Amorphous Ferromagnetic Metal in van der Waals Materials

Amorphous solids are non‐equilibrium states of matter that lack long‐range structural order, and are recognized as key materials in electronics. Although 2D van der Waals materials have been intensively studied in the wide field of materials science, their amorphous states have been less studied experimentally. Here, a van der Waals ferromagnetic semiconductor CrGeTe3 transforms into an amorphous ferromagnetic metal upon irradiation with high‐energy Xe ions. Notably, the Curie temperature of the amorphous state reaches 200 K, which is three times higher than that of the crystalline phase. The anomalous Hall conductivity in the amorphous phase is governed by the extrinsic skew‐scattering mechanism, although conventional theory predicts that skew scattering is dominant only in ultra‐clean ferromagnetic metals. The present results call for a new theory of the anomalous Hall effect in highly disordered ferromagnetic conductors. Moreover, the unique change in magnetic and transport properties due to amorphization of the van der Waals material is expected to open up a new research field in materials science.


Introduction
Since the breakthrough of graphene in 2004, 2D materials have attracted much interest because of different physical and chemical properties from 3D materials. [1]The possibility of layer-bylayer control and the absence of surface dangling bonds allow arbitrary stacking of different 2D materials to form diverse van der Waals heterostructures without regard to lattice mismatch. [2]owever, although 2D materials with various properties have DOI: 10.1002/aelm.202300609been studied intensively, intrinsic ferromagnetism had not been experimentally discovered in 2D materials until recently. [2,3]This is mainly because the long-range magnetic order is strongly suppressed by thermal fluctuations in 2D systems according to the Mermin-Wagner theorem.In 2017, two 2D materials, CrGeTe 3 and CrI 3 , were found to host intrinsic ferromagnetic order down to bilayer and monolayer limit thanks to magnetic anisotropy counteracting the thermal fluctuations. [4,5]Such 2D ferromagnetic materials provide an ideal platform for exploring new spintronic phenomena. [6]oreover, the recent discovery of twist engineering [7,8] has enhanced the potential of 2D magnetic materials, and research on 2D magnetism has become extremely vigorous in recent years.While typical 2D ferromagnet CrGeTe 3 has been intensively studied in the research field of 2D materials, this material has recently been shown to be an excellent phase-change material. [9]otably, CrGeTe 3 exhibits an inverse resistance change, that is, a low electrical resistance in the amorphous phase and a high electrical resistance in the crystalline phase.The crystalline state is a semiconductor with a band gap of 0.74 eV, while the amorphous state is still a semiconductor but has a smaller band gap. [10]he origin of the inverse resistance change has been attributed to local structural change around Cr atoms that is linked to the change in electronic state. [11]A theoretical study based on ab initio molecular dynamics (AIMD) simulation pointed that there are short Cr-Cr bonds in the amorphous phase, leading to the ptype conduction observed in the amorphous phase. [12]It has been confirmed that Cr nanoclusters are present even in as-deposited CrGeTe 3 films. [13]Unfortunately, amorphous CrGeTe 3 samples have been limited to thin films [9] and powders, [14] and systematic experiments using bulk samples are still lacking.
In this study, we tried to prepare amorphous CrGeTe 3 bulk samples by means of high-energy heavy-ion irradiation.The irradiation with fast heavy ion beam forms nanocolumnar amorphous defects in samples. [15]If the density of heavy ions is sufficiently high, the amorphous phase is expected to spread uniformly throughout the samples.According to a model of energy transfer from incident ions known as the thermal spike model, [16] the amorphization due to heavy ion irradiation should be a highly non-equilibrium process, since the time scale of temperature increase/decrease is as fast as ∼10 ps. [17]In fact, the very rapid quenching by Xe +14 irradiation to bulk CrGeTe 3 crystals produces an amorphous metallic phase, which has not been demonstrated before by usual thermal quenching or room-temperature sputtering.Interestingly, the amorphous metallic phase exhibits ferromagnetic order with a Curie temperature (T C ) of up to 200 K, as shown below.

