Improved magnetostriction in Galfenol alloys by aligning crystal growth direction along easy magnetization axis

Galfenol (Iron-gallium) alloys have attracted significant attention as the promising magnetostrictive materials. However, the as-cast Galfenols exhibit the magnetostriction within the range of 20–60 ppm, far below the requirements of high-resolution functional devices. Here, based on the geometric crystallographic relationship, we propose to utilize the 90°-domain switching to improve the magnetostriction of Galfenols by tuning the crystal growth direction (CGD) along the easy magnetization axis (EMA). Our first-principles calculations demonstrate that Pt doping can tune the CGD of Galfenol from [110] to [100], conforming to the EMA. Then, it is experimentally verified in the (Fe0.83Ga0.17)100−xPtx (x = 0, 0.2, 0.4, 0.6, 0.8 and 1.0) alloys and the magnetostriction is greatly improved from 39 ppm (x = 0, as-cast) to 103 ppm (x = 0.8, as-cast) and 188 ppm (x = 0.8, directionally solidified), accompanying with the increasing CGD alignment along [100]. The present study provides a novel approach to design and develop high-performance magnetostrictive materials.

possesses a body-centered cubic (BCC) A2 structure, with Fe and Ga atoms distributed disorderedly 5 ; the EMA is along <100> 20 and the CGD is along <110> 21 . Herein, we have considered the EMA along [100] and CGD along [110] to conveniently illustrate and describe the magnetostrictive model, which does not influence the proposed methodology. In the case of CGD deviating from EMA, the corresponding magnetostrictive process is illustrated in Fig. 1a,b1,c1. Figure 1a presents the normal elongation of the crystal along EMA below Curie temperature, i.e., δa, where a refers to the lattice constant and δ represents the elongation coefficient of the lattice distortion. The 90°-domain switching ends with the external magnetic field (H) parallel to the CGD [110]. If a single domain state is considered (Fig. 1b1), the magnetostriction along H is calculated to be ~ √ 2 2 . δa. The calculations of the magnetostriction (∆L 1(s) in Fig. 1b1) are as below: The experimentally measured magnetostriction (10-100 ppm) demonstrates that δ is of the order of magnitude of 10 −4 . Therefore, the angle θ is approximately equal to 45°. Consequently, the magnetostriction ∆L 1(s) is: If a multi-domain state is considered (Fig. 1c1), the magnetostriction is equal to the elongation multiplied with a domain configuration factor. For simplicity, the domain configuration factor is fixed as 2/3, corresponding to the homogeneous distribution of domains along six axes of the BCC structure. Hence, the magnetostriction for the multi-domain state is calculated to be ~ 0.47δa.
In another case, if the CGD is parallel to the EMA along [100], the shape distortion of the 90°-domain switching completely contributes to the measured magnetostriction. This is illustrated in Fig. 1a,b2,c2. The 90°-domain switching ends with the external magnetic field H parallel to the EMA [100]. For the 90° switching of a single domain, the value of magnetostriction is equal to δa (Fig. 1b2). If a multi-domain state is considered (Fig. 1c2), the calculated magnetostriction is ~ 0.67δa, which is obtained by multiplying the multi-domain factor (2/3). In brief, if the CGD [110] can be tuned to the EMA [100], a large improvement in magnetostriction is expected.
However, the experimental realization of such domain switching process remains a challenge. Given the relationship between surface formation energy and the growth surface (growth plane) that correlates to the crystal growth direction, the preferred growth direction can be determined from the plane with the lowest surface formation energy 22,23 . Therefore, if elemental doping can tune the plane with the lowest surface formation energy of FeGa alloy, from (110) to (100), it is expected to improve the magnetostriction.
