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Magnetic skyrmions are topological magnetization textures that are characterized by the homotopy group of two dimensional spheres. Despite years of intensive research on skyrmions, the fundamental problem of the inertia of a skyrmion in driven motion remains unresolved. By properly taking into account a direct coupling between skyrmion motion and the correspondingly excited magnons, we identify a dynamical mass for the skyrmion in motion. The direct coupling between skyrmion motion and magnons can be employed to engineer skyrmion dynamics with magnons through ingenious material and geometry design., 16 pages, 4 figures

Skyrmionic textures are being extensively investigated due to the occurrence of novel topological magnetic phenomena, and their promising applications in a new generation of spintronic devices take advantage of the robust topological stability of their spin structures. The development of practical devices relies on a detailed understanding of how skyrmionic structures can be formed, transferred, detected, and annihilated. In this work our considerations go beyond static skyrmions and theoretically show that the formation/annihilation of both skyrmions and antiskyrmions is enabled by the transient creation and propagation of topological singularities (magnetic monopolelike Bloch points). Critically, our results predict that during the winding/unwinding of skyrmionic textures, the Bloch-point propagation will give rise to an emergent electric field with a substantial amplitude and in the terahertz frequency range. We also demonstrate ways for controlling Bloch-point dynamics, which directly enable the tunablility on generation of this signal, as well as its frequency and amplitude. Our studies provide a concept of directly exploiting topological singularities for terahertz skyrmion-based electronic devices., Physical Review Research, 2 (3), ISSN:2643-1564

Various recent experiments have proven the theoretical prediction that domain walls in planar magnetic structures can channel spin waves as magnonic waveguides, establishing a platform for building magnonic devices. Recently, three-dimensional nanomagnetism has been boosted and become a significant branch of magnetism, because three-dimensional magnetic structures expose much emerging physics hidden behind planar ones and will provide broader room for device engineering. Skyrmions and antiskyrmions, as natural three-dimensional magnetic configurations, are not considered yet in the context of spin-wave channeling and steering. Here, we show that skyrmion tubes can act as nonplanar magnonic waveguides, if excited suitably. An isolated skyrmion tube in a magnetic nanoprism induces spatially separate internal and edge channels of spin waves; the internal channel has a narrower energy gap, compared with that of the edge channel and, accordingly, can transmit signals at lower frequencies. Additionally, we verify that those spin-wave beams along the magnetic nanoprism are restricted to the regions of potential wells. Transmission of spin-wave signals in such waveguides results from the coherent propagation of locally driven eigenmodes of skyrmions, i.e., the breathing and rotational modes. Finally, we find that spin waves along the internal channels are less susceptible to the magnetic field than those along the edge channels. Our work will open up an arena for spin-wave manipulation and help to bridge between skyrmionics and magnonics.

Magnetization reversal in cylindrical nanowires depends on the sample diameter. In thin nanowires, effectively one-dimensional reversal takes place, and at finite temperatures soliton-antisoliton pairs may be nucleated with energy barriers proportional to the cross-sectional area of the nanowires. In soft nanowires of larger diameter of the order of the exchange length, magnetization reversal is initiated by the well-known curling mode. As reversal progresses, skyrmion lines are formed which emanate from the center of the nanowire. As long as these skyrmion lines remain intact, the magnetization process is reversible. Irreversibility occurs when the skyrmion lines break leading to the formation of hedgehog-antihedgehog pairs. These topological spin textures move rapidly away from each other toward the center and the end of the nanowire, respectively. Their high speed between 1 and 3 km/s produces significant emergent electric fields of solenoidal type thus characterizing the hedgehog as an emergent magnetic monopole. These emergent electric fields imply significant forces which correspond to a real electric field of the order of dielectric breakthrough in air.

