Introduction

Electric-field-modulated magnetic properties of materials with perpendicular magnetic anisotropy (PMA) have potential for developing energy-efficient spintronic memory and computing devices1,2,3. Significant progress has been obtained in heterostructures4,5,6,7,8, magnetic tunnel junctions9,10, and spin–orbit torque devices3,11, where magnetic properties of the ferromagnetic (FM) single layer and synthetic antiferromagnetic layer can be tuned through electric-field-induced piezoelectric strains, establishing the relationship between the magnetic properties and strains. Recently, two-dimensional van der Waals (2D-vdW) FM materials have emerged as one of the promising candidates for investigating the manipulation of the magnetic properties under piezoelectric strains, due to their high flexibility, excellent compatibility, and atomic-scale stability12,13,14,15,16. Because of their layered features, these materials are highly sensitive to lattice deformation, making strains from the piezoelectric substrates an effective way to alter the lattice and electronic structures of 2D-vdW FM materials17,18,19. Strain-modulated magnetic properties of the vdW ferromagnets (e.g., CrI3, Fe3GeTe2, CrSBr, FePS3) have been investigated17,18,19,20,21; however, the low Curie temperature (Tc) of these vdW ferromagnets limits their applications in spintronic devices13,15,18. Thus, the strain-modulated magnetic properties of the vdW ferromagnets at room temperature remain elusive.

Most recently, the vdW ferromagnet Fe3GaTe2, with a record-high Tc of 350–380 K and strong PMA with a constant Ku of ~3.88 × 105 J m-3, has attracted considerable attention for the development of room-temperature 2D-vdW spintronic devices22,23,24,25. These include magnetic tunnel junctions with a room-temperature tunneling magnetoresistance of ~85%26, spin–orbit torque devices with a low switching current density of ~1.69 × 106 A cm-227,28 and magnetic skyrmion devices29,30,31,32,33. The performance of these devices is highly dependent on the magnetic properties (especially PMA) of Fe3GaTe2, which is determined by the interplay between local magnetic moments and itinerant electrons34. Therefore, an effective method to modulate the PMA is critical for achieving ultralow-power 2D-vdW Fe3GaTe2-based spintronic devices. The compressive and tensile piezoelectric strains induced by the electric field (E) through the Pb(Mg1/3Nb2/3)0.7Ti0.3O3 (PMN-PT) substrates are significant and easily controllable due to their large piezoelectric coefficient4,5,6,7,8,9,10,11. Hence, the piezoelectric strains provide a promising and effective way to manipulate the magnetic properties of Fe3GaTe2, offering valuable insights into the underlying physical mechanism.

In this study, we systematically investigate the modulation of the PMA in Fe3GaTe2 flakes under the compressive and tensile piezoelectric strains from PMN-PT substrates. To understand the modulation mechanism of the PMA under the different E at room temperature, the anomalous Hall resistance (Rxy) versus (vs.) the external magnetic field (Hext) loops of Fe3GaTe2 flakes were measured. The Rxy vs. Hext loops exhibit a transition from an irregularly to regularly rectangular shape on the (001)-oriented PMN-PT substrate, while a rapid change from irregularly rectangular to narrow-waist shape is observed on (111)-oriented PMN-PT substrate, suggesting a significant change in the PMA. The electric-field-regulated Raman spectra, showing pronounced blueshift and redshift, further reveal that the compressive and tensile piezoelectric strains could reduce and elongate the bond lengths, respectively, leading to corresponding increase and decrease in the vibrational energy of Fe3GaTe2. In addition, first-principles calculations and macrospin simulations are utilized to investigate the modulation of the crystalline structures (e.g. band structures) and magnetic anisotropy energy constants (e.g. K1 and K2) under compressive and tensile strains. Our findings will open a way to design 2D-vdW spintronic devices, based on E regulation of the PMA at room temperature.

