The subject of the study is an MgO(111)(0.5 mm)/Ru(5 nm)/Mn₃Sn(80 nm)/Si(3 nm) sample. In Fig. 1a, we show the optical pump-THz emission geometries used in our experiments. When presenting a data set we will refer to the experiment geometry in which this data was collected as configuration1, 2 or 3. To indicate different directions we introduce two Cartesian coordinate systems, also indicated in Fig. 1(a): (x, y, z)—fixed with respect to the experimental setup; (a, b, c)—fixed with respect to the sample. Laser pulses of 50 fs duration with a central wavelength of 800 nm propagate along the z-axis. A quarter-wave plate (QWP) placed in the pump path is used to control the polarisation and helicity of the pulses. In-plane rotations of the QWP by an angle φ allow changing between linear (φ = 0° ± nπ/2), left-handed circular (LHCP) (φ = 45° ± nπ), right-handed circular (RHCP) (φ = − 45° ± nπ), and intermediate elliptical polarisations. The angle between the laser beam and the sample surface can be varied by rotating the sample away from normal incidence about the x-axis (configuration 2) or y-axis (configuration 3). We define the tilting angles as θ_x and θ_y respectively. Additionally, the sample can be rotated in-plane, about the c-axis by an angle defined as θ_c. An external magnetic field up to μ₀H_x ≈ 860 mT can be applied along the x direction. Unless stated otherwise, the experiments presented in the main body of the paper were performed at room temperature (RT).Fig. 1

a Experiment schemes in different geometries. Ultrafast laser pulses travelling along z-axis are incident on the sample, leading to the emission of broadband THz electro-dipole emission s_i(t) with integrated peak amplitude S_i. In the experiments, we resolve the two orthogonal components of the transient THz signals: s_x(t) and s_y(t). θ_x, θ_y and θ_z label the rotation angles around the x, y and z axis respectively. Configuration 1 corresponds to a measurement in the standard geometry with normal laser incidence, in which θ_x = 0 and θ_y = 0. In configuration 2 and configuration 3 the sample is rotated about the x (θ_x ≠ 0 and θ_y = 0) or y (θ_x = 0 and θ_y ≠ 0) axes respectively. Please note that the scheme of configuration 2 is presented in a different perspective than configuration 1 and 3. b shows THz signals detected along y, emitted from Mn₃Sn optically pumped with laser pulses of different polarisations. The measurements were performed in configuration 1 without an external magnetic field. The experimental data set is fitted with function introduced in Eq. (1) to find H_y, L_y, and B_y. Here, Hi(φ)=hisin(2φ+φ1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{i}(\varphi )={h}_{i}\sin (2\varphi +{\varphi }_{1})$$\end{document} is the magnitude of the circular polarisation helicity-dependent component with a phase shift φ1,Li(φ)=lisin(4φ+φ2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{1},{L}_{i}(\varphi )={l}_{i}\sin (4\varphi +{\varphi }_{2})$$\end{document} is the linear polarisation-dependent component with a phase shift φ₂, and B_i is the polarisation-independent background component. These are presented in (c) with the extracted values of the amplitudes ∣h_y∣, ∣l_y∣, and B_y.

The optically induced charge currents J_i(t) result in broadband THz electro-dipole emission s_i(t). The subscript i indicates the polarisation components i = x or i = y, along the two axes of the experimental setup x and y. As shown in Fig. S2 in Supplementary Note 2, THz transients detected from the Mn₃Sn sample switch the polarity upon changing the pump helicity from RHCP (right-hand circular polarisation) to LHCP (left-hand circular polarisation). This behaviour indicates the presence of pump-polarisation-dependent photocurrent generation mechanisms.

We define S_i as the integrated peak amplitude of the emitted THz pulse (we refer the reader to Fig. S2, S3 and S4 in Supplementary Notes 2 to 4 for a more precise definition in the different measurement configurations). Figure 1b shows the φ-dependence of S_y, measured at zero magnetic field (μ₀H_x = 0) and at normal pump incidence (configuration 1). The different polarisations of the pump pulse that correspond to the different values of φ are also indicated to facilitate the reading. The data is decomposed into different harmonics by fitting with the equation¹⁸:1Si(φ)=Hi(φ)+Li(φ)+Bi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S}_{i}(\varphi )={H}_{i}(\varphi )+{L}_{i}(\varphi )+{B}_{i}$$\end{document}