(1)  , special quasirandom structure (SQS) approximation was used to construct a 3 × 3 × 3 BCC supercell, which has the stoichiometry of Fe 45 Ga 9 , whereas the nominal composition is Fe 0.83 Ga 0.17 26 . The bulk structure of Fe 45 Ga 9 was completely relaxed. Based on the relaxed bulk structure, six-layered atomic slabs of FeGa, perpendicular to (100) and (110) surfaces, were built with different surface configurations. Only one Pt atom was doped into each surface of FeGa slabs to examine the influence of Pt. The total energy and surface area of the above-mentioned structures are summarized in Table 1. The surface formation energy can be defined as , where E slab and E bulk refer to the total energy of slab and bulk, respectively, and S represents the surface area. Considering multiple surface configurations, E S is determined by an average value of all slabs. As illustrated in Fig. 2, only one slab is depicted as a representative. The surface energy of (100) and (110) in FeGa slab is E S(100) = 132 meV/Å 2 and E S(110) = 127.4 meV/Å 2 , respectively ( Fig. 2a,b). The difference between the surface energy of (100) and (110) is �E S = E S(100) − E S(110) = 4.6 meV/Å 2 , which implies that (110) is more stable than (100) and easily forms during solidification. The replacement of Fe or Ga by Pt on the surface of the above slabs hardly changes the atomic structure, as shown in Fig. 2c,d. However, the surface formation energy of (100) and (110) is changed to E S−Pt(100) = 125.9 meV/Å 2 and E S−Pt(110) = 131.9 meV/Å 2 , respectively. Hence, the difference in surface formation energies becomes �E S−Pt = E S−Pt(100) − E S−Pt(110) = −6.0 meV/Å 2 . Apparently, the surface formation energy relationship is reversed, which indicates that (100) is more stable than (110) and becomes a preferred growth plane after Pt doping. The DFT calculations indicate that doping of Pt can tune the CGD of FeGa from [110] to [100] (parallel to the EMA), which is expected to improve the magnetostriction, as depicted in Fig. 1. X-ray diffraction analysis. For verification, we prepared both as-cast and directionally solidified (DS) Ptdoped FeGa crystals. The X-ray diffraction (XRD) patterns of the selected compositions are shown in Fig. 3a. The as-cast and the DS-treated samples exhibit only characteristic (110), (200) and (211) peaks within the 2theta range from 30° to 90°, demonstrating that pure body-centered cubic (BCC) A2 structure is retained after Pt doping 15,27 . Figure  Magnetostriction and magneto-crystalline anisotropic constant K 1 . Figure 4a presents the Pt content dependent magnetostriction curves at room temperature. The un-doped FeGa sample (x = 0) shows the magnetostriction of 39 ppm, which is consistent with the previously reported values of 20-60 ppm and theoretical prediction 28 . The composition x = 0.8 shows the highest magnetostriction of 103 ppm for as-cast sample and 188 ppm for DS-treated sample. It should be noted that as for the trace-amount element doped FeGa polycrystalline alloys without treatment of magnetic annealing and prestress during measurement, the reported maximum value of magnetostriction (even DS-treated FeGa alloys) is 160 ppm [29][30][31][32][33][34] . Meanwhile, the Pt doping causes a higher magnetostriction without increasing the saturation field, which can be quantified as dλ/dH, as shown in Fig. 4b. For as-cast and DS-treated samples, the largest dλ/dH appears at x = 0.8 and reaches the maximum value of 0.11 ppm/Oe and 0.17 ppm/Oe, respectively. This feature is also desirable in practical applications. The higher www.nature.com/scientificreports/ the value of dλ/dH is, the lower field is needed to trigger large magnetostriction. In practical applications, the magnetic materials with higher value of dλ/dH can help realize the miniaturization of devices. Because the samples are polycrystalline, the magneto-crystalline anisotropic constant K 1 cannot be measured directly. Using the methods proposed by Vazquez et al. and Andreev et al. 35,36 , the magneto-crystalline anisotropic constant K 1 is calculated from the magnetization as a function of magnetic field (Fig. 4c, details can be referred to the supplementary materials). For our samples, the calculated K 1 ranges 3.7-4.0 × 10 5 erg/cm 3 , while Rafique. S et al. have reported that the K 1 of FeGa alloy ranges 3-7 × 10 4 J/m 337 . Considering the relation that 1 erg/cm 3 = 10 -1 J/m 3 , the values of calculated K 1 for our FeGa samples are in good agreement with the previous reports. From the inset of Fig. 4c, it can be seen that compared with x = 0.8, the sample of x = 0 is harder to be magnetized, reflected from both the saturated magnetization and the slope of the curve. This result agrees well with Fig. 1c1,c2. The FeGa-xPt alloy of x = 0.8 exhibits the highest magneto-crystalline anisotropic constant K 1 of 3.97 * 10 5 erg/cm 3 and 4.00 * 10 5 erg/cm 3 for as-cast and DS-treated samples, respectively. The trend of K 1 variation with Pt content is also consistent with the intensity ratio I 200 /I 110 . The increase of K 1 with the increase of Pt content, up to x = 0.8, demonstrates the increase of magneto-crystalline anisotropy and, consequently, the increase of δ (Fig. 1), which further improves the magnetostriction.  (Figs. 3c, 4a).
