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Topological solitons have been studied for decades in classical field theories, and have started recently to impact condensed matter physics. Among those solitons, magnetic skyrmions are two-dimensional particle-like objects with a continuous winding of the magnetization, and magnetic Hopfions are three-dimensional topological solitons that can be formed from a closed loop of a twisted skyrmion string. Whereas intense research is underway with magnetic skyrmions towards a fundamental understanding and potential applications in advanced storage and logic devices, the experimental creation and confirmation of magnetic Hopfions has been elusive so far. Theoretical models suggest that Hopfions can be stabilized in frustrated or chiral magnetic systems, and that target skymions can be transformed into Hopfions by adapting their perpendicular magnetic anisotropy. Here, we present experimental evidence of magnetic Hopfions that were created in magnetic Ir/Co/Pt multilayers shaped into nanoscale disks, which are known to host target skyrmions. The three-dimensional spin texture, which distinguishes magnetic Hopfions from target skyrmions was confirmed by combining two advanced element-specific magnetic X-ray microscopy techniques with about 20-30nm lateral resolution, using X-ray magnetic circular dichroism effect as magnetic contrast mechanism in surface-sensitive X-ray photoemission electron microscopy and bulk-sensitive soft x-ray transmission microscopy. We anticipate that these results will stimulate further investigations of Hopfions with different topologies and their potential application in three-dimensional spintronics devices.
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Paradigmatic knotted solitons, Hopfions, that are characterized by topological Hopf invariant, are widely investigated in the diverse areas ranging from high energy physics, cosmology and astrophysics to biology, magneto- and hydrodynamics and condensed matter physics. Yet, while holding high promise for applications, they remain elusive and under-explored. Here we demonstrate that Hopfions emerge as a basic configuration of polarization field in confined ferroelectric nanoparticles. Our findings establish that Hopfions govern a wealth of novel functionalities in the electromagnetic response of composite nanomaterials opening route to unprecedented technological applications.
Hopfions are an intriguing class of string-like solitons, named according to a classical topological concept classifying three-dimensional direction fields. The search of hopfions in real physical systems is going on for nearly half a century, starting with the seminal work of Faddeev. But so far realizations in solids are missing. Here, we present a theory that identifies magnetic materials featuring hopfions as stable states without the assistance of confinement or external fields. Our results are based on an advanced micromagnetic energy functional derived from a spin-lattice Hamiltonian. Hopfions appear as emergent particles of the classical Heisenberg model. Magnetic hopfions represent three-dimensional particle-like objects of nanometre-size dimensions opening the gate to a new generation of spintronic devices in the framework of a truly three-dimensional architecture. Our approach goes beyond the conventional phenomenological models. We derive material-realistic parameters that serve as concrete guidance in the search of magnetic hopfions bridging computational physics with materials science.
We consider a quasi one-dimensional configuration consisting of two small pieces of ferromagnetic material separated by a metallic one and contacted by two metallic leads. A spin-polarized current is injected from one lead. Our goal is to investigate the correlation induced between the magnetizations of the two ferromagnets by spin-transfer torque. This torque results from the interaction between the magnetizations and the spin polarization of the current. We discuss the dynamics of a single ferromagnet, the extension to the case of two ferromagnets, and give some estimates for the parameters based on experiments.
We present micromagnetic simulations on resonant spin wave modes of magnetic Hopfions up to 15 GHz driven by external magnetic fields. A sharp transition is found around 32 mT coinciding with a transition from Hopfions to magnetic torons. The modes exhibit characteristic amplitudes in frequency space accompanied by unique localization patterns in real space, and are found to be robust to damping around topological features, particularly vortex lines in Hopfions and Bloch points in torons. The marked differences in spin wave spectra between Hopfions, torons and target skyrmions can serve as fingerprints in future experimental validation studies of these novel 3d topological spin textures.
Using spin dependent specular and off-specular polarized neutron reflectivity (PNR), we report the observation of a twisted helical magnetic structure with planar 2{pi} domain wall (DW) and highly correlated magnetic domains in a Gd/Co multilayer. Specular PNR with polarization analysis reveals the formation of planar 2{pi}DWs below a compensation temperature (TComp), resulting to positive exchange bias in this system. Off-specular PNR with spin polarization showed development of magnetic inhomogenities (increase in magnetic roughness) for central part (thickness ~ 25-30 {AA}) of each Gd layer, where magnetization is aligned perpendicular (in-plane) to an applied field. These magnetic roughness are vertically correlated and results into Bragg sheet in spin flip channel of Off-specular PNR data, which is contributing towards an antisymmetric magnetoresistance at TComp in the system. The growth and tunability of highly correlated magnetic inhomogeneities (roughness) and domain structure around TComp in combination of twisted helical magnetic structure with planar 2{pi}DWs will be key for application in all-spin-based technology.
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