Here, Hi(φ)=hisin(2φ+φ1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{i}(\varphi )={h}_{i}\sin (2\varphi +{\varphi }_{1})$$\end{document} is the magnitude of the circular polarisation helicity-dependent component with a phase shift φ1,Li(φ)=lisin(4φ+φ2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{1},{L}_{i}(\varphi )={l}_{i}\sin (4\varphi +{\varphi }_{2})$$\end{document} is the linear polarisation-dependent component with a phase shift φ₂, and B_i is the polarisation-independent background component. As displayed in Fig. 1(c), the decomposition of S_y shows that H_y(φ), L_y(φ), and B_y all contribute to the measured signal. For comparison, S_x measured in the same experimental geometry (configuration 1) displays a relatively smaller contribution from the helicity-dependent H_x(φ) component, and is dominated by L_x(φ) (Supplementary Note 5). We attribute this difference to a small unintentional rotation around the y-axis, as it will be further justified in the analysis that follows. In our set-up, the sample’s mount orientation can be freely adjusted around the y-axis, but not around the x-axis, so an unintentional tilting around the y-axis is more likely. In the following considerations, we focus on polarisation-dependent components of the signal, H_y(φ), L_y(φ). The remaining contribution, B_i does not have any dependence on optical polarisation, and can therefore be correlated to heating¹⁹. When the optical pump hits the sample surface its energy is absorbed by the electron bath and induces gradients in the electron temperature distribution at sub-picosecond timescales. The asymmetric diffusion of carriers along the gradient direction can lead to photo-currents. In our measurement layout, only the photo-currents generated parallel to the sample surface are radiative and can be detected. This is possible in the lateral photo-Dember effect²⁰, if the pump hits the sample close to one edge (we need to consider that the pump beam diameter is 1 mm, comparable to the sample size). This is also validated by the fact that the background value does not have any clear correlation with sample rotation angle, as shown in Table S1 in the Supplementary Note 6. We also exclude any magnetic field dependent effect such as the anomalous Hall effect because we do not observe any dependence on magnetic field or flipping of the sign when the magnetic field direction is flipped (please refer to the section Magnetic field dependence below and Supplementary Note 8).

Here we study how both polarisation and amplitude of the photocurrent-generated THz emission depend on the direction of the optical wavevector q_z relative to the sample surface. For this purpose we tilt the sample whilst leaving the direction of the pump wavevector q_z unchanged with respect to the laboratory frame of reference, along the z-direction. For θ_x (configuration 2) or θ_y (configuration 3) different from zero, q_z has a non-zero projection along the b and a directions on the plane of the Mn₃Sn film, which we label q_b and q_a respectively. Consequently, the components of the wavevector relative to the sample frame are [0, q_b, q_c] in configuration 2 and and [q_a, 0, q_c] in configuration 3.

Figure 2a and b show the components of the THz emission polarised along the x and the y directions as a function of φ, measured in configuration 2 (a) and configuration 3 (b). S_x(φ) and S_y(φ) are fitted with Eq. (1) to extract the coefficients h_x and h_y. While in Fig. 2a h_x ≫ h_y, in Fig. 2b the trend is inverted and h_x ≪ h_y. This suggests that the direction of the helicity-dependent photocurrent, and therefore of the THz polarisation, depends on the projection of the pump wavevector on the sample plane and is perpendicular to it. Due to finer control of θ_y in comparison to θ_x in our setup, we restrict the following analysis to configuration 3 only. In Fig. 2c we show that the THz emission amplitude increases with tilting angle θ_y. We now study the symmetry of the THz emission for opposite tilting angles by decomposing S_i(φ) into even and odd contributions as:2Si(φ)even(θy=±15∘)=Si(φ)(θy=+15∘)+Si(φ)(θy=−15∘)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S}_{i}{(\varphi )}_{even}({\theta }_{y}=\pm \! 1{5}^{\circ })={S}_{i}(\varphi )({\theta }_{y}=+1{5}^{\circ })+{S}_{i}(\varphi )({\theta }_{y}=-1{5}^{\circ })$$\end{document}3Si(φ)odd(θy=±15∘)=Si(φ)(θy=+15∘)−Si(φ)(θy=−15∘)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S}_{i}{(\varphi )}_{{{\mbox{odd}}}}({\theta }_{y}=\pm \! 1{5}^{\circ })={S}_{i}(\varphi )({\theta }_{y}=+1{5}^{\circ })-{S}_{i}(\varphi )({\theta }_{y}=-1{5}^{\circ })$$\end{document}Fig. 2

