Hans-Benjamin Braun

Topological effects in nanomagnetism: from superparamagnetism to chiral quantum solitons

Micromagnetics has been the method of choice to interpret experimental data in the area of microscopic magnetism for several decades. In this article, we show how progress has been made to extend this formalism to include thermal and quantum fluctuations in order to describe recent experimental developments in nanoscale magnetism. For experimental systems with constrained dimensions such as nanodots, atomic chains, nanowires, and thin films, topological defects such as solitons, vortices, skyrmions, and monopoles start to play an increasingly important role, all forming novel types of quasiparticles in patterned low-dimensional magnetic systems. We discuss in detail how soliton–antisoliton pairs of opposite chirality form non-uniform energy barriers against thermal fluctuations in nanowires or pillars. As a consequence of their low barrier energy compared to uniform reversal, they limit the thermal stability of perpendicular recording media. For sufficiently short samples, the non-uniform energy barrier continuously merges into the conventional uniform Néel–Brown barrier. Partial formation of chiral domain walls also determines the magnetic properties of granular nanostructured magnets and exchange spring systems. For a long time, the reconciliation between micromagnetics and quantum mechanics has remained an unresolved challenge. Here it is demonstrated how inclusion of Berrys phase in a micromagnetic action allows for a semiclassical quantization of spin systems, a method that is demonstrated by the simple example of an easy-plane spin. This powerful method allows for a description of quantum dynamics of solitons and breathers which in the latter case agrees with the anisotropic spin-½ XYZ-model. The domain wall or soliton chirality plays an important role as it is coupled to the wavevector of the quasiparticle dispersion. We show how this quantum soliton chirality is detected by polarized neutron scattering in one-dimensional quantum antiferromagnets.

Impurity-ion pair induced high-temperature ferromagnetism in Co-doped ZnO

Magnetic 3d-ions doped into wide-gap oxides show signatures of room temperature ferromagnetism, although their concentration is two orders of magnitude smaller than that in conventional magnets. The prototype of these exceptional materials is Co-doped ZnO, for which an explanation of the room temperature ferromagnetism is still elusive. Here we demonstrate that magnetism originates from Co oxygen-vacancy pairs with a partially filled level close to the ZnO conduction band minimum. The magnetic interaction between these pairs is sufficiently long-ranged to cause percolation at moderate concentrations. However, magnetically correlated clusters large enough to show hysteresis at room temperature already form below the percolation threshold and explain the current experimental findings. Our work demonstrates that the magnetism in ZnO:Co is entirely governed by intrinsic defects and a phase diagram is presented. This suggests a recipe for tailoring the magnetic properties of spintronics materials by controlling their intrinsic defects.

Dynamically stabilized magnetic skyrmions

Magnetic skyrmions are topologically non-trivial spin textures that manifest themselves as quasiparticles in ferromagnetic thin films or noncentrosymmetric bulk materials. So far attention has focused on skyrmions stabilized either by the Dzyaloshinskii–Moriya interaction (DMI) or by dipolar interaction, where in the latter case the excitations are known as bubble skyrmions. Here we demonstrate the existence of a dynamically stabilized skyrmion, which exists even when dipolar interactions and DMI are absent. We establish how such dynamic skyrmions can be nucleated, sustained and manipulated in an effectively lossless medium under a nanocontact. As quasiparticles, they can be transported between two nanocontacts in a nanowire, even in complete absence of DMI. Conversely, in the presence of DMI, we observe that the dynamical skyrmion experiences strong breathing. All of this points towards a wide range of skyrmion manipulation, which can be studied in a much wider class of materials than considered so far.

Berry's phase and quantum dynamics of ferromagnetic solitons

We study spin parity effects and the quantum propagation of solitons (Bloch walls) in quasi-one-dimensional ferromagnets. Within a coherent state path integral approach we derive a quantum field theory for nonuniform spin configurations. The effective action for the soliton position is shown to contain a gauge potential due to the Berry phase and a damping term caused by the interaction between soliton and spin waves. For temperatures below the anisotropy gap this dissipation reduces to a pure soliton mass renormalization. The quantum dynamics of the soliton in a periodic lattice or pinning potential reveals remarkable consequences of the Ferry phase. For half-integer spin, destructive interference between opposite chiralities suppresses nearest-neighbor hopping. Thus the Brillouin zone is halved, and for small mixing of the chiralities the dispersion reveals a surprising dynamical correlation. Two subsequent band minima belong to different chirality states of the soliton. For integer spin the Ferry phase is inoperative and a simple tight-binding dispersion is obtained. Finally it is shown that external fields can be used to interpolate continuously between the Bloch wall dispersions for half-integer and integer spin.

Fluctuations and instabilities of ferromagnetic domain-wall pairs in an external magnetic field.