Results
Xe +14 -ion-beam irradiation was performed at the tandem accelerator in Japan Atomic Energy Agency.The ion energy was 200 MeV and the beam fluence was 1 × 10 14 cm −2 .Here, the samples were fixed on thermally oxidized Si substrates with silver paste to avoid sample dropping during ion-beam irradiation.See also Figure S1 (Supporting Information) for the sample images.Figure 1a shows the X-ray diffraction (XRD) results for a CrGeTe 3 single crystal before ion-beam irradiation and for three irradiated samples (#1, #2, and #3).The XRD data for the singlecrystalline sample shows clear (006) and (0012) peaks, consistent with previous reports. [18]The small additional peaks observed at approximately 40°are attributed to silver paste on thermally oxidized Si substrates, as demonstrated in Figure S1 (Supporting Information).
Notably, the XRD spectra are completely different for the irradiated samples; both the (006) and (0012) XRD peaks are strongly suppressed, as shown in Figure 1a.Tiny crystalline peaks are discernible in #1, but are lower than the detection limit for #2 and #3.The irradiation dose appears to be higher in #2 and #3 than in #1.Although the set ion-beam fluence is the same between the samples, the irradiation dose depends on the sample position during the irradiation (see Methods).Also, no additional peaks due to sample decomposition are observed.The strong suppression of the XRD peaks indicates the amorphization of CrGeTe 3 by ion beam irradiation.
To confirm the amorphization of CrGeTe 3 , we performed micro-Raman measurements.As shown in Figure 1b, some Raman active modes are observed in a single crystal, whereas only background signals are observed for the irradiated samples (#1, #2, and #3).The Raman modes in the single crystal are assigned according to the previous report. [18]For example, the E 3 g mode involves the twisting vibration of Cr-Ge octahedra and the shear vibration of the Ge atoms, while the A 1 g mode involves the rocking vibration of three Te atoms around one Cr atom and the stretching vibration of two Ge modes. [18]The absence of crystalline signals in the irradiated samples supports the amorphization of CrGeTe 3 .
Transmission electron microscopy (TEM) measurements were performed for #3 in Figure 1c.No signs of crystalline order were observed as far as we measured.The diffuse rings in the diffraction pattern in the inset to Figure 1c are typical of amorphous materials with well-defined nearest-neighbor coordination and interatomic distances.We also performed elemental mapping in the amorphous phase, as shown in Figure S2 (Supporting Information).Cr, Ge, and Te elements are distributed uniformly, and no aggregation of the elements is observed.

Metallic transport and ferromagnetic order in amorphous samples
Temperature (T) dependence of longitudinal resistivity  xx for a single crystal and the irradiated samples is shown in Figure 2a.
Here the silver paste residue on the back side of the samples was carefully removed.The single-crystalline sample shows a semiconducting behavior and the  xx value is above the detection limit < 80 K.The magnitude and overall temperature dependence is similar to those reported in previous papers. [19,20]In contrast, the irradiated samples show completely different transport properties.The  xx magnitude at room temperature decreases from that of the crystalline phase, and remains small even at 2 K.The finite resistivity at the lowest temperature means that the amorphous CrGeTe 3 is not semiconducting, but metallic.The resistivity weakly increases with decreasing temperature, which can be attributed to significant scattering due to structural disorder.Although smaller resistivity in the amorphous phase than in the crystalline phase has been reported for CrGeTe 3 films in T > 77 K, [10] metallic resistivity has never been observed in the amorphous phase.
The magnetic properties also change dramatically from those of the crystalline phase.Figure 2b shows temperature dependence of magnetization M for the single-crystalline sample and the irradiated samples.The magnetization of the single crystal increases rapidly at ≈70 K owing to the ferromagnetic transition.[21] By contrast, the magnetic property for the irradiated samples is totally different from the single crystal and also from the paramagnetic behavior reported for amorphous films. [22]As shown in Figure 2b, ferromagnetic order is still observed in all the amorphous samples.Notably, T C reaches ≈200 K for #2 and #3, which is three times higher than that of the crystalline phase.The magnetization value of the irradiated samples is 40−80% of that of the single crystal at 2 K.The resistivity and magnetization measurements thereby show that the bulk CrGeTe 3 amorphized by Xe-ion irradiation is a ferromagnetic metal with a high T C .

