Alan Molinari,Federico Balduini,Lorenzo Rocchino,Rafał Wawrzyńczak,Marilyne Sousa,Holt Bui,Christian Lavoie,Vesna Stanic,Jean Jordan-Sweet,Marinus Hopstaken,Serguei Tchoumakov,Selma Franca,Johannes Gooth,Simone Fratini,Adolfo G. Grushin,Cezar Zota,Bernd Gotsmann,Heinz Schmid
Disorder-Induced Magnetotransport Anomalies in Amorphous and Textured Co1–xSix Semimetal Thin Films
CoSi,topological semimetals,amorphous thin films,magnetotransport,Hall effect
In recent times the chiral semimetal cobalt monosilicide (CoSi) has emerged as a prototypical, nearly ideal topological conductor hosting giant, topologically protected Fermi arcs. Exotic topological quantum properties have already been identified in CoSi bulk single crystals. However, CoSi is also known for being prone to intrinsic disorder and inhomogeneities, which, despite topological protection, risk jeopardizing its topological transport features. Alternatively, topology may be stabilized by disorder, suggesting the tantalizing possibility of an amorphous variant of a topological metal, yet to be discovered. In this respect, understanding how microstructure and stoichiometry affect magnetotransport properties is of pivotal importance, particularly in case of low-dimensional CoSi thin films and devices. Here we comprehensively investigate the magnetotransport and magnetic properties of ≈25 nm Co1–xSix thin films grown on a MgO substrate with controlled film microstructure (amorphous vs textured) and chemical composition (0.40 < x < 0.60). The resistivity of Co1–xSix thin films is nearly insensitive to the film microstructure and displays a progressive evolution from metallic-like (dρxx/dT > 0) to semiconducting-like (dρxx/dT < 0) regimes of conduction upon increasing the silicon content. A variety of anomalies in the magnetotransport properties, comprising for instance signatures consistent with quantum localization and electron–electron interactions, anomalous Hall and Kondo effects, and the occurrence of magnetic exchange interactions, are attributable to the prominent influence of intrinsic structural and chemical disorder. Our systematic survey brings to attention the complexity and the challenges involved in the prospective exploitation of the topological chiral semimetal CoSi in nanoscale thin films and devices.
Disorder-Induced Magnetotransport Anomalies in Amorphous and Textured Co1–xSix Semimetal Thin Films

In recent times the chiral semimetal cobalt monosilicide (CoSi) has emerged as a prototypical, nearly ideal topological conductor hosting giant, topologically protected Fermi arcs. Exotic topological quantum properties have already been identified in CoSi bulk single crystals. However, CoSi is also known for being prone to intrinsic disorder and inhomogeneities, which, despite topological protection, risk jeopardizing its topological transport features. Alternatively, topology may be stabilized by disorder, suggesting the tantalizing possibility of an amorphous variant of a topological metal, yet to be discovered. In this respect, understanding how microstructure and stoichiometry affect magnetotransport properties is of pivotal importance, particularly in case of low-dimensional CoSi thin films and devices. Here we comprehensively investigate the magnetotransport and magnetic properties of ≈25 nm Co1–xSix thin films grown on a MgO substrate with controlled film microstructure (amorphous vs textured) and chemical composition (0.40 < x < 0.60). The resistivity of Co1–xSix thin films is nearly insensitive to the film microstructure and displays a progressive evolution from metallic-like (dρxx/dT > 0) to semiconducting-like (dρxx/dT < 0) regimes of conduction upon increasing the silicon content. A variety of anomalies in the magnetotransport properties, comprising for instance signatures consistent with quantum localization and electron–electron interactions, anomalous Hall and Kondo effects, and the occurrence of magnetic exchange interactions, are attributable to the prominent influence of intrinsic structural and chemical disorder. Our systematic survey brings to attention the complexity and the challenges involved in the prospective exploitation of the topological chiral semimetal CoSi in nanoscale thin films and devices.

