Terahertz Probing of Anisotropic Conductivity and Morphology of CuMnAs Epitaxial Thin Films

Antiferromagnetic CuMnAs thin films have attracted attention since the discovery of the manipulation of their magnetic structure via electrical, optical, and terahertz pulses, enabling convenient approaches for switching between magnetoresistive states of the film for information storage. However, the magnetic structure and, thus, the efficiency of the manipulation can be affected by the film morphology and growth defects. In this study, the properties of CuMnAs thin films are investigated by probing the asymmetrical growth‐related uniaxial anisotropy of electric conductivity by contact‐free terahertz transmission spectroscopy. It is shown that the terahertz measurements conveniently detect the conductivity anisotropy that is consistent with conventional DC Hall‐bar measurements. Moreover, the terahertz technique allows for considerably finer determination of anisotropy axes, and it is less sensitive to the local film degradation. Thanks to the averaging over a large detection area, the THz probing also allows an analysis of strongly non‐uniform thin films. Using scanning electron and near‐field terahertz microscopies, the observed anisotropic conductivity of CuMnAs is related to the elongation and orientation of growth defects, which both originate in the anisotropic growth of the films. In addition, control over the morphology of defects is demonstrated by using vicinal substrates.

). (e) σ THz,0 measured with 20-nm-thick CuMnAs on GaAs substrate on two different areas, separated by ~ 1 mm (in the horizontal [1-10] substrate direction for α = 0).Dashed curves are the twofold, uniaxial contributions of the fit by Eq. ( 3), the one-fold, unidirectional contributions are shown in dash-anddot curves.These components are shifted vertically for clarity.(f) A close-up on σ THz,0 data of (d).2Δ 2 / ̅ as a function of the film thickness  for three substrates (circles: GaP, squares: GaAs, triangles: Si) obtained from fits of THz data (Mar.22) in Fig. 4. Error bars are the magnitude of the one-fold component ±Δ 1 / ̅.In correspondence with Ref. [8], a 1/-dependence is plotted as guides for an eye for GaP (solid blue curve) and GaAs substrate (grey curve) and a constant function for Si substrate (solid red line).The grey dashed line stresses the rising trend with  for GaAs substrate experimentally observed in our data.The opposite phase of σ 0,THz (α) for CuMnAs(20)/Si is stressed by plotting it as a negative number.

Introduction
Antiferromagnets (AF) have appeared on the roadmap towards future spintronic applications in the information memory technology thanks to their advantages as compared to ferromagnets: their insensitivity to external magnetic fields up to units or tens of T improving the memory robustness 1,2 , no stray fields, and the associated possibility of a denser memory bit integration 3 , significantly faster coherent dynamics of the magnetic order reaching or exceeding THz frequency scale 4 , and availability of a large variety of AF materials ranging from insulators to metals 5,6 .
However, the lack of a net magnetic moment of antiferromagnets also brings a significant challenge for the concept of room-temperature device operation as impractically strong magnetic fields would be needed to manipulate the AF order.In this regard, the room-temperature collinear antiferromagnet CuMnAs has gained significant attention thanks to a theoretical prediction 7 and recent demonstrations of a coherent switching of the Néel vector by electrical current pulses [8][9][10][11] .Besides its coherent reorientation, the magnetic order of CuMnAs can be also manipulated incoherently through heatactivated processes induced by electrical 12 , optical 2 , and THz pulses 13,14 , resulting in a transient metastable nano-fragmentation of AF domains 2,15,16 .The nano-fragmentation is accompanied by a switching of the resistive state by tens of percent, and has been explored in the context of logic-inmemory devices for spiking neuromorphic applications 2,12 .
Consistently with previous studies [11][12][13][14] , we prepare the tetragonal CuMnAs films (space group P4/nmm) by molecular beam epitaxy (MBE) on GaP, GaAs, and Si substrates 17,18 .A detailed characterisation 19 of MBE-grown CuMnAs showed that the crystal growth is accompanied by a formation of several types of defects associated with externally controlled parameters, such as stoichiometry, choice of substrates, and layer thickness .For example, polar GaP and GaAs substrates promote a growth mode that starts from a formation of isolated elongated islands.Upon increasing the deposition time, the islands gradually evolve into a percolated layer containing an array of elongated holes whose density decreases with increasing .In contrast, the shape of islands formed during the growth on the non-polar Si substrate remains isotropic for all .
All the types of defects contribute to film inhomogeneities and induce local variations of conductivity.In addition, the elongated defects also create local morphologic anisotropy which can explain the observed global anisotropy of conductivity of CuMnAs thin films 14,19 .Moreover, it could also contribute to the magnetic anisotropy 20 and, thus, be linked to the efficiency of the switching of the magnetic order.Therefore, a convenient detection method, a detailed understanding, and even a manipulation of the morphologic anisotropy are desirable for improving the overall performance of CuMnAs-based devices and could bring new functionalities.
In this paper, we show that a reliable contactless non-destructive detection of the elongated-defectrelated anisotropy of electrical conductivity of CuMnAs is possible by means of the time-domain THz spectroscopy.This method probes the electrical properties averaged over a large film area defined by the THz spot size (~1 mm 2 ).These are orders of magnitude larger dimensions than the typical defect size (< 1 m).Benefiting from this low sensitivity to local layer inhomogeneities and the high azimuthal angle resolution of the method, we find a correlation between the conductivity anisotropy and the anisotropy of elongated defects of defects.In addition, we show that Si substrates with vicinal (step-like) surfaces can be used to control the morphologic and conductivity anisotropy.Finally, by employing a scanning near-field THz microscopy, we directly observe local variations of the electrical conductivity in elongated defects, providing a microscopic insight into the origins of the global anisotropy of the conductivity in CuMnAs.

