Systematic Study of Ferromagnetism in CrxSb2−xTe3 Topological Insulator Thin Films using Electrical and Optical Techniques

Ferromagnetic ordering in a topological insulator can break time-reversal symmetry, realizing dissipationless electronic states in the absence of a magnetic field. The control of the magnetic state is of great importance for future device applications. We provide a detailed systematic study of the magnetic state in highly doped CrxSb2−xTe3 thin films using electrical transport, magneto-optic Kerr effect measurements and terahertz time domain spectroscopy, and also report an efficient electric gating of ferromagnetic order using the electrolyte ionic liquid [DEME][TFSI]. Upon increasing the Cr concentration from x = 0.15 to 0.76, the Curie temperature (Tc) was observed to increase by ~5 times to 176 K. In addition, it was possible to modify the magnetic moment by up to 50% with a gate bias variation of just ±3 V, which corresponds to an increase in carrier density by 50%. Further analysis on a sample with x = 0.76 exhibits a clear insulator-metal transition at Tc, indicating the consistency between the electrical and optical measurements. The direct correlation obtained between the carrier density and ferromagnetism - in both electrostatic and chemical doping - using optical and electrical means strongly suggests a carrier-mediated Ruderman-Kittel-Kasuya-Yoshida (RKKY) coupling scenario. Our low-voltage means of manipulating ferromagnetism, and consistency in optical and electrical measurements provides a way to realize exotic quantum states for spintronic and low energy magneto-electronic device applications.

The term "topological insulator" (TI) was first introduced in 2007 to generalize the two-dimensional quantum spin Hall state to three dimensions 1,2 . The key reasons were the presence of time reversal symmetry (TRS) and spin-momentum locking 3,4 . Since then, researchers have been in search of exotic quantum phenomena which can potentially revolutionize the field of condensed matter physics. Transition metal doping in TIs is predicted to break TRS which opens a surface gap at the Dirac point 5,6 . This has led to the recent experimental observations of the topological magnetoelectric effect 7 , induction of a magnetic monopole 8 and the quantum anomalous Hall effect (QAHE) 9 . Hence a wide range of potential industrial applications have found their way into the literature such as magnetic sensing 10 , information storage 10 , phase change memories 11 and various spin injectors for spintronic devices 12 . In the quantized version of the anomalous Hall effect (AHE), the topologically protected state has a dissipationless current flowing along the edge of a 2D surface of a magnetically doped TI in the absence of a magnetic field. In this context, Cr-doped Sb 2 Te 3 has been the object of consideration since the discovery that it Scientific  becomes ferromagnetic when Cr replaces Sb 13 . The AHE is a well-recognized phenomenon and has been extensively studied in transition metal doped dilute magnetic semiconductors (DMS) and complex oxide ferromagnets 14 . To ascertain the general origin of the AHE, various theories have also been put forward 14 . In TIs, on the other hand, it is now well established that the origin relies on a scattering-independent, intrinsic mechanism which can be described in terms of the Berry phase effect in crystal momentum space 9, [14][15][16] . The evolution of the AHE with temperature and magnetic field can be linked to the magnetization, M, of the sample through the following relationship 14 : ρ xy = R o B + R s M, where ρ xy is the total Hall resistivity, B is the applied magnetic field, R o = 1/nec (e being the electron charge and n the carrier concentration) is the ordinary Hall coefficient arising from the Lorentz force experienced by electrons/holes, and R s is the anomalous Hall coefficient. On dividing this equation by ρ xx 2 , we see that the equation expresses the additivity of the Hall currents, that is, the total Hall conductivity σ xy T . As ρ ρ   2 , hence enabling the field and temperature dependence in M to be extracted directly from magnetotransport data. Given this context, there is also a strong motivation to understand the mechanism of the magnetic behaviour in TIs. Two models have been proposed in the literature: the Van Vleck mechanism 17 which is