Topological materials, comprising for instance topological insulators, Dirac and Weyl semimetals, are characterized by exotic electronic band structures, which give rise to a variety of unconventional physical properties. The emergence of giant magnetoresistance, photogalvanic and thermoelectric effects, the evidence for the violation of the Wiedemann–Franz law and the conservation of chirality, and the presence of unusual quantum phenomena make topological materials highly attractive for the exploration of novel device concepts in the areas of valleytronics, quantum computing, sensing, and catalysis. Recently, novel types of chiral fermions—spin-1 and charge-2 fermions—as well as giant Fermi arcs traversing the entire surface Brillouin zone have been observed in the topological chiral semimetal CoSi. In particular, the giant surface Fermi arcs of CoSi are orders of magnitude larger than those detected in the majority of chiral Weyl fermion semimetals. Besides, CoSi benefits from quasi-symmetry-protected topology, which makes it particularly resilient to perturbations such as strain-induced crystalline symmetry breaking. The combination of these nontrivial topological properties highlights CoSi as a prospective, ideal topological conductor. Experimental works on CoSi bulk single crystals have already shown a remarkable modulation in magnetoresistance (MR) up to 400% at 2 K and prominent quantum oscillations in both MR and thermoelectric signals. However, CoSi is known for being sensitive to nonstoichiometries and disorder even in the case of bulk single crystals, which in turn provoke a marked variability in the magnetotransport and magnetic properties. Therefore, the question arises whether the topological properties of CoSi bulk single crystals survive in the case of less-ideal, low-dimensional systems such as thin films and nanowires, which are required for nanoscale device applications. On the one hand, an increased surface-to-volume ratio should be beneficial for the exploitation of charge carrier transport along surface Fermi arcs, which, for instance, is envisioned as a promising route to overcome the resistivity bottleneck scaling of conventional metallic interconnects. On the other hand, it is still unclear if low-dimensionality and structural and chemical disorder are compatible with topological magnetotransport. Focusing on thin films, early works—well before the discovery of the topological nature of CoSi—already pointed out the difficulties in stabilizing a pure cobalt monosilicide phase, owing to the tendency of formation of Co2Si or CoSi2 spurious phases, as also evidenced by the Co1–xSix phase diagram. A careful control of the chemical composition in CoSi is also important since a variation in the Co content can trigger the formation of magnetic exchange interactions, which in turn affect the magnetotransport properties, particularly at low dimensionality. CoSi single crystals present rather weak diamagnetism with the possible onset of paramagnetism at temperatures below 25 K owing to the alignment of defect-generated paramagnetic centers in the presence of an external magnetic field. Differently, unusual surface ferromagnetism and magnetic textures have been experimentally observed as the length scale of CoSi is brought to the nanoscale, such as in single-crystalline CoSi nanowires, CoSi flakes, and polycrystalline CoSi films above a critical cobalt excess of about 2.9%. Besides, since band crossings typically realize Berry curvature monopoles in topological materials, inserting controllably magnetic centers in CoSi may offer new opportunities to tailor its topological properties by breaking time-reversal symmetry. The film microstructure represents another crucial parameter. Indeed, in topological materials crossing of linear bands in nontrivial nodal points or multifold degeneracies is stabilized by crystalline symmetries or quasi-symmetries. In this respect, epitaxial CoSi films are desirable, for they are expected to better reflect the symmetry constraints, and in turn also the topological properties, of CoSi bulk single crystals. Yet, to date there has been no experimental realization of high-quality epitaxial CoSi thin films. Besides, from a device technological perspective, it is of interest to determine if topological protection may suffice to reveal signatures of topological transport in systems with large disorder, such as textured, polycrystalline or even amorphous CoSi thin films. Concerning the latter, a new research direction has recently sparked the search for possible exotic topological phases in amorphous systems, despite the absence of crystal symmetries. Notably, amorphous topological metals have been predicted but remain undetected. In this work, we systematically investigate the influence of microstructure (amorphous vs textured) and chemical composition (0.40 < x < 0.60) on the magnetic and magnetotransport properties of Co1–xSix thin films with a thickness of ≈25 nm grown by molecular beam epitaxy (MBE) on (001)-oriented MgO substrates. The results show that the resistivity of amorphous Co1–xSix thin films is comparable to the one of textured Co1–xSix thin films. Furthermore, regardless of the very different microstructures, both amorphous and textured Co1–xSix thin films reveal an evolution from metallic-like (dρxx/dT > 0) to semiconducting-like (dρxx/dT < 0) regimes of conduction upon progressively increasing the silicon content. The prominent effects of disorder and inhomogeneities on the magnetotransport and magnetic properties are manifested in various ways. For instance Co-rich Co1–xSix thin films display enhanced magnetic interactions (ferromagnetic in textured films, superparamagnetic in amorphous films), as confirmed by pronounced magnetic hysteresis loops, butterfly-like MR, and anomalous Hall effect. The resistivity of amorphous Co-rich films exhibits an upturn at temperatures below 20 K, which can be explained in terms of the Kondo effect due to electron scattering with localized magnetic nanoparticles. We observe a transition from parabolic to quasi-linear MR in Co1–xSix thin films at temperatures below 50 K, which we attribute to disorder-induced quantum corrections potentially due to electron–electron interactions. Our results reveal the influence of structural and chemical disorder on the magnetotransport properties of low-dimensional Co1–xSix thin films, thus opening the path to the implementation of the prototypical topological chiral semimetal CoSi into future electronic and Weyltronic devices.