Samples and setups
The sample set consists of thin films of CuMnAs of various thicknesses (9-50 nm) grown by MBE on the three different (001)-oriented substrates (in most cases double-side polished): Si, GaP and GaAs, as summarized in the Supplementary material, Table S1.Since our aim is to study the defect morphology associated with elongated islands formed in the initial stages of the growth, we intentionally select samples in which this initial island growth-mode was well pronounced.The [100] crystal direction of the CuMnAs epilayer is oriented along the [110] direction of the substrate 19 .In the following text and Figures, the marked crystallographic directions refer to the substrate.The CuMnAs films were capped by 3 nm of Al which almost fully oxidized in the air and formed a protective AlOx cap.The surface was then lithographically patterned according to the experimental scheme used to determine the film conductivity (see Fig. 1 and Section 6: Experimental methods for more details).
The main, contactless technique used in our work is the THz time-domain transmission spectroscopy 21 [scheme shown in Fig. 1(a)], which is an established method for probing electrical currents [22][23][24][25] and conductivity 26,27 .Here, linearly polarized picosecond pulses of THz radiation, generated by an excitation of a spintronic emitter 28,29 by a train of ultrashort optical pulses (see Section 6 for more details), are focused to a ~860-m-wide spot (see Supplementary Fig. S1).The radiation is further transmitted through the CuMnAs film and substrate, with the substrate crystallographic axis [110] rotated by an angle  with respect to the polarization direction of the THz pulse.The transmitted radiation () is detected by the electrooptical sampling resulting in a signal ().Since its image in the frequency domain, (), equals the product of the transmitted field () and the transfer function of the setup, we can relate the detected signals to the conductivity () of the CuMnAs film by the Tinkham formula 21,22,30 : where   () and   = 1 are refractive indices of the substrate and air, respectively,  0 ≈ 377 Ω is the vacuum impedance,  is the thickness of CuMnAs, and  ′ (, α) = (ω, α)/ ref (ω, α).Here,  ref is the electrooptical signal for transmission through the bare substrate (see Section 6 and Supplementary Note 1 for more details).For switching between  and  ref , a chessboard-like pattern was created by non-etched and etched squares of the film [Fig.1(c) and Experimental methods for details] to directly access the reference transmission through the substrate.
To get an additional insight into the local variations of conductivity, a THz scanning near-field optical microscopy (THz-SNOM) setup 31 was employed (see Sec. 6 for details about the setup).Although the scattered THz electric field depends on complicated near-field interactions between the sample and the SNOM tip, it can provide a qualitative relation between the growth defects, their topology, and the local conductivity of the CuMnAs film.Measurements by all techniques are performed at room temperature.From the above qualitative findings, we conclude that the observed modulation of the THz signal originates in the thin film and is directly related to the anisotropic conductivity of CuMnAs.Moreover, the modulation has a phase consistent with the orientation of previously reported elongated surface defects (their elongated direction was observed to be parallel to the [110] crystallographic direction of the substrate) 19 .