caused by the large spin susceptibility of the valence electrons in the band-inverted TI materials and the Rudderman-Kittel-Kasuya-Yosida (RKKY) 5 coupling, where the magnetic ions can indirectly couple with the assistance of itinerant electrons. Consequently, the former is independent of the carrier density and is referred as "bulk ferromagnetism", while in the latter case the neighbouring magnetic moments couple via a carrier-mediated mechanism. Electrically controlling the magnetic properties of doped TIs also holds great importance for future device applications. For example, by gate tuning the carrier density, the coercivity or AHE may be modulated 18,19 . The use of electrolyte gating has also been demonstrated in undoped TIs 20 , while it has not been applied to magnetically doped TIs. Recently, we characterized Cr x Sb 2−x Te 3 magnetic topological insulator (MTI) samples using x-ray magnetic circular dichroism (XMCD) and observed carrier mediated coupling 21 . In addition, we also reported that a good crystalline order is maintained in molecular beam epitaxy (MBE) grown ~60 quintuple layer (QL) thick films of Cr x Sb 2−x Te 3 (x = 0.15, 0.26, 0.42) using x-ray diffraction (XRD) and atomic force microscopy 13 . In this study, we present a comprehensive comparison of the variation in ferromagnetism in highly doped Cr x Sb 2−x Te 3 films (x ranging from 0.15 to as high as 0.76) through gated electrical transport, magneto-optical Kerr measurements and terahertz time domain spectroscopy. We conclude that the ferromagnetic order in the films is via the carrier-mediated RKKY mechanism.

Results and Discussion
Cr-doped Sb 2 Te 3 thin films with a typical thickness of 20 nm were grown by MBE in an ultra-high vacuum chamber (UHV) with a base pressure lower than 2 × 10 −10 Torr using a two-step growth process described in the Methods section. X-ray diffraction (XRD) was carried out to confirm their tetradymite-type crystal structure, shown in the Fig. 1(a). All samples display the (0 0l) peaks (l = 3, 6, 9, …), confirming that the films grow along the c-axis direction. After comparing possible characteristic diffraction peaks from pure Sb, Te and their other compounds such as SbTe, SbTe 2 and Sb 2 Te 5 , no traces of any secondary phase formation were found in any of the samples, up to and including the highest doped sample (x = 0.76). For increasing Cr doping concentration, a reduction in the c-axis lattice parameter from 30.393 Å in a sample with x = 0.15 to 30.177 Å (x = 0.41), 30.057 Å (x = 0.58) and 29.834 Å (x = 0.76) for the highest doped samples was observed, marked by a shift in the (0 0l) peaks (dotted line), consistent with a substitutional doping scenario. XPS measurements were performed to explore the effect of Cr doping on the bonding properties. For the XPS analysis the samples were prepared in a similar manner as for electrical and optical measurements discussed below. Figure 1(b) shows the shift in the spectra of the Sb 3d peaks upon introducing the Cr dopant. In pristine sample of Sb 2 Te 3 the Sb 3d peak is expected at 528-529 eV. A small shift to 530.5 eV in the present case for the sample with the lowest doping concentration (x = 0.15) can be attributed to surface oxidation (labelled with arrows). Upon increasing the Cr concentration, the peaks shift towards the un-oxidized, pristine value of 528 eV, thus indicating that the doping with Cr prevents further oxidation of Sb 2 Te 3 , consistent with earlier reports 11,22 . In other words, Cr atoms are more prone to oxidation compared to the Sb atoms, and upon substitution, the degree of surface oxidation of the sample is reduced. This conceivably demonstrates that Cr atoms are substituting the Sb atoms in the structure. Correspondingly, upon fitting the peaks, we observe that it is possible to change the doping levels in Cr x Sb 2−x Te 3 from x = 0.15 to x = 0.76. A negligible shift in the XPS pattern of Te 3d (Supplementary Figure S1) is observed upon increasing the dopant concentration for the peaks at 573, 583 eV (Te 3d), and 575, 586 eV (Te-O). Moreover, it is difficult to ascertain the substitution of the Cr at Te sites due to the fact that the peaks corresponding to the Te (3d) and Cr (2p) binding energies closely resemble each other. Nevertheless, we have demonstrated in our previous work that Cr substitutes an ion of a smaller ionic radius, i.e., Sb 13 .