A series of Co1–xSix thin films (thickness of about 25 nm) with finely tailored stoichiometry and microstructure were grown on (001)-oriented MgO substrates by the MBE method (see summary sketch in Figure 1). The chemical composition was varied in the 0.40 < x < 0.60 range by carefully adjusting the fluxes of Co and Si electron-beam sources during a layer-by-layer MBE growth process; quantitative determination of the Co1–xSix films’ stoichiometry was carried out by means of Rutherford backscattering spectroscopy (RBS). The growth temperature was found to be the main parameter affecting the microstructure of the Co1–xSix films with an amorphous-to-polycrystalline transition occurring at temperatures above the range of 100–175 °C, similarly to a previous work. In the present study a maximum growth temperature of 360 °C was employed, because a substantial increase in surface roughness due to island formation was observed upon increasing the growth temperature from 360 °C to 450 °C (see Figure S1). Grazing-incident X-ray diffraction (GIXRD) analysis of the fabricated Co1–xSix samples reveals that all the films deposited at room temperature feature a broad and low-intensity peak in proximity to 2θ ≈ 45.9°, which is the fingerprint of an amorphous microstructure with an average interatomic distance of 1.97 Å (Figure 2a bottom). As a comparison, the Co1–xSix films grown at a temperature of 360 °C have several sharp peaks, which are characteristic of a polycrystalline microstructure with an average domain size of about 10 nm, as calculated by the Scherrer formula (Figure 2a top). Considering the Co1–xSix films grown at 360 °C, the X-ray peaks fit well with the reference CoSi reflections, thus suggesting that cobalt monosilicide is the predominant phase formed within the compositional range of 0.40 < x < 0.60. This further suggests that in first approximation Co1–xSix can be treated as a solid-solution type alloy, although according to the bulk phase diagram a deviation less than 2% from the ideal 1-to-1 Co/Si ratio is required in order to stabilize the cobalt monosilicide phase. Still, we underline that the vicinity of the reference CoSi peaks with reflections from other phases makes the interpretation of XRD results not always straightforward, in particular in the case of the Co0.60Si0.40 and Co0.43Si0.57 films grown at 360 °C (e.g., in the latter there is a small CoSi2 peak at 2θ ≈ 48°), which conspicuously deviate from the ideal 1-to-1 Co/Si ratio. The results of GIXRD analysis and additional pole figure analysis carried out by means of synchrotron characterization reveal that the crystalline grains of the Co1–xSix films grown at 360 °C are not randomly oriented, but they rather present a pronounced in-plane and out-of-plane texture orientation with respect to the MgO substrate (more details in Figure S2). The results of the XRD survey are supported by the scanning transmission electron microscopy (STEM) and fast Fourier transform (FFT) analyses of representative cross sections of nearly stoichiometric Co1–xSix films (see Figure 2b). The lack of long-range order and the blurred ring in the STEM and FFT images of the Co0.49Si0.51 films grown at room temperature confirm an amorphous film microstructure. In contrast, the Co0.48Si0.52 sample grown at 360 °C displays a coherent stacking of the CoSi unit cells in proximity of the interface with the MgO substrate. The local interfacial area analyzed in Figure 2b (top) denotes an out-of-plane epitaxial relation between film and substrate given by CoSi (00l) ∥ MgO (00l). The size of the Co1–xSix grains having a nearly epitaxial relation with the MgO substrate is on the order of 20–30 nm. Concerning the chemical composition, local inspection via energy dispersive X-ray analysis reveals a uniform distribution of Co and Si elements in the Co0.48Si0.52 film grown at 360 °C (see Figure 2c). The absence of oxygen or other elements overlapping with the Co and Si signals demonstrates the lack of film oxidation through the film thickness or interfacial interdiffusion, thus supporting the high quality of the fabricated films. As mentioned, the chemical composition of all the investigated Co1–xSix films has been quantitatively inspected by means of the RBS method; more details about sample preparation and characterization can be found in the Experimental Section and in Figures S3–S6.

We now analyze the electrical resistivity ρxx of amorphous and textured Co1–xSix films with 0.40 < x < 0.60 in the temperature range of 2–300 K (see Figure 3). At room temperature the values of ρxx progressively increase in the range of 150–360 μΩ cm and 220–530 μΩ cm respectively for textured and amorphous Co1–xSix films upon substitution of Co with Si sites; in particular, in the case of the Co1–xSix samples approaching the ideal 1-to-1 CoSi stoichiometry, i.e., textured Co0.48Si0.52 in Figure 3c and amorphous Co0.49Si0.51 in Figure 3g, ρxx is on the order of 330–370 μΩ cm. Considering the trend of the temperature-dependent curves, one can notice a systematic change of slope of ρxx(T) upon increasing the silicon content. Textured and amorphous Co1–xSix films with about 10% Co excess Co0.60Si0.40 films display a monotonic decrease in ρxx as the temperature decreases, similarly to the behavior of conventional metals. Textured Co0.60Si0.40 films achieve the largest residual resistivity ratio (RRR) = ρxx(300 K)/ρxx(2 K) ≈ 2.3, whereas all the other investigated Co1–xSix samples have an RRR close to unity. As the composition approaches x ≈ 0.5, the temperature-dependent ρxx curves reveal a nonmonotonic behavior; in particular a characteristic plateau is formed in the temperature range of 120–250 K. Such plateau, which is commonly observed in semimetals and narrow-gap semiconductors, lies at higher or lower temperatures in relation to a slight excess of Co or Si, respectively. Then, at even higher values of silicon content x ≈ 0.57 the amorphous and textured Co1–xSix films display a quasi-monotonic increase in resistivity as the temperature is decreased, similarly to the case of semiconductors or strongly disordered metals. We note that the Co-rich and Si-rich amorphous Co1–xSix films, i.e., Co0.61Si0.39 in Figure 3e and Co0.43Si0.57 in Figure 3h, display some peculiar features not exhibited by the other samples; in particular, there is a distinct upturn in ρxx below 20–30 K followed by a logarithmic temperature dependence of ρxx down to 2 K (see also Figure S7). This behavior may be a consequence of the Kondo effect due to strong interaction of charge carriers with localized magnetic impurities, or quantum corrections to electrical conduction due to weak localization, or disorder-enhanced electron–electron interaction. In 2D films these different mechanisms provide a similar logarithmic temperature-dependence of ρxx, thus making a distinction between them not trivial. The analysis of MR and magnetization described in the following is helpful to disentangle the different phenomena. Regardless of the various degrees of intrinsic structural order (and thus also of transport mechanisms), both textured and amorphous Co1–xSix films manifest a similar change of slope in the temperature-dependent