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This Roadmap provides an overview of the critical role of materials in exploiting spin and topology for next-generation quantum technologies including computing, sensing, information storage and networking devices. We explore the key materials systems that support spin and topological phenomena and discuss their figures of merit. Spin and topology-based quantum technologies have several advantages over their classical, charged-based counterparts, including non-volatility, faster data processing speeds, higher integration densities and lower power consumption. We discuss the main challenges facing the field, identify strategies to overcome them, and provide a realistic outlook on future possibilities of spin-based and topological materials in quantum technology applications., Comment: Roadmap of the UKRI EPSRC Materials for Quantum Network (M4QN) Spin & Topology group. 25 pages, 5 figures, includes supplement. Comments welcome!

Skyrmion-hosting multilayer stacks are promising avenues for applications, although little is known about the depth dependence of the magnetism. We address this by reporting the results of circular dichroic resonant elastic x-ray scattering (CD-REXS), micromagnetic simulations, and low-energy muon-spin rotation (LE-$\mu^+$SR) measurements on a stack comprising [Ta/CoFeB/MgO]$_{16}$/Ta on a Si substrate. Energy-dependent CD-REXS shows a continuous, monotonic evolution of the domain-wall helicity angle with incident energy, consistent with a three-dimensional hybrid domain-wall-like structure that changes from N\'eel-like near the surface to Bloch-like deeper within the sample. LE-$\mu^+$SR reveals that the magnetic field distribution in the trilayers near the surface of the stack is distinct from that in trilayers deeper within the sample. Our micromagnetic simulations support a quantitative analysis of the $\mu^+$SR results. By increasing the applied magnetic field, we find a reduction in the volume occupied by domain walls at all depths, consistent with a crossover into a region dominated by skyrmions above approximately 180 mT., Comment: 9 pages, 4 figures

Crystal geometry can greatly influence the emergent properties of quantum materials. As an example, the kagome lattice is an ideal platform to study the rich interplay between topology, magnetism, and electronic correlation. In this work, combining high-resolution angle-resolved photoemission spectroscopy and ab-initio calculation, we systematically investigate the electronic structure of XMn6Sn6 (X = Dy, Tb, Gd, Y) family compounds. We observe the Dirac fermion and the flat band arising from the magnetic kagome lattice of Mn atoms. Interestingly, the flat band locates in the same energy region in all compounds studied, regardless of their different magnetic ground states and 4f electronic configurations. These observations suggest a robust Mn magnetic kagome lattice across the XMn6Sn6 family, thus providing an ideal platform for the search and investigation on new emergent phenomena in magnetic topological materials., Comment: PRB accepted

Three-dimensional topological insulators (TIs) are a perfectly tuned quantum-mechanical machinery in which counter-propagating and oppositely spin-polarized conduction channels balance each other on the surface of the material. This topological surface state crosses the bandgap of the TI, and lives at the interface between the topological and a trivial material, such as vacuum. Despite its balanced perfection, it is rather useless for any practical applications. Instead, it takes the breaking of time-reversal symmetry (TRS), and the appearance of an exchange gap to unlock hidden quantum states. The quantum anomalous Hall effect, which has first been observed in Cr-doped (Sb,Bi)$_2$Te$_3$, is an example of such a state in which two edge channels are formed at zero field, crossing the magnetic exchange gap. The breaking of TRS can be achieved by magnetic doping of the TI with transition metal or rare earth ions, modulation doping to keep the electronically active channel impurity free, or by proximity coupling to a magnetically ordered layer or substrate, in heterostructures or superlattices. We review the challenges these approaches are facing in the famous 3D TI (Sb,Bi)$_2$(Se,Te)$_3$ family, and try to answer the question whether these materials can live up to the hype surrounding them., Comment: 13 pages, 3 figures, published in Applied Physics Letters

Heterostructures composed of ferromagnetic layers that are mutually interacting through a nonmagnetic spacer are at the core of magnetic sensor and memory devices. In the present study, layer-resolved ferromagnetic resonance was used to investigate the coupling between the magnetic layers of a Co/MgO/Permalloy magnetic tunnel junction. Two magnetic resonance peaks were observed for both magnetic layers, as probed at the Co and Ni L3 x-ray absorption edges, showing a strong interlayer interaction through the insulating MgO barrier. A theoretical model based on the Landau-Lifshitz-Gilbert-Slonczewski equation was developed, including exchange coupling and spin pumping between the magnetic layers. Fits to the experimental data were carried out, both with and without a spin pumping term, and the goodness of the fit was compared using a likelihood ratio test. This rigorous statistical approach provides an unambiguous proof of the existence of interlayer coupling mediated by spin pumping., Comment: 11 pages, 7 figures