We used magneto-transport and magneto-optical measurements down to 1.8 K to characterize the ferromagnetic ordering in a series of samples with progressively increasing Cr doping, x from 0.15 to 0.76. Hall traces show that all Cr x Sb 2−x Te 3 films have hole-type carriers and display a similar trend, hence we take the highest doped samples with x = 0.76 and 0.58 as examples and all further data presented here are recorded for these samples unless specified otherwise. Figure 1(b,f and c,g) shows the evolution of the Hall resistance, R xy , and polar Kerr angle, θ K , respectively, as a function of temperature and magnetic field, B. Clear, long-range ferromagnetic ordering indicating the easy axis of orientation pointing out-of-plane is observed in both MOKE and transport measurements. We also detected that the coercive field, H c , and the saturated Hall resistance at B = 0 were higher for the sample with x = 0.58 than for x = 0.76 although its Curie temperature, T c , was lower. Furthermore, we studied the Hall transport, R xy , with different directions of the magnetic field, B, with respect to the sample as shown in Supplementary Figure S3.1. As the angle θ of the sample changes from out-of-plane (θ = 90°) to in-plane (θ = 0°), the value of R xy reduces and the slope gradually changes from positive to negative until we see a parabolic dependence at θ = 0°. This parabolic behaviour at θ = 0° indicates a strong out-of-plane spontaneous magnetization at zero field, confirming that the magnetic moments of the sample prefer to be in the perpendicular direction. This feature may be favourable for spintronic applications, where perpendicular magnetic anisotropy is more common than in plane magnetism 18,23 . Figure 1 xx xx xx 0 measured from 180 K to 1.8 K. The butterfly shaped hysteresis characterizes the negative MR caused by spin dependent scattering of carriers 24 as local magnetic ordering comes into play at T c . The distance between the two peaks for all temperatures corresponds to the coercive field H c . T c can be estimated as the temperature when H c becomes zero. At this point, the long-range ordering disappears and a positive MR is observed corresponding the weak anti-localization (WAL) commonly observed in pristine TI samples 25,26 . An undoped 20-nm-thick Sb 2 Te 3 sample was also measured which showed WAL [see Figure  To understand this further we studied the trend comparing the anomalous Hall conductivity, σ xy A , and Kerr rotation, θ K , as a function of temperature for both samples as shown in Fig. 3(a,c). Both curves are strikingly concave over a broad range of temperatures, similar to the data reported by Chang et al. 18 in their transport data, but different from that of Zhou et al. 28 in their SQUID data (both in Cr-doped TIs). Furthermore, the surface-favoured sensitivity of MOKE measurements might account for the discrepancy with transport measurements 29 , which probe the whole film. Magnetic properties of Cr-doped Sb 2 Te 3 can also be affected by the laser illumination during MOKE measurements. When the laser is focused to a 3 μm spot size on the sample at T = 10 K, the coercivity decreases with increasing laser intensity as shown in Fig. 3(b). This relation fits well to a power law (dashed line) from 0.1 V to 3 V photovoltage, which corresponds to approximately 0.1 mW to 3 mW energy incident on the film. Locally induced heat from the laser is likely to account for this coercivity relation 30 . Below 0.05 mW laser power (0.05 V photovoltage) the coercivity plateaus at ~0.215 T, showing good agreement with AHE measurements at 10 K. This suggests, as compared to electrical transport measurements, that the laser power below 0.5 mW is unlikely to significantly affect magnetism in the film. Figure 3(d) shows the H c dependence on temperature carried out at laser power = 0.5 mW. Both measurement sets are in good agreement with each other. Theoretically, T c can be established as the point when σ xy A and H c both fall to zero at zero magnetic field, but in experiments, a tail is commonly observed above T c . This may be due to sample inhomogeneity or a finite remanent field arising from the superconducting magnetic coils in the cryostat 31 . Hence it is best to accurately determine T c by using Kouvel-Fisher (K-F) 32 and Arrott-Noakes 33 plots.  