ρxx curves. Typically, electrical transport in polycrystalline films is dominated at high temperature by scattering of the charge carriers with phonons and at low temperature by scattering with intrinsic defects, such as the sample surface, interfaces, and grain boundaries. Differently, amorphous systems are characterized by intrinsic short-range structural order, which causes the carriers’ mean free path to be on the order of the interatomic distance. In general, the charge carriers contributing to the electrical transport in amorphous systems can be distinguished in localized or extended states being separated in energy by a mobility edge or a mobility gap; the metallic/insulating character of the material is then determined by the position of the Fermi energy with respect to the localized region. In amorphous semiconductors, such as a-Si, localized states dominate and conduction typically occurs through a thermally induced, variable range hopping process, with a conductivity that follows the Mott relation where T is the absolute temperature. The compounds under study, however, lie outside the domain of applicability of activated hopping since all exhibit a small overall change in resistance (less than a decade, and thus hardly attributable to an exponential). As the composition is varied, we observe a progressive reduction and change of sign of the slope of the temperature-dependent resistivity at room temperature, a phenomenology that is commonly observed in strongly disordered metals. The resistivity curves indicate that the present samples exhibit so-called Mooij correlations: dρxx/dT decreases linearly with the interpolated intercept ρ0, changing sign at a value of ρ0 that is comparable to the Mott–Ioffe–Regel value ρMIR, the latter defined as the resistivity of a metal where the carrier mean-free-path equals the lattice spacing (see Figure S8 and Table S1 for numerical values and in-depth analysis). Possible microscopic mechanisms that have been advanced to explain this behavior include quantum localization corrections and polaron formation favored by disorder. Highly relevant to the present compounds, this phenomenology also arises in disordered systems when the Fermi energy is tuned across a band edge, corroborating the semimetallic nature of the Co1–xSix films. Remarkably, the band tuning scenario naturally implies sizable changes of the carrier density with composition x (see Hall measurements below) and leads to the emergence of resistivity maxima at intermediate temperatures, both observed here. To put our resistivity data into a broader context, we note that previous works report a room temperature ρxx ≈ 100–150 μΩ cm for CoSi bulk single crystals and ρxx ≈ 100–350 μΩ cm for CoSi polycrystalline thin films. First, we remark that the order of magnitude of ρxx of our Co1–xSix films is consistent with literature, though the value of nearly stoichiometric films appears to be slightly higher. Second, it is quite surprising that the values of ρxx are very similar in amorphous and textured Co1–xSix films and even comparable to some single-crystalline samples with low RRR. This may be attributed to the fact that CoSi—even in the form of single crystals—belongs to the category of strongly disordered metals, thus reflecting a situation where intrinsic defects and disorder heavily impact the electronic transport. Yet, it is well established that amorphous materials are typically much worse conductors than their crystalline counterparts. We further discuss this aspect in connection to the values of mobilities and charge carrier concentration provided in the Hall effect analysis below. In order to gain deeper insights into the conduction mechanisms of Co1–xSix thin films, we have investigated the transverse MR (Figure 4), the magnetization (Figure 5), and the Hall effect (Figure 6) in the 2–300 K temperature range with applied magnetic fields up to ±9 T. Textured Co0.60Si0.40 films present a negative transverse MR with a maximum variation of −1.5% upon decreasing the temperature from 300 K to 50 K. Below 50 K the transverse MR progressively turns from negative to positive and reaches a value of +1% at 2 K and high magnetic fields (see Figure 4a). The occurrence of negative transverse MR in the textured Co-rich Co0.60Si0.40 films already hints toward the possible presence of robust ferromagnetism. In textured Co1–xSix films with compositions x = 0.47, 0.52, and 0.57 the transverse MR is dominated by a positive response with a systematic decrease in its magnitude from 1.2% to 0.18% for increasing x (see Figure 4b–d). Concerning the amorphous Co1–xSix films, the samples with x = 0.39, 0.47, and 0.51 have a positive transverse MR with a modulation of about 1% (see Figure 4e–g). It is worth noticing that the amorphous Co-rich Co0.61Si0.39 film, unlike its textured Co-rich counterpart, does not present an evident sign of negative transverse MR, except for a small hint at 2 K and low magnetic fields (see also Figure S10). The amorphous Co0.43Si0.57 film shows the most atypical transverse MR behavior, with an abrupt transition from positive to negative response below 5 K (see Figure 4h). As mentioned above, such amorphous Si-rich Co0.43Si0.57 sample is also the one displaying an unusual low-temperature upturn in ρxx. The behavior of ρxx and MR curves indicates the possible presence of localization effects or electron–electron interaction (EEI), similarly to the case of topological semimetal Cd3As2 films and topological insulator Bi2Se3 films. Localization effects can appear in the form of weak localization (WL) or weak antilocalization (WAL). WL (WAL) occurs due to the constructive (destructive) interference of electron wave functions with defects and impurities along a back scattering path in a quantum diffusive conduction regime. WL (WAL) brings about an enhanced (diminished) probability of electron localization. A distinctive characteristic of WL (WAL) is that it gives rise to negative (positive) transverse MR often accompanied by cusp-like features, which are suppressed as the magnetic field is increased. Therefore, the sharp increase in ρxx at low temperature (see Figure 3h) and the negative transverse MR (see Figure 4h) in amorphous Si-rich Co0.43Si0.57 films point toward a possible contribution of a WL effect. The variation from positive to negative transverse MR upon decreasing temperature in the Si-rich Co0.43Si0.57 sample may indicate a transition from WAL to WL. However, EEI can affect the magnetotransport properties in a similar manner to localization effects. EEI is triggered by enhanced Coulomb interactions between electrons in highly disordered metals. The origin of this anomaly is related to the fact that in disordered metals the electrons can only propagate by diffusion, and thus a sudden variation in charge distribution is screened with a certain delay. In contrast to WL or WAL, EEI is much less sensitive to the orientation and magnitude of the applied magnetic fields. In this sense, the isotropic character of transverse MR and longitudinal MR signals, whose curves can be nearly superimposed (see Figure S11), is compatible with an EEI scenario. In addition, WL and WAL are