Normalised THz emission amplitude S_x(φ) and S_y(φ) data sets measured in configuration 2 and configuration 3 are plotted in (a, b) respectively. The sample was rotated around the x-axis by θ_x = + 25° ± 5° or θ_y = + 15° ± 2° respectively. c shows THz signals measured along y in configuration 3 for tilting angles θ_y between 0 and 30°. The data sets were fitted with Eq. (1) to extract the values of ∣h_y∣ and ∣l_y∣ parameters, respectively the magnitude of the circular polarisation helicity-dependent component and the near polarisation-dependent component. d shows even (see Eq. (2)) and odd (see Eq. (3)) responses with respect to θ_y, the rotation angle around the y-axis. The figure displays normalised THz signals measured along y in configuration 3. All measurements in (a–d) were performed at room temperature with no magnetic field. Data sets shown in (a, b–d) were fitted with Eq. (1) prior to normalisation to subtract the polarisation-independent backgrounds, B_i.

In Fig. 2d we observe that the odd component of S_y is dominant. Analogous behaviour is presented in Supplementary Note 7 for S_x. Our observations suggest that the helicity-dependent photocurrents are generated in the direction perpendicular to the in-plane projection of the pump wavevector and are proportional to it.

In this section we want to understand whether the photocurrents have a magnetic origin and depend on the magnetic phase of Mn₃Sn. Figure 3a shows S_y measured for two opposite directions of the magnetic field ±0.860 mT. According to Reichlova et al.²¹, 0.860 mT may be too low to switch the magnetic ordering in Mn₃Sn thin films at RT, while it is sufficient to reverse the spins at temperatures close to T_N. Hence, for these measurements we followed a cool down procedure with the magnetic field continuously applied from 420 K to 380 K, at which the experiment was performed. No significant dependence on magnetic field is measured. We also do not observe a qualitative difference in the time-domain THz transients measured at different fields as shown in the SI.Fig. 3

a THz signals measured at 380 K in configuration 3 after field-cooling from 420 K with opposite directions of external magnetic field continuously applied along x. b Normalised THz emission amplitude S_x(φ) and S_y(φ) data sets obtained prior, and after an in-plane rotation of the film by 90°. Prior to the measurements the sample was cooled down from 420 K to room temperature with the magnetic field of +860 mT. The field was switched off at room temperature, and S_i(φ)(θ_c = 0) were measured. Without repeating the field-cooling procedure and at zero magnetic field, the film was rotated in plane by +90° to obtain S_i(φ)(θ_c = + 90°). The experiment was performed in configuration 3. The plots show normalised signal values. Prior to normalisation the data sets were fitted with Eq. (1) to subtract the polarisation-independent backgrounds, B_i.

We further confirm that the polarisation and amplitude of the emitted THz pulse is not correlated with the magnetic phase of Mn₃Sn by repeating the measurement after rotating the sample by 90° around the c-axis. Figure 3b shows S_x(φ) and S_y(φ) prior and after the rotation by θ_c = + 90°. If the direction of the photoinduced currents, hence the polarisation of the THz emission, were correlated with the orientation of the spins we would have expected a rotation of the THz polarisation plane by 90°, which we do not observe. Instead, the two graphs of S_x(φ) and S_y(φ) overlap, as is discussed further in the SI.

In this section, we investigate nonlinear optical effects in Mn₃Sn as an explanation of the observed signal. Other possible sources of helicity-dependent photocurrents are discussed in the subsequent section.

We consider a phenomenological expression for the induced photocurrent J_i that in turn generates THz emission via electro-dipole interaction. Using the notation from ref. ²² and expanding to second order in the light wave amplitude E(ω) for a frequency ω we write:4Ji=χijk(2)EjEk*+χijkl(3)qjEkEl*\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${J}_{i}={\chi }_{ijk}^{(2)}{E}_{j}{E}_{k}^{* }+{\chi }_{ijkl}^{(3)}{q}_{j}{E}_{k}{E}_{l}^{* }$$\end{document}where all indices run over the Cartesian coordinates of the sample i, j, k, l ∈ (a, b, c) and q is the momentum of the incoming light. At normal incidence (configuration 1), only q_c, E_a and E_b are non-zero. The first term describes the photogalvanic effect (PGE), whereas the second term describes the photon-drag effect (PDE). We further decompose each of these tensors into symmetric and antisymmetric components with respect to the light wave amplitude which respectively give rise to the linear photogalvanic/photon drag effect (LPGE/LPDE) and the circular photogalvanic/photon drag effect (CPGE/CPDE)²³. Note that all quantitative features of these effects depend crucially on the details of the band structure. We show the ab-initio bulk and surface band structures in Fig. 4, for an energy-window of ℏω ≈ 1.55 eV, corresponding to the central wavelength of the laser pulses. Due to the large number of bands involved, we focus on a qualitative phenomenological symmetry analysis of the tensors in Eq. (4).Fig. 4