THz and DC conductivities
To address the quantitative comparison of both methods, we first extract the complex-valued conductivity,  THz (), from the THz data for  = 0, 45, 90° using Eq. ( 1) and correct it for possible phase shifts due to a variation of the substrate thickness [see also Supplementary Note 1].We fit the data by the Drude model 32 : where σ THz,0 is the conductivity at ω = 0, and τ is the electron scattering time.The data and the fits are shown in Fig. 3. Apart from a significant variation of  THz,0 versus α (by ~30%) due to the anisotropy, we observe that the real part of  THz remains nearly constant over the studied frequency range.This implies that (i) we can view the film as fully percolated with no significant portion of insulated islands of CuMnAs.In non-percolated films, σ THz (ω) typically differs from the Drude behavior and would be manifested by an increase of Re( THz ) with increasing frequency 27,33 .Also, (ii) the real part of  THz (ω) can be approximated by constant  THz,0 .The conclusions hold also for other samples (see Supplementary Fig. S2).We can directly compare  THz,0 to the DC conductivity σ DC = /( DC ) where  and  are the length and width of Hall bar segments between the voltage contacts (data points at ω = 0 in Fig. 3).
The conclusion (ii) allows us to avoid extraction of the spectral dependence of the conductivity and to simplify the subsequent systematic anisotropy study by disregarding the time dependence of () and only evaluating its RMS, rms[()].The quantity σ ,0 is then obtained by using Eq. ( 1) and substituting  ′ = rms[()]/rms[ ref ()].The full dependence of  THz,0 and σ DC on α, is plotted in Fig. 4(a) by full red and open red data points, respectively.We observe a good quantitative agreement between the two methods, yielding the same conductivity anisotropy 2Δσ/ ̅ = 29.3%,where 2Δσ is the full amplitude of modulation of conductivity and  ̅ is the α-averaged mean conductivity.
An example of the analysis of samples on other substrates is shown in Fig. 4 [  (α) and  THz,0 (α) for the whole sample set are available in Supplementary Fig. S2 and S3, respectively].In contrast to GaP and GaAs substrates [Fig.4(a,b)], we observe a significant discrepancy between  THz,0 (full red points) and σ DC (open red points) for CuMnAs films grown on the Si substrate [Fig.4(c,d)].To address the possible impact of an inhomogeneity and gradual oxidation of the films on both methods, we repeated the experiments after 7-8 months on the same samples: at a different location on the surface (THz data, full blue points), at the same location using the original Hall bar devices (DC data, blue open points) and on a new location using newly patterned devices (DC data, grey open points).We observe that, apart from CuMnAs(50)/GaAs, all DC measurements differ significantly from each other and even their scatter increased over the time period, while the THz data are significantly more consistent.These findings indicate that the DC electrical detection of the σ anisotropy is more prone to the local degradation of CuMnAs due to oxidation, an effect which was reported even on capped films 19 .The oxidation affects more likely the edges and holes of the film, leading to possible damages of the devices and deterioration of their functionality.The THz detection does not suffer from the oxidation to this extend as it averages over the area of the sample probed by the THz spot.For this reason, only the THz data will be analysed in the reminder of this section.
Although noticeably more reproducible, the THz data still show a certain deviation from the expected cos (2) dependence with indications of different symmetry with respect to α.Therefore, we evaluate the relative contribution of the uniaxial (two-fold, Δσ 2 ) and unidirectional (one-fold, Δσ 1 ) components by fitting the THz data by an empirical function where α 1 and α 2 are the corresponding phases of modulations, i.e., orientations of the anisotropic axes for unidirectional and uniaxial components, respectively.Results of the fits of all the studied samples are summarized in Supplementary Table S1 and later in Fig. 5.While Δσ 2 ≫ Δσ 1 and phase α 2 ≈ 90° stays constant for all films on GaP and GaAs substrates, this does not hold for the Si substrate: the phase reverses its sign in Fig. 4(c), and the weaker anisotropy of σ THz,0 can even be dominated by Δσ 1 , as seen in Fig. 4(d) and its close-up Fig. 4(f).Here, we see that Δσ 1 changed dramatically with changing the probing position and the measurement time period.To get more insight into the nature of Δσ 1 , we repeated the experiment with CuMnAs(20)/GaAs on the same day and in two different sample locations separated by roughly 1 mm in the [1-10] direction [Fig.4e].While Δσ 2 stays the same for both locations, the Δσ 1 component significantly changes.A consistent observation is made for the corresponding phases: α 1 varies randomly for all measured samples (illustrated in Supplementary Fig. S4).From these observations, we draw a conclusion that the unidirectional (onefold) symmetry is an artifact.A slight misalignment of the sample rotation axis and the propagation axis of the THz pulses can lead to an effective motion of the THz spot over the surface.Indeed, the characterization of the maximal possible displacement of the THz spot on the sample surface during the sample rotation yielded ∼ 40 μm (Supplementary Note 2 and Fig. S5).This, in combination with large-scale gradients of the film and the substrate, can lead to an apparent non-zero Δσ 1 .Therefore, the genuine anisotropy of the electrical conductivity seems to be only the uniaxial component.
The elongated-defect-related uniaxial anisotropy component of the conductivity, 2Δσ 2 / ̅, for different  and substrates is shown in Fig. 5, complemented by a guide to the eye (blue curve) to highlight the expected trends for the samples on the GaP substrate 19 .Conservatively, the error bars are set as the magnitude of the corresponding unidirectional anisotropy component Δσ 1 / ̅.We observe that 2Δσ 2 / ̅ measured on CuMnAs/GaP decreases with the film thickness, while the sample on GaAs yields an unexpected increasing trend.Similarly, relatively small values of 2Δσ 2 / ̅, approaching zero within the error bars, on the two CuMnAs/Si samples for  < 14 nm are contrasted by a 20-nm-thick CuMnAs/Si sample with 2Δσ 2 / ̅ = 17.2% and an opposite phase to the films on GaP and GaAs.To stress this phase change, the value of 2Δσ 2 / ̅ is plotted with a negative sign in Fig. 5.We note that all samples were remeasured on multiple surface regions, consistently yielding the presented results.To understand these trends, we explored further the morphology of the film defects.