Applying an ion gel as a gate dielectric allows for the efficient control of the carrier densities at very low operating voltages, making it superior compared to other gating methods which suffer from high leakage currents, slow polarization responses, and limited transistor operation speeds at less than 100 Hz 35,36 . A DEME-TFSI based ion gel was used (we refer the reader to the methods section on device fabrication and electrical transport for further details). By applying a positive gate voltage, the DEME + cations accumulate on the flat surface of the Hall bar channel and an electric double layer which acts as a capacitor with nanoscale thickness forms at the liquid/ solid interface. Figure 4(a) shows the Hall resistance R xy modulation with gate bias fixed at −3 V, 0 V and +3 V at 200 K for a sample with x = 0.58 cooled to 1.8 K. The amplitude of the hysteresis loop increases, showing an increase in the AHE as the gate bias is lowered from +3 V to −3 V. The leakage current in the ion gel dielectric was less than 100 nA. The total carrier density p changes from 1.89 × 10 14 cm −2 at −3 V to 9.31 × 10 13 cm −2 at +3 V. The inset on the top of Fig. 4(a) shows R xx vs V g sweep at 200 K (the temperature where gel modulation is possible before cooling to 1.8 K) displaying R xx increasing as V g increases. The bottom inset of Fig. 4(a) shows the temperature dependent σ xy A deduced from the saturated behaviour at +3, 0 and −3 V. An increase in the σ xy A at −3 V is explained by a larger hole concentration on applying an electric field, resulting in enhanced ferromagnetic properties (AHE), directly suggesting a hole-mediated ferromagnetic interaction among local Cr spins. Note that there is no apparent change in T c with gate voltage. To check if the gate control of the magnetic properties is reproducible, the measurements were repeated in the opposite sequence, i.e., first +3 V, followed by 0 V, and then −3 V as shown in Supplementary Figure S4(b). The results were replicated within ~10%, which can be attributed to slow polarization relaxation of the gel 20 . In Fig. 4(b) we plot the total Hall resistance versus perpendicular magnetic field at 1.8 K for different Cr concentrations. The coercive field and saturated Hall resistance increase with Cr concentration, except for the sample with x = 0.76. A similar trend was also reported by Lee et al. in Mn doped Bi 2 Te 3 37 , which they attributed to structural flaws arising from a Bi bilayer sandwiched between two QLs. Our XRD data shows no parasitic peaks [see Fig. 1(a)] over the entire scan range, even for the highest doped sample, where a reduction in the c-lattice parameter corresponds to Sb being replaced by Cr. The homogeneity of magnetic ordering in transition metal doped TIs has been under debate and a few possible scenarios are proposed such as super-paramagnetism 38 , long-range ferromagnetism, antiferromagnetism 39 and cluster formation 40 . These scenarios depend on the location and concentration of the Cr atoms in the crystal. For example, Cr atoms sitting at interstitial sites may form clusters and couple antiferromagnetically, while Cr replacing Sb coupled ferromagnetically 41 . Our results may perhaps be explained by the spontaneous coexistence of ferro-and antiferromagnetic coupling in the highest doped sample leading to a lower saturation resistance at 0 T for x = 0.76. In order to further our understanding and elucidate the mechanism of magnetism, a detailed study was carried out to comprehend the relationship between carrier densities, T c , and Cr concentration trends using terahertz time domain spectroscopy (THz-TDS). It is well-known that device processing makes it more challenging to probe the surface states of pristine TI thin films 42 , as TIs are very sensitive to water and organic solvents. To circumvent this issue, we employed contact-free and non-invasive THz-TDS to study optical conductivities and determine the carrier densities and mobilities for all the samples, and compare them directly with the results from electrical transport measurements. The carrier damping rate in TIs (typically~10 −13 s −1 ) lies in the THz frequency range (0.1-2.2 THz), making broadband THz spectroscopy a particularly sensitive probe of TI carrier dynamics. Moreover, the energies typical of collective quasiparticles such as optical phonons, have a fingerprint across the energetic range of the THz radiation (0.4-4 meV) making it a powerful technique to study TIs 27 . The time-resolved THz transmission through all Cr x Sb 2−x Te 3 thin films was measured at 4 K as shown in Fig. 5(a). The primary transmitted THz field intensity shows a systematic reduction with increasing Cr concentration x [see inset in Fig. 5(a)] which signifies an increased free carrier absorption in the film. To further quantify this behaviour, we extracted the carrier densities of each sample.
