## Abstract

Topology and strong electron correlations are crucial ingredients in emerging quantum materials, yet their intersection in experimental systems has been relatively limited to date. Strongly correlated Weyl semimetals, particularly when magnetism is incorporated, offer a unique and fertile platform to explore emergent phenomena in novel topological matter and topological spintronics. The antiferromagnetic Weyl semimetal Mn_{3}Sn exhibits many exotic physical properties such as a large spontaneous Hall effect and has recently attracted intense interest. In this work, we report synthesis of epitaxial Mn_{3+x}Sn_{1−x} films with greatly extended compositional range in comparison with that of bulk samples. As Sn atoms are replaced by magnetic Mn atoms, the Kondo effect, which is a celebrated example of strong correlations, emerges, develops coherence, and induces a hybridization energy gap. The magnetic doping and gap opening lead to rich extraordinary properties, as exemplified by the prominent DC Hall effects and resonance-enhanced terahertz Faraday rotation.

## INTRODUCTION

Band structure topology is becoming an increasingly important aspect in materials research and design and is responsible for many of the exotic behaviors found in quantum materials such as strongly correlated two-dimensional (2D) electron systems (*1*), graphene (*2*), and topological insulators (*3*). More recently, band structure topology has been critical to the understanding and development of gapless topological semimetals (*4*–*6*), including Weyl semimetals (WSMs), Dirac semimetals, and nodal line semimetals. In WSMs, the conduction and valence bands cross at certain points in momentum (*k*−) space known as Weyl nodes (*6*). Weyl nodes appear in nondegenerate pairs with opposite chirality and act as monopoles of Berry curvature (i.e., sources or sinks of Berry flux). The spacing of the Weyl nodes in *k*-space is determined by the crystal and/or magnetic structure that break inversion or time-reversal symmetry and, in turn, dictates the magnitude of the intrinsic anomalous Hall effect (*7*, *8*).

While much of the work on WSMs to date has focused on weakly interacting systems, there is a growing need to address and include the effects of strong electron correlations (*9*–*12*). A classic example of strongly correlated behavior is the Kondo effect (*13*), which originates from the coupling between the spins of conduction electrons and local magnetic moments. As local magnetic moments form a lattice, the Kondo effect develops coherence and leads to the Kondo insulator (*14*, *15*). Inclusion of topological order in Kondo insulators leads to topological Kondo insulators, among which SmB_{6} is an example that has attracted substantial attention (*16*). Recently, there have been increased theoretical efforts (*17*–*19*) to address the Kondo effect in WSMs and, particularly, the emergence of a Weyl-Kondo semimetal in nonmagnetic Ce_{3}Bi_{4}Pd_{3} bulk samples (*20*). Unusual properties such as giant spontaneous Hall effect were predicted (*21*). These works suggest that strongly correlated WSMs are a fertile platform to explore new quantum phases, resulting from the interplay between Weyl and Kondo physics.

A promising material in which to study both Weyl and Kondo physics is the antiferromagnetic (AFM) WSM Mn_{3}Sn (*22*–*25*). Mn_{3}Sn has a hexagonal structure with lattice constants *a* = 5.67 Å and *c* = 4.53 Å (Fig. 1A), with a Néel temperature (*T*_{N}) of 420 K (*25*). The Mn atoms form a 2D Kagome lattice on the (0001) plane (i.e., *ab* plane) with Sn atoms sitting at the hexagon centers (Fig. 1B). Two neighboring Kagome Mn_{3}Sn layers are stacked along the *c* axis with an in-plane lattice offset (Fig. 1A). The Mn moments (~3 μ_{B}/Mn) form various noncollinear spin orders at different temperatures, including inverted triangular structures, spin spiral, and spin glass (fig. S1 and note S1) (*26*). The most interesting are the inverted triangular spin textures (Fig. 1B) with nearly zero spontaneous magnetization (~3 × 10^{−3} μ_{B}/Mn). The magnetic symmetry of the inverted triangular spin textures includes mirror symmetry that ensures the appearance of the pairs of Weyl nodes at a *k* line along the local easy axis in the *ab* plane, as demonstrated by the angle-resolved photoemission spectroscopy (ARPES) measurements (*22*). The Berry curvature induced by the Weyl nodes generates a large anisotropic anomalous Hall effect (*22*, *25*). Under an external field, tilting of the triangular spin textures results in noncoplanar spin structures and generates a topological Hall effect arising from the spin Berry curvature in real space (*27*). Moreover, novel magnetic spin Hall and inverse spin Hall effects, which demonstrate field-controllable conversion between spin current and charge current, have been discovered (*24*). In addition to these unusual topological and spintronic properties, substantial bandwidth renormalization is observed because of strong correlations among Mn 3*d* electrons (*22*). These outstanding topological/spintronic properties and strong electron correlations make Mn_{3}Sn an ideal platform to explore the multifaceted physics of the interplay between topology, magnetism, and strong correlations, as well as the emerging topological AFM spintronics (*28*, *29*) in which thin films play a crucial role.