Surface defect morphology
The morphology of surface defects can be observed directly by performing a scanning electron microscopy (SEM) imaging of the sample surfaces and inferring the corresponding anisotropy of the surface morphology .We illustrate the analysis on two samples that differ significantly in their conductivity anisotropy: 10-nm-thick CuMnAs/GaP (2Δ 2 / ̅ = 63.4 %) and 9-nm-thick CuMnAs/Si (2Δ 2 / ̅ < 3%), whose SEM images are shown in Figs.6(a) and (b), respectively.The SEM images for all samples are shown in Supplementary Fig. S6.A clear elongation of defects is observed along the [110] GaP substrate direction (indicating  > 0), while rather isotropic surface defects are evidenced in the film on Si substrate ( ≈ 0).
To quantify  of the defects, we numerically processed the SEM images by the edge-finding method, described in Section 6, yielding histograms of defect dimensions, , in ) where   are the means of the distribution in the respective direction .The analysis yields  = 45.5% and 0.05% for the CuMnAs/GaP and the CuMnAs/Si sample, respectively.The results of the analysis for all samples are summarized in Fig. 6(e), where their 2Δ 2 / ̅ are plotted as a function of the corresponding defect .The observed trend directly reveals a correlation between these two quantities [shown in Fig. 6 (e) by a guide to the eye].Remarkably, the scaling between the conductivity anisotropy and  holds also for the measurements on GaAs and Si substrates where we found unexpected trends of the conductivity anisotropy vs. thickness  (Fig. 5).The increased 2Δ 2 / ̅ in thicker CuMnAs/GaAs is, indeed, related to more elongated defects in this sample, and the surprisingly large conductivity anisotropy in CuMnAs(20)/Si also scales well with the determined .Moreover, the reversed phase α 2 of σ THz,0 (α) in this sample is consistent with the elongation of defects in the [1-10] substrate direction (opposite to CuMnAs on GaP and GaAs), yielding  < 0. This motivates us to verify whether such a large  of CuMnAs films on non-polar Si substrates can be related to the substrate parameters.

