| The introduction of topology into condensed matter physics opens a new perspective to understand the properties of materials,which leads to the discovery of a series of new quantum effects and corelated quantum materials.The topological properties of electron energy band in reciprocal space and the topology of electron spin structure in real space are the typical features of topological quantum materials.The energy band topology comes from the topological properties of the electron wave function in the reciprocal space,which leads to the discovery of topological insulators,topological metals(semimetals),topological superconductors and the topological order of correlated electron systems.The topology of electron spin structure in real space comes from soliton physics.Bogdanov et al.for the first time,found the magnetic solitons in spiral magnets by considering the Dzyaloshinskii-Moriya interaction(DMI)caused by inversion symmetry broken.This magnetic soliton is similar to Skyme’s localized soliton proposed for heavy mesons,and has topological properties such as emergent electrodynamics.However,these topological phases are mainly concentrated in the crystalline systems with long-range translational symmetry,while the topological properties of amorphous materials,a large category of materials in contrast to crystalline systems in the material world,have not been explored.We look for topological phases in amorphous systems for the following two reasons:The first one is scientific meaning.The first property of topological phase is the robustness to disorder,so what is the upper limit of robustness?It is known that on-site disorder on a lattice can induce topological phases,but it will eventually lead to a trivial Anderson insulator.So,can a completely structure disordered system without lattice also has topological phases?If so,how to define and calculate the invariants of amorphous topological phases and their physical properties?The second one is the application of technology.Due to the strong spin-momentum locking at the surface of energy band topological materials and the real-space emergent electrodynamics of topological spin structure,topological materials have great application prospects.However,at present,most topological properties are only observed in carefully grown single crystals,so the production costs will be very high and the application field will be limited.In contrast,amorphous solids are easy to grow,which is one of the reasons why they are ubiquitous in technological applications.Therefore,finding the topological phase in amorphous system is a possible way to realize the practical application of topological materials.Taking the amorphous magnetic metal alloy Fe78Si9B13(FeSiB)as the object of study,this work explores the transport properties and topological phases.The main results are the following two aspects:The first part studies the transport properties of FeSiB,especially the anomalous Hall effect(AHE).We find that the minimum resistivity of FeSiB at low temperature is independent of the applied magnetic field,indicating the origin is the two-level scattering caused by the amorphous structure effect.The high field magnetoresistance has a linear relationship with the applied magnetic field,which is consistent with the less scattering of magneton-electron in high field.The magnetic excitation of FeSiB originates from the fluctuations of independent long spin waves,showing M-T3/2 scaling law,which is the characteristic of strong itinerant ferromagnet.We further find a very well linear relationship between the anomalous Hall conductivity σAH and the magnetization Mz,the anomalous Hall resistivity ρAH equals SHρxx2Mx meanwhile.This shows that the AHE comes from the intrinsic contribution caused by energy band.Using the magnetic excitation of strong itinerant ferromagnet,we give a qualitative explanation,that is the linear relationship between σAH and Mz originates from the fluctuations of independent long spin wave.In addition,the largest anomalous Hall angle θAH and σAH at low temperature can be comparable to the values of some magnetic topological metals,which means that FeSiB may inherit some topological properties of energy band from BCC-Fe.The second part studies the topological spin structure in FeSiB.Firstly,we find that there are two magnetization stages in the magnetization curve,which means that the spin will flip during the out-of-plane magnetization.At this process,there are both in-plane and out-of-plane spin components in the system.Then we find a much large topological Hall effect(THE)at above room temperature,which has a peak in the low and high field,respectively.The absolute values of the negative THE in the low field increase with the increase of temperature,which has the feature of thermal driven topology,while the positive THE in the high field decreases with the increase of temperature.We explained the negative THE by topological transport theory,and the calculated spin canting angle between non collinear magnetic moments is consistent with the previous results obtained by Mossbauer spectrum.In addition,according to the previous neutron scattering,the local coordination numbers of Fe-Fe in FeSiB are different,which means the intensity of magnetic frustration also changes.And the region with high coordination numbers corresponds to strong frustration and the region with low coordination numbers corresponds to weak frustration.While the size of the spin vortex is negatively correlated with the magnetic frustration,that is,the strong frustration corresponds to the small vortex.Therefore,due to the global close-packed structure of amorphous alloy,the size of vortex in the system show a Gaussian distribution dominated by small clusters.Thus,the detection technology with different resolution will find clusters with different sizes.Then,we use Lorentz transmission electron microscope(LTEM)with the scale bar 1μm to study the topological spin structure in FeSiB,and the image did show a few sparse spin vortices(～50nm).Finally,starting from the competing interaction between ferromagnetic and antiferromagnetic,combined with the DMI due to inherent inversion symmetry broken of amorphous structure,the detailed configuration of topological spin structure in FeSiB is studied through Monte Carlo(MC)simulation.We find that these topological spin structures are topologically equivalent to skyrmion.And the competing interaction is the fundamental mechanism of topological spin structure,while the role of DMI is providing anisotropy,so the system could have non-zero topological charge.Furthermore,the size of the topological vortex under frustration can reach the order of about 1nm,which is very important for high-density magnetic storage.Therefore,our findings provide a unique candidate for magnetic memory devices with ultra-high density. |