suppressed in the presence of large magnetic fields because of the destruction of electron phase coherence. In our case below 20 K the temperature-dependent ρxx curves of amorphous Si-rich Co0.43Si0.57 films in the presence and absence of an applied magnetic field of 9 T have a nearly perfect overlap (see Figure S12). This is a clear indication that the low-temperature quantum corrections to conductivity in amorphous Si-rich Co0.43Si0.57 films are dominated by EEI rather than one-body localization effects, though a small contribution of the latter cannot be completely excluded. We note that the concurrent presence of EEI and WL (or WAL) effects is not uncommon in amorphous and topological systems. Moreover, we note that textured Si-rich Co0.43Si0.57 films reveal a small cusp-like feature at 2 K and low magnetic fields (see Figure 4d and Figure S9), which can be possibly attributed to WAL or EEI effects. A closer inspection of the transverse MR curves permits to grasp further details. First, differently from the classical parabolic MR due to the contribution of the Lorentz force in metals and semimetals, the transverse MR curves of amorphous and textured Co1–xSix thin films undergo a transition from quadratic to nonsaturating, quasi-linear response upon increasing the magnetic field at temperatures below ≈50 K. This behavior is more clearly visualized in the derivatives of the transverse MR curves (see Figure S13), which present a crossover field BL of about 1–2 T. Below we delve deeper into the possible phenomena that give rise to a transition from quadratic to quasi-linear MR in Co1–xSix thin films. Second, by sweeping back and forth the direction of the magnetic field in the range of ±1.5 T, the transverse MR curves trace a butterfly-like shape (see the Figures S9, S10), which is especially pronounced for the films with higher Co concentration. Such butterfly-like shape is a fingerprint of the occurrence of magnetism in amorphous and textured Co1–xSix films. Magnetic characterization (see Figure 5) confirms the presence of robust magnetic exchange interactions, whose strength is directly correlated to the amount and distribution of Co in amorphous and textured Co1–xSix films. Textured Co0.60Si0.40 films achieve the largest values of magnetization saturation, Ms ≈ 39 emu/cm3, and coercivity, Hc ≈ 1000 Oe, whereas amorphous Co0.61Si0.39 films feature a comparable Ms ≈ 36 emu/cm3, but a markedly smaller Hc ≈ 100 Oe. The other Co1–xSix thin films still display magnetic hysteresis loops with a tendency toward a lower Ms as the cobalt concentration is progressively decreased. The main influence of the microstructure is that textured Co1–xSix films have larger values of Hc as compared to the amorphous counterparts. The analysis of the temperature-dependent magnetization (M(T)) (see Figure S14) reveals a net separation between zero field and field cooled (ZFC–FC) curves in textured Co1–xSix films with a maximum blocking temperature TB of about 150 K for x = 0.40. Differently, in case of amorphous Co1–xSix films the ZFC–FC curves have a near perfect overlap onto each other. Besides, we note that the M(T) curves do not undergo any steep transition in the range of 2–300 K, thus suggesting that the Curie temperature (TC) lies above room temperature. The steep increase in M(T) occurring below 15 K is likely related to the contribution of paramagnetic impurities intrinsic in the bulk MgO substrate, as also confirmed by the M(T) measurement on a reference MgO substrate. From the breadth of the M(H) curves and the behavior of the ZFC–FC curves, it is inferred that textured Co1–xSix thin films include ferromagnetic nanoparticles in the microstructure, whereas amorphous Co1–xSix thin films comprise soft ferromagnetic particles close to the threshold of superparamagnetism. The different ferromagnetic and near-superparamagnetic responses are likely ascribed to a different distribution of cobalt within the amorphous and textured microstructures as a consequence of the growth temperatures employed during MBE deposition. In a plausible scenario, textured Co1–xSix films deposited at a temperature of 360 °C experience an enhanced diffusion and nucleation of Co into larger magnetic clusters during the MBE growth process. In contrast, Co species are embedded more uniformly in the disordered lattice of amorphous Co1–xSix films grown at room temperature, thus forming smaller, isolated superparamagnetic nanoparticles. The tendency for the formation of Co-rich clusters with a size of several nanometers in textured Co0.60Si0.40 films is confirmed by the EDX analysis (see Figure S5); such clusters could not be detected in the case of nearly stoichiometric Co1–xSix thin films (see Figure 2c). The presence of Co-rich clusters with different size and distribution in amorphous and textured Co1–xSix films may also explain some of the apparent anomalies observed in the ρxx and transverse MR curves. As mentioned above, the characteristic increase in ρxx with logarithmic temperature dependence below 20 K in the amorphous Co0.61Si0.39 film (see Figure 3e) can be explained in terms of the Kondo effect due to the coupling of electrons with localized magnetic impurities. The Kondo effect is not expected to occur in ferromagnetic materials, thus explaining why there is no low-temperature upturn in ρxx in the case of textured Co0.60Si0.40 films (see Figure 3a). Moreover, the negative transverse MR occurring in the textured Co0.60Si0.40 film (see Figure 4a) is consistent with the presence of robust ferromagnetic interactions and consequent reduction in spin-flip scattering; yet, a small hint of negative transverse MR is actually also visible in the amorphous Co0.61Si0.39 film at low temperature and magnetic field (see Figure S10). To make a comparison of our magnetization data with literature, we mention that CoSi single crystals are diamagnetic at a temperature as low as 20 K, below which paramagnetism may occur due to the contribution of paramagnetic centers generated by self-doping effects. Nonetheless, a quantum-phase transition from Pauli paramagnetism to a magnetically ordered state was found in polycrystalline Co1–xSix ribbons above a critical cobalt excess of about 2.9%. Besides, room-temperature skyrmions were identified after thinning down the samples to about 50 nm by means of focused ion beam milling. Moreover, it has been suggested that surface ferromagnetism may emerge in nominally diamagnetic CoSi flakes, possibly due to the presence of distorted bonds and ordered vacancies near the sample surface. Our results on magnetic characterization unambiguously demonstrate that structural and chemical disorder brings about signatures of magnetic ordering not only in Co-rich Co1–xSix films but also in the nearly stoichiometric Co1–xSix samples within a range of x ≈ ±3% (i.e., not only for Co, but also for Si excess) and even in the case of amorphous Co1–xSix films with only a 1% Si excess. The latter is particularly relevant, because in general from an experimental perspective the control of the stoichiometry of thin films with an accuracy better than 1% using conventional thin films deposition methods poses a serious challenge.