Results and discussion

The crystalline structure and magnetic properties of Fe3GaTe2

Figure 1 presents the crystalline structure and magnetic properties of the bulk Fe3GaTe2 sample. The vdW Fe3GaTe2 possesses a hexagonal unit cell with space group P63/mmc22,23,24,25. Its X-ray diffraction pattern (XRD) exhibits only the (00l) diffraction peaks, indicating the oriented growth and high crystallinity, as shown in Fig. 1a. To further analyze the crystal structure, high-resolution scanning transmission electron microscopy (HR-STEM) was performed. The high-angle annular dark field (HAADF) image in Fig. 1b clearly resolves the atomic arrangement along the [110] zone axis, with FeI (red), FeII (orange), Ga (green) and Te (blue) atoms distinctly identified, confirming the high quality of the bulk Fe3GaTe2 sample. To characterize the magnetic properties, the temperature-dependent magnetization curves were measured using field-cooled protocols with an applied Hext of 1000 Oe, along both out-of-plane and in-plane directions, as plotted in Fig. 1c. From these curves, the Curie temperature (Tc) of the bulk Fe3GaTe2 sample is estimated to be around 360 K. Meanwhile, the out-of-plane magnetization of the bulk Fe3GaTe2 sample is significantly larger than the in-plane magnetization in the temperature-dependent magnetization (M−T) curves, indicating strong PMA32. This behavior is further confirmed by the magnetic-field dependence of spontaneous magnetic hysteresis (M−H) loops at different temperatures from 10 to 350 K, as presented in Figs. 1d and S1 (Supplementary Note 1). Typical rectangular M−H loops along out-of-plane orientation are obtained, providing further evidence of the out-of-plane easy axis and the strong PMA, with in-plane saturation field Bs = ~4 T and saturation magnetization Ms = ~40 emu g−1. The Ku of the bulk Fe3GaTe2 sample is calculated to be ~3.5 × 105 J m−3 using the formula \({K}_{{{{\rm{u}}}}}=\frac{{\mu }_{0}{B}_{{{{\rm{s}}}}}{M}_{{{{\rm{s}}}}}}{2}\) (where μ0 is the permeability in free space), consistent with previous works22,33. The magnetic force microscopy (MFM) image also confirms the large-sized labyrinthine domain in the Fe3GaTe2 flakes (146 nm) in Fig. S2 (Supplementary Note 1), which can be effectively modulated by the strain35,36.

Fig. 1: Characterization of Fe3GaTe2 single crystal.
Fig. 1: Characterization of Fe3GaTe2 single crystal.The alternative text for this image may have been generated using AI.
Full size image

a The out-of-plane θ−2θ X-ray diffraction (XRD) pattern of the Fe3GaTe2 single crystal sample (the inset is the crystal structure of Fe3GaTe2). b High-angle annular dark field-scanning transmission electron microscopy (HADDF-STEM) image of the Fe3GaTe2 sample viewed along [110] zone axis. The zoomed HADDF-STEM image exhibits atomic arrangement of FeI (red), FeII (orange), Ga (green) and Te (blue) without lattice distortion. c Temperature-dependent magnetization (M−T) curves of the Fe3GaTe2 flake by using field-cooled protocols with a magnetic field of 1000 Oe along out-of-plane and in-plane directions. d Magnetic hysteresis (M−H) loops of the bulk Fe3GaTe2 sample along the out-of-plane direction under different temperatures from 10 to 350 K.

Piezoelectric-strain-modulated PMA of vdW Fe3GaTe2

Figure 2a illustrates the schematic of the Fe3GaTe2/PMN-PT stack, where the (001)-oriented and (111)-oriented PMN-PT substrates are utilized to generate compressive and tensile piezoelectric strains by applying E, respectively. The XRD patterns of (001)-oriented and (111)-oriented PMN-PT substrates confirm their high crystallinity, as shown in Fig. S3 (Supplementary Note 2). Figures S4–S7 (Supplementary Note 2) present the piezoelectric force microscopy (PFM) images, polarization hysteresis loops and corresponding current (I) vs. E loops of (001)-oriented and (111)-oriented PMN-PT substrates, with micro-patterned surface electrodes in the same device geometry as shown in Fig. 2b (without Fe3GaTe2 flakes). It can be found that the ferroelectric domains of PMN-PT (001) and (111) substrates undergo local reversal under the relatively low E of 6.25 and 12.5 kV m−1. However, both PMN-PT (001) and (111) substrates present large-scale ferroelectric domain reversal as the E increases from 625 to 3750 kV m−1, suggesting the capability of PMN-PT substrates for ferroelectric domain reversal and piezoelectric strain generation4,5,6,7,8,9,10,11,37.

