We investigate the anomalous Hall effect in a van der Waals material Fe5GeTe2. We find a distinct difference in the temperature dependence of the anomalous Hall effect associated with the evolution of magnetic states in Fe5GeTe2 films. In the low-temperature region, the anomalous Hall conductivity changes with the longitudinal conductivity, which highlights the substantial contribution from the extrinsic mechanism. The extracted skew scattering coefficient in the Fe5GeTe2 films is an order of magnitude larger than that in transition metal ferromagnets. This result sheds light on the role of the extrinsic mechanism in the anomalous Hall effect in van der Waals magnets.

Ever since graphene was first discovered by developing a simple mechanical exfoliation method,1 quasi-two-dimensional (2D) van der Waals materials have been actively studied in the pursuit of the understanding of the underlying physics and the potential applications of their non-trivial behavior.2–7 Van der Waals materials that exhibit phase transitions, such as superconductivity, ferromagnetism, and antiferromagnetism, have been reported. In particular, van der Waals ferromagnetic materials have drawn great attention as building blocks for spintronic devices.8 So far, Fe3GeTe2 is found to be a promising van der Waals ferromagnetic material with a high Curie temperature (TC ≈ 230 K).9–16 It has been reported that the Curie temperature TC of Fe3GeTe2 thin films can be increased to near room temperature by ionic liquid gating.17 

Recently, inspired by the itinerant ferromagnetism with even higher Curie temperature, research on a van der Waals ferromagnet Fe5GeTe2 has become active.18–25 Fe5GeTe2 has Fe(1), Fe(2), and Fe(3) sites18,19 [see Fig. 1(a)]. The complex magnetic structure of Fe5GeTe2 gives rise to multiple magnetic phase transitions, which may involve a transition between ferromagnetic and ferrimagnetic states.18 The Curie temperature of Fe5GeTe2 has been reported to be around room temperature (TC ≈ 270–310 K). Despite its promise as a 2D ferromagnet for spintronic devices, the spin-dependent transport in Fe5GeTe2 has not been fully understood.

FIG. 1.

(a) A schematic illustration of the crystal structure of Fe5GeTe2. The Te, Fe, and Ge atoms are shown in yellow, orange, and purple, respectively. (b) A schematic illustration of the device structure for the Hall measurement, where the numbers in parentheses represent the thickness. The Au/Pt electrodes are also shown. In order to make good contact with electrodes, the side of Fe5GeTe2 flakes was etched by an Ar ion beam milling process. (c) The cross-sectional profile of the Fe5GeTe2 flake before processing. (d) An optical microscopic image of the Fe5GeTe2 device.

FIG. 1.

(a) A schematic illustration of the crystal structure of Fe5GeTe2. The Te, Fe, and Ge atoms are shown in yellow, orange, and purple, respectively. (b) A schematic illustration of the device structure for the Hall measurement, where the numbers in parentheses represent the thickness. The Au/Pt electrodes are also shown. In order to make good contact with electrodes, the side of Fe5GeTe2 flakes was etched by an Ar ion beam milling process. (c) The cross-sectional profile of the Fe5GeTe2 flake before processing. (d) An optical microscopic image of the Fe5GeTe2 device.

Close modal

In this Letter, we report a large extrinsic anomalous Hall effect in Fe5GeTe2 flakes. We investigate the anomalous Hall effect in mechanically exfoliated Fe5GeTe2 at different temperatures T. At T < 100 K, where the magnetization is almost independent of T, we find that the anomalous Hall conductivity changes with the longitudinal conductivity, which enables the extraction of the intrinsic and extrinsic contributions to the anomalous Hall effect. We find that the extrinsic skew scattering coefficient in the Fe5GeTe2 thin films is an order of magnitude larger than that in transition metal ferromagnets. This result sheds light on the role of the extrinsic mechanism in the anomalous Hall effect in van der Waals ferromagnets.