Anomalous Hall effect in CrGeTe 3 irradiated with Xe ions
To further investigate the ferromagnetic properties of the amorphous samples, the magnetic field (H) dependence of magnetization M and Hall resistivity  yx is shown in Figure 3.For the single crystal, although ferromagnetic order is observed in the M -H curve, ferromagnetic transport is not observed owing to the high resistivity at low temperatures.As shown in Figure 3a, the Hall resistivity is linear with the magnetic field over the entire temperature range, and its slope increases with decreasing temperature.The transport carrier is dominated by holes, and the hole density is estimated to be 3.5 × 10 16 cm −3 at 200 K.
In contrast to the results for the single crystal, the anomalous Hall effect, a typical ferromagnetic transport proportional to magnetization, is clearly observed for the irradiated samples, as shown in Figure 3b-d.In line with the ferromagnetic order observed in isothermal magnetization curves, the anomalous Hall resistivity ( A yx ) is observed ˂ 150 K for #1.The sign of the anomalous Hall resistivity is negative, and the anomalous Hall contribution decreases with increasing temperature.The anomalous Hall resistivity almost disappears at 150 K, which is consistent with the M -H results.This onset temperature is notably higher than the T C of the single crystal.
For #2 and #3, the anomalous Hall effect is also observed; notably, it is accompanied by a high coercive field.As shown in Figure S3 (Supporting Information), the magnitude of the coercive fields at 2 K is similar for magnetic fields applied parallel and perpendicular to the sample plane.This suggests that the magnetic anisotropy is small in the amorphous samples, while the single crystal exhibits a strong magnetic anisotropy with an out-of-plane easy axis. [21,23,24]The sign of the anomalous Hall resistivity is negative, as in #1.The anomalous Hall contribution decreases with increasing temperature and almost disappears at 250 K, which is consistent with the magnetization measurements.
Another interesting feature of the anomalous Hall effect for #2 and #3 is that an additional anomalous Hall resistivity with a positive sign is observed.This is especially apparent for #3 in Figure 3d; see also the magnified view of the high-temperature  yx data in Figure S4 (Supporting Information).Hence, in the heavily irradiated samples, there are two ferromagnetic parts showing the anomalous Hall resistivities with opposite signs.Judging from the lowest resistivity of #3, the proportion of the ferromagnetic part with positive anomalous Hall resistivity increases as the irradiation dose increases.
Transverse magnetoresistance also varies systematically between the irradiated samples.As shown in Figure S5 (Supporting Information), negative magnetoresistance is observed for all the irradiated samples, and its magnitude decreases in the order of #1, #2, and #3.A clear butterfly-shaped hysteresis appears at low temperatures for #2 and #3.These results confirm the emergence of long-range ferromagnetic order in the amorphous samples.
Temperature dependence of anomalous Hall conductivity Here,  A xy is calculated from the anomalous Hall resistivity at 0 T for #2 and #3, whereas it is estimated by extrapolating the  yx data from a high field for #1.As shown in Figure 4a, the  A xy magnitude increases in the order of #1, #2, and #3, as the longitudinal conductivity  xx increases in the same order.Notably, | A xy | is ≈ 10 −1 Ω −1 cm −1 , which is much smaller than the magnitude of anomalous Hall conductivity for typical ferromagnetic crystals (100-1000 Ω −1 cm −1 ).We also examine the scaling relation between the Hall and longitudinal conductivities in Figure 4b.This plot indicates that | A xy | ∝  xx .This is consistent with the extrinsic skew-scattering mechanism, [25] but the skew-scattering mechanism is usually dominant over the intrinsic Berrycurvature mechanism in ultra-clean metals with very high conductivity. [26]Note that even if  xx is divided by the carrier density n and  A xy is plotted against the carrier lifetime ≈  xx /n (Figure S6, Supporting Information), the experimental results cannot be explained by the intrinsic mechanism.The observed scaling relation is difficult to explain using conventional theories of the anomalous Hall effect established in ferromagnetic crystals.However, it may not be surprising that the extrinsic contribution related to impurity scattering is dominant in the anomalous Hall effect, because disorder scattering significant in the xx -T curves (Figure 2a).Moreover, because the wave number k is not a good quantum number in amorphous systems lacking a periodic structure, the k-space Berry curvature is ill-defined and thus, the intrinsic contribution can be significantly reduced in our amorphous samples.The greater skew scattering contribution than the intrinsic one was indeed reported for amorphous CoFeB thin films sputtered at room temperature. [27]