Fig. 2: Piezoelectric-strain-modulated perpendicular magnetic anisotropy (PMA) of Fe3GaTe2.
Fig. 2: Piezoelectric-strain-modulated perpendicular magnetic anisotropy (PMA) of Fe3GaTe2.The alternative text for this image may have been generated using AI.
Full size image

a Schematic of the Fe3GaTe2/PMN-PT stack. b Optical image of the Fe3GaTe2 device on the Pb(Mg1/3Nb2/3)0.7Ti0.3O3 (PMN-PT) substrate, and the schematic of the measurement of the electric-field-modulated anomalous Hall effect (AHE) loops. The green and orange dashed lines demarcate the Fe3GaTe2 and top h-BN layers, respectively. The electric field (E) was applied along the direction of the angular bisector of the current (I) and voltage (V) directions. c, d The anomalous Hall resistance (Rxy) versus an external magnetic field (Hext) loops of the Fe3GaTe2 devices on the (001)-oriented and (111)-oriented PMN-PT substrates at different E. With the increase of E, the irregularly rectangular Rxy vs. Hext loops of the Fe3GaTe2 devices gradually tend to more rectangular loops on the (001)-oriented PMN-PT substrate, but change to narrow-waist shape on the (111)-oriented PMN-PT substrate. e, f The corresponding variation in the coercivity (HC) of the Fe3GaTe2 devices on the (001)-oriented and (111)-oriented PMN-PT substrates at room temperature. The Fe3GaTe2 devices show a dramatic increase of HC by more than ~+89% on the (001)-oriented PMN-PT substrate but a dramatic decrease of HC by more than ~−100% on the (111)-oriented PMN-PT substrate.

To investigate the piezoelectric-strain-modulated PMA, Fe3GaTe2 flakes were exfoliated and transferred onto the PMN-PT substrates with the Ti (5.0 nm)/Pt (15.0 nm) contact electrodes, and then capped with h-BN flakes. Figure 2b exhibits the optical image of the Fe3GaTe2/PMN-PT stack, where the green and orange dashed lines demarcate the Fe3GaTe2 and top h-BN layers, respectively. The thickness of the Fe3GaTe2 flakes on the (001)-oriented and (111)-oriented PMN-PT substrates is characterized to be ~187 and ~128 nm, respectively (see Fig. S8 in Supplementary Note 3). The Rxy vs. Hext loops of Fe3GaTe2 flakes were measured by applying I and measuring the voltage (V), under the in situ E = 0–6.25 kV m−1 along the angular bisector of the I and V directions, as shown in Fig. 2c. In the absence of E, the Rxy vs. Hext loops of Fe3GaTe2 device on the (001)-oriented PMN-PT substrate present irregularly rectangular shapes, consistent across three measurements (see Fig. S9 in Supplementary Note 4). It is also found that the Rxy vs. Hext loops differ from the M–H loops of Fe3GaTe2 single crystal, likely due to the reduced dimensionality and surface effects in the exfoliated flakes22. With increasing positive E from 0.125–6.25 kV m−1, Rxy vs. Hext loops become progressively more rectangular. The coercivity (HC) extracted from Rxy vs. Hext loops displays a dramatic increase from 240 to 454 Oe (see Fig. 2e) with a variation of over +89%. A similar trend is also observed under increasing negative E, where the loops also become more rectangular, and HC gradually increases, as shown in Fig. S10a (Supplementary Note 5). When the E increases from 6.25 to 1125 kV m−1, Rxy vs. Hext loops show progressively more rectangular characteristics and the corresponding HC gradually increases, consistent with the behavior observed at E ≤ 6.25 kV m−1 (see Fig. S11 in Supplementary Note 6). These results indicate that the compressive piezoelectric strain generated by the (001)-oriented PMN-PT substrate significantly enhances the PMA of the vdW Fe3GaTe2.