We shall now focus on the results of the Hall effect analysis of amorphous and textured Co1–xSix films at different temperatures and applied magnetic fields (see Figure 6). The antisymmetrized Hall resistivity ρxy of textured Co1–xSix films in the range of 0.4 < x < 0.6 is characterized by a linear, negative slope, i.e., a negative Hall coefficient RH, with the only exception being the textured Co0.60Si0.40 film at fields below 1 T. The predominance of a negative sign of RH strongly indicates that electrons are the main charge carriers contributing to the electrical transport properties. The Hall response of amorphous Co1–xSix films is somewhat more complex and displays different regimes. In the case of the amorphous Co0.61Si0.39 film, ρxy reveals initially a steep positive response for fields below 0.7 T, followed by a pronounced kink with nearly saturation of the Hall signal. The amorphous Co1–xSix samples with x = 0.47 and 0.51 present a transition from positive to negative Hall coefficient at about 1 T, followed by linear ρxy at high fields, whereas a negative, quasi-linear Hall response prevails for the amorphous Co0.43Si0.57 film. At first glance, the transition from low-field, positive to high-field, negative Hall coefficients occurring in some of our Co1–xSix thin films may suggest a crossover from hole- to electron-dominated transport regimes. A nonlinear Hall response with reversal of its sign is not uncommon in semimetals, and often a two-band Hall model is employed to fit ρxx and ρxy curves in order to extrapolate the charge carrier density and mobility of holes and electrons pockets. However, as explained in another work and akin to the situation of our Co1–xSix thin films, in the presence of quasi-linear MR the condition on ρxx cannot be fit to the standard two-carrier model, as the linear component is not described by it. The interpretation of the Hall effect data is further entangled by the presence of magnetism in our Co1–xSix thin films. Indeed, reversal of the sign of the Hall coefficient from positive to negative upon increasing the applied magnetic field is known in polycrystalline films of cobalt and also amorphous, Co-based alloys owing to the different contributions of anomalous and ordinary Hall effects. The former provides a positive (similar to holes), low-field Hall signal until magnetic saturation is reached; at larger fields the Hall coefficient turns negative, because only the ordinary Hall component associated with electrons concurs to the transport. Given the presence of magnetic ordering in our Co1–xSix thin films (particularly for the Co-rich samples), it is not too surprising that some of our CoSi films display an anomalous Hall effect at low magnetic fields. A tentative analysis of the anomalous Hall effect in amorphous Co0.61Si0.39 films with the aim to distinguish between the intrinsic mechanism caused by Berry curvature and extrinsic skew scattering and side-jump mechanisms is proposed in the Supporting Information (Figure S15). Regardless of the low-field, nonlinear Hall response displayed by some of our Co1–xSix thin films, the high-field Hall resistivity of all Co1–xSix samples is linear and negative (with the amorphous Co0.61Si0.39 film as the only exception). First, the negative slope provides a strong indication that electrons are the charge carriers dominating the magnetotransport properties. Second, the linear character of ρxy at high fields motivates the use—in first approximation—of a single-carrier Drude band model to estimate the charge carrier density n and the Hall mobility μH of electrons according to the relations (with RH as the Hall coefficient and q ≈ 1.602 × 1019 C the elementary charge) and . Notably, a one-band model was used to interpret Hall effect data also in the case of single crystals of the topological Weyl semimetal NbP displaying nonlinear Hall behavior at low magnetic fields. The charge carrier density and Hall mobility of amorphous and textured Co1–xSix thin films are plotted as a function of temperature in Figure 7. No abrupt variations in n or μH with temperature were found, with the only exception of the amorphous Co0.61Si0.39 film. According to a one-band model, textured Co1–xSix films have a maximum n ≈ 1 × 1022 cm–3 for x = 0.40, whereas for the other compositions n drops to 1020–21 cm–3. The tendency toward lower values of charge carrier density upon increasing the Si content is another indication of the aforementioned evolution from metallic to semiconducting-like behavior in Co1–xSix films. The charge carrier density of the textured Co0.48Si0.52 film, virtually the one resembling most the condition of crystalline, stoichiometric CoSi, is about n ≈ 7 × 1020 cm–3 at 2 K, which is slightly higher than the values of (1–3) × 1020 cm–3 reported for stoichiometric CoSi single crystals. Notably, the amorphous Co1–xSix samples in the range 0.39 < x < 0.51 feature an electron carrier density of n ≈ 1 × 1023 cm–3, which is about 1 to 2 orders of magnitude higher than in textured Co1–xSix films. Such large values of charge carrier densities are more consistent with metallic rather than semimetallic behavior, which could be explained by the large amount of disorder-induced states dramatically increasing the density of states (DOS) of the semimetal. Furthermore, when the silicon content is increased to x = 0.57 in amorphous Co1–xSix the charge carrier density drops by nearly 2 orders of magnitude. Taken together, the drop in charge carrier density and the change in carrier type to full electron-like as a function of x could be interpreted as a transition through a band touching point, crossed upon silicon doping the cobalt bands at the Fermi energy. An evident effect of the film microstructure