Discussion
The amorphous state observed in the Xe-ion irradiated CrGeTe 3 is totally different from the one obtained by thermal quenching or room-temperature sputtering for thin films before; [9,10,14] while our samples are amorphous ferromagnetic metals, the amorphous state in thin films was a narrow-gap semiconductor and basically nonmagnetic with a spin-glass behavior at very low temperatures. [14]This difference is attributable to the different local atomic structures in the amorphous phases between the samples obtained by thermal quenching/room-temperature sputtering and heavy-ion irradiation.Thermal quenching is usually performed by electric pulses with a width of tens of nanoseconds, [9] while a time scale of temperature increase/decrease is as fast as ≈10 ps in the quenching by heavy ion irradiation. [17]Amorphous samples synthesized under different conditions can present different local atomic structures, although both lack a longrange structural order.We also note that in amorphous ferromagnetic thin films such as CoFeB obtained by sputtering at room temperature, [27,28] the conductivity decreases naturally due to disorder, but M and  A xy are rather robust against disorder.Unlike previous studies on amorphous magnetic films, our CrGeTe 3 samples irradiated with heavy ions are more significantly affected by amorphization and exhibit totally different transport and magnetic properties from those of the crystalline phase.
The irradiated CrGeTe 3 samples are fragile, and the exfoliation is no longer possible, indicating that the amorphous state lacks a layered structure.To evaluate the local Cr environment, we have performed Cr K-edge X-ray absorption fine structure (XAFS) experiments for #2.As shown in Figure S7 (Supporting Information), the Fourier-transformed extended XAFS intensity reveals that the Cr─Te bond length of #2 is 2.70 Å, which is shorter than the Cr─Te bond lengths of single crystals (2.78 Å) and the amorphous thin film (2.72 Å). [11] Notably, the Cr─Te bond length of #2 is close to that reported for bulk single crystals under an external pressure of 4.8 GPa. [21]The shorter Cr─Te bond length than that of single crystals is consistent with the increase in conductivity.
Theoretical calculations [12,14] also suggest that modulation of the local atomic structure leads to modulation of the electronic structure, resulting in an increase in conductivity from the crystalline phase.Although precise simulation of local structure in the disordered system may be a formidable task, Previous AIMD simulations showed that the local structural change due to amorphization modifies electronic structure of CrGeTe 3 significantly and the density of states becomes nonzero at the Fermi level. [12,14]t is also noted that, because CrGeTe 3 is not a band insulator but a Mott insulator, [19] strong electron correlation needs to be considered in the electronic structure of the amorphous state.The disordered structure could weaken the correlation effect and decrease the Mott gap.
It is necessary to point out that a ferromagnetic metallic state with T C of 200-250 K has been reported for CrGeTe 3 crystals, when high carrier density is doped by intercalation [20] or ionic liquid gating, [6] as well as when the bandwidth is controlled by pressure. [19]The ferromagnetic order with T C ≈66 K in the initial bulk crystal has been attributed to super-exchange interaction at Cr 3+ ─Te─Cr 3+ bonds with the bond angle of 90 • .As the origin of the enhanced T C in the metallic phase, two mechanisms have been proposed: the double-exchange interaction mediated by carriers [20] and the boost of the ferromagnetic super-exchange interaction due to the change in the charge transfer energy. [19,29]imilar mechanisms can be applied to our case, because the amorphization alters both the carrier density and the local atomic structure.However, the Hall-effect data suggest hole doping by amorphization (Figure S6, Supporting Information), which is incompatible with the double exchange mechanism assuming Cr 3+ ─Te─Cr 2+ hopping.The shortened Cr─Te bond length confirmed by the XAFS measurements and the enhanced conductivity are likely to modify the super-exchange interaction and produce a high-T C ferromagnetic state, as observed in the study of the pressure-induced insulator-metal transition. [19]Note that it was very recently reported that the increase in Cr-Cr distance due to lattice expansion enhances T C of CrGeTe 3 crystals. [31]The ferromagnetic properties of CrGeTe 3 can be significantly altered by slight structural modifications.