Quantum spin liquids are materials that feature quantum entangled spin correlations and avoid magnetic long-range order at T = 0 K. Particularly interesting are two-dimensional honeycomb spin lattices where a plethora of exotic quantum spin liquids have been predicted. Here, we experimentally study an effective S = 1/2 Heisenberg honeycomb lattice with competing nearest and next-nearest-neighbour interactions. We demonstrate that YbBr3 avoids order down to at least T = 100 mK and features a dynamic spin–spin correlation function with broad continuum scattering typical of quantum spin liquids near a quantum critical point. The continuum in the spin spectrum is consistent with plaquette type fluctuations predicted by theory. Our study is the experimental demonstration that strong quantum fluctuations can exist on the honeycomb lattice even in the absence of Kitaev-type interactions, and opens a new perspective on quantum spin liquids., npj Quantum Materials, 5 (1), ISSN:2397-4648

We predict that complete magnetization reversal in simple metallic ferromagnetic nanoparticles is directly linked to the pair creation of topological point defects in the form of hedgehog-antihedgehog pairs. These dynamical point defects move at exceptionally high speeds in excess of $1500\text{ }\text{ }\mathrm{m}/\mathrm{s}$, faster than any other known magnetic object. Their rapid motion generates unprecedented solenoidal emergent fields on the order of megavolts per meter, in analogy to the magnetic field of a moving electric charge, providing a striking example that a moving hedgehog constitutes an emergent magnetic monopole.

Recent years have seen tremendous progress in the understanding of topological phenomena in magnetism, in particular at the nanoscale. In this overview, we consider smooth topological textures such as smooth domain walls, meron or vortices, and most importantly skyrmions. These structures derive their topological stability from the fact that they cannot be undone without violating the continuity of the magnetization field, similar to a knot in a rope. Owing to their topological stability, domain walls and skyrmions are prominent candidates in racetrack-type memories introduced by Parkin and co-workers. These smooth textures should be contrasted with singular topological point defects where the magnetization field is forced to vanish in a submanifold. Such point defects include Ising domain walls, vortices of easy-plane spins, and 3D Bloch points, ‘hedgehogs’, or ‘monopoles’. As domain walls, vortices, and skyrmions including their dynamical versions will be discussed in detail in later chapters by Thiaville and Miltat, Behncke and Meier, Chen, Bauer et al., and Akerman, we give analytical arguments how domain walls emerge in quasi 1D nanowires, how magnetization reverses via nucleation, and why skyrmions exist in thin films. A variational ansatz for skyrmions that is derived from an exact \(2\pi \) domain wall profile provides an excellent approximation to numerical and experimental observations in films that include Dzyaloshinskii-Moriya interaction (DMI) and dipolar interactions. In systems of vanishing DMI, the two helical states of a skyrmion are degenerate, and switching between the two helicities occurs in a topologically allowed fashion. This mechanism is closely related to domain wall nucleation in nanowires. Finally we show that dynamical skyrmions may be regarded as 2D siblings of domain wall breathers, and can be described by the same variational ansatz inspired from \(2\pi \) domain walls as static skyrmions in thin films.

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 c...

Magnetic domain wall racetrack memory samples allow for the controlled motion of isolated magnetic domain walls in a quasi one-dimensional geometry. Here we consider the possibility of the dynamical formation of bound states of domain walls that can be prepared via a suitably chosen external field. Upon switching off the external field, these domain walls oscillate around their common center of mass, with a frequency depending on the relative initial handedness of the domain wall. Such breather states may be observed by detecting the resulting magnetization oscillations.

Small-angle neutron scattering (SANS) experiments on nanostructured Fe reveal grain-size-dependent magnetic correlations with a minimal correlation length for grain sizes on the order of the bulk domain-wall width. To investigate the evolution of these correlations during the magnetization process, we performed SANS experiments in external fields of various strengths. In intermediate fields, we find anisotropic scattering profiles with an unusual intensity enhancement for scattering vectors parallel to the field direction. These observations are compared with a modeled granular microstructure containing magnetic domains of arbitrary size and orientation, demonstrating that magnetic domains extend over several grains and have a magnetization that is tilted considerably away from the external field direction. Since the domain size does not change significantly with the magnitude of the external field, we conclude that the magnetization process does not proceed via domain-wall motion. Rather, our SANS data suggests that the magnetization process proceeds by simultaneous reversal of a few adjacent domains, presumably in the form of small avalanches. The latter supposition is supported by theoretical arguments showing the existence of marginally stable domains within the random-anisotropy model.