We mechanically exfoliated a Fe5GeTe2 crystal with Nitto tape (Nitto Denko Co., SPV) and subsequently transferred Fe5GeTe2 flakes onto a MgO(4 nm)/Ti(3 nm)/SiO2-substrate. The MgO and Ti layers were sputtered by radio frequency (RF) magnetron sputtering before the mechanical exfoliation because of their potential to enhance the adhesion with Fe5GeTe2 like plasma oxidation of the substrate.26,27 In order to achieve large-area flakes, after placing the tape with Fe5GeTe2 on the substrate, we moved the substrate onto a hot plate of 100 °C for 2 min to promote the adhesion between the Fe5GeTe2 flakes and substrate and then removed the adhesive tape after the sample was cooled down to room temperature. All the exfoliation processes were done under inert conditions in a glovebox with an N2 atmosphere and an O2 concentration of around 10 ppm. Without being exposed in air, the exfoliated sample was immediately transferred into a sputtering chamber, and a 4-nm-thick SiO2 capping layer was subsequently deposited on top of the Fe5GeTe2 flakes to prevent oxidation. The structure of the sample is shown in Fig. 1(b), where the thickness tF of the Fe5GeTe2 flake was determined by atomic force microscopy [Fig. 1(c)]. For electric measurements, the Fe5GeTe2 flake was patterned into a six-probe Hall bar by standard photolithography technique with a negative resist mask, followed by an Ar ion beam milling process. The probe of the Hall bar outside the rectangle area indicated in Fig. 1(d) was elongated by a sputter-deposition of Pt(60 nm)/Ti(3 nm) to improve the contact between Au(220 nm)/Ti(3 nm) electrode and the Hall bar. We investigate the anomalous Hall effect for the Fe5GeTe2 devices with thicknesses of tF = 38.6 and 52.4 nm. The out-of-plane field sweeping measurements were performed at T ranging from 5 to 300 K with the applied field up to 1 T. During the measurements of longitudinal and Hall resistances, we applied an AC with a frequency of 17 Hz and tune its amplitude between 10 and 30 μA to reduce any damage from possible thermal effects.

Figure 2(a) shows the T dependence of the longitudinal resistivity ρxx for the Fe5GeTe2 devices. A kink of ρxx appears around T = 150 K, indicating a gradual magnetic transition of the Fe(1) site with decreasing temperature.18 This temperature is consistent with the magnetic transition temperature where the magnetic anisotropy of Fe5GeTe2 changes from in-plane to out-of-plane.28 In Fig. 2(b), we show T dependence of the magnetization M for a bulk Fe5GeTe2 crystal under a magnetic field of 2 T. This result shows that M is almost constant in the low-temperature region (T < 100 K), which is consistent with previous reports.24,29,30 Here, we note that the thickness of the Fe5GeTe2 devices, tF = 38.6 and 52.4 nm, is thick enough to ensure that the magnetic properties of these devices are the same as those of the bulk crystal.14 In Fig. 2(c), we show the Hall resistance Rxy measured at different T. The magnetic transition temperature, which is derived from changes in magnetic anisotropy, can also be determined whether the hysteresis loop is closed in the Hall resistance Rxy data, and it is found to be around 150 K.28 The anomalous Hall resistance RAHE can be extracted from the intercept of a linear fit to the data of Rxy as a function of external fields, whose magnitude are large enough to saturate the magnetization of Fe5GeTe2 [see the dashed lines in Fig. 2(d)]. RAHE at each T is obtained by using RAHE=(Rxy+Rxy)/2.

FIG. 2.

(a) Temperature T dependence of the longitudinal resistivity ρxx measured for the Fe5GeTe2 films with tF = 38.6 nm (blue) and 52.4 nm (red). (b) T dependence of the magnetization M for a bulk Fe5GeTe2 crystal under a magnetic field of 2 T measured using a magnetic property measurement system based on a superconducting quantum interference device. (c) The Hall resistance Rxy for the Fe5GeTe2 film with tF = 52.4 nm as a function of a magnetic field H applied perpendicular to the film at different temperatures. (d) Perpendicular magnetic field H dependence of the Hall resistance Rxy for the Fe5GeTe2 film with tF = 52.4 nm at T = 90 K. Rxy+() represents extrapolated values obtained by fitting Rxy using a linear function at the positive(negative) high magnetic fields. W and L are the width and length of the Hall bar, respectively. (e) T dependence of the anomalous Hall resistivity ρAHE of the Fe5GeTe2 films with tF = 38.6 nm (blue) and 52.4 nm (red).

FIG. 2.

(a) Temperature T dependence of the longitudinal resistivity ρxx measured for the Fe5GeTe2 films with tF = 38.6 nm (blue) and 52.4 nm (red). (b) T dependence of the magnetization M for a bulk Fe5GeTe2 crystal under a magnetic field of 2 T measured using a magnetic property measurement system based on a superconducting quantum interference device. (c) The Hall resistance Rxy for the Fe5GeTe2 film with tF = 52.4 nm as a function of a magnetic field H applied perpendicular to the film at different temperatures. (d) Perpendicular magnetic field H dependence of the Hall resistance Rxy for the Fe5GeTe2 film with tF = 52.4 nm at T = 90 K. Rxy+() represents extrapolated values obtained by fitting Rxy using a linear function at the positive(negative) high magnetic fields. W and L are the width and length of the Hall bar, respectively. (e) T dependence of the anomalous Hall resistivity ρAHE of the Fe5GeTe2 films with tF = 38.6 nm (blue) and 52.4 nm (red).