Last but not least, CrGeTe 3 is potentially decomposed into other materials that exhibit ferromagnetism and high conductivity during the amorphization.This possibility cannot be ruled out, because the precise structural characterization of amorphous samples is difficult.Regarding the magnetic properties, magnetization and the anomalous Hall effect showed that there are two ferromagnetic components (Figure 3), although these have not been confirmed by polar magneto-optical Kerr effect measurements (Figure S8, Supporting Information).A candidate material as the secondary phase is amorphous Cr─Te binary alloys; in the case of crystals, Cr─Te alloys with various compositions are ferromagnetic metals with high T C up to 300 K:, e.g., CrTe, Cr 2 Te 3 , Cr 3 Te 4 , Cr 5 Te 8 , and CrTe 2 . [30]These binary crystalline alloys have different Cr─Te bond lengths in their local structural motifs.Notably, these Cr─Te binary alloys have a Cr─Te bond length of 2.68─ ─2.73 Å, which is close to the observed value (2.7 Å) for the amorphous sample.Hence, the decrease in the Cr─Te bond length and the change to a local structure close to the Cr─Te alloys potentially give rise to a ferromagnetic metallic state with a high T C .Moreover, the sign of anomalous Hall resistivity for Cr─Te crystalline alloys changes sensitively depending on their composition [32] and strain. [33]This could explain the two anomalous Hall components observed in the heavily irradiated CrGeTe 3 .
In summary, we experimentally investigated the magnetic and transport properties of bulk CrGeTe 3 samples amorphized using a highly non-equilibrium approach of Xe-ion irradiation.Whereas amorphous topological materials have attracted great interest recently, [34,35] less attention has been paid to amorphous 2D materials in condensed matter physics.Our results demonstrated that amorphization has a significant influence on a 2D ferromagnet CrGeTe 3 , and that the initial ferromagnetic semiconductor transforms into an amorphous ferromagnetic metal with an enhanced T c reaching 200 K.The anomalous Hall conductivity is dominated by the skew-scattering mechanism in contrast to conventional theory claiming that the skew scattering makes a major contribution in ultra-clean ferromagnetic metals.The ultra-fast quenching by heavy-ion irradiation could be a valuable approach to investigate the correlation between crystallinity and ferromagnetism in the 2D limit and to explore novel physics in amorphous materials.
Sample Preparation for Heavy Ion Irradiation: Before heavy ion irradiation, CrGeTe 3 single crystals were mechanically exfoliated to a typically 5-30 μm thickness using a scotch tape and then fixed on a SiO 2 /Si wafer using silver paste (Dupont 4922N).After heavy ion irradiation, the samples were immersed in acetone thinner to separate irradiated CrGeTe 3 samples from SiO 2 /Si wafers and remove the remaining silver paste.Photographs and X-ray diffraction data for each step of the sample preparation were shown in Figure S1 (Supporting Information).
Heavy Ion Irradiation: Heavy ion irradiation was performed using the tandem accelerator at Japan Atomic Energy Agency, Japan.The samples were irradiated with 200 MeV Xe 14+ ions at a particle current of 120 nA.Nine samples were simultaneously irradiated with a horizontal scanning beam with the fluence of 1 × 10 14 cm −2 ; however, the irradiation dose varied from sample to sample depending on the sample position during the irradiation.This is mainly because the beam density was distributed in the vertical direction.The samples #1, #2, and #3 had thicknesses of 10 m, 3.5 m, and 4.0 m, respectively.Note that the penetration depth of the ion beam was estimated to be ≈10-20 m using the density of 5.6 g cm −3 for CrGeTe 3 .
Sample Characterization: Primary characterization of the crystal structure of CrGeTe 3 before and after irradiation was carried out using X-ray diffraction (Rigaku) with Cu K radiation.Micro-Raman measurement was performed using a 532 nm laser (LabRAM HR Evolution equipped with an EMCCD camera, HORIBA Scientific) at room temperature.The laser power is 180 μW, and the exposure time was 30 s.The data were accumulated 30 times.Transmission electron microscopy (TEM) was conducted using JEM-2100F (JEOL) with an acceleration voltage of 200 kV.To prepare TEM samples, the irradiated CrGeTe 3 was first placed in a mortar with ethanol and ground into fine particles.The resulting mixture was then transferred onto a microgrid mesh using a syringe.After drying in ethanol for one day, TEM measurements were performed.For elemental mapping measurements, JEM-ARM200F Thermal FE STEM (JEOL) was also used.