For Fe3GaTe2 device on the (111)-oriented PMN-PT substrate, Rxy vs. Hext loops initially exhibit irregularly rectangular shapes without an applied E. When applying E from 0 to 0.125 kV m−1 then to 0.625 kV m−1, Rxy vs. Hext loops transform from an irregularly rectangular shape into a narrow-waist shape in Fig. 2d. Correspondingly, HC decreases rapidly from 475 to 325 Oe and eventually to 0 Oe with a variation of more than −100% (see Fig. 2f). A similar trend is observed under increasing negative E, as shown in Figure. S10b (Supplementary Note 5). This dramatic modulation demonstrates that the tensile piezoelectric strain from the (111)-oriented PMN-PT substrate can tilt the magnetic easy axis from the out-of-plane direction to the in-plane direction by weakening the PMA of vdW Fe3GaTe2. Furthermore, Rxy vs. Hext loops of Fe3GaTe2 flakes transition from irregularly to regularly rectangular shapes on the (001)-oriented PMN-PT substrate, while evolving to narrow-waist shapes on the (111)-oriented PMN-PT substrate with increasing the E. This suggests that piezoelectric strain can modulate large-sized labyrinthine domain in the thick Fe3GaTe2/PMN-PT stacks under the E, which could enable long-range and significant modulation of the PMA.

Piezoelectric-strain-modulated vibrational energy of vdW Fe3GaTe2

The PMN-PT substrate has a rhombohedral phase with eight spontaneous polarization directions along the body diagonal, as shown in the inset (red cube) of Fig. 3a. The in-plane compressive or tensile piezoelectric strains arise from ferroelectric domain reversal of PMN-PT substrates. The micro-patterned surface electrodes facilitate local ferroelectric domain reversal in the PMN-PT substrates near the morphotropic phase boundary (MPB), generating effective local strains concentrated around the small-sized Fe3GaTe2 flakes under relatively low E37,38,39,40,41,42. When the E is applied along [110] directions of the (001)-oriented PMN-PT (green cube) or [−101] directions of the (111)-oriented PMN-PT (blue cube), the ferroelectric polarization tends to align with [110] or [−101] directions, which induces a phase transition of PMN-PT from the rhombohedral to monoclinic phase with generating strains of ~0.1% in magnitude40,41. This phase transition probably results in either a decrease or an increase in the lattice plane areas of the (001)-oriented PMN-PT or (111)-oriented PMN-PT substrates, as indicated by the change from the blue dotted line to the orange line. The vdW force between the Fe3GaTe2 and PMN-PT surfaces, as well as the vdW gaps of the layers in Fe3GaTe2 flakes, is strong enough to enable efficient strain transfer43,44. Furthermore, the excellent crystallinity, low defect density and labyrinthine domain of vdW Fe3GaTe2 flakes could further enable efficient piezoelectric strain transmission across the Fe3GaTe2/PMN-PT interface, facilitating long-range propagation while minimizing strain relaxation in the Fe3GaTe2 flakes36,43,44,45.

Fig. 3: Strain-dependent vibrational energy of van der Waals (vdW) Fe3GaTe2.
Fig. 3: Strain-dependent vibrational energy of van der Waals (vdW) Fe3GaTe2.The alternative text for this image may have been generated using AI.
Full size image

a The mechanisms of electric field (E) induced in-plane piezoelectric compressive and tensile strains and further modulating the vibrational energy of vdW Fe3GaTe2. The compressive and tensile strains derive from the electric-field-induced phase change of Pb(Mg1/3Nb2/3)0.7Ti0.3O3 (PMN-PT) from the rhombohedral to monoclinic phases, which decreases and increases the bonds of the Fe3GaTe2, leading to the modulation of the vibrational energy. b, c Raman spectra of the Fe3GaTe2 flakes on the (001)-oriented and (111)-oriented PMN-PT substrates as a function of E. The solid and dotted black lines label the peak positions at different E, respectively. d, e The corresponding Raman shifts of the Fe3GaTe2 flakes on the (001)-oriented and (111)-oriented PMN-PT substrates. With the increase of E, the Raman peak positions of Fe3GaTe2 flakes increase (blueshift) on the (001)-oriented PMN-PT substrate but decrease (redshift) on the (111)-oriented PMN-PT substrates, indicating the in-plane compressive and tensile strains induced by E, respectively.