Considering that DS is one type of heat treatment process, the differences between x = 0 (as-cast) and x = 0 (DStreated) are probably due to the nanoheterogeneities (m-D03 phase nano-inclusions or precipitates) that have been studied extensively [11][12][13][14]38 .  www.nature.com/scientificreports/ Last but not least, let us return to the previously reported methods to improve the magnetostriction of FeGa alloys. The XRD patterns of the FeGa alloys prepared by magnetic annealing 15 , melt-spinning 9,39 , and single crystal growth 27 all indicate the positive correlation between the magnetostriction and the preferred growth direction along [100]. This validates our proposed model and indicates the presence of a common physical mechanism behind these different approaches. Compared with previous work, the fundamental scientific objective of the present work is to tune the intrinsic factor to enhance the magnetostriction, without considering complex treatments and measurement auxiliary conditions. Besides, with the assistance of DFT calculations, the design and fabrication of high-performance FeGa alloys will be more efficient.
In conclusion, based on a crystallographic geometric model, we propose an approach to improving the magnetostriction of FeGa alloys by aligning the crystal growth direction with the easy magnetization axis, and the DFT calculations indicate that the doping of Pt can facilitate such process through tuning the crystal surface formation energy. Furthermore, the proposed model is experimentally verified: accompanying with the increasing preference of the crystal growth along [100] direction, the magnetostriction of FeGa with Pt doping is greatly improved from 39 ppm (x = 0) to 103 ppm (x = 0.8) and 188 ppm (x = 0.8, DS). The present study provides an effective approach to explore and design high-performance magnetostrictive materials.

Methods
Sample preparation and characterization. The (Fe 0.83 Ga 0.17 ) 100−x Pt x polycrystalline samples (x represents the atomic percentages; x = 0, 0.2, 0.4, 0.6, 0.8 and 1.0) were prepared by using high purity metals of Fe (99.95%), Ga (99.99%) and Pt (99.99%) by arc-melting techniques under argon atmosphere. Considering the lower melting point of Ga, excessive 1 mol% of Ga was added to compensate the losses during the melting process. To ensure compositional homogeneity, each sample (~ 7 g) was melted four times and the weight loss of the ingots was less than 1%. The as-cast ingots were sectioned into slices with a thickness of 1 mm by wirecutting and sealed into a quartz tube, filled with argon gas, followed by a heat treatment at 1000 °C for 3 h, and then quenched into water. The directionally solidified samples were prepared at 1680 °C with the pulling rate of 5 µm/s. The X-ray diffraction (XRD) patterns were measured by using a Bruker D8 ADVANCE Diffractometer (Cu-Kα, λ = 1.5406 Å) and the lattice constants of FeGa-Pt alloys were calculated by using Nielsen extrapolation method.
Property measurements. The magnetic characterization was carried out on the superconducting quantum interference device-vibrating sample magnetometer (MPMS-SQUID VSM-094). The magnetostriction was tested with a standard strain gauge at room temperature.
Computational methods. The Vienna Ab-initio Simulation Package (VASP) was used to conduct DFT calculations with the projector augmented wave method 40 . The spin-polarized generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional was adopted 41 . The kinetic energy cutoff for wavefunction expansion was set to 400 eV. Monkhorst-Pack k-point grid of 3 × 3 × 3 and 3 × 3 × 1 was used for bulk and slab supercell, respectively. Atomic positions and lattice constants were completely relaxed in bulk. For the slab models, two surface atomic layers were completely relaxed, but two middle atomic layers were fixed in lattice constants of the relaxed bulk model to simulate the surface influence. Both relaxations were terminated once the difference of energy and force was less than 10 -5 eV and 0.01 eV/Å, respectively. The periodic boundary conditions were applied in calculations, while the vacuum space was added along the z-axis for slab model at least 20 Å to safely avoid artificial interaction between the periodic images.

Data availability
The data that support the findings of this study are available from the corresponding authors on request. www.nature.com/scientificreports/