Magnetization and Transport Measurements:
Longitudinal resistivity  xx , Hall resistivity  yx , and magnetoresistance were measured using the standard four-probe technique in a Physical Properties Measurement System (PPMS, Quantum Design).Electrodes were formed using silver paste (Dupont 4922N).The maximum magnetic field is ± 9 T. The raw data are symmetrized (anti-symmetrized) with respect to the magnetic field to subtract the influence of electrode misalignment on magnetoresistance (Hall resistivity).Temperature dependence of  xx was measured at a rate of 2 K/min.Magnetization measurement was carried out using a superconducting quantum interference device magnetometer (MPMS3-VSM, Quantum Design).The maximum magnetic field is ± 7 T. Temperature dependence of magnetization was measured at a rate of 2 K min −1 in a field-cooling process under the magnetic field of 0.1 T applied perpendicular to the sample plane.

Figure 1 .
Figure 1.Experimental evidence for amorphous atomic structure of irradiated CrGeTe3.(a).X-ray diffraction (XRD) patterns for an exfoliated single crystal without irradiation, and three irradiated CrGeTe3 samples: #1, #2, and #3.The (006) and (0012) peaks observed in #1 indicate that the crystalline phase remains partially in the sample, while the crystalline peaks are absent in #2 and #3.Small additional peaks due to silver paste on SiO2/Si substrates are also observed at approximately 40°; see also Figure S1 (Supporting Information).b).Raman spectra for the single crystal and irradiated samples.Raman active modes labelled by e.g.E 3 g in the single crystal are not observed in the irradiated samples.c).A high-resolution TEM image for #3.The inset shows the diffraction pattern.

Figure 2 .
Figure 2. Temperature dependence of resistivity and magnetization for irradiated CrGeTe3.a).Temperature (T) dependence of longitudinal resistivity  xx of the single crystal and the irradiated samples.The  xx (T) of the single crystal exhibits a semiconducting trend with a ≈0.2 eV band gap.After the ion irradiation,  xx (T) becomes metallic as shown for #1, #2, and #3.(b).Temperature (T) dependence of magnetization M measured in a field-cooling process under a magnetic field of 0.1 T applied perpendicular to the sample plane.TC of the single crystal is estimated to be 66.7 K from the dM/dT analysis.The irradiated samples exhibit higher TC values.

Figure 3 .
Figure 3. Magnetization and anomalous Hall effect in irradiated CrGeTe3.a-d.Magnetic field (H) dependence of magnetization M (top panel) and Hall resistivity  yx (bottom panel) for the single crystal and the irradiated samples.A magnetic field is applied perpendicular to the sample plane.In the M-H curves, the data shown in blue are at 2 K, and > 25 K, the data were recorded every 25 K up to 100 K (single crystal), 150 K (#1), and 250 K (#2 and #3).In the  yx data for the single crystal (a), the data were taken every 25 K from 100 K to 200 K.For #1 (#2 and #3), the  yx data were taken at 2 K, and > 25 K, every 25 K up to 150 K (250 K).The arrows in the figures indicate the direction from low temperature to high temperature.

Figure 4 .
Figure 4. Anomalous Hall conductivity and scaling relation for irradiated CrGeTe 3 .a). Temperature (T) dependence of anomalous Hall conductivity  A xy (≈  A yx ∕ 2 xx ) defined at zero field for the single crystal and the irradiated samples.b).Scaling relation between | A xy | normalized by the magnetization (M) and longitudinal conductivity  xx for #1, #2, and #3 at 2 K.