Raman micro-spectroscopy is a valuable technique to study the local strain state, as the characteristic wavenumbers of phonon modes are sensitive to lattice expansion and contraction18. For Fe3GaTe2, the\({E}_{2g}^{2}\)Raman modes represent the in-plane vibrations of Fe, Ga, and Te34,46,47. The piezoelectric strains (ɛ) can be calculated based on the\({E}_{2g}^{2}\) Raman peak using the equation \(\varepsilon =-\frac{\varDelta \omega }{2\gamma {\omega }_{0}}\), where ω0 is the Raman frequency at zero strain, \(\varDelta \omega\) is the strain-induced Raman shift under E, and γ is the Grüneisen parameter48. In this work, the γ ~ 2 is chosen to calculate the ɛ for Fe3GaTe2 with reference to Fe3GeTe249. In this case, the compressive strain reduces the bond lengths and further increases the vibrational energy while the tensile piezoelectric strain elongates bond lengths and decreases vibrational energy18,46,47, which could result in the blueshift and redshift of Raman spectra, as shown in Fig. 3a. To confirm the mechanism behind PMA modulation via piezoelectric strain, the Raman spectra of Fe3GaTe2 flakes were measured under the in-situ E. The Raman spectra as a function of the E for the Fe3GaTe2 flakes on (001)-oriented and (111)-oriented PMN-PT substrates are plotted in Fig. 3b and c, respectively. As the E increases, the\({E}_{2g}^{2}\)Raman peak of Fe3GaTe2 flakes on the (001)-oriented PMN-PT substrate shifts to a higher wavenumber (blueshift), however, the \({E}_{2g}^{2}\)Raman peak on the (111)-oriented PMN-PT substrate shifts to lower wavenumber (redshift). The positions of the\({E}_{2g}^{2}\)Raman peaks increase from 127.05 to 128.34 cm−1 for the Fe3GaTe2 flakes on the (001)-oriented PMN-PT substrate, as plotted in Fig. 3d, indicating that the Fe3GaTe2 flake experiences compressive piezoelectric strain. On the contrary, the position of the\({E}_{2g}^{2}\)Raman peaks of the Fe3GaTe2 flake on the (111)-oriented PMN-PT substrate decreases from 128.15 to 127.01 cm−1, as presented in Fig. 3e, suggesting that the Fe3GaTe2 flake sustains tensile piezoelectric strain. The values of the ɛ are estimated to be −0.10% ~ −0.19% and 0.14% ~ 0.16% transferred to Fe3GaTe2 flakes from PMN-PT (001) and (111) substrates under applied the E from 1.25 to 6.25 kV m−1, respectively. The compressive (tensile) piezoelectric strains reduce (elongate) the bond lengths and further increase (decrease) the vibrational energy of Fe3GaTe2, resulting in the blueshift (redshift). The piezoelectric-strain-induced blueshift and redshift in the Raman spectra agree with both the theoretical calculations of Γ-point phonon energy variations for the \({E}_{2g}^{2}\) mode under strains in phonon spectra and previously reported experimental results18,50, confirming that the observed Raman shifts are indeed strain-driven modifications. However, precisely determining the magnitude and type of piezoelectric strains in Fe3GaTe2 flakes on the (001)-oriented and (111)-oriented PMN-PT substrates remains challenging due to the undetermined magnitude and sign of the γ of the Fe3GaTe2.

Mechanism of piezoelectric-strain-modulated magnetic anisotropy energy

The magnetic anisotropy energy (MAE) is defined as the difference in total energy per Fe atom between the in-plane and out-of-plane magnetization configurations. A positive MAE value indicates an enhancement of PMA of Fe3GaTe251. To understand the physical mechanism behind the piezoelectric-strain-modulated PMA of Fe3GaTe2 flakes, the electronic structures and magnetic properties under different strains were calculated based on the density functional theory to estimate the MAE value. Figure 4a shows the MAE values as a function of the in-plane strains for the vdW bulk Fe3GaTe2 structure. The selected ɛ of −0.4% ~ +0.4% for the DFT simulation appropriately matches our calculated values based on the experimental results. The calculated MAE for pristine Fe3GaTe2 is ~0.62 meV per Fe atom (or 2.6 × 106 J m−3), consistent with the previously reported value of 0.55 meV per Fe atom (or 2.3 × 106 J m−3)51. Under in-plane compressive strains from 0% to −0.4%, the MAE value presents an increasing trend with ~0.5% increment. However, under tensile strains from 0% to 0.4%, the MAE value decreases, with a reduction of about 2.1%. These calculated results match the experimental observation in Fe3GaTe2 devices on the (001)-oriented and (111)-oriented PMN-PT substrates, where compressive strain enhances the PMA, while tensile strain weakens it. To understand the origin of strain-dependent MAE, we calculated the electronic band structures of the vdW bulk Fe3GaTe2 structure under varying compressive and tensile strains, as shown in Fig. 4b. Notable band shifts are observed around K and Γ points under both types of strain, indicating that the MAE of Fe3GaTe2 is sensitive to these changes51,52,53. When increasing the compressive or tensile strains, the electron pockets around K point and hole pockets around Γ point can gradually shift downward (the left panel of Fig. 4b) or upward (the right panel of Fig. 4b). The MAE contribution from electron (hole) pockets around K (Γ) point is positive (negative)53. The electronic bands, with large spin–orbit induced changes around K and Γ points, are pushed close to the Fermi energy through the compressive strain. Hence, the contribution from the electron pockets is strongly enhanced, thereby increasing the energy gain and the MAE. The negative contribution for the MAE from the downward hole pockets is probably smaller compared to the electron pockets since they are farther away from the Fermi surface. On the contrary, under the tensile strain, the electron pockets shift away from the Fermi energy, further decreasing the energy gain and the MAE. Consequently, the compressive and tensile strains enhance and weaken the PMA, respectively, as explained by the changes in the electronic structures of Fe3GaTe2.