Close modal

Figure 2(e) shows the T dependence of the anomalous Hall resistivity ρAHE = RAHEtF for the Fe5GeTe2 devices with tF = 38.6 and 52.4 nm. We find that the T dependence of ρAHE is nonmonotonic, consisting of an increase of ρAHE upon lowering the temperature, followed by a decrease in magnitude starting around 100 K. This tendency is quite similar to that observed in a single crystal Fe5GeTe2 from a previous study.19 

When the temperature is in the range of 100 K <T<TC, Fe5GeTe2 has been suggested to be ferrimagnetic or a canting of magnetic moments.18 In this temperature range, the observed change in ρAHE can be attributed to the change in M with T. The change in ρAHE resulting from the change in T from 100 to 260 K is at most ∼50%, which can be roughly explained by the change in M [as seen in Fig. 2(e)]. At T < 100 K, the magnetic phase of Fe5GeTe2 evolves to a state with glassy cluster24 or helical magnetism.25 

Now, by using the results for ρAHE and ρxx, we can plot the T dependence of anomalous Hall conductivity, σAHE=ρAHE/ρxx2, which is valid when ρxxρAHE [see Fig. 3(a)].31, Figure 3(a) shows a peak of σAHE around 100 K, which is lower than the magnetic transition temperature of T = 150 K where the magnetic anisotropy of Fe5GeTe2 changes between in-plane and out-of-plane. In the following, we focus on the anomalous Hall effect observed for the Fe5GeTe2 films at T < 100 K. In this low-temperature region, we neglect the change in the magnetization M induced by changing T for simplicity [see Fig. 2(b)]. To explore the mechanism of the anomalous Hall effect and separate each contribution to the observed σAHE, we employ an empirical relation for the AHE analysis given as31 
σAHE=(ασxx01+βσxx02)σxx2σint,
(1)
where σxx is the longitudinal conductivity and σxx0 is the residual longitudinal conductivity. The first, second, and third terms correspond to the contributions from the extrinsic skew scattering, side-jump, and intrinsic Berry phase mechanisms, respectively. Here, σint is assumed to be independent of the thickness, while the extrinsic skew scattering conductivity σSK is different in the two Fe5GeTe2 devices with different thicknesses. The reason for this difference is that σint is independent of σxx and σxx0, while the anomalous Hall conductivity due to the skew scattering, σSK=ασxx01σxx2, depends on σxx and σxx0, where the skew scattering coefficient α is assumed to be independent of the thickness. In Fig. 3(b), we plot the σAHE as a function of σxx2 for the Fe5GeTe2 flakes. It can be seen that the σAHE changes linearly with σxx2 when T < 100 K, indicating a coexistence of the intrinsic and extrinsic contributions to the anomalous Hall conductivity. Using Eq. (1), α and σint in the Fe5GeTe2 devices with different thicknesses can be obtained from T dependence of σAHE, and they are determined to be α38.6 nm = −3.80%, α52.4 nm = −3.11%, σint 38.6 nm = 178 Ω−1 cm−1, and σint 52.4 nm = 147 Ω−1 cm−1, where αtF and σinttF are the skew scattering coefficient and intrinsic anomalous Hall conductivity with a thickness of tF. Note that we approximate σxx at 5 K as σxx0 and neglect the side-jump contribution because it is generally negligible compared to the intrinsic and skew scattering contributions.32,33
FIG. 3.

(a) T dependence of σAHE for the Fe5GeTe2 devices with tF = 38.6 and 52.4 nm. (b) The anomalous Hall conductivity σAHE plotted as a function of σxx2 for the Fe5GeTe2 films with tF = 38.6 nm (blue and light blue) and 52.4 nm (red and light red), where σxx is the longitudinal electric conductivity. The blue and red lines show the linear fitting results for each device in the temperature range from 5 to 80 K. The inset shows σAHE plotted as a function of σxx for the Fe5GeTe2 films. (c) T dependence of σint in the Fe5GeTe2 device together with the measured values of σSK for the Fe5GeTe2 devices with tF = 38.6 and 52.4 nm at T from 5 to 80 K. (d) T dependence of σxx for the Fe5GeTe2 devices with tF = 38.6 and 52.4 nm at T from 5 to 80 K.

FIG. 3.

(a) T dependence of σAHE for the Fe5GeTe2 devices with tF = 38.6 and 52.4 nm. (b) The anomalous Hall conductivity σAHE plotted as a function of σxx2 for the Fe5GeTe2 films with tF = 38.6 nm (blue and light blue) and 52.4 nm (red and light red), where σxx is the longitudinal electric conductivity. The blue and red lines show the linear fitting results for each device in the temperature range from 5 to 80 K. The inset shows σAHE plotted as a function of σxx for the Fe5GeTe2 films. (c) T dependence of σint in the Fe5GeTe2 device together with the measured values of σSK for the Fe5GeTe2 devices with tF = 38.6 and 52.4 nm at T from 5 to 80 K. (d) T dependence of σxx for the Fe5GeTe2 devices with tF = 38.6 and 52.4 nm at T from 5 to 80 K.