Here, we report the fabrication of high-quality epitaxial films of Mn_{3+x}Sn_{1−x} with greatly extended compositional range (*x* up to ~0.55). We observe the Kondo effect in films with excess Mn, which substitutes for Sn and acts as a magnetic dopant in the system. Upon increased Mn doping, the system develops Kondo coherence and opens a hybridization gap. Films with *x* > 0.4 behave like Kondo insulators with topological features, as manifested in the DC Hall and terahertz Faraday rotation measurements.

## RESULTS

### Fabrication of epitaxial Mn_{3+x}Sn_{1−x} films with greatly extended compositional range

Mn_{3}Sn has layered Kagome planes and exhibits a strongly anisotropic Hall effect. Thus, it is important to realize epitaxial films with two different orientations: (0001) films where the Kagome plane is in the plane of the film, and _{3}Sn films, including (0001) Mn_{3}Sn films on Ru seed layer (*30*), (0001) and _{3}Sn films on MgO and Al_{2}O_{3} substrates (*31*), and polycrystalline films on Si/SiO_{2} substrate (*32*). In this work, we used cosputtering of Mn and Sn targets and realized epitaxial growth of (0001) and _{3+x}Sn_{1−x} films (see Materials and Methods).

We took advantage of the small lattice mismatch (~2%) between Pt (111) (cubic, _{3}Sn (*a* = 5.67 Å), and fabricated high-quality epitaxial (0001) Mn_{3+x}Sn_{1−x} films on a Pt seed layer, which is grown on C-Al_{2}O_{3} substrate via magnetron sputtering. The θ/2θ x-ray diffraction (XRD) pattern (Fig. 2A) shows a strong (0002) Mn_{3}Sn peak without any noticeable impurity peaks. High-resolution XRD (HR-XRD) rocking curves, collected with monochromating incident optics and a triple-axis analyzer, show a very sharp peak with full width at half maximum (FWHM) of 0.002° (Fig. 2B, for *x* = 0.5), indicating that the film has exquisite planar alignment between the (0001) crystalline plane and the film plane. Rocking curves with a double-axis analyzer showed a sharp peak with a slightly larger FWHM of 0.07° (fig. S2A), indicating a small *d*-spacing spread. For Sn-rich samples (e.g., *x* = 0.1), crystalline quality decreases slightly with a rocking curve FWHM of 0.21° (double axis, fig. S2B) and in-plane φ scan FWHM of 0.8° (fig. S2C). In-plane φ scans (Fig. 2C) of Mn_{3}Sn, Pt, and Al_{2}O_{3} show six diffraction peaks, confirming the epitaxial relation of Al_{2}O_{3} _{3}Sn _{3}Sn are further confirmed by x-ray reflectivity measurements (fig. S2E). We attribute the high quality of Mn_{3}Sn to the high-quality Pt seed layer as indicated by the Laue oscillations of the XRD Pt (111) peak (inset of fig. S2E). We note that the flat surface of (0001) Mn_{3}Sn is critical for future work attempting to interface Mn_{3}Sn with other quantum materials. Toward that end, we also grew (0001) Mn_{3}Sn on the integrated circuit (IC) technology–compatible substrate Si(111) with a Ag(111) seed layer (fig. S2F) and _{3}Sn on R-Al_{2}O_{3} substrate (fig. S3).

It has been shown previously that hexagonal Mn_{3}Sn is stable with excess Mn. Specifically, earlier work on bulk Mn_{3+x}Sn_{1−x} found that a maximum Mn excess of *x* = 0.2 could be achieved (*22*, *23*, *33*). The extra Mn atoms replace Sn atoms and randomly occupy the Sn sites (i.e., Mn_{3+x}Sn_{1−x}, *x* > 0). The replacement of nonmagnetic Sn atoms with magnetic atoms is expected to alter real space spin ordering and affect the spacing of Weyl nodes in the system. Density functional theory (DFT) calculations also suggest that extra Mn may raise the Fermi energy *E*_{F} (*22*). Therefore, doping with Mn should be an effective way to tune band structure topology and the Hall effects in Mn_{3+x}Sn_{1−x}.