Fig. 4: Calculated magnetic anisotropy energy and electronic band structures as a function of strain.
Fig. 4: Calculated magnetic anisotropy energy and electronic band structures as a function of strain.The alternative text for this image may have been generated using AI.
Full size image

a Magnetic anisotropy energy (MAE) as a function of in-plane strain by first-principles calculations. The in-plane compressive and tensile strains can increase and decrease MAE, respectively. b Electronic band structures under the compressive and tensile strains. The compressive and tensile strains can push the electron pockets near and away Fermi energy, thereby enhancing and diminishing the MAE of Fe3GaTe2.

To further understand the effect of piezoelectric-strain-modulated MAE in the vdW Fe3GaTe2, the M–H loops are simulated to compare with experimental results, as shown in Fig. 5. We systematically adjusted first-order (K1) and second-order (K2) magnetic anisotropy constants to emulate the strain-dependent MAE, using our experimentally measured MAE value (Ku = ~3.5 × 105 J m−3) as the baseline. The resulting various shapes of the M–H loops are consistent with the experimental piezoelectric-strain-modulated Rxy vs. Hext loops in Fig. 2. In Fig. 5a, when K1 = Ku and K2 = −2Ku (with Ku serving as the reference PMA constant for tuning MAE under different strain conditions), an irregularly rectangular M–H loop is obtained, matching with the shapes of the Rxy vs. Hext loops of Fe3GaTe2 devices on the (001)-oriented and (111)-oriented PMN-PT substrates without an applied E. As K2 increases a more positive values with K1 = Ku, the M–H loops evolve to regularly rectangular shapes, accompanied by a significant increase in Hc (Figs. 5a–e and S12 in Supplementary Note 7), consistent with the experimental results for Fe3GaTe2 device on the (001)-oriented PMN-PT substrate (Fig. 2c). This suggests that increasing K2 probably enhances PMA of the Fe3GaTe2 due to compressive piezoelectric strain16, which is schematically illustrated in Fig. 5g. Conversely, when K2 is held at −2Ku and K1 is decreased to 0 or a negative value, the M–H loops change from irregularly rectangular to arrow-waist shape, with a significant decrease in Hc, as shown in Fig. 5a, f and i. This matches well with the Rxy vs. Hext loops in the Fe3GaTe2 device on the (111)-oriented PMN-PT substrate, indicating that the tensile piezoelectric strain mainly modulates the K1 that contributes to in-plane easy axis. Hence, the variation in K2 and K1 of MAE is responsible for the change in the magnetic easy axis and the various Rxy vs. Hext loops. As shown in Fig. 5m, a tilted magnetic easy axis can be obtained at zero field with K1 < 0 and K2 > 0. The specific angles between the easy axis and the z-axis in Fig. 5a–m and S12, obtained by varying K1 and K2, are summarized in Table S1. The variation in K2 and in K1 can influence the direction of magnetic easy axis and the switching of the magnetic easy axis. Figure 5n–q illustrate the magnetization dynamics at different points labeled in Fig. 5a, c, f and m. Following a similar precession process, the magnetization (m) eventually stabilizes at different tilt angles. As K2 increases (K1 decreases), the energy near the out-of-plane (in-plane) orientation becomes lower, resulting in a gradual enhancement (reduction) of the z-component of m under the same Hext.