In (a), we show the bulk band structure, for an energy window corresponding to the frequency of the laser. In (b), we show the same plot, but with the colour and opacity of the bands indicating the value of minm{En(k)−(Em(k)±ℏω)}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop{\min }\limits_{m}\{{E}_{n}({{{{{{{\boldsymbol{k}}}}}}}})-({E}_{m}({{{{{{{\boldsymbol{k}}}}}}}})\pm \hslash \omega )\}$$\end{document} for band n, with ± indicating whether the band is above/below the Fermi surface. This is a rough indicator of the possibility of a vertical transition from band n occurring. The flat bands around K may also allow non-vertical transitions. In (c, d), we show the surface band structure for the c-directed top and bottom surface respectively, with the colour indicating how well-localised the states are on the surface.

Another way in which helicity-dependent photocurrents can be generated is through a combination of the inverse Faraday effect (IFE) and inverse spin Hall effect (ISHE), as described recently for Bismuth thin-films in ref. ¹⁴. This could be an important mechanism in Mn₃Sn, where effects related to the nonzero Berry curvature are significant⁸ and may result in strong responses of the Faraday effect²⁹. Furthermore, Mn₃Sn has been shown to have a large spin Hall angle³⁰. However, we believe this mechanism does not play a significant role in our experimental results. Firstly, for an efficient conversion of IFE-induced spin currents into charge currents and THz electric fields the spins must travel relatively long distances¹⁴. This is not the case in Mn₃Sn, where the reported spin propagation length is below 1 nm³¹. Secondly, a Berry curvature related effect, such as the IFE, would show a strong dependence on the magnetic phase of Mn₃Sn. We do not observe this behaviour in our temperature measurements reported in Fig. S8 in Supplementary Note 9. Previous studies have reported that at temperatures above 420 K Mn₃Sn becomes paramagnetic and that upon cooling below RT the material can undergo transitions into the spiral and spin glass phases¹. Our investigation in the temperature range of 50 − 400 K does not reveal any abrupt changes in the magnitude of THz signals that could indicate the role of magnetic phase-dependent mechanisms. We do not, however, rule out that our sample remains in the same magnetic state over the entire investigated temperature range. Finally, the mechanism relying on the IFE and ISHE could only explain the helicity-dependent photocurrents and cannot account for the generation of photocurrents that show linear dependence on the pump polarisation. As shown in Fig. 1c, the magnitudes of H_y and L_y are comparable, and therefore we suggest their main contributions originate from related mechanisms, namely the CPDE and LPDE.

Epitaxial Mn₃Sn films were grown using magnetron sputtering in a BESTEC ultra-high vacuum (UHV) system with a base pressure of <2 × 10⁻⁹ mbar and a process gas (Ar 5 N) pressure of 3 × 10⁻³ mbar. The target to substrate distance was fixed at 20 cm and the substrates were rotated during deposition to ensure homogeneous growth. The underlayer was deposited using a Ru (5.08 cm) target by applying 40 W DC power with the substrate held at 400 °C. Following cooling back to room temperature, Mn₃Sn was grown from Mn (7.62 cm) and Sn (5.08 cm) sources in confocal geometry, using 47 W and 11 W DC power respectively. The stack was then annealed in-situ under UHV at 350 °C for 10 min. The stoichiometry is Mn₇₅Sn₂₅ (±2 at. %), estimated by using energy dispersive x-ray spectroscopy (see Fig. S1 in Supplementary Note 1). Finally, a Si capping layer was deposited at room temperature using an Si (5.08 cm) target at 60 W RF power to protect the film from oxidation. Magnetotransport studies on films grown under the same conditions and with comparable crystal quality are presented in ref. ³² and show a large anomalous Hall effect at room temperature and a transition to topological Hall effect below 50 K.

The electronic band structure was calculated using density-functional theory (DFT) as implemented in Quantum Espresso^33,34 with a fully-relativistic norm-conserving pseudopotential, generated using the ONCVPSP package³⁵. We used the experimental crystal parameters a = b = 5.67 Å and c = 4.53 Å, with an 8 × 8 × 8 k-grid and a kinetic-energy cutoff of 870 eV. The magnetic structure was relaxed by constraining the total direction of the magnetization. The bands were then Wannierised using Wannier90³⁶, with all d-orbitals of Mn considered in the projector. Finally, the slab band structure was computed using WannierTools³⁷.