As shown in the inset of Fig. 2A, for two distinct *x* values, the (0002) XRD peaks are well separated, indicating distinct values of lattice constant *c*. The lattice constant *a* is obtained from the *c* and *a* decrease as *x* increases, supporting replacement of Sn atoms by smaller Mn atoms. We found that the amount of Mn excess can be greatly extended to *x* ≈ 0.55 in our epitaxial films without the introduction of an impurity phase. This result sharply contrasts the small compositional window seen in bulk samples and is likely related to the nonequilibrium growth conditions that exist during vacuum deposition processes. As *x* increases from 0.06 to 0.55, the *c* axis lattice constant decreases from 4.57 to 4.53 Å. Similar dependence of lattice parameters as a function of *x* is observed in (0001) Mn_{3+x}Sn_{1−x} grown on Ag(111) seed layer on Si(111) wafer (Fig. 2D). The lattice parameters of _{3+x}Sn_{1−x} show different dependence on *x*, but the unit cell volume still decreases as *x* increases (fig. S3). The greatly extended compositional range for replacing Sn with magnetic Mn in thin films allows for the exploration of new and unusual physics in Mn_{3}Sn, as exemplified below.

### Kondo effect and gap opening by extended Mn doping

Figure 3A shows normalized resistance γ(*T*) [=*R*(*T*)/*R*(295 K)] as a function of temperature (*T*) for 60-nm (0001) Mn_{3+x}Sn_{1−x} films. Strictly speaking, a rigorous identification of metallicity requires demonstration that resistance extrapolates to a finite value at zero temperature, which is possible even if *R* is increasing as *T* decreases throughout the measurement range (*34*). For simplicity, here, we adopt the popular nomenclature that γ(*T*) curves have a “metallic” (“insulating”) characteristic if resistance decreases (increases) as *T* decreases. For reference, we note that bulk Mn_{3+x}Sn_{1−x} (*x* < 0.15) single crystals show metallic behaviors with carrier density *n* about 2 × 10^{22} cm^{−3}. The resistivity of such bulk crystals is about 250 μΩ·cm at room temperature along the *ab* plane, indicating a mean-free path on the order of 1 nm (*35*). Broadly speaking, the γ(*T*) character of our films is metallic for compositions below *x* ~ 0.40 and insulates above. For *x* = 0.06, γ decreases nearly linearly from room temperature to *T* = 50 K and reaches a residue value of about 0.76 at *T* = 5 K. As *x* increases to 0.11, metallic behavior remains, but with a larger γ at 5 K, consistent with the elevated scattering from Mn dopants randomly replacing the centers of the hexagons in the Kagome plane. Note that the transport contributions from the buffer and capping layers are minimized by using highly resistive materials (Materials and Methods).

The strong correlation among Mn *3d* electrons (*22*) in Mn_{3}Sn and its topological band structure suggest that Mn_{3}Sn is an ideal platform to explore the interplay between Weyl and correlation physics. In this material, Mn moments in the Kagome lattice are strongly antiferromagnetically coupled to each other, leading to various spin orders such as a planar 120° spin orientation with negligibly small net magnetization (*25*). The substituting Mn_{Sn} atom sitting at the hexagon center of the Kagome lattice could interact with its six neighbors via the Heisenberg exchange. However, the vanishing of total magnetic moment of the six neighbors results in the same energy no matter what direction the center spin points toward, to lowest order. Therefore, substitutional Mn spins may behave as magnetic impurities exchange coupled to the *d*-like conduction band states on the Mn-Kagome sublattice, leading to Kondo physics if the correlation is considerable. In the metallic regime, for example, the *x* = 0.27 film Fig. 3B shows a resistance upturn instead of a residue below the resistance minimum temperature *T*_{m} = 25 K. The −ln*T* increase in resistance with decreasing temperature at *T* < *T*_{m} and the deviation of ln*T* scaling at lower temperature are characteristics of the Kondo effect (*36*). For simplicity, we adopt the deviation point of ln*T* scaling (Fig. 3B) as an estimation of the Kondo temperature *T*_{K}, which reflects the strength of Kondo interaction (*36*). The resistance increases as a result of Kondo scattering of magnetic impurities. As temperature further decreases, the Kondo scattering is inhibited because of the formation of a singlet state between a localized Mn moment and a conduction electron, which screens the magnetic moments of the impurities (*37*).