Close modal
On the other hand, Eq. (1) can be converted to a resistivity counterpart given as
ρAHE=(αρxx0+βρxx02)+σintρxx2,
(2)
which is valid when ρxxρAHE.31 According to the Matthiessen rule, Eq. (2) can be simplified to ρAHE0=αρxx0+(β+σint0)ρxx02 at 5 K. By substituting the values of ρAHE = ρAHE0 and ρxx = ρxx0 at 5 K for the Fe5GeTe2 films with tF = 38.6 and 52.4 nm, the skew scattering coefficient is determined to be α = −4.60%.31 Since in Eq. (2), only the third term depends on the resistivity of the sample, by using ρxx at each T for the Fe5GeTe2 films with tF = 38.6 and 52.4 nm with the parameters of ρxx0 and α determined at 5 K, we can extract the intrinsic σint contribution of anomalous Hall conductivity as a function of T, where we neglect the side-jump contribution because it is generally negligible compared to the intrinsic and skew scattering contributions.32,33 As shown in Fig. 3(c), σint is almost independent of the temperature ranging from 5 to 80 K. The determined intrinsic anomalous Hall conductivity, σint ≈ 200 Ω−1 cm−1, is comparable to that reported for bulk Fe5GeTe2 (90 Ω−1 cm−1)34 and Fe5GeTe2 bilayers35 estimated from first principle calculations. The values of α and σint is consistent with αtF and σinttF obtained from Eq. (1). Also, we show the T dependence of the anomalous Hall conductivity due to the skew scattering σSK=ασxx01σxx2 and the longitudinal conductivity σxx for the Fe5GeTe2 flakes [see Figs. 3(c) and 3(d)]. Since σSK is proportional to the square of σxx, σSK is enhanced by decreasing T.

It is worth noting that the skew scattering coefficient α = −4.60% of the Fe5GeTe2 films obtained in this work is larger than that of 3d transition metal ferromagnets and materials with sizable skew scattering contributions, such as Pt/Co/Pt/Cr/MgO(001) (α = −0.165%), Fe/MgO(001) (α = −0.149%), Co/MgO(001) (α = −0.151%), Ni/MgO(001) (α = −0.070%), Fe/GaAs(001) (α = −0.370%), Fe–Co alloy (α ≈ 1.12%), and KV3Sb5 (α varying from 0.75% to 1.72%).31–33,36–39 Regarding the sizable skew scattering, recently, Fujishiro et al. reported a giant Hall angle 18% mainly from the skew scattering contribution in a chiral magnet MnGe thin film.40 By establishing an Anderson impurity model, the large anomalous Hall effect is attributed to the skew scattering through the formation of a three-spin cluster, namely spin-cluster scattering. The large skew angle may modify the scaling plot of the AHE, making this contribution even dominant in the moderately dirty regime.41 At T < 100 K, a possible transition to a state with glassy cluster24 or the presence of helical magnetism25 may alter the scaling plot of the AHE similar to the scenario of the spin-cluster scattering, leading to a large contribution of the skew scattering.

In summary, we have investigated the anomalous Hall effect in van der Waals ferromagnet Fe5GeTe2 flakes with a thickness in the scale of tens of nanometers. We found that the T dependence of the anomalous Hall conductivity is nonmonotonic with a peak value appearing around 100 K. At T < 100 K, we found that the anomalous Hall conductivity is linear to the longitudinal conductivity, which evidences the substantial extrinsic contribution to the anomalous Hall effect in the Fe5GeTe2 films. We found that the skew scattering coefficient associated with glassy cluster24 or helical magnetism25 is an order of magnitude larger than that of transition metal ferromagnets. This finding demonstrates the importance of the extrinsic mechanism in the anomalous Hall effect in the van der Waals magnet, providing a fundamental understanding of spin-dependent transport in this class of materials.

This work was supported by JSPS KAKENHI (Grant Nos. 22H04964 and 22K14561), JST FOREST Program (Grant No. JPMJFR2032), and Spintronics Research Network of Japan (Spin-RNJ). R.S. was supported by JSPS Grant-in-Aid for Research Fellowship for Young Scientists (DC1) (Grant No. 21J22062).

The authors have no conflicts to disclose.

Ryuki Suzuki: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Project administration (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). Tenghua Gao: Investigation (supporting); Methodology (supporting); Supervision (supporting); Writing – review & editing (supporting). Hiroki Nakayama: Investigation (supporting); Methodology (supporting); Supervision (supporting); Writing – review & editing (supporting). Kazuya Ando: Conceptualization (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (equal); Project administration (lead); Supervision (lead); Visualization (lead); Writing – original draft (equal); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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