Effect of vicinal substrates
Inducing anisotropic properties of thin films by growth on vicinal substrates is a known technique used in MBE deposition 35 .For example, a significant anisotropy in the conductivity of isotropic metals 36 , semiconducting quantum wells 37 , or in the morphology of microstructural defects in semiconducting thin films 38 has been observed on miscut (100) Si substrates.To address whether an unintentional miscut of the used substrates could explain the negative and large  of the CuMnAs(20)/Si film, the atomic force microscopy (AFM) imaging of the etched-off substrate part of the sample was performed in Fig. 6(f).Here, we can indeed observe small terraces-like features in the form of asymmetric "saw-like" modulation of the surface, indicating a possible small vicinality in the order of 0.1°.On the other hand, an AFM imaging performed on the substrate part of CuMnAs(9)/Si, where small and positive  and 2Δ 2 / ̅ were observed, shows a considerably different surface morphology of etched substrates (Fig. S7).
To further test the hypothesis, the sample set was complemented by three 20-nm-thick CuMnAs films grown in a series under identical conditions on two intentionally miscut GaAs substrates of the vicinality of 2° in [110] or [1-10] directions and on a reference non-vicinal GaAs substrate.The obtained conductivity modulation  THz,0 (α) is plotted in Fig. 7(a).The sample grown on the reference nonvicinal GaAs substrate shows consistently a similar modulation, 2Δ 2 / ̅ = 9.1% with α 2 = 95°, as compared to the CuMnAs(20)/GaAs sample shown in Fig. 5 and grown in a different MBE chamber.In contrast, the sample on the [1-10]-vicinal substrate shows a considerably higher anisotropy (2Δ 2 / ̅ = 16.1%, 2 = 93°), caused by a formation of defects elongated in the [110] direction.Interestingly, the [110]-miscut substrate even leads to an anisotropy in the perpendicular direction (2Δ 2 / ̅ = 7.1%,  2 = 4°), surpassing the original anisotropy related to the polarity of the non-vicinal GaAs.From these findings, we conclude that the vicinality of substrates can affect the nucleation of defects during growth and it can even be used to control the resulting conductivity anisotropy.

Local conductivity and morphology
Finally, we extend the phenomenological correlation of the conductivity anisotropy and  of defects to a more microscopic understanding.The local conductivity of the CuMnAs(10)/GaP film was investigated by THz-SNOM, yielding both the AFM-like maps of the surface, shown in Fig. 7(b) as color maps, and the amplitude of the scattered THz pulses, presented as contours with labels indicating the relative THz amplitude decrease in percent.We observe a clear correlation between the defects of the film and the locally scattered THz amplitude.If we limit ourselves only to a qualitative observation, we can interpret the findings as a clear correspondence between the surface morphology and the local conductivity, confirming the defect-related origin of the macroscopic anisotropy of the conductivity in CuMnAs films.

Discussion
The presented experiments show that the time-domain THz spectroscopy is a reliable, fast, and versatile method to quantify the anisotropic conductivity of CuMnAs and, potentially, of other thin films.The extracted angular modulation of the conductivity is consistent over multiple repeated measurements and with conventional DC electrical characterization.Compared to the DC probing using Hall bars, it brings several advantages: (i) It is non-destructive and contactless as it requires no surface patterning.(ii) It provides a high angular resolution of practically arbitrary precision, which is limited in the case of DC characterization by the number of patterned devices, allowing for a precise determination of anisotropic axes and exclusion of parasitic contributions of other than uniaxial (twofold) symmetries in the signal.(iii) Since the THz probing of the conductivity is averaged over an arbitrarily large area according to a chosen spot size (in our case ~1 mm 2 ), a single experiment can yield statistically averaged conductivity and its anisotropy even in strongly non-uniform samples.
The anisotropic conductivity of all the studied CuMnAs films, including samples on GaAs and Si substrates that did not follow the expected thickness dependence 19 , was entirely explained by the induced anisotropy of the growth defects.Their anisotropy of the surface morphology, , was directly determined from the SEM images and the local variation of the conductivity inferred from the THz-SNOM technique.Vice versa, the THz conductivity  THz,0 (α) was used for a fast and nondestructive determination of the orientation and  of the growth-induced defects.Indeed, the method revealed unexpected defect anisotropy on non-polar Si substrate, indicating an unintentional miscut in the used Si wafer.
The possibility of the control of the induced defect  and related anisotropic conductivity using intentionally vicinal substrates can play an important role in the magnetic recording in CuMnAs.The shape and orientation of defects with a size on the order of tens of nanometers, i.e., the same range as observed in our samples [Fig.6 (c)], were shown to affect also the magnetic anisotropy in AF.They lead to an effective shape-induced magnetic anisotropy 20 , even though AF possess vanishingly small net magnetization.Indeed, very recently, Reimers et al. directly experimentally showed by photoemission electron microscopy and X-ray diffraction techniques that a magnetic domain structure in CuMnAs thin films is correlated with their growth defects 39 .