As *x* increases further and more Sn atoms are replaced by Mn atoms, *T*_{m} and *T*_{K} shift gradually to higher temperatures, indicating a stronger Kondo effect. For *x* = 0.39, *T*_{m} (*T*_{K}) is 47 K (23 K) (Fig. 3C). Above *x* > 0.40 (Fig. 3, D and E), the resistance shows an upturn at a much higher temperature (e.g., 192 K for *x* = 0.44, and >300 K for *x* = 0.50), consistent with the transition to a Kondo insulator as Kondo effect develops coherence in the dense Kondo lattice (*14*). The ground state of such a system features a hybridization gap, on the order of a few millielectron volts to tens of millielectron volts, near the Fermi energy (*14*, *15*), and because of the featured band inversion therein, most Kondo insulators are topologically nontrivial (*16*). A prominent example is the topological Kondo insulator SmB_{6}, which shows a small insulator gap of about 3 meV and a saturation resistance plateau at low temperatures (*38*). The γ(*T*) curves of our highly doped films (*x* > 0.40) show a similar temperature dependence. As shown in Fig. 3E, for *x* = 0.55, the resistance exhibits a −ln*T* increase from room temperature to *T*_{K} ~ 130 K, then increases at a slower rate, and eventually reaches a near-saturated value at low temperature. Following the analysis in (*38*), we divide the measured conductance *G*_{measured} into two parallel contributions: *G*_{measured} = *G*_{T=5K} + *G*_{insulator}, where *G*_{T=5K} represents the near-saturated conductance at low temperature. *G*_{T=5K} may originate from a topological surface state or an in-gap state (*39*). We plot *G*_{insulator} as a function of 1/*T* from 300 to 150 K (inset of Fig. 3E). The linearity indicates that this analysis is appropriate and gives a gap value of 10.2 meV (i.e., 118 K ≈ *T*_{K}), which corresponds well with reported gap values of other Kondo insulators (*15*). The gap opening at *x* > 0.40 is also evidenced by the decrease in carrier density as a function of temperature (fig. S4) due to reduced thermal activation at low temperature.

We briefly note that the Kondo effect and gap opening are also observed in thicker (0001) Mn_{3+x}Sn_{1−x} films, as well as *T*) curves (fig. S4). Terahertz transmission measurements (Fig. 3F) at *T* = 2 K on a 60-nm _{3+x}Sn_{1−x} (*x* = 0.47) show a prominent dip at 1.3 THz (~5.5 meV), which is less obvious in a metallic sample (*x* = 0.13). These terahertz transmission results echo the resistivity measurements and corroborate the notion of a gap opening. Even stronger evidence for the gap opening can be seen in terahertz Faraday rotation measurements discussed below.

### Resonance-enhanced terahertz Faraday rotation

Here, we present a notable consequence of the gap opening in the terahertz Hall effect (i.e., Faraday rotation). Figure 4 shows the real (*x* = 0.13) shows a small Faraday rotation on the order of a few milliradians (Fig. 4A), which is similar to the observed value in a recent study on polycrystalline Mn_{3}Sn films (*40*). In sharp contrast, for the gapped sample (*x* = 0.47), the imaginary part of the Faraday rotation, which is related to the ellipticity (_{3}Sn films (*40*). The gap-induced resonance feature in optical rotations was also recently observed in a magnetic topological insulator (*41*). The resonance-enhanced terahertz Faraday rotation described here may represent an entirely new phenomenon in the world of the Kondo insulator, which was not observed in SmB_{6} (*42*).

These above transport and terahertz results demonstrate a gap opening of WSM by doping of magnetic Mn atoms whose 3*d* electrons have strong correlations, and thus a possible transition from Kondo effect to Kondo insulator in new class of topological matter. These effects are independent of the crystalline growth orientation.