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 nano- contact. Arranged in a periodic array, such nanocontacts allow the creation of a skyrmion lattice that causes a periodic modulation of the waveguide's 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.

The interface and magnetic properties of sputter-deposited FeCoV/NiO(tNiO)/FeCoV trilayers were analyzed by X-ray reflectivity, bulk magnetization, and polarized neutron reflectivity measurements. The layer depth profile, interface roughness, interface oxidation, etc. are obtained from specular X-ray reflectivity. The dc magnetization shows a coupled reversal of both FeCoV layers for tNiO < 20 nm, whereas for tNiO ≥ 20 nm, a step appears in the MH loop, which widens until tNiO reaches 40 nm. We investigated the magnetization state of the FeCoV layers during the magnetization reversal process by polarized neutron reflectivity measurements at selected points of the hysteresis loop. We conclude that the exchange coupling between the FM layers is accomplished by a spin twist mediated by the AF.

Left- and right-handed chiral matter is present at every scale ranging from seashells to molecules to elementary particles. In magnetism, chirality may be inherited from the asymmetry of the underlying crystal structure, or it may emerge spontaneously. In particular, there has been a long-standing search for chiral spin states1 that emerge spontaneously with the disappearance of antiferromagnetic long-range order. Here we identify a generic system supporting such a behaviour and report on experimental evidence for chirality associated with the quantum dynamics of solitons2,3,4,5 in antiferromagnetic spin chains. The soliton chirality observed by polarized neutron scattering is in agreement with theoretical predictions and is a manifestation of a Berry phase6. Our observations provide the first example of the emergence of spin currents and hidden chiral order that accompany the disappearance of antiferromagnetic order, a scheme believed to lie at the heart of the enigmatic normal state of cuprate superconductors.

Ferromagnetic/antiferromagnetic/ferromagnetic (FM/AF/FM) trilayers are investigated by polarized neutron reflectivity (PNR) with polarization analysis to obtain the layer resolved magnetization profile at various states of magnetization. The trilayers are composed of FeCoV (FM) layers which are separated by NiO (AF) layers of varying thickness. The spin-dependent reflectivities are analyzed by modeling the magnetic states of the FeCoV layers. First, we study magnetization configurations during the magnetization reversal as a function of AF thickness. It is found that for thin AF layers the magnetization reversal of the FM layers occurs simultaneously, whereas for thick AF layers the reversal occurs in a two-step process. In a second part of the experiments we follow, by PNR, the reorientation of the top FM layer in an in-plane perpendicular field starting from a state with the magnetization in the adjacent FM layers oriented antiparallel. It is observed that the magnetization of the top FeCoV layer gradually rotates into the direction of the applied field while the bottom FeCoV layer remains pinned in its state perpendicular to the field.

Magnetic profiles of FM/AF/FM trilayers (FM=ferromagnet, AF=antiferromagnet), as a function of AF thickness t have been investigated by bulk magnetization and polarized neutron reflectivity measurements. DC magnetization results show a t -dependence of the magnetization reversal. From the analysis of polarized neutron reflectivity in conjunction with the DC magnetization we conclude that the thickness dependence of magnetization reversal is a direct consequence of domain wall formation across NiO.

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., Nature Communications, 6, ISSN:2041-1723

Magnetic skyrmions are envisioned as ideal candidates as information carriers for future spintronic devices, which have attracted a great deal of attention in recent years. Due to their topological protection, the creation and annihilation of magnetic skyrmions have been a challenging task. Here, we numerically demonstrate that a magnetic skyrmion can be created by chopping a chiral stripe domain with a static uniaxial strain/stress pulse. This mechanism not only provides a method to create skyrmions in magnetic nanostructures but also offers promising routes for designing tunable skyrmionic-mechanic devices.