is that textured Co1–xSix films present a Hall mobility on the order of μH ≈ 20 cm2/V s, which is nearly 2 orders of magnitude larger than in the case of amorphous Co1–xSix films having μH ≈ 0.22 cm2/V s. As expected, both amorphous and textured Co1–xSix films feature lower values of Hall mobilities as compared to CoSi single crystals (μH ≈ 230–7300 cm2/V s). We note that the amorphous Co0.43Si0.57 film presents a higher mobility μH ≈ 7.5 cm2/V s at 2 K as compared to the other amorphous samples. Typically, Hall mobilities in amorphous materials are close to about 0.1 cm2/V s with relatively little sensitivity to structural and compositional variations. The seeming discrepancy in the mobility of the amorphous Co0.43Si0.57 film is possibly another manifestation of EEI, which, differently from localization effects, can cause an increase in the Hall coefficient. After extracting the values of n and μH with a one-band model, it becomes clearer why the resistivities of amorphous Co1–xSix films are comparable to textured Co1–xSix films regardless of their very different microstructures (see Figure 3). Considering ρxx = (nqμH)−1, the lower Hall mobilities of amorphous Co1–xSix films are compensated by their larger values of charge carrier densities. After completing the surveys on the magnetotransport and magnetic properties on amorphous and textured Co1–xSix films, we shall now shed some light on the change in sign and the crossover from parabolic to quasi-linear observed in the MR results. Several mechanisms, comprising quantum MR, conductivity fluctuations, and quantum electron–electron interference, can induce nonsaturating, quasi-linear positive transverse MR in metals and semimetals. Quantum MR implies the charge carriers to be in the quantum limit and occupy the lowest Landau level according to the condition (with n the charge carrier density, H the magnetic field, c the speed of light, and h the Planck constant). Our Co1–xSix films do not fulfill this condition, because a charge carrier density ne ≈ 1021–23 cm–3 would require much larger values of magnetic fields as compared to the crossover field BL of about 1–2 T, above which a transition from parabolic to quasi-linear transverse MR is observed. Conductivity fluctuations take place in inhomogeneous conductors with macroscopic spatial fluctuations in carrier density and/or mobility. In these circumstances charge carriers may scatter with low-mobility islands, thus causing the electrical current to deviate from the direction of the applied electric field E due to the emergence of a Hall component perpendicular to both E and B. Such an additional Hall contribution is responsible for the onset of linear, nonsaturating MR response. Given the large intrinsic disorder of our Co1–xSix films, it is tempting to invoke conductivity fluctuations as a possible mechanism for the observed quasi-linear MR response. One of the fingerprints of conductivity fluctuations is that sizable differences in mobility and charge carrier density take place upon the crossover from quadratic to quasi-linear regimes. As mentioned, at high temperature the transverse MR curves of our Co1–xSix films can be well described with a parabolic dependence as a function of the applied magnetic field, whereas below 50 K the transverse MR curves undergo a crossover to a quasi-linear response. However, as can be seen from Figure 7, the values of charge carrier density and mobility of our Co1–xSix films vary smoothly throughout the whole investigated temperature range (apart from the amorphous Co0.43Si0.57 film). Besides, another feature of conductivity fluctuations is that when the orientation of the magnetic field is turned from perpendicular to parallel with respect to the direction of the current flow, the magnitude of the transverse MR decreases and, depending on the film thickness, can even turn from positive to negative. As a matter of fact, conductivity fluctuations are one of the possible phenomena, such as also chiral anomaly or current jetting, that can give rise to negative longitudinal MR in topological semimetals. However, there is a quite good overlap between the transverse and longitudinal MR curves in our Co1–xSix films, thus indicating a rather isotropic MR response upon modification of the orientation of the magnetic field (see Figure S11). For these reasons, this effect alone cannot adequately explain our MR results. In an alternative scenario, the unusual MR may be correlated to the intrinsic magnetism of our Co1–xSix films. Ferromagnetic materials typically exhibit negative MR owing to the strong spin–orbit coupling suppressing spin-flip interband scattering of electrons. This explanation is compatible with the negative MR observed in the textured Co0.60Si0.40 film at low temperature and magnetic fields (see Figure 4a), which is also the sample with the most prominent ferromagnetic signal in terms of both Ms and Hc. Nonetheless, the dominant transverse MR response of Co1–xSix thin films is positive with a transition from parabolic to quasi-linear MR at low temperature upon increasing the magnetic field. In this respect, we notice that linear and positive MR is not unusual in disordered ferromagnetic systems such as Fe1–yCoySi and thin films of Fe, Ni, Co, and their granular mixtures with nonmagnetic materials as a consequence of quantum corrections to the conductivity due to EEI. The positive and linear MR generated by EEI is typically isotropic with respect to the applied magnetic field and can occur at temperatures as high as 100 K. These two features indicate that quantum corrections to conductivity due to EEI remain a plausible scenario for the explanation of the linear and positive MR observed in our Co1–xSix films.