### DC Hall resistances arising from Berry curvatures in reciprocal and real spaces

One of the most salient transport features in bulk Mn_{3}Sn is the large spontaneous anomalous Hall resistance (AHR), arising from the Berry curvatures of the Weyl nodes (*22*, *25*). Therefore, the Weyl nature of our Mn_{3+x}Sn_{1−x} thin film can be checked by Hall measurements. The total Hall resistivity includes various contributions and can be described as *M* is the magnetization, *R*_{0} (*R*_{S}) is the ordinary (anomalous) Hall coefficient (both *R*_{0} and *R*_{S} are positive), and μ_{0} is the magnetic permeability. Unlike conventional ferromagnets such as Fe and Co, where the Hall resistances only include the first two terms, there is an additional term *B* or *M* (*25*). Because usual antiferromagnets do not exhibit measurable spontaneous Hall resistances, *43*) and oxide heterostructures (*44*). It is important to note that the exchange bias in Mn_{3+x}Sn_{1−x}/Py bilayers is observed at *T* = 5 K (fig. S5) in both metallic and gapped states. This is strong evidence that antiferromagnetism in our Mn_{3+x}Sn_{1−x} films is robust over the whole compositional range we studied. Above the saturation field of the uncompensated spins (but below the spin-flop transition), *M* to *B* = 0. Therefore, above the saturation field, _{B}/Mn at room temperature, close to the resolution limit of the magnetometers used in this work (fig. S6 and note S2). In the following, we use bulk value χ ~ 3 × 10^{−3} for our estimations (note S1).

We first consider the Hall effect in *x* < 0.4). Figure S7A shows Hall resistance as a function of field for Mn_{3+x}Sn_{1−x} (*x* = 0.18) at *T* = 300 K. The Hall loops indicate *B* = 9 T) is negative. The negative AHR is a signature of the intrinsic contribution of Berry curvature in *k*-space, as observed in bulk single-crystal samples (*25*). Figure 5A shows the *x*. For *x* = 0.10 and 0.18, *T*_{1} ≈ 225 K, which is also observed in bulk Mn_{3}Sn single crystals (*35*), indicates changes from triangular spin order at higher temperatures to spin glass or spin spiral at low temperatures. Between *T*_{N} *=* 420 K and *T*_{1}, a WSM state exists because of the magnetic symmetry of triangular spin order (*22*). Below *T*_{1}, the intrinsic negative AHR decreases drastically due possibly to the disappearance of Weyl nodes in spin glass/spinal state. The ρ_{H} (*T* < *T*_{1}) is only about −0.2 μΩ·cm and depends weakly on temperature. At *x* = 0.26, where Kondo physics manifests at low temperature (Fig. 3B and fig. S4), a similar temperature dependence of *x* = 0.10 and 0.18.

However, at *x* > 0.40, the gapped state is realized, and *T* = 300 K, *x* = 0.10. This may be a direct consequence of a gap opening, which likely annihilates Weyl nodes and greatly reduces the Berry curvature. Alternatively, extended doping could also disrupt the triangular spin texture, which protects the Weyl nodes. *T*_{1} (Fig. 5A). With extended doping (*x* > 0.40), the doped localized Mn moments start to form a lattice and disrupt the spin glass/spiral state at *T* < *T*_{1}. The doped Mn spins, along with Mn spins in the Kagome sites, are likely lying in the Kagome plane that is perpendicular to the film. These spins are “polarized” by the out-of-plane field (in the Kagome plane) and give rise to positive conventional AHR

_{3+x}Sn_{1−x} films are summarized in a *T*-*x* phase diagram shown in Fig. 5B. Large negative Hall resistance presumably induced by Weyl nodes exists at *T* > 225 K and *x* < 0.40. Notably, driven by the Kondo effect with higher Mn doping, a gapped state (possibly a Kondo insulator) emerges at *x* > 0.40 and shows positive Hall resistance at *T* < 225 K. These results indicate that magnetic doping is an effective way to tune electron correlations and Berry curvatures in the reciprocal space.