Using the Tinkham's equation for thin films 43 and substituting for the complex Drude conductivity as , we obtain the following relationship between the imaginary and the real parts [see Figure S5.1(a,b) of the Supplementary Information] of the transmission coefficient: where φ is the phase angle between the sample and substrate waveforms, ω is the angular frequency and τ is the scattering lifetime for the carriers. Plotting tan φ as a function of frequency [ Fig. 5(b)], and fitting it with a linear regression, the slope yields the scattering lifetime τ [inset to Fig. 5(b)]. Furthermore, the scattering lifetime τ, obtained from THz-TDS, was used to calculate the THz mobility using μ = τe/m*(assuming the bulk hole effective mass m* in Sb 2 Te 3 is 0.78 m e , with m e as the electron rest mass), as shown in Fig. 5(c).The carrier concentration p can then be obtained using the following relationship between sheet conductance G 2D and p: G 2D = G(ω → 0) = μep. This yields the plot shown in Fig. 5(c), directly comparing the values of p and μ extrapolated from the slope of R xy vs B at high fields [from Fig. 4(b)]. The carrier densities (and mobilities) in both measurements increase (decrease) roughly linearly with the Curie temperature T c [T c obtained from Fig. 3(f,h)] yielding the carrier dependence of the magnetic ordering temperature. It is interesting to note that the values of p obtained from the THz measurements tend to be smaller than those deduced from the Hall transport measurements. We used the bulk hole effective mass m* = 0.78 m e in calculating the values for the THz measurements 44 . Due to the anisotropic nature of the upper and lower valence bands in Sb 2 Te 3 the effective mass varies from m* = 0.034 m e to m* = 1.24 m e 44,45 . This is likely to be one of the origins for the quantitative discrepancy in the parameters obtained from THz and transport measurements. Furthermore, Ar + ion milling used during the Hall bar processing has been reported to increase the transport carrier density in topological insulators 46 . Figure 5(d) shows the relationship between T c and xp 1/3 . In the case when magnetism is mediated through carriers in the mean field approximation, the Curie temperature is given by 39 : , where S is the spin quantum number of Cr, n is the number density of Cr in the material, J is the exchange interaction constant between localized Cr spin and itinerant holes, and χ is susceptibility of itinerant hole spins. In the above equation, χ is characterized as: , where m* is hole effective mass, h is Planck constant, and p is hole density. The above two equations indicate that in mean field theory, T c will be proportional to xp 1/3 . We plotted T c with respect to xp 1/3 in all samples with results obtained from electrical transport and THz measurements [ Fig. 5(d)]. Our results demonstrate a good proportionality between T c and xp 1/3 , clearly supporting the validity of the mean field approximation in the parabolic band model, and strongly suggesting RKKY mediated magnetism in our Cr x Sb 2− x Te 3 films. This behaviour is similar to that reported by Zhou et al. 28 and Li et al. 47 . The inset of Fig. 5(d) illustrates the proportionality between the Cr concentration x and the carrier density p with a monotonic increase in p with x also consistent with the mean field theory.