Magnetic doping with transition metal ions is the most widely used approach to break timereversal symmetry in a topological insulator, a prerequisite for unlocking the TIs exotic potential. Recently, we reported the doping of Bi2Te3 thin films with rare earth ions, which, owing to their large magnetic moments, promise commensurately large magnetic gap openings in the topological surface states. However, only when doping with Dy has a sizable gap been observed in angle-resolved photoemission spectroscopy, which persists up to room-temperature. Although disorder alone could be ruled out as a cause of the topological phase transition, a fundamental understanding of the magnetic and electronic properties of Dy:Bi2Te3 remained elusive. Here, we present an X-ray magnetic circular dichroism, polarized neutron reflectometry, muon spin rotation, and resonant photoemission study of the microscopic magnetic and electronic properties. We find that the films are not simply paramagnetic but that instead the observed behavior can be well explained by the assumption of slowly fluctuating, inhomogeneous magnetic patches with increasing volume fraction as the temperature decreases. At liquid helium temperatures, a large effective magnetization can be easily introduced by the application of moderate magnetic fields, implying that this material is very suitable for proximity coupling to an underlying ferromagnetic insulator or in a heterostructure with transition metal-doped layers. However, the introduction of some charge carriers by the dopants cannot be excluded at least in these highly doped samples. Nevertheless, we find that the magnetic order is not mediated via the conduction channel in these rare earth doped samples and therefore magnetic order and carrier concentration are expected to be independently controllable. This is not generally the case for transition metal doped topological insulators., Comment: 9 pages, 5 figures

We report on the electronic structure of the elemental topological semimetal $\alpha$-Sn on InSb(001). High-resolution angle-resolved photoemission data allow to observe the topological surface state (TSS) that is degenerate with the bulk band structure and show that the former is unaffected by different surface reconstructions. An unintentional $p$-type doping of the as-grown films was compensated by deposition of potassium or tellurium after the growth, thereby shifting the Dirac point of the surface state below the Fermi level. We show that, while having the potential to break time-reversal symmetry, iron impurities with a coverage of up to 0.25 monolayers do not have any further impact on the surface state beyond that of K or Te. Furthermore, we have measured the spin-momentum locking of electrons from the TSS by means of spin-resolved photoemission. Our results show that the spin vector lies fully in-plane, but it also has a finite radial component. Finally, we analyze the decay of photoholes introduced in the photoemission process, and by this gain insight into the many-body interactions in the system. Surprisingly, we extract quasiparticle lifetimes comparable to other topological materials where the TSS is located within a bulk band gap. We argue that the main decay of photoholes is caused by intraband scattering, while scattering into bulk states is suppressed due to different orbital symmetries of bulk and surface states.

We report grazing incidence small angle neutron scattering (GISANS) and complementary off-specular neutron reflectometry (OSR) of the magnetic order in a single-crystalline epitaxial MnSi film on Si(111) in the thick film limit. Providing a means of direct reciprocal space mapping, GISANS and OSR reveal a magnetic modulation perpendicular to the films under magnetic fields parallel and perpendicular to the film, where additional polarized neutron reflectometry (PNR) and magnetization measurements are in excellent agreement with the literature. Regardless of field orientation, our data does not suggest the presence of more complex spin textures, notably the formation of skyrmions. This observation establishes a distinct difference with bulk samples of MnSi of similar thickness under perpendicular field, in which a skyrmion lattice dominates the phase diagram. Extended x-ray absorption fine structure measurements suggest that small shifts of the Si positions within the unstrained unit cell control the magnetic state, representing the main difference between the films and thin bulk samples.

We have investigated the band structure at the $\Gamma$ point of the three-dimensional (3D) topological insulator Bi$_2$Se$_3$ using magneto-spectroscopy over a wide range of energies ($0.55-2.2$\,eV) and in ultrahigh magnetic fields up to 150\,T. At such high energies ($E>0.6$\,eV) the parabolic approximation for the massive Dirac fermions breaks down and the Landau level dispersion becomes nonlinear. At even higher energies around 0.99 and 1.6 eV, new additional strong absorptions are observed with a temperature and magnetic-field dependence which suggest that they originate from higher band gaps. Spin orbit splittings for the further lying conduction and valence bands are found to be 0.196 and 0.264 eV.