Although Kondo physics is similar in (0001) films, the Hall resistance shows different compositional dependence therein because of the anisotropy of the Hall effect in these materials. In bulk single crystals (*x* < 0.15), the *25*). In the spin glass state, *25*). In (0001) Mn_{3+x}Sn_{1−x} films, a positive *x* > 0.40; Fig. 5C and fig. S8) is much smaller than that of the metallic state. ^{TH}) (*45*), arising from the spin chirality in the real space (*27*). Considering a triangle spin structure shown in Fig. 5C, tilting of spins (*S** _{i}*,

*i*= 1,2,3) toward the

*c*axis gives a scalar spin chirality

*S*_{1}∙ (

*S*_{2}×

*S*_{3}) (

*27*), which induces a spin Berry phase (magnetic flux) Φ = 2

*r*Φ

_{0}, where Φ

_{0}is the flux quantum (2000 T·nm

^{2}), and

*r*reflects the fraction of the flux quantum (

*r*is 1 for a magnetic skyrmion). The spin Berry phase gives rise a fictitious field

*B*

_{eff}= Φ/

*A*=

*r*× 1.18 × 10

^{5}T, where

*A =*0.034 nm

^{2}is the area of each triangle. Therefore, a tiny value of

*r*(note S3) can generate large

*B*

_{eff}that induces a topological Hall resistivity ρ

^{TH}=

*R*

_{0}

*B*

_{eff}(e.g., ρ

^{TH}=0.33 μΩ·cm for 60-nm films). In thicker films such as 120 nm with lower crystalline quality, tilting can easily take place, resulting in a larger

*r*. The larger

*r*thus corresponds to a larger ρ

^{TH}, as echoed in the experiment (fig. S8). In contrast with

^{TH}increases from

*T*= 300 K to

*T*≈

*T*

_{1}(225 K), but decreases noticeably at

*T*< 100 K, which suggests a spin glass transition at

*T*

_{g}~ 100 K (note S1). As mentioned above, for gapped states (

*x*> 0.40), nearly half of hexagon centers are occupied by magnetic Mn atoms with spins randomly orienting in the Kagome plane. These doped (random) spins contribute to the spin chirality [

*S*_{1}∙ (

*S*_{2}×

*S*_{3})] with opposite signs so that the net spin chirality is (nearly) zero. These unusual Hall resistances in

### Unusual magnetoresistance

Another important transport feature in WSMs is their negative magnetoresistance (NMR) due to the chiral anomaly. When a magnetic field is applied along the current direction, a chiral charge current is driven from one Weyl node to its counterpart with opposite chirality (*6*). This chiral current leads to additional electric conductivity and gives rise to NMR. The NMR effect is largest when ** B** ||

**and vanishes when**

*I***(**

*B*⊥*I**6*,

*22*). The NMR effect has been observed in bulk Mn

_{3}Sn single crystals, where it is very small (~0.1% at

*B*= 9 T and

*T*= 300 K) (

*22*). Moreover, the NMR decreases quickly as the energy difference (Δ

*E*) between Fermi energy and Weyl nodes increases. NMR is inversely proportional to Δ

*E*

^{2}and is reduced by ~60% as Δ

*E*increases from 5 meV (

*x*= 0.06) to 8 meV (

*x*= 0.03) (

*22*). As shown in Fig. 6A and fig. S9A, a small ordinary positive magnetoresistance (PMR) due to Lorentz force is observed from

*T*= 300 K to

*T*= 2 K in our films for

*x*< 0.40. The absence of NMR is likely due to the larger Δ

*E*in those films. For the gapped state (Fig. 6B and fig. S9B), PMR is observed at

*T*> 70 K, but NMR is observed at

*T*< 70 K inside the spin glass regime (i.e.,

*T*

_{g}~ 70 K). The nearly linear NMR at low temperatures weakly depends on the orientation of the applied magnetic field. This isotropic NMR can originate from the suppressed Kondo scattering and/or spin-dependent scattering as magnetic field polarizes the randomly oriented doped Mn spins at the center of the hexagon (note S4). Nevertheless, the NMR well correlates with the γ(

*T)*and Hall results induced by Mn doping, providing complementary transport consequences by the magnetic doping of Mn atoms.

## DISCUSSION

In this work, we show that AFM WSM Mn_{3+x}Sn_{1−x} thin films with superior sample quality are a class of exciting materials to study the interplay between strong correlation, topology, and magnetism. By replacing Sn with magnetic Mn atoms, a Kondo effect, which often appears in strongly correlated metals, emerges, evolves, and leads to opening of a hybridization gap. As a consequence, Hall resistances inherent to Berry curvatures in the reciprocal space decreases. Notably, resonance-enhanced terahertz Faraday rotation emerges as the gap is opened. Our work calls for further studies of related materials. For example, one may increase electron localization (hence electron correlations) by doping atoms with 3*d* (e.g., Fe, Co, and Cu) or 5*f*/4*f* (e.g., Gd) electrons (*14*). It is also interesting to tune the spin-orbit coupling by doping (especially isostructural and/or isoelectronic doping) of heavy elements (e.g., Pb).