Magnetization measurements and small-angle neutron scattering (SANS) were performed on nanostructured Fe, Co and Ni samples, produced by inert-gas condensation. The grain size, which is 10–20 nm in the as-prepared state, was increased incrementally up to 100 nm by thermal annealing. The coercive field shows a pronounced variation with grain size. In Fe, it passes a maximum at around 35 nm and shows a steep decrease towards smaller grain sizes. Small-angle neutron scattering experiments show that magnetic correlations which extend over several grains form spontaneously in zero-field. The correlation length depends strongly on grain size and has in Fe a minimum at around 35 nm. We explain the results at low grain sizes on the basis of an extended random-anisotropy model. Within this model, we take into account that the intergrain exchange coupling constant is smaller than the intragrain exchange constant. We further demonstrate that the random-anisotropy model will break down for grain sizes exceeding a critical value L crit = πδ , with δ approximately the bulk domain-wall width. For grain sizes above L crit , the coercive field follows a 1/ D behavior and the magnetic correlation length increases approximately linearly with grain size, i.e. the magnetic properties approach those of coarse-grained ferromagnetic materials.

Chirality is shown to emerge as a novel degree of freedom of a quantum soliton in the anisotropic spin-12 compound CsCoBr3. The soliton chirality, detected via polarized neutron scattering, is in agreement with theoretical predictions and is a manifestation of Berry's phase. Our observations provide an explicit example of the emergence of spin currents and hidden chiral order that accompany the disappearance of antiferromagnetic order.

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 gauge potential strongly affects the quantum dynamics of the soliton in a periodic lattice or pinning potential. For half-integer spin, destructive interference between soliton states of opposite chirality 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 Berry 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., 20 pages, RevTex 3.0 (twocolumn), to appear in Phys. Rev. B 53, 3237 (1996), 4 PS figures available upon request

We consider the quantum dynamics of spin solitons in a variety of low-dimensional magnetic systems in the semiclassical and the extreme quantum limit. Introducing the concept of chirality of the soliton we derive the dispersion of spin solitons moving through a periodic pinning potential and show that for half-odd integer spin the topological part of the Berry phase induces a halving of the Brillouin zone as well as chirality correlations between subsequent band minima. We demonstrate that these chirality and spin parity effects are universal by considering quasi-one-dimensional ferromagnets and antiferromagnets with local anisotropies and large spins, as well as spin-½ ferromagnetic and antiferromagnetic Heisenberg chains in the Ising limit. For large spin systems, the tunneling rate between states of opposite chiralities is derived and shown to provide a novel scenario for macroscopic quantum phenomena. The results are extended to solitons moving as holes in a two-dimensional antiferromagnetic background, leading to a hole spectrum which is in remarkable agreement with recent ARPES measurements on high-Tc compounds.

Bloch walls in mesoscopic ferromagnets are shown to tunnel coherently between periodically arranged pinning sites and to form a band similar to a Bloch electron in a crystal lattice. Eliminating the spin wave degrees of freedom we derive an effective action for the Bloch wall position. The dissipative term in this action involves a spectral function with a gap and therefore damping due to spin waves is negligible at low temperatures. It is shown that the Berry phase gives rise to a spin-parity-dependent shift in the dispersion. We show that this band structure can give rise to Bloch oscillations of the magnetization in response to a static external field, which provides a magnetic analog to the Josephson effect.

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.

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 c...