Fig. 5: Simulated magnetic hysteresis loops and magnetization dynamics with varied first-order (K1) and second-order (K2) magnetic anisotropy constants.
Fig. 5: Simulated magnetic hysteresis loops and magnetization dynamics with varied first-order (K1) and second-order (K2) magnetic anisotropy constants.The alternative text for this image may have been generated using AI.
Full size image

a–e K1 = Ku, K2 = −2Ku ~ 2Ku, f, h K1 = 0, K2 = −2Ku and 2Ku, i–m K1 = −Ku, K2 = −2Ku ~ 2Ku. g Schematics of spin orientation with different K1 and K2. n–q Time evolution of the magnetization m for points A–D marked in a, c, f, and m. The Ku serves as the reference perpendicular magnetic anisotropy constant for tuning magnetic anisotropy energy under different strain conditions.

Conclusions

In summary, we investigate the piezoelectric-strain-modulated PMA in the vdW ferromagnet Fe3GaTe2 flakes on PMN-PT substrates with (001) and (111) orientations at room temperature. The experimental results reveal that Rxy vs. Hext loops transit from irregularly to regularly rectangular shapes on the (001)-oriented PMN-PT substrate, while evolving to narrow-waist shapes on the (111)-oriented PMN-PT substrate under increasing E at room temperature. Significant HC changes of +89% for the Fe3GaTe2 on the (001)-oriented PMN-PT substrate and −100% for the Fe3GaTe2 on the (111)-oriented PMN-PT substrate could indicate effective modulation of the PMA through electric-field-induced compressive and tensile piezoelectric strains, which will benefit the development of the ultralow power Fe3GaTe2-based spintronic devices. Meanwhile, the theoretical calculations reveal that the band structure of the Fe3GaTe2 is highly sensitive to the piezoelectric strains. The simulated M–H loops further confirm that the increase in K2 and the decrease in K1 contribute to the switching of the magnetic easy axis and the variations in Rxy vs. Hext loops. These results advance the understanding of piezoelectric-strain-modulated magnetic properties in 2D-vdW ferromagnets and pave the way for innovative 2D-vdW FM spintronic devices.

Methods

Crystal growth and property characterizations

High-quality Fe3GaTe2 single crystal samples were prepared using the self-flux method. The Fe powder (99.95%), Te powder (99.999%) and Ga balls (99.9999%) in a stoichiometric molar ratio of 2:2:1 were mixed in an evacuated quartz tube, which was sealed using a hydrogen-oxygen cutting machine and then placed in a muffle furnace. The synthesis process involved heating the tube to 1000 °C within 60 min, maintaining 1000 °C for 1440 min, cooling down rapidly to 780 °C, and finally quenching in ice water. To characterize the crystalline structure of Fe3GaTe2 single crystal, powder X-ray diffraction (XRD) and high-resolution scanning transmission electron microscopy (HR-STEM) were carried out. The magnetic properties of the Fe3GaTe2 were also measured using a physical property measurement system (PPMS) and a vibrating sample magnetometer (Model 3107, East Changing Technologies, China).

Device fabrication and transport-property measurements

The contact electrodes with a stack of Ti (5.0 nm)/Pt (15.0 nm) for the Fe3GaTe2 devices on the PMN-PT substrates were fabricated by standard photolithography. The distance between the two electrodes for applying E is 80.0 μm, and the widths of the electrodes for applying current and measuring the Hall signal are 12.0 and 4.0 μm, respectively. Then, the 2D-vdW ferromagnet Fe3GaTe2 was mechanically exfoliated and transferred onto the electrodes of the (001)-oriented and (111)-oriented PMN-PT substrates. A layer of h-BN was applied to encapsulate the Fe3GaTe2 flakes to protect them from oxidation. All steps were performed in a glove box with water and oxygen levels below 0.1 ppm.