Conclusion
In summary, we have shown that THz time-domain spectroscopy can be used to measure the growthdefect related anisotropic conductivity of CuMnAs thin films in a reliable, contactless, and versatile manner.The method also proved to be less sensitive to the film degradation as compared to the electrical characterization by Hall bars, requiring a lithographical processing.At the same time, it allows for an analysis of strongly non-uniform thin films due to the averaging of the conductivity over the large area of the THz spot size.The uniaxial conductivity anisotropy was observed on samples with various thicknesses and grown on GaP, GaAs, and Si substrates.Its magnitude and orientation with respect to the crystallographic directions in the sample were fully explained by the elongation and orientation of growth defects and related to the corresponding THz-SNOM detected local change of the conductivity.We demonstrated that the anisotropic conductivity can be controlled not only by the film thickness but also by using vicinal Si substrates.The understanding and control of defect morphology, presented in this paper, can lead to a future optimization of spintronic functionality in antiferromagnetic devices based on CuMnAs.

Hall bar fabrication
For the fabrication of the chessboard like structure [Fig.1(c)] and the Hall-bar devices, first, a positive photoresist was deposited on the sample by spin-coating it at 4000 RPM and baked on the hotplate.Next, the resist was exposed using Microwriter ML3 PRO, developed using an alkaline developer, and etched in a 1:400 solution of phosphoric acid.

Electrical measurements
Electrical measurements were carried out with two electrical setups, one consisting of Keithley SourceMeter 2400 (current source) and Keithley MultiMeter 2000 (voltmeter) and the other utilizing NI DAQ card USB-6211.In the first setup, the readout current was set to 100 µA to prevent heating, and, in the case of the second setup, the reading voltage was set to 0.2 V, and the readout current was measured as a voltage drop over a known resistor.Corresponding voltages were measured with a four-point method for each segment in the Hall bar.The conductivity in the corresponding direction was calculated from the known dimensions of segments.

THz measurements Time domain THz spectroscopy
The linearly polarized picosecond pulses of THz radiation were generated by exciting the spintronic emitter 29 by a train of laser pulses (1030 nm, 170 fs long, fluence 0.15 mJ/cm 2 , repetition rate 10 kHz) and focused on the sample, forming a ~ 800-m-wide spot (FWHM).The transmitted radiation () was detected by the electrooptical sampling using a 110-cut 2-mm-thick GaP crystal 21 , yielding the electrical signal ().Since its image in the frequency domain, (), equals the product of the transfer function of the setup and the transmitted field (), the transfer function cancels in ratio (ω, α)/  ref (ω, α) = (, α)/ ref (, α) =  ′ where  ref and  ref are the electrooptical signal and electric field for transmission through the bare substrate.
To study the anisotropy of transmission, the sample was attached to a rotational holder with an angular resolution of 0.2°.If the THz beam axis and the axis of rotation of the holder do not coincide, small displacements of the beam spot on the sample surface are induced during the sample rotation.
To avoid this, a special alignment technique was introduced (see Supplementary Note 2).After the alignment, samples were installed with a precision ~2° into the rotational holder without moving it.The measured angular dependence of THz transmission was globally shifted by 3° due to the THz polarisation rotation tilt from the vertical direction induced by parabolical mirrors (see Fig. S8).

