Nanoscale magneto-structural coupling in as-deposited and freestanding single-crystalline Fe₇Pd₃ ferromagnetic shape memory alloy thin films

As illustrated in figure 2(a), a surface corrugation pattern correlated to nanotwinning is readily resolved for sample M1. An exemplary XRD spectrum to confirm the fct phase of sample M1 is presented in figure 3. AFM measurements reveal c/a ≈ 0.92 ± 0.03, which additionally corroborates the presence of the fct phase.

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An area of 10 × 10 μm² was investigated using MFM and AFM. Instead of topographies, the amplitude error images are shown in figure 2, since they yield a better contrast especially for weak features such as a twin variant corrugation pattern. As for sample M1, bright and dark magnetic domain stripes can be observed, indicating moments that point in opposite directions (see figure 2(a)). Correlations between magnetic domains and martensite structure are readily identified: while smooth plateaus exhibit stripe domains oriented normal to the twin variant pattern, angular deviations are observed at steep descents. The domain stripe width amounts to λ = 400 ± 30 nm. The average twin variant width is found to be 95 ± 15 nm.

In figure 2(b), combined AFM/MFM measurements of sample M2 can be seen. They exhibit microscopic regions, where the regular surface corrugation pattern is absent. Instead, a much weaker surface corrugation with a twice greater periodicity is present. The MFM micrograph reveals magnetic domains located only within these stripe areas separated by the corrugation lines. Moreover, the phase shift between these domains is more pronounced than in regular corrugated areas, indicating a larger out-of-plane magnetization. A closer insight into structural features occurring beneath the surface is given in the cross-sectional SEM images depicted in figure 4. While regions with the regular twinned surface corrugation pattern reveal a 45° angle between twin boundary orientation and the film normal (in accordance with the scheme in figure 1(a)), areas exhibiting weak corrugation stripes are characterized by variant twinning in the surface plane, meaning that crystal orientation is rotated by 90° with respect to the usual structure and one of the two easy a-axes is always aligned normal to the surface plane.

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Although martensitic samples are of central relevance for magnetically induced actuation or sensing, it is, however, instructive to address micromagnetic characteristics of the parental austenitic phase (see figure 2(c)). It is surprising, at first glance, that a well-ordered domain stripe pattern with significant out-of-plane magnetization and λ = 360 ± 10 nm can be observed, which will be discussed in section 4.

By applying a lift-off approach as suggested earlier [10, 11], structurally intact freestanding films are prepared. As visible in the topography signal of figure 5, a hierarchical martensite structure occurs. It is dominated by a micrometer-sized stripe variant pattern of 1400–2000 nm periodicity. Elevated microvariants (EM) show no morphological subfeatures at the surface but the FIB cut (not shown here) reveals twin boundaries oriented normal to the substrate plane in some areas. In contrast, lower microvariants (LM) yield regions of regular nanotwinning. A well-pronounced magnetic domain stripe pattern can be seen in EM, whereas almost no out-of-plane magnetization is observed in LM. Only within nanotwinned regions, a weak magnetic domain stripe contrast forms. Taking a closer look at the connection between different microvariants (figure 5(c)), those of EM coincide with the domain walls in LM.

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Similar micromagnetic characteristics can be obtained at the sample's back side (formerly attached to the substrate) as depicted in figure 6. The topography furthermore contains a residual island pattern originating from early stage growth mechanisms at elevated temperatures [14]. A microvariant superstructure—similar to that of the front side—is, however, absent.

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Referring back to specimen A, appearing in the austenite phase at room temperature, we performed a partial lift-off to examine its domain structure in detail. It turns out that as-deposited regions remain unchanged, but the magnetic domain pattern illustrated in figure 2(c) is absent in freestanding regions (not shown here).

Temperature-dependent AFM/MFM measurements across the austenite–martensite transition on as-deposited sample M3 and lift-off specimen FS1 are described in the following.

Figures 7(a)–(f) show the results for M3 at five temperatures between 293 and 370 K. At room temperature, the regular surface corrugation structure (AFM) and corresponding stripe domain pattern (MFM) can be observed again.

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A gradual austenite transition already occurs at 325 K (figure 7(b)) where a major fraction of the twin variant corrugation pattern disappears and the maximum MFM contrast Δφ drops slightly. At 370 K the surface is free from any features related to variant twinning and the austenite phase established completely. The contrast of the magnetic stripe domain pattern steadily decreases with higher temperatures, but does not disappear even at 370 K. During the heating process, some minor regions exhibit domain stripe alignment tendencies. The structural phase transition extends over a temperature range of a few tens of kelvins. Noteworthy is the fact that the domain stripe width λ remains unaffected. Comparing the initial surface morphology with the one at room temperature after a heating cycle, minor changes concerning the twin orientation can be seen. A domain reconfiguration to its initial state could not be observed during cooling.