Nanoscale chiral skyrmions in noncentrosymmetric helimagnets are promising binary state variables in high-density, low-energy nonvolatile memory. Skyrmions are ubiquitous as an ordered, single-domain lattice phase, which makes it difficult to write information unless they are spatially broken up into smaller units, each representing a bit. Thus, the formation and manipulation of skyrmion lattice domains is a prerequisite for memory applications. Here, using an imaging technique based on resonant magnetic x-ray diffraction, we demonstrate the mapping and manipulation of skyrmion lattice domains in Cu2OSeO3. The material is particularly interesting for applications owing to its insulating nature, allowing for electric field-driven domain manipulation., Comment: 4 pages, 3 figures

We report a study of the strain state of epitaxial MnSi films on Si(111) substrates in the thick film limit (100-500~\AA) as a function of film thickness using polarization-dependent extended x-ray absorption fine structure (EXAFS). All films investigated are phase-pure and of high quality with a sharp interface between MnSi and Si. The investigated MnSi films are in a thickness regime where the magnetic transition temperature $T_\mathrm{c}$ assumes a thickness-independent enhanced value of $\geq$43~K as compared with that of bulk MnSi, where $T_\mathrm{c} \approx 29~{\rm K}$. A detailed refinement of the EXAFS data reveals that the Mn positions are unchanged, whereas the Si positions vary along the out-of-plane [111]-direction, alternating in orientation from unit cell to unit cell. Thus, for thick MnSi films, the unit cell volume is essentially that of bulk MnSi --- except in the vicinity of the interface with the Si substrate (thin film limit). In view of the enhanced magnetic transition temperature we conclude that the mere presence of the interface, and its specific characteristics, strongly affects the magnetic properties of the entire MnSi film, even far from the interface. Our analysis provides invaluable information about the local strain at the MnSi/Si(111) interface. The presented methodology of polarization dependent EXAFS can also be employed to investigate the local structure of other interesting interfaces., Comment: 11 pages, 10 figures

We report the study of the skyrmion state near the surface of Cu$_2$OSeO$_3$ using soft resonant elastic x-ray scattering (REXS) at the Cu $L_3$ edge. Within the lateral sampling area of $200 \times 200$ $\mu$m$^2$, we found a long-range-ordered skyrmion lattice phase as well as the formation of skyrmion domains via the multiple splitting of the diffraction spots. In a recent REXS study of the skyrmion phase of Cu$_2$OSeO$_3$ [Phys. Rev. Lett. 112, 167202 (2014)], Langner et al. reported the observation of the unexpected existence of two distinct skyrmion sublattices that arise from inequivalent Cu sites, and that the rotation and superposition of the two periodic structures leads to a moir\'{e} pattern. However, we find no energy splitting of the Cu peak in x-ray absorption measurements and, instead, discuss alternative origins of the peak splitting. In particular, we find that for magnetic field directions deviating from the major cubic axes, a multidomain skyrmion lattice state is obtained, which consistently explains the splitting of the magnetic spots into two - and more - peaks., Comment: 6 pages, 3 figures

Magnetic skyrmions in chiral magnets are nanoscale, topologically-protected magnetization swirls that are promising candidates for spintronics memory carriers. Therefore, observing and manipulating the skyrmion state on the surface level of the materials are of great importance for future applications. Here, we report a controlled way of creating a multidomain skyrmion state near the surface of a Cu$_{2}$OSeO$_{3}$ single crystal, observed by soft resonant elastic x-ray scattering. This technique is an ideal tool to probe the magnetic order at the $L_{3}$ edge of $3d$ metal compounds giving a depth sensitivity of ${\sim}50$ nm. The single-domain sixfold-symmetric skyrmion lattice can be broken up into domains overcoming the propagation directions imposed by the cubic anisotropy by applying the magnetic field in directions deviating from the major cubic axes. Our findings open the door to a new way to manipulate and engineer the skyrmion state locally on the surface, or on the level of individual skyrmions, which will enable applications in the future., Comment: 19 pages, 5 figures

We present the results of transverse-field muon-spin rotation measurements on an epitaxially grown 40 nm-thick film of MnSi on Si(111) in the region of the field-temperature phase diagram where a skyrmion phase has been observed in the bulk. We identify changes in the quasistatic magnetic field distribution sampled by the muon, along with evidence for magnetic transitions around $T\approx 40$ K and 30 K. Our results suggest that the cone phase is not the only magnetic texture realized in film samples for out-of-plane fields., Comment: 5 pages, 4 figures

We present the results of transverse field (TF) muon-spin rotation (muSR) measurements on Cu2OSeO3, which has a skyrmion lattice (SL) phase. We measure the response of the TF muSR signal in that phase along with the surrounding ones, and suggest how the phases might be distinguished using the results of these measurements. Dipole field simulations support the conclusion that the muon is sensitive to the SL via the TF lineshape and, based on this interpretation, our measurements suggest that the SL is quasistatic on a timescale tau > 100 ns., Comment: 8 pages, 8 figures, version 4, corrected typos, increased typeface size on figures