THz-sSNOM
A THz scanning near-field optical microscope THz-SNOM (Neaspec) was used to investigate local changes in conductivity.Broadband THz pulses (0.2-1.5 THz) are focused on a PtIr tip (50 nm radius) which oscillates above the film surface with the typical tapping frequency of 50-100 kHz [Fig.1(b)].
The detected scattered THz electric field carries information about the local conductivity.Scanning the sample surface with the tip thus provides local conductivity measurements with a spatial resolution of ~ 50 nm.The simplest models used to describe the underlying physics consider the electrostatic approach.In this case, the near-field contribution to the scattered THz electric field can be expressed as  scatt ∝ (1 +  p ) 2 α eff  inc , where  inc is the incident field, α eff is the effective tip polarizability and  p the Fresnel reflection coefficient for p-polarized light. 40,41The near-field interaction between the sample and the tip (and consequently the local conductivity) is incorporated in α eff which depends nonlinearly on the tip-sample distance.As a result of the tip oscillation α eff is modulated at the tip frequency as well as at higher harmonics of the tip frequency.By demodulating the THz signal at higher demodulation orders, we can efficiently extract the useful signal, which depends on the local conductivity.A 2D scan of the sample surface [Fig.7(b)] was obtained by scanning the sample surface at the peak electric field of the scattered THz pulse detected at the second demodulation order.The quantitative determination of the local conductivity requires an appropriate model for the description of the whole system.However, on a qualitative level, we can relate THz signals to variations of local conductivity.

Scanning electron microscopy
Defects in CuMnAs lead to a modification of morphology of the film surface; thus, we studied the surface of the samples by SEM as well as by AFM.To analyse the observed defects, SEM image processing was performed.The used approach is based on looking for certain characteristics of the defects along the two orthogonal directions (x and y-axis).For this, several cuts were applied along the x and y directions of the recorded image.In between those cuts, a peak finder method was applied and the found peaks were fitted by a set of Gaussian distributions.From the obtained data sets, histogram analysis was performed, for more details, see Supplementary Note 3.

Atomic force microscopy
For all AFM scans, Bruker Dimension ICON AFM was operated in semi-contact Peak Force QNM mode using Aspire conical force modulation (CFM) probes.The symmetrical shape and combination of small tip radius (guaranteed < 10 nm) and sharp tip cone angle (30°) of these probes ensure true and symmetrical representation of all sample features.For processing the data, Gwyddion software 42 was used with a focus on local surface roughness, disregarding the natural slope of the sample surface.

Supplementary Figures
Fig. S1: Scanning edge measurement and determination of beam size.The EOS signal  of the maximum of the transmitted THz waveform (points) as a function of the knife edge position  with a corresponding fit by Eq.S4.The fit yields the full width at half maximum (FWHM) of (865 ± 63) μm.The inset shows a zoomed part for a variation of  corresponding to the modulation observed with a rotating razor (cf.Fig. S4).The dashed lines show the maximal modulation of 8.5%, which yields an estimated mismatch of rotation axes ~40 µm.S2.  3) and summarized in Table S1  The RMS of THz transmission signal () as a function of rotation angle α in the rotating razor method, detailed in Supplementary Note 2. The maximum observed variation of () is 8.5 %, whose major part (~7.2%) originates from the unidirectional component (UAD, ∝ sin()).Apart from the UAD component, we also observe small contributions (< 2%) corresponding to the uniaxial (UAX, ∝ sin(2)) and the mixed unidirectional-uniaxial components (UAM, ∝ sin(3)).The UAX and UAM components originate likely from the asymmetry of the THz beam spot.Using the measurement in Fig. S1(a) and its inset, we determine the maximal apparent movement of the beam over the sample surface of 40 μm.This value is considerably smaller than FWHM of the THz spot size (828 μm).The same measurement but with an empty holder is shown in b), demonstrating a negligible contribution of the rotating holder itself.

Fig. 1 |
Fig. 1 | Samples and experimental schemes.(a) A schematic of the THz transmission probing of the conductivity σ THz of CuMnAs films.The incident linearly polarized THz pulse is transmitted through the film with [110] substrate crystal direction forming an angle α with the polarization plane.The transmitted beam has a reduced amplitude due to the local anisotropic σ THz = σ THz (α), resulting in a measured electrooptical signal ().(b) A sketch of the SNOM setup where the THz pulse is focused on the sample surface and a scanning tip, resulting in a near-field interaction with resolution ~50 nm.The scattered THz radiation is related to the local σ THz .(c) The chessboard pattern of CuMnAs films (orange areas) used for THz experiments.The drawing depicts the advantage of the contactless method: accessing the global characteristics by averaging local responses with an arbitrary angular resolution of α without an impact of inhomogeneity of the film.(d) A sketch of the lithographically prepared Hall bar device for DC electrical characterization.The electrical current (~100 μA) is sent through Hall bar segments (black arrows) oriented under four angles α = 0°, 45°, 90°, and 135° with respect to [110] substrate crystal direction; the measured drop of potential provides the local resistance R(α).