Analogous investigations on the freestanding specimen FS1 (figures 8(a)–(c)) reveal different behavior. During the heating process, a minor fraction of nanotwins vanished. It could, however, not be verified whether the film traverses a phase change locally or whether vanishing of surface corrugation is only artificial due to thermally induced noise by the sample heater. At higher temperatures, the magnetic contrast in EM decreases and the magnetic domain pattern gets blurry and the domains are not strictly limited to one type of microvariant anymore. Due to limited heating power of the Peltier element used, only temperatures up to 400 K could be achieved. On cooling down to room temperature, the magnetic contrast in EM increases again.

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The experimental results given in the previous section can be summarized as follows. (i) A magnetic stripe domain pattern with detectable out-of plane magnetization occurs in regularly twinned martensite Fe–Pd thin films and is aligned predominantly perpendicular to the twin corrugation pattern. (ii) In several martensitic samples—as exemplarily shown on M2—regions without this regular corrugation pattern also occur. They contain an in-plane twinning with larger variant width and the corresponding magnetic domain pattern is characterized by stronger z magnetization M_z. These domains are furthermore confined within variants rather than forming a pattern similar to regular twinned areas. (iii) As-deposited austenite reveals a distinct out-of-plane magnetic domain stripe pattern, which vanishes after lift-off. (iv) A hierarchical stripe morphology emerges in freestanding martensite films. It is characterized by varying EM and LM, where the latter partially contain a corrugation pattern due to regular twinning. Despite the fact that EM do not yield any similar surface features detectable by AFM, cross-sectional SEM micrographs reveal the partial presence of in-plane variant twinning as schematically drawn in figure 5(b). Magnetic domains with strong out-of-plane components can be readily resolved in EM, whereby domain walls are mainly visible in LM.

In general, the occurrence of magnetic domains in ferromagnets originates from the long-range dipole–dipole interaction occurring between atomic magnetic moments. By introducing such domains of different magnetic orientation, a loop closure of magnetic flux lines is achieved and stray fields effectively reduce. The overall magnetostatic energy—correlated to this interaction—can in turn be minimized at the macroscopic level. As a consequence, this contributor to the overall magnetic energy of a ferromagnet forces magnetic moments into the surface plane if they are located close to open boundaries. The long-range character of the underlying magnetic dipole interaction makes it moreover sensitive to a specimen's geometry ('shape anisotropy energy'). This energy term therefore heavily impacts on domain characteristics in systems such as thin films, where the surface-to-volume ratio attains extremal values. As already frequently observed, a domain stripe pattern with altering in-plane magnetization often occurs in such films. This highly ordered configuration further reduces stray fields appearing at the film sides.

Once significant (but not too high) uniaxial magnetocrystalline anisotropy arises in the surface plane, the domain stripe pattern aligns along the easy axis. If the easy axis is oriented normal to the surface, magnetization slightly rotates out-of-plane and is detectable by MFM. Once the amount of this magnetocrystalline anisotropy increases, not only moment M_z components and domain stripe widths/wall widths are affected [15] but also the order of the stripe pattern may transform to a maze structure or even toward unordered island-like domain configurations in the case of a dominating magnetocrystalline energy contribution [16]. This explanation leads to the discussion of finding (i). A nanostructural influence in the form of regular twinning—as a predominant structural feature in as-deposited thin films—causes an angular alternation of one easy a-axis. Variants having both easy axes in-plane clearly prefer moments to lie in-plane as well since this state is additionally supported by the strong magnetostatic energy fraction. Neighboring variants with one a-axis normal to the film surface, however, allow for a significant M_z component. The low lateral variant extension of about 100 nm additionally promotes magnetic coupling [17]. The occurrence of variant twinning at small scales may therefore be associated with a reduced average out-of-plane magnetocrystalline easy axis causing an ordered stripe pattern with lower out-of-plane magnetization. This is in accordance with comparable low MFM phase shifts compared to those observed in microvariants of lift-off films (see figure 2(a) versus figure 5(a)) as well as irregular twinned areas (figure 2(a) versus figure 2(b)).

This leads us to the consideration of finding (ii). As mentioned before, smooth areas with a weak irregular surface corrugation pattern are characterized by in-plane twinning (twin boundaries parallel to the (100) and (010) planes, respectively). A similar irregular corrugation pattern has been reported for Ni–Mn–Ga, and an explanation was given in terms of tilted modulated variants [18, 19]. The origin in Fe–Pd has not been discovered yet but intrinsic stresses as well as a phase reconfiguration close to the substrate interface are reasonable causes.