We further performed temperature dependent THz-TDS on the Cr 0.76 Sb 1.24 Te 3 sample (largest Cr concentration) and deduced the corresponding THz conductance spectra [ Fig. 5(e)], also see Supplementary Figure S5.2 for the time domain measurement. A detailed description of the method used to obtain the THz conductance is discussed elsewhere 27 . The THz conductance spectra in Fig. 5(e) shows a Drude type response with a characteristic phonon signature at 1.9 THz, consistent with previous reports of THz measurements on Sb 2 Te 3 and other TIs 48,49 . Figure 5(f) shows the THz conductance response of Cr 0.76 Sb 1.24 Te 3 plotted as a function of temperature. As the temperature is reduced from 300 K to 4 K, the THz conductance decreases rapidly indicating a freezing of the bulk carriers in the TI film. However, the THz conductance begins to gradually increase with a further reduction in temperature due to an insulator-to-metal transition at ~175 K. Such a behaviour can be attributed to the spin disorder scattering that sets in at the paramagnetic to ferromagnetic transition 50,51 . The temperature (~175 K) obtained from our THz measurements is in close agreement with the T c value obtained from the transport measurements, and also matches the resistance vs temperature plot from transport shown in the inset of Fig. 5(f). Introducing a magnetic dopant in TI breaks time reversal symmetry 52 and a bulk type insulator response is expected from the film (conductance decreasing with decreasing temperature). However below 175 K, the THz conductance shows a metallic response as shown in Fig. 5(f), indicating that the magnetism could be RKKY mediated. Table 1 summarizes all sample properties.
In conclusion, we have carried out MBE growth, structural characterization by XRD, and electrical and optical measurements on magnetically doped Cr x Sb 2−x Te 3 TI thin films using XPS, electric transport, MOKE, and THz-TDS. On increasing the Cr doping concentration, the crystal structure remains intact up to x = 0.76 with Cr being incorporated on Sb sites. AHE and MOKE measurements plotted as a function of magnetic field and temperature confirm out-of-plane ferromagnetic ordering and are consistent with each other. We measured a T c of 176 K for the highest doped sample and employed ion gel gating on a sample with x = 0.58 to vary the chemical potential. We observed an increase in the magnitude of the AHE as the level of hole doping was increased by up to 50% with a gate bias variation of only ±3 V, which corresponded to an increase in carrier density by 50%. This directly suggests a strong correlation between carrier concentration and ferromagnetism originating from RKKY interaction. On plotting carrier densities and mobilities for all Cr doped samples obtained entirely from optical THz-TDS, and comparing them directly to transport measurements, we found that the T c obtained from transport was proportional to xp 1/3 , further supporting a mean field approximated RKKY interaction scenario. Our work presents a unique comparison of optical measurements using THz-TDS and MOKE, and electrical transport measurements to achieve a complete characterization of Cr doping in Sb 2 Te 3 thin films and their

Methods
MBE growth of Cr-doped Sb 2 Te 3 . High purity Sb (6N) and Te (6N) were co-evaporated from standard effusion cells along with a high temperature cell for Cr (5N) to obtain high quality stoichiometric Cr-doped Sb 2 Te 3 . We started with a 5-nm-thick, undoped Sb 2 Te 3 seed layer (see ref. 13 for details). The flux ratio of Te per (Sb + Cr) was kept at ~10:1. The Te overpressure ensures reduction in vacancies commonly observed in this material system 53 . The Cr doping concentration was precisely controlled by adjusting the cell temperature to grow the next 15 nm of Cr-doped Sb 2 Te 3 . It was found that the Cr concentrations follow approximately the measured beam flux monitor fluxes. The typical growth rate for our experiment was ~1 quintuple layer/minute (QL/min). Finally, we grew a 3-nm-thick amorphous Te capping layer at room temperature prior to taking the sample out of ultra-high vacuum to avoid contamination.
XPS. X-ray photoelectron spectroscopy (XPS) was measured using a Kα (Thermo Fisher Scientific) x-ray photoelectron spectrometer, equipped with a monochromatic Al Kα source. All XPS spectra were fitted by Gaussian/ Lorentzian convolution functions with simultaneous optimization of the background parameters. The background was modelled using a combination of a Shirley and a Tougaard background.