Soliton excitations and their stability in anisotropic quasi-1D ferromagnets are analyzed analytically. In the presence of an external magnetic field, the lowest lying topological excitations are shown to be either soliton-soliton or soliton-antisoliton pairs. In ferromagnetic samples of macro- or mesoscopic size, these configurations correspond to twisted or untwisted pairs of Bloch walls. It is shown that the fluctuations around these configurations are governed by the same set of operators. The soliton-antisoliton pair has exactly one unstable mode and thus represents a critical nucleus for thermally activated magnetization reversal in effectively one-dimensional systems. The soliton-soliton pair is stable for small external fields but becomes unstable for large magnetic fields. From the detailed expression of this instability threshold and an analysis of nonlocal demagnetizing effects it is shown that the relative chirality of domain walls can be detected experimentally in thin ferromagnetic films. The static properties of the present model are equivalent to those of a nonlinear sigma-model with anisotropies. In the limit of large hard-axis anisotropy the model reduces to a double sine-Gordon model.

NUCLEATION IN FERROMAGNETIC NANOWIRES-MAGNETOSTATICS AND TOPOLOGY

Magnetization reversal in nanowires can be accomplished locally via thermal nucleation of soliton-antisoliton pairs. It is demonstrated that the total nonlocal magnetostatic energy can be reduced to a local anisotropy if the particle diameter is smaller than the magnetic length scale. Topological restrictions of the curling mode are discussed. Barrier energies for nucleation at sample ends are computed and close agreement with recent experiments on Ni-nanowires is found.

Transition rates of a non‐Markovian Brownian particle in a double well potential

The transition rate of a non‐Markovian Brownian particle in a double well potential is determined analytically by means of asymptotic methods and compared with both current theories and numerical simulations by Straub, Borkovec, and Berne [J. Chem. Phys. 83, 3172 (1985)]. We obtain good agreement with these simulations. The ranges of validity for the different current theories which we find do, however, not exhaust the complete parameter range. In particular, for large static friction we identify a region of bath correlation times in which the rate differs grossly from the value predicted by either Grote–Hynes theory or non‐Markovian energy diffusion. Additionally, corrections to the Grote–Hynes rate are determined and an analytical expression for the non‐Markovian energy diffusion rate is obtained.

Kramers’s rate theory, broken symmetries, and magnetization reversal (invited)

The theory of thermally induced magnetization reversal in small particles is reviewed. The conventional Neel–Brown theory for uniform magnetization reversal and its derivation from Kramers’s rate theory are first discussed. For sufficiently elongated particles, however, a nonuniform energy barrier (‘‘nucleus’’) has lower energy than the uniform barrier and thus yields a lower coercivity. This coercivity reduction is shown to occur also for vanishing hard‐axis anisotropy when the nucleus breaks the rotational symmetry around the easy axis. The prefactor of the Arrhenius factor is calculated for uniform and nonuniform barriers.

NONUNIFORM SWITCHING OF SINGLE DOMAIN PARTICLES AT FINITE TEMPERATURES

It has recently been shown that nonuniform thermal fluctuations are able to significantly reduce the coercivity of elongated ferromagnetic particles compared to the uniform rotation model of Neel and Brown. In particular, this theory revealed that even for particles that are single domain in the remanent state, a nonuniform energy barrier exists which is proportional to the product of the particle cross‐sectional area and the domain wall energy. For sufficiently long particles, this energy barrier is therefore always lower than that of uniform reversal. Here, several implications of this theory are discussed. It is shown that the coercivity of a particle with fixed volume decreases with increasing aspect ratio. For a fixed particle shape, the coercivity is lower with decreasing exchange constant. For small particle aspect ratios the theory is shown to merge continuously into the Neel–Brown theory. The angular dependence of the coercivity is evaluated explicitly. The reduction from the Stoner–Wohlfarth val...

Skyrmion-Based Dynamic Magnonic Crystal

A linear array of periodically spaced and individually controllable skyrmions is introduced as a magnonic crystal. It is numerically demonstrated that skyrmion nucleation and annihilation can be accurately controlled by a nanosecond spin polarized current pulse through a nanocontact. Arranged in a periodic array, such nanocontacts allow the creation of a skyrmion lattice that causes a periodic modulation of the waveguides magnetization, which can be dynamically controlled by changing either the strength of an applied external magnetic field or the density of the injected spin current through the nanocontacts. The skyrmion diameter is highly dependent on both the applied field and the injected current. This implies tunability of the lowest band gap as the skyrmion diameter directly affects the strength of the pinning potential. The calculated magnonic spectra thus exhibit tunable allowed frequency bands and forbidden frequency bandgaps analogous to that of conventional magnonic crystals where, in contrast, the periodicity is structurally induced and static. In the dynamic magnetic crystal studied here, it is possible to dynamically turn on and off the artificial periodic structure, which allows switching between full rejection and full transmission of spin waves in the waveguide. These findings should stimulate further research activities on multiple functionalities offered by magnonic crystals based on periodic skyrmion lattices.