The magnetization reversal rate via thermal creation of soliton pairs in quasi-1D ferromagnetic systems is calculated. Such a model describes e.g. the time dependent coercivity of elongated particles as used in magnetic recording media. The energy barrier that has to be overcome by thermal fluctuations corresponds to a soliton-antisoliton pair whose size depends on the external field. In contrast to other models of first order phase transitions such as the phi^4 model, an analytical expression for this energy barrier is found for all values of the external field. The magnetization reversal rate is calculated using a functional Fokker-Planck description of the stochastic magnetization dynamics. Analytical results are obtained in the limits of small fields and fields close to the anisotropy field. In the former case the hard-axis anisotropy becomes effectively strong and the magnetization reversal rate is shown to reduce to the nucleation rate of soliton-antisoliton pairs in the overdamped double sine-Gordon model. The present theory therefore includes the nucleation rate of soliton-antisoliton pairs in the double sine-Gordon chain as a special case. These results demonstrate that for elongated particles, the experimentally observed coercivity is significantly lower than the value predicted by the standard theories of N\'eel and Brown., Comment: 21 pages RevTex 3.0 (twocolumn), 6 figures available on request, to appear in Phys Rev B, Dec (1994)

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.

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 value is maximal for external fields parallel and perpendicular to the particle axis and the coercivity shows an asymmetric angular dependence. Both features are in accordance with recent experiments on an elongated single domain particle.

Elongated ferromagnetic single-domain particles are believed to exhibit a high stability of their remanent magnetization. However, here it is shown that for elongated particles thermal fluctuations lower the coercivity much more drastically than predicted by current theories. The rate for magnetization reversal is calculated for a classical model of a ferromagnet that allows for a spatially nonuniform magnetization distribution along the sample. The prefactor of the Arrhenius factor is explicitly evaluated and analytical results are obtained in the experimentally important limit of external magnetic fields close to the anisotropy field and for moderate damping.

The dynamics of a classical continuum model of a ferromagnet with exchange and anisotropy energies of hard- and easy-axis type is considered. Exact solutions of soliton pairs with vanishing center of mass velocity are presented. They reveal the counterintuitive existence of a family of bound states of a repulsive, twisted domain wall (soliton) pair. These breather states have energies which lie above the continuum of the corresponding scattering states of two solitons

On etablit une solution plane generale de ces equations. De la, on evalue l'evolution dans le temps de petites deviations planes de forme arbitraire. On developpe en detail l'exemple d'une paroi se deplacant dans un champ magnetique brusquement eteint. Analyse des effets d'un champ magnetique dependant de l'espace et du temps et des modifications de l'anisotropie

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.

Classical bound states of solitons (“breathers”) in continuum spin chains are semiclassically quantized via Berry’s phase. Remarkably, our results at zone center and zone boundary as well as the whole continuum match the exact Bethe ansatz result of the discrete, XYZ spin-1/2 chain with arbitrary anisotropies.

Small-angle neutron scattering experiments on nanostructured Fe reveal spatial magnetic correlations across the interfaces which depend strongly on grain size, with a minimum at around 35 nm. This grain size is comparable with Lcrit=πδ, with δ the bulk domain-wall width. We present an extended random-anisotropy model to explain the magnetic properties in the low grain size regime and explain the crossover of the magnetic properties for grain sizes comparable with Lcrit.

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 ${\text{Co}}^{2+}$ 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.

We examine the effects of long-range dipolar forces on metamagnetic transitions and generalize the theory of Condon domains to the case of an itinerant electron system undergoing a first-order metamagnetic transition. We demonstrate that within a finite range of the applied field, dipolar interactions induce a spatial modulation of the magnetization in the form of stripes or bubbles. Our findings are consistent with recent observations in the bilayer ruthenate Sr$_3$Ru$_2$O$_7$., Comment: 4 pages, 3 figures, minor changes, references added

We use polarized neutron reflectivity to study the evolution of the magnetization profile during the hysteresis of FeCoV (20 nm)/NiO (tNiO) /FeCoV (20 nm) trilayers. For small tNiO, we find that the magnetization in the two ferromagnetic layers remains parallel, indicating a strong exchange coupling across the anti-ferromagnetic NiO layer. Beyond a film thickness tNiO = 40 nm, the observed step in the hysteresis is seen to correspond to an antiparallel orientation of the two ferromagnetic layers. Since this length scale agrees with the domain wall width of NiO, our results suggest that the interlayer exchange coupling involves a partial domain wall formation in the antiferromagnetic layer.