The piezoelectric-strain-modulated Rxy vs. Hext loops of the Fe3GaTe2 devices on the (001)-oriented and (111)-oriented PMN-PT substrates were measured using a self-built source meter (Keithley, model 2400) and electromagnet. The thickness and magnetic domain of the Fe3GaTe2 flakes were characterized by atomic force microscopy (AFM, Bruker icon) and magnetic force microscopy (MFM, Bruker icon), respectively. The ferroelectric domains, polarization hysteresis loops and corresponding I vs. E loops of (001)-oriented and (111)-oriented PMN-PT substrates were measured by piezoelectric force microscopy (PFM, Bruker icon) and ferroelectric analyzer (AIX ACT model TF2000), respectively. The strain-regulated structures of the Fe3GaTe2 devices were analyzed using in situ laser confocal Raman spectroscopy (Raman, LabRAM Odyssey). All transport measurements were carried out at room temperature.

Theoretical calculation

The structural optimization and electronic properties were calculated by utilizing the projector augmented wave (PAW) method implemented in the Vienna ab-initio simulation package (VASP)54. The calculations employed the generalized gradient approximation of the Perdew–Burke–Ernzerhof (GGA-PBE) exchange-correlation functional55,56. Convergence was achieved with a total energy threshold of 10−8 eV and a Hellman–Feynman force convergence of 10−4 eV Å−1. A kinetic energy cutoff of 600 eV was used, and the irreducible Brillouin zone (BZ) was sampled with the dimensions of 15 × 15 × 3 k-mesh. To incorporate vdW interactions between layers, Grimme-D3 dispersion corrections were applied57. Our first-principles calculations revealed relaxed lattice parameters of a = b = 4.039 Å, c = 16.118 Å for Fe3GaTe2, with two atomic layers per unit cell stacked along the c direction, separated by an interlayer spacing of 8.06 Å. The PMA is calculated including the spin–orbit coupling. The PMA of Fe3GaTe2 is obtained by simultaneously straining the lattice constants of the a-axis and b-axis, and the strain range of a-axis and b-axis is −0.4% to 0.4%.

The magnetization dynamics was simulated by solving the Landau–Lifshitz–Gilbert–Slonczewski (LLGS) equation \({{{\rm{d}}}}{{{\bf{m}}}}/{{{\rm{d}}}}t=-\gamma {{{\bf{m}}}}\times {{{{\bf{H}}}}}_{{{{\rm{e}}}}{{{\rm{f}}}}{{{\rm{f}}}}}+\alpha {{{\bf{m}}}}\times {{{\rm{d}}}}{{{\bf{m}}}}/{{{\rm{d}}}}t\)58,59, where the damping constant α = 0.02, the gyromagnetic ratio γ = 1.76 × 1011 rad s−1 T−1), the reduced Planck constant ћ = 6.58 × 10−16 eV s, the saturation magnetization Ms = 3.76 × 105 A m−1, the electron charge e = 1.6 × 10−19 C, and the reference PMA constant Ku = 3.5 × 105 J m−3, experimentally measured in our work for the zero-strain condition, is used as the baseline for simulations, consistent with previous work33. The effective magnetic field Heff consists of the magnetic anisotropy field Han, the demagnetizing field Hdemag, and Hext. To understand the continuous rotation of magnetization trajectory under the voltage modulation, both the first-order and second-order anisotropy constants K1 and K2 are included in our analysis. The Hamiltonian of magnetic anisotropy is\({ {\mathcal H} }_{{{{\rm{ani}}}}}={K}_{1}{\sin }^{2}\theta +{K}_{2}{\sin }^{4}\theta\), resulting in the effective field \({{{{\bf{H}}}}}_{{{{\rm{a}}}}{{{\rm{n}}}}{{{\rm{i}}}}}=2{K}_{1}\,\cos \theta +4{K}_{2}\,\cos \theta -4{K}_{2}{\cos }^{3}\theta\). \({{{{\bf{H}}}}}_{{{{\rm{d}}}}{{{\rm{e}}}}{{{\rm{m}}}}{{{\rm{a}}}}{{{\rm{g}}}}}=-({N}_{x}{m}_{x}\hat{{{{\bf{x}}}}}+{N}_{y}{m}_{y}\hat{{{{\bf{y}}}}}+{N}_{z}{m}_{z}\hat{{{{\bf{z}}}}})\) with the demagnetizing tensors (Nx, Ny, and Nz) calculated based on the sample geometry (the rectangular sample with a length, width, and thickness of 50, 50, and 1.5 nm, respectively).