In summary, this work reveals the strong correlation between microstructure, chemical composition, magnetotransport, and magnetic properties in ≈25 nm Co1–xSix thin films with 0.40 < x < 0.60. Both amorphous and textured Co1–xSix thin films undergo a progressive transition from metallic to semiconducting-like conduction regimes upon increasing the silicon content. Most importantly, the values of resistivities are on the same order of magnitude independently of the film microstructure; this is quite unexpected since electrical conduction is heavily hampered in conventional disordered materials as compared to their crystalline counterparts. A possible reason comes from the results of one-band Hall effect analysis: amorphous Co1–xSix thin films have a lower mobility, but also a higher charge carrier concentration than textured Co1–xSix thin films, likely resulting from a disorder-enhanced DOS in the semimetallic region which almost entirely compensates for the much lower carrier mobilities. Other factors possibly contributing to the increase of carrier density include the presence of dangling bonds and topological surface states. The latter find support in a recent theoretical work reporting that amorphous metals can host exotic topological phases despite the lack of long-range translational symmetry. Our findings, notably the semimetallic nature of the Co1–xSix samples, the abrupt drop in charge carrier density, and the change of carrier type to full electron-like as a function of x, are consistent with the survival of band touchings with low density of states. We also note that some of the transport anomalies, such as EEI and localization effects, observed in our Co1–xSix films have also been reported in other studies on thin films of the topological semimetal Cd3As2 and the topological insulator Bi2Se3. However, discerning whether topological features survive structural disorder and what is their potential correlation with transport anomalies (e.g., Kondo, WL, EEI, and anomalous Hall effects) requires developing models for amorphous and textured CoSi, currently unavailable. Experimentally, a promising strategy to evaluate the possible occurrence of topological surface states in amorphous and textured Co1–xSix films would be to analyze the scaling behavior of the film resistivity as compared to conventional materials upon reducing the film thickness. The MR of Co1–xSix films displays a variety of responses, such as sign reversal and transition from quadratic to quasi-linear regimes, which can be ascribed to quantum corrections due to EEI. All the Co1–xSix films present signatures of magnetic exchange interactions, whose strength is directly correlated to the amount and distribution of cobalt, even in the case of nearly stoichiometric Co1–xSix films. This result poses a challenge concerning the realization of Co1–xSix films with transport, magnetic, and topological characteristic similar to CoSi bulk single crystal. On the other hand, a careful adjustment of the concentration and size of magnetic centers in low-dimensional Co1–xSix films may also offer new degrees of freedom to tailor the properties of CoSi beyond bulk systems. In conclusion this work will serve as a valuable case study to pinpoint the sensitivity of low-dimensional Co1–xSix thin films with respect to structural and chemical disorder and to critically evaluate the potential implementation of the chiral semimetal CoSi in nanoscale thin films and topological devices.

Prior to insertion in vacuum (001)-oriented, epi-polished MgO substrates (size 10 mm × 10 mm × 1 mm) were ultrasonically cleaned for 5 min in isopropyl alcohol. After that, the MgO substrates were outgassed at about 450 °C for 30 min under ultra-high-vacuum conditions. The base pressure of the MBE system was around 10–10 mbar, which increased to 10–9–10–8 mbar during film growth. Co and Si elements were deposited from electron-beam sources at a deposition rate of ≈0.1 Å/s. The Co and Si fluxes were calibrated prior to MBE deposition via a quartz crystal microbalance and maintained constant during MBE deposition using quadrupole mass spectrometers coupled to the electron-beam sources. Co1–xSix thin films were deposited following a layer-by-layer growth process by opening/closing the metal shutters in front of the electron-beam sources. The MBE growth temperature was monitored via a type K thermocouple after calibration with a pyrometer. After MBE growth the structural characterization of the Co1–xSix thin films have been done via atomic force microscopy, grazing-incident X-ray diffraction, synchrotron pole figures, and scanning transmission electron microscopy. The preparation of cross sectional lamellas was done by means of focused ion beam (FIB) milling; to mitigate the damage induced by FIB preparation, a protective Al2O3 layer (about 40 nm) grown by atomic layer deposition was added onto the Co1–xSix films. For chemical characterization Rutherford backscattering spectroscopy, energy dispersive X-ray analysis, and X-ray photoelectron spectroscopy were employed. Additional details can be found in the Supporting Information.

The original Co1–xSix thin films grown on a MgO substrate were sliced into Hall bars with a size of about 10 mm × 1.5 mm × 1 mm (length, width, thickness) using a diamond cut tool. Metallic contacts for 4-point probe resistance and Hall effect measurements were prepared via wire bonding. The current leads were covered with silver paste in order to provide better uniformity of the current flow. The input current was set to 0.05 mA. The resistivity, MR, Hall effect, and magnetization of Co1–xSix thin films were characterized via a physical properties measurement system (PPMS) in the range of 2–300 K and applied magnetic fields up to ±9 T. The analysis of the Hall effect data was carried out after removal of the symmetric Hall contribution due to the misalignment of the voltage probes.