The density of monopoles in spin ice can be enhanced by rapid cooling. After the creation of significant numbers of monopoles, magnetization measurements show that, much like charges in an electric field, monopoles can be driven by a magnetic field.

The magnetization process in nanostructured $(n\text{\ensuremath{-}})$ Fe and Co was investigated via small-angle neutron scattering (SANS). In a zero field, the magnetization exhibits correlations extending over several grains. In intermediate applied magnetic fields around $1\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$, $n\text{\ensuremath{-}}\mathrm{Fe}$ and $n\text{\ensuremath{-}}\mathrm{Co}$ samples with small grain sizes exhibit an anisotropic scattering profile with an unusual intensity enhancement for scattering vectors parallel to the field direction. Comparing the experimental data with a modeled granular microstructure containing magnetic domains of arbitrary size and orientation, we conclude that magnetic domains extending over several grains are tilted considerably out of the external field direction in intermediate fields. Since the domain size does not change significantly with the magnitude of the external field, we conclude that the magnetization process does not proceed via domain-wall motion. Together with theoretical arguments showing the existence of marginally stable domains within the random-anisotropy model, our SANS data suggests that the magnetization process proceeds by simultaneous reversal of a few adjacent domains, presumably in the form of small avalanches. This resembles the magnetization process predicted for random-field Ising magnets. Our theoretical analysis of SANS data is general and applies to other systems consisting of magnetic nanoclusters embedded in a nonmagnetic matrix.

Bloch walls in mesoscopic ferromagnets can tunnel between periodically arranged pinning sites leading to a Bloch band. The quantum spin phase gives rise to a spin parity dependent shift in the dispersion. Static external magnetic fields induce magnetization oscillations and provide a magnetic analogue of the Josephson effect.

A 10 nm Fe/5 nm NiO/10 nm Co polycrystalline trilayer prepared by magnetron sputtering has been investigated by resonant magnetic reflectivity of linearly polarized soft x rays (transversal magneto-optical Kerr effect geometry) at the L 3 edges of Fe, Ni, and Co. The exchange coupling in the trilayer, introduced during synthesis, has been altered by cooling through the Neel temperature T N of NiO at three different cooling fields H F C . We show that the chemical structure at the interfaces, the grain size and the magnetic properties of the trilayer are governed by factors such as successive heat treatment, magnetic field applied during synthesis and cooling through T N of NiO. Clear evidence for oxidation of Fe and Co states has been obtained, suggestive for the formation of mixed oxides at the Fe/NiO and NiO/Co interfaces. Oxidized Fe and Co are found to carry a net magnetic moment, which couples to the moments of the metallic states. We find that the coupling between oxidized and metallic Co spins is ferromagnetic, whereas the coupling between oxidized and metallic Fe spins is antiferromagnetic. We observe the presence of two types of excess Ni spins. A rigid excess Ni magnetic moment is induced at the interface during synthesis as follows from the strong asymmetry of the x-ray Kerr loops of the oxidized Co spins at H F C = 0 Oe and metallic Co spins at H F C =240 Oe. Heat treatment leads to appearence of a soft excess Ni magnetic moment, which is ferromagnetically coupled to the metallic Fe and Co spins and exhibits a conventional hysteresis loop. Competing interactions lead to frustrated magnetization at the NiO/Fe interface and cause a tilt of the Fe spins away from the direction of applied magnetic field. This manifests itself in the presence of characteristic humps in the Fe Kerr loops.

A biaxial ferromagnet in an external magnetic field is considered. A metastable state is realized when the magnetization is uniform and pointing antiparallel to the external field. At finite temperature, fluctuations drive the configuration over the lowest lying saddle point of energy. A known unstable structure is identified as this saddle point and nucleation rates are calculated by mean of the Brinkman/Laundauer-Swanson/Langer (BLSL) approach. >