Fig. 3 |
Fig. 3 | THz conductivity.Extracted real (full symbols) and imaginary parts (open symbols) of THz conductivity σ THz (ω) for 20-nm-thick CuMnAs on GaP using Eq.(1) for three different orientations α of the sample.The solid curves are fits by the Drude model [Eq.(2)].The value of the fit parameter σ 0,THz is obtained from Eq. (2) and plotted by dashed horizontal lines.The data points at ω = 0 are the DC conductivities σ DC .

Fig. 5 |
Fig. 5 | Thickness dependence of conductivity anisotropy.Conductivity contrast of the two-fold component

Fig. 6 |
Fig. 6 | Correlation of THz conductivity contrast with defect morphology.SEM images of (a) CuMnAs(10)/GaP and (b) CuMnAs(9)/Si films with (c, d) corresponding histograms of defect size () distributions in [110] and [1-10] substrate directions.(e) Two-fold component of the conductivity contrast 2Δ 2 / ̅ as a function of the anisotropy of the surface morphology  of defects.The blue line is a guide for the eye.Error bars are considered as ±Δ 1 / ̅.(f) An AFM image of the etched-off substrate part of CuMnAs(20)/Si sample, probing terrace-like surface structures.

Fig. 7 |
Fig. 7 | Manipulation of conductivity contrast by vicinal substrates and THz-SNOM measurements.(a) Anisotropy of  THz,0 in CuMnAs(20)/GaAs samples grown on normal (green points) and vicinal substrates with vicinality of 2° in direction [110] (black points) and [1-10] (red points).Curves with the corresponding colors are fits by Eq. 3. (b) The relative amplitude decrease in percent of the scattered THz pulses from CuMnAs(10)/GaP measured by the THz-SNOM scanning of the sample surface (contours with labels).The corresponding AFM image of the same area is shown by the color map.
As a reference, the DC conductivity is determined by conventional electrical 4-probe measurements on lithographically defined Hall bars (length 250 μm, width 50 μm) patterned along selected crystallographic directions [Fig.1(d)],including the [110] and[1-10] directions where the anisotropy of conductivity is the most pronounced.The Hall bars are distributed over an area comparable to the dimensions of the THz spot (~1 mm 2 ), however, each individual Hall bar probes only ~1% of this area.

Fig. 2 (
Fig.2(a) shows typical THz transmission waveforms () through a 20-nm-thick CuMnAs film on a GaP substrate, and the corresponding spectra.When we rotate the polarization direction from [110] axis of the substrate, i.e., increase α from 0 to 90°, the amplitude is clearly reduced.Since the overall shape of the THz trace is not changed, we can explore the α-dependence of the signal amplitude by taking the root-mean-square (RMS) of each waveform (), normalizing its offset (average over α) to unity and plotting it in Fig.2(b).The observed two-fold symmetry of the RMS amplitude  N (α) is emphasized by fitting the data by ΔScos[2(α + α 0 )] + 1; the fit yields a modulation of 2Δ = 16.6% and  0 =1.5°.

Fig. S2 :
Fig.S2: THz conductivities  THz extracted for the rest of the listed samples.Full and empty points correspond to the real and imaginary parts of  THz , respectively, and full lines are fits by the Drude model [Eq.(2)].Dashed lines, corresponding to  ,0 , show that approximation by a constant function is legitimate.Regression coefficients corresponding to the presented figures are summarized in TableS2.
Fig. S3: Modulation of THz signals for all the listed CuMnAs thin films.Normalized THz transmission signal   plotted as a function of angle α for all CuMnAs samples grown on different substrates.The unidirectional and uniaxial components were extracted by fitting the modulations to Eq. (3) and summarized in TableS1.

Fig. S9 :
Fig. S9: Dispersion of refractive indices of GaP and GaAs from literature.(a) The dispersion relations of GaP in the THz spectral range according to Wei et al 5 .in the temperature range from 290 to 295 K (coloured lines) and Tanabe et.al 1 .(dashed black line).(b) The relative change in the refractive indices according to both references.(c) The dispersion relation of GaAs in the THz spectral range according to Moore et al 2 .

Table S2 : Summary of regression coefficients from the spectral dependence of the conductivity according to Eq. (2).
The last subscript  in  , ,  corresponds to the angle of the sample rotation.The samples from the study of the impact of the substrate vicinality are marked by an asterisk. .