by pure diffusive spin currents in a nonlocal spin valve structure based on two ferromagnetic Permalloy elements with copper as the nonmagnetic spin conduit. The injected spin current is absorbed by the second Permalloy structure with a domain wall, and from the dependence of the wall depinning field on the spin current density we find an efficiency of 6×10{-14} T/(A/m{2}), which is more than an order of magnitude larger than for conventional current induced domain-wall motion. Theoretically we find that this high efficiency arises from the surface torques exerted by the absorbed spin current that lead to efficient depinning.

Size-dependent spin structures in iron nanoparticles.

Using photoemission electron microscopy, we study the magnetization orientation in single 5-25 nm iron particles coupled to a ferromagnetic cobalt support. We find a noncollinear alignment between the particle and substrate magnetization above a particle size of approximately 6 nm and a parallel alignment for smaller sizes. Numerical calculations reveal a transition from an exchange-dominated to an anisotropy-dominated regime on increasing the particle height: the smaller particles are in a single-domain collinear state while larger particles exhibit a spin-spiral magnetic structure determined by the magnetic anisotropy energy.

Imaging of domain wall inertia in Permalloy half-ring nanowires by time-resolved photoemission electron microscopy.

Using photoemission electron microscopy, we image the dynamics of a field pulse excited domain wall in a Permalloy nanowire. We find a delay in the onset of the wall motion with respect to the excitation and an oscillatory relaxation of the domain wall back to its equilibrium position, defined by an external magnetic field. The origin of both of these inertia effects is the transfer of energy between energy reservoirs. By imaging the distribution of the exchange energy in the wall spin structure, we determine these reservoirs, which are the basis of the domain wall mass concept.

Direct determination of large spin-torque nonadiabaticity in vortex core dynamics.

We use a pump-probe photoemission electron microscopy technique to image the displacement of vortex cores in Permalloy discs due to the spin-torque effect during current pulse injection. Exploiting the distinctly different symmetries of the spin torques and the Oersted-field torque with respect to the vortex spin structure we determine the torques unambiguously, and we quantify the amplitude of the strongly debated nonadiabatic spin torque. The nonadiabaticity parameter is found to be ß=0.15±0.07, which is more than an order of magnitude larger than the damping constant α, pointing to strong nonadiabatic transport across the high magnetization gradient vortex spin structures.

Relationship between nonadiabaticity and damping in permalloy studied by current induced spin structure transformations.

By direct imaging we determine spin structure changes in Permalloy wires and disks due to spin transfer torque as well as the critical current densities for different domain wall types. Periodic domain wall transformations from transverse to vortex walls and vice versa are observed, and the transformation mechanism occurs by vortex core displacement perpendicular to the wire. The results imply that the nonadiabaticity parameter beta does not equal the damping alpha, in agreement with recent theoretical predictions. The vortex core motion perpendicular to the current is further studied in disks revealing that the displacement in opposite directions can be attributed to different polarities of the vortex core.

Spatially resolved dynamic eigenmode spectrum of Co rings.

The spatially resolved eigenmode spectrum of micrometer-sized Co ring elements has been determined by means of combined vector network analyzer ferromagnetic resonance and time resolved magneto-optic Kerr effect measurements. Up to 5 resonant eigenmodes were observed in the frequency range from 45 MHz to 20 GHz as a function of an external magnetic bias field. A well-defined mode structure was found for the two equilibrium states (vortex and onion) which correspond to distinctive spatial modes. The effect of dynamic inter-ring coupling on the modes in the remanent states was evinced. The experimental results are found to be in good agreement with those of micromagnetic simulations. Our results demonstrate that, in analogy to the well-defined static equilibrium magnetic states of ring elements, the eigenmode spectra of this high symmetry geometry consist of a well-defined and simple mode structure.

Controlled and reproducible domain wall displacement by current pulses injected into ferromagnetic ring structures.

In a combined numerical and experimental study, we demonstrate that current pulses of different polarity can reversibly and controllably displace a magnetic domain wall (DW) in submicrometer permalloy (NiFe) ring structures. The critical current densities for DW displacement are correlated with the specific spin structure of the DWs and are compared to results of micromagnetic simulations including a spin-torque term. Using a notch, an attractive local pinning potential is created for the DW resulting in a highly reproducible spin structure of the DW, critical for reliable current-induced switching.