Device fabrication and electrical transport. After removing the films from the UHV chamber, 5 mm × 5 mm chips were cleaved in a clean room for device fabrication. Micro meter sized Hall bar geometries of dimensions L = 800 µm and W = 200 µm were produced, schematically shown in Figure S4(a) of the Supplementary Information. Standard S1813 photoresist was first spin coated onto the sample, followed by an optical lithography process using a mask pattern and an aligner. The mesa was then defined using Ar ion milling in a vacuum chamber with a calibrated rate of ~100 Å/min. 20/80 nm of Ti/Au were then evaporated as Ohmic contacts for the Hall bar in a thermal evaporator, followed by a standard lift-off process with acetone and isopropanol. The chips were then glued to chip carriers and Au wires were used to bond the contacts onto the pads using a ball bonder. Commercially purchased ionic-liquid N, N-diethyl-N-(2-methoxyethyl)-N-methylammonium bis (trifluoromethylsulphonyl-imide) (DEME-TFSI) was then drop-casted carefully using a micropipette on top of the channel of the Hall bar as shown in Figure S4(b) of the Supplementary Information. The samples were screwed to a probe and dipped into a continuous flow cryostat with a base temperature of 1.8 K equipped with a 9 T superconducting magnet. The Hall, R xy , and longitudinal, R xx , resistances were measured using a standard AC lock-in four-terminal method with the current applied in-plane (along x) and the magnetic field perpendicular to the film. All measurements were carried out with an excitation current of 1 µA at a frequency of 77 Hz. For gating measurements, the ion gel was biased at 200 K to fix the voltage at +3 V or −3 V, before cooling the gel along with the sample to 1.8 K.

MOKE.
The magnetic properties of all Cr-doped Sb 2 Te 3 thin films were characterized by magneto-optic polar Kerr effect (MOKE) measurements. The MOKE describes the polarization change of an electromagnetic wave reflected from the surface of a magnetic material. When a linearly polarized laser is incident and reflected perpendicular to the sample surface, i.e., polar MOKE, the change of polarization degree will be proportional (to first order) to the material's out-of-plane magnetization. The optical path of the polar MOKE experiment is illustrated in Supplementary Figure S2. The sample was mounted on a piezoelectric XYZ stage with 10 nm step size, in the same cryostat as used for the transport measurements. The linearly polarized laser beam from an 850-nm diode laser was focused down to 3 μm diameter onto the sample via an objective lens, and reflected back into the same path. Modulation at 100 kHz was achieved by passing light through a photoelastic modulator (PEM). To minimize unwanted contribution from photoexcitation and room lighting, an 850-nm bandpass filter was placed in front of the photodetector. The Kerr rotation angle 54 can be calculated as: , where J 2 (A) is the first kind Bessel function, A is the PEM retardation angle (kept at π), V AC is the photovoltage at 100 kHz due to the PEM modulation, and V DC is the DC photovoltage.
Terahertz time domain spectroscopy. Broadband terahertz time domain spectroscopy was carried out on all samples with different Cr concentrations, using a Tera K15-T-Light MENLO system. A 60 mW pump laser with 90 fs pulse duration at 1560 nm (repetition rate of 100 MHz) was split into two beam paths: (i) first the beam was focused down to a 40 μm spot onto the THz emitter, resulting in a broadband THz emission with a spot size of ~1 mm, and (ii) the second beam went through the delay stage for THz detection. The temperature dependent Sample p transport (10 13 cm −2 ) p Thz (10 13 cm −2 ) µ transport (cm 2 /Vs) µ Thz (cm 2 /Vs) T c (K) measurements were carried out using a Janis continuous flow cryostat with optical access capable of reaching a base temperature of 4 K. In the ultrathin-film limit, THz conductance spectra were obtained from the normalized transmission using Tinkham's theory 43 . A detailed account of the optical setup and measurement is described elsewhere 27 .