One of the major challenges in AFM spintronics is the electric detection of AFM spin order. In this respect, conventional collinear AFMs, which do not exhibit AHRs due to vanishingly small magnetization, are not good candidates for AFM spintronics (*28*). The rich noncollinear spin textures and the substantial Hall resistances in the Mn_{3}Sn family of compounds make it a promising contender for such applications. Moreover, the noncollinear spin orders and/or the topological aspects in Mn_{3}Sn present new opportunities for spin-charge conversion and spin orbit torque switching of AFM spin orders. These Mn_{3+x}Sn_{1−x} films with greatly extended compositional range, tunable strong correlations, unusual Hall resistances, and resonance-enhanced terahertz Faraday rotation, offer new prospects, as exemplified in this work, and may further propel the nascent field of topological AFM/terahertz spintronics and the development of novel spin-based devices.

## MATERIALS AND METHODS

The Mn_{3+x}Sn_{1−x} films were synthesized by DC cosputtering of Mn (99.99%) and Sn (99.99%) targets at a sputtering rate of about 2 Å/s in a high-vacuum magnetron sputtering system with base pressure better than 5 × 10^{−8} torr. Each batch of films with compositional wedge (pure phase) was grown on a wafer with dimensions approximately 7 mm by 50 mm. After growth, the wafer was cut into 13 to 14 pieces (each of them had a size of around 3.5 mm by 7 mm) along the wedge direction for XRD measurements. Each piece was further cut for transport (~2 mm by 3.5 mm; electrodes were made by wire bonder) and/or other characterizations. (0001) Mn_{3+x}Sn_{1−x} films were grown at substrate temperature of *T*_{S} ≈ 300°C on C-Al_{2}O_{3} substrate with Pt seed layer and Si (111) substrate with Ag seed layer. _{3+x}Sn_{1−x} films were grown at substrate temperature of *T*_{S} ≈ 400°C on R-Al_{2}O_{3} substrate without seed layer. The samples presented in this work are listed in table S1. The compositions of films were measured/calibrated on 150-nm (0001) Mn_{3+x}Sn_{1−x} films by energy-dispersive spectroscopy (EDS) in a scanning electron microscope. For transport measurements on (0001) films, the buffer layer (Pt) is slightly doped (or the thickness is reduced) to increase the resistivity but retains its crystalline quality, so that the contribution from the buffer layer is minimized. The magnetization measurements were done in a Quantum Design PPMS system equipped with a vibrating sampling magnetometer (VSM) and a room temperature VSM. The DC transport measurements were done in a 9-T cryogen-free Quantum Design PPMS system with transport rotator assembly. Terahertz measurements were done in a home-built spectrometer that is coupled to a cryogen-free 7-T split-coil superconducting magnet with a base temperature of 1.6 K.

## SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/35/eabc1977/DC1

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is **not** for commercial advantage and provided the original work is properly cited.

## REFERENCES AND NOTES

**Acknowledgments:**

**Funding:**X.H. and L.W. acknowledge support by the Amy Research Office under the grant W911NF1910342. The Penn NSF MRSEC DMR-1720530 supported part of the magneto-terahertz instrumentation development (L.W.) and the electrical transport measurements (S.H.P. and J.M.K.). J.Z. acknowledges the financial support by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under award no. DE-SC0020221. J.W. acknowledges the support by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515. R.F.N. acknowledges support from the National Research Council Research Associateship Program. Research was performed, in part, at the NIST Center for Nanoscale Science and Technology. P.K. and W.W. acknowledges support by the NSF under the grant DMR-1905783.

**Author contributions:**S.X.H. conceived the project. D.K. synthesized the films and performed the XRD measurements. T.R.T., S.H.P., and J.M.K. performed the DC transport measurements. X.H. and L.W. performed the terahertz measurements and analyzed the data. J.W., P.K., and W.W. performed magnetic measurements. R.F.N. did HR-XRD and EDS measurements. S.X.H. analyzed the data with assistance from T.R.T. and D.K. and inputs from all authors. S.X.H. and J.Z. discussed the results and gave explanations. S.X.H. wrote the manuscript, with revisions from J.Z., J.M.K., L.W., and R.F.N. and comments from all authors.

**Competing interests:**The authors declare that they have no competing interests.

**Data and materials availability:**All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

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