Engineering new limits to magnetostriction through metastability in iron-gallium alloys

Abstract

Magnetostrictive materials transduce magnetic and mechanical energies and when combined with piezoelectric elements, evoke magnetoelectric transduction for high-sensitivity magnetic field sensors and energy-efficient beyond-CMOS technologies. The dearth of ductile, rare-earth-free materials with high magnetostrictive coefficients motivates the discovery of superior materials. Fe_1-xGa_x alloys are amongst the highest performing rare-earth-free magnetostrictive materials; however, magnetostriction becomes sharply suppressed beyond x = 19% due to the formation of a parasitic ordered intermetallic phase. Here, we harness epitaxy to extend the stability of the BCC Fe_1-xGa_x alloy to gallium compositions as high as x = 30% and in so doing dramatically boost the magnetostriction by as much as 10x relative to the bulk and 2x larger than canonical rare-earth based magnetostrictors. A Fe_1-xGa_x - [Pb(Mg_1/3Nb_2/3)O₃]_0.7-[PbTiO₃]_0.3 (PMN-PT) composite magnetoelectric shows robust 90° electrical switching of magnetic anisotropy and a converse magnetoelectric coefficient of 2.0 × 10^-5 s m^-1. When optimally scaled, this high coefficient implies stable switching at ~80 aJ per bit.

Fig. 1. Epitaxial stabilization of A2 Fe_1−xGa_x on (001) PMN-PT.

a Electron energy loss spectroscopy (EELS) of the PMN-PT substrate and Fe_1−xGa_x film as a function of film thickness, showing abrupt concentration edges and a nominal thickness of ~15 nm for the Fe_1−xGa_x film. Ti signal comes from the capping layer to prevent oxidation. b High-angle annular dark-field scanning transmission electron micrographs (HAADF-STEM) along the PMN-PT [100] / Fe_1−xGa_x [110] zone axis, showing the single crystalline, epitaxial relationship along the [100]_s substrate direction. c Diagram showing the epitaxial relationship of PMN-PT (blue) and Fe_1−xGa_x (red) normal to the interface ([001] direction); crystallographic directions of the film and the substrate are shown. d Interfacial selected area electron diffraction (SAED) confirming that the Fe_1−xGa_x thin film is in the disordered A2 phase due to the absence of superlattice peaks which would appear in the ordered D0₃ phase. Bragg peaks of the Fe_1-xGa_x (red) only appear when the sum of reciprocal lattice indices is even (missing peaks shown as yellow dashed circles), indicating a solid solution BCC crystal structure. Parts (a), (b), and (d) are collected from a representative 30% Ga sample, full diffraction data are shown in Sup. Fig. S1.

Fig. 2. Magnetoelectric switching.

a Schematic of the Fe_1−xGa_x/PMN-PT device. Voltage is applied across the substrate, using the device as a top ground, and resistance is measured along the bar as a function of magnetic field strength and direction ($\varphi$). b Colormap of low-field (50 Oe) AMR curves fit to $\cos \left(2\theta \right)$, showing the normalized resistance as a function of magnetic field direction ($\theta$) and applied electric field. The overlain points correspond to the calculated phase shift from the data, which is the direction of magnetization, $\varphi$. The two saturated polarization states of the ferroelectric show a 90${}^{\circ }$ phase shift in the curve, demonstrating a 90${}^{\circ }$ switching of magnetization. c Hysteresis of the anisotropy axis, with respect to the direction of the device (x), as a function of electric field, and effective converse magnetoelectric coefficient $\left(\mid {\alpha }_{\mathrm{eff}}\mid \right)$, reaching a maximum value of ~2.0 × 10⁻⁵ s m⁻¹ during switching. The error bars represent the $\pm 5^{\circ }$ angular resolution with one standard deviation of the fit to $\cos \left(2\theta \right)$. Parts (b) and (c) show the representative 30% Ga sample with the largest magnetoelectric coefficient. The full data set is shown in Sup. Fig. S3.

Fig. 3. Local shear strains arising from 109° polarization switching in PMN-PT.

a Polarizations within the (110)_s (substrate) plane, blue, and the ($\overline{1}$10)_s plane, green, are associated with shear distortion in the (001)_pc plane. b indicated by the blue and green dashed frame. The corresponding shear strain arising from a 109° polarization switching can be calculated based on the coordinates of points $r_i$ (i=1,2,3,4), where the translation from $r_1$ to $r_2$ results in a 0.192% shear strain per unit cell. This is then scaled by the fraction of ferroelectric domains that undergo a 109° switch (${\eta }_{109^{\circ }}$) to calculate the total strain seen by the device. c PFM switching map that allows us to experimentally determine ${\eta }_{109^{\circ }}$. This map is made by overlaying PFM micrographs before switching (+4 kV cm^-1) and after switching (−4 kV cm⁻¹) and calculating the 3D switching angle per pixel. The directions of the ferroelectric vectors were determined by combining in-plane and out-of-plane piezoresponse patterns before and after rotating the sample by 90° to allow for the determination of in-plane directionality. The full data set is shown in Sup. Fig. S5. d Histogram of the switching events from 14 composite images, with standard deviations shown as error bars. The analysis indicates that 23%$\pm$ 4% of the domains undergo 109° switchings.

Fig. 4. Enhanced magnetostriction coefficient through epitaxial stabilization.

a Plot of mechanical coefficient $\frac{1}{2}\left(c_{11}-c_{12}\right)$ extracted from literature (red) and simulated here with DFT (blue). Both data sets follow approximately the same trend and show no deviation from linear behavior following the ~19% phase limit. The blue error bars correspond to the error of the calculation, the black error bars are one standard error of the linear fit, and the shaded area is the sum of the errors fixed about the trendline. Literature values are from ref. . b Plot of magnetoelastic coefficients ($B_1$) taken from the previous thin film (red) and bulk (gray) works compared to our measured values. We note that in previous work, there is a sharp decline in $B_1$ following the phase change at ~19% Ga (dotted line), which we do not observe. Bulk (gray) values are from refs. ^,, and film (red) values are from ref. . c The extracted magnetostriction values as a function of Ga concentration with our values (red, open circles) compared to the measured bulk coefficients (blue) from ref. . The values from this work are plotted as $\frac{3}{2}{\lambda }_{100}$ to facilitate comparison with the bulk, polycrystalline values. Above 19% Ga, we do not observe a decrease in the magnetostriction associated with the formation of the ordered D0₃ phase and we extend the regime of the disordered A2 phase via epitaxial stabilization. As the concentration approaches the second phase change at ~30% Ga, the shear modulus $c_{11}-c_{12}$ approaches 0, leading to extremely large values of the magnetostriction. Calculation of the error bars, ${\sigma }_{\lambda }$, is detailed in Sup. Note 4. d Comparison of the magnetostriction coefficients from this work to other magnetostrictive materials. The largest magnetostrictive tensor component ${\lambda }_{ijk}$ of each respective material is plotted here for ease of comparison. Comparative data in (b) from refs. ^–.