However, the occurrence of variant twinning within a surface plane is connected to a shift in energetic balance with respect to the regular type addressed in (i). The magnetocrystalline influence benefits from the fact that one easy a-axis permanently aligns to the surface normal and the angular alternation of the magnetically hard c-axis within the surface partially weakens the influence of shape anisotropy. Moreover, variant widths are approximately twice as large as in regular twinned regions, leading to a less pronounced magnetic coupling via stray fields. As a consequence, magnetic domain extension is predominantly limited within a variant type and yields significantly stronger M_z components causing higher MFM phase shifts.

As mentioned in finding (iii), an austenite specimen should exhibit cubic magnetocrystalline anisotropy. Indeed, Cui et al reported on magnetocrystalline anisotropy with the easy axes aligned to the 〈111〉 directions for single-crystalline austenite bulk Fe₇Pd₃. However, this anisotropy constant amounts to K_cubic = (− 5 ± 2) × 10² J m⁻³ [3] and is two orders of magnitude lower compared to the uniaxial counterpart measured in the martensite phase. Obviously, the magnitude of K_cubic as well as the symmetry of cubic magnetocrystalline anisotropy are not sufficient to face the magnetostatic anisotropy term.

We demonstrated that films grow virtually stress free during deposition at high temperatures [9]. Major stresses arise during sample cooling due to different thermal expansions of both substrate and thin film. Many studies examined the invar properties of Fe₇Pd₃ [10, 20, 21], and Matsui et al determined the linear thermal expansion coefficient as α_Fe−Pd ≈ 9 × 10⁻⁶ K⁻¹ for Fe₆₈Pd₃₂ at room temperature. Considering a value of α_MgO = 10.8 × 10⁻⁶ K⁻¹ for the MgO substrate [22], this results in a biaxial compressive stress acting on Fe₇Pd₃ during cooling [10]. Due to volume conservation, the austenite fcc cell should be tetragonally distorted and the unit cell vector normal to the film plane slightly extends. Since Fe₇Pd₃ prefers a long axis to be the magnetically easy one, a stripe domain pattern with detectable M_z may occur once the thermally induced uniaxial K_stress is large enough. The disappearance of magnetic domains in lifted austenitic films confirms the suggestion of a stress-induced magnetocrystalline anisotropy as a reasonable origin.

According to Kittel's theory [15], a modified model system of partial flux closure [17] was utilized to estimate K_stress in our austenite Fe₇Pd₃ thin film A. The total magnetic energy per unit area—consisting of the sum of magnetostatic energy, stress-induced anisotropy energy and a wall energy—is therefore calculated analytically. Material-specific exchange constant A (≈ 2 × 10⁻¹¹ J m⁻¹), saturation magnetization M_s and film thickness t have to be considered as well. The total energy is minimized with respect to the domain width and to a parameter η, which determines the amount of flux closure [17]. In the case of the austenite specimen A with a domain width of λ = 360 nm, we estimate a stress-induced uniaxial second-order anisotropy constant of K_stress ≈ (3.8 ± 0.4) × 10⁴ J m⁻³ that is basically sufficient to explain the presence of the domain stripe pattern observed by MFM.

The formation of a hierarchical variant pattern and correlated magnetic features as addressed in finding (iv) and illustrated in figures 5(a) and 6 is clarified in the following. As is generally known, the introduction of lattice misfit dislocations at substrate interfaces is the preferred mechanism to reduce film stresses beyond a critical thickness of several nanometers. In the case of epitaxially grown Fe–Pd films presented here, such dislocations can also be found as stated in [9]. After film lift-off, some of these defects relax toward the surface, but others remain within the film. As pinning centers, they affect the phase transitions probably occurring after lift-off as well as the formation of hierarchical structures as a mechanism of stress relaxation [11]. Further intrinsic stresses may arise due to the formation of Fe precipitates. They can be observed at the film's substrate side and occur during the deposition to minimize lattice misfits [9]. Iron precipitates may therefore be a reason for a more distinct roughness at the sample back side and the absence of an ordered microvariant surface morphology (see figure 6). In general, a hierarchical twin structure indicates the compensation of shear stress fields arising in the specimen [23]. Currently, transmission electron microscopy measurements are in progress to investigate in more detail which mechanism is the major origin.

However, EM—characterized by a strong magnetic contrast—can be treated like those discussed in point (ii), where one long magnetically easy a-axis permanently points normal to the film plane. Crystal orientation in LM is rotated by 90° with respect to that observed in EM. Both easy axes are aligned in the surface plane, resulting in poor MFM contrast. Only in subregions of regular twinning—partially occurring therein—the formation of a weak stripe domain pattern can be observed again. The distinct height difference between both microvariant types originates from the tetragonality of martensite unit cells. The coincidence of domain walls at neighboring microvariants implies an interplay between their demagnetization fields.

In as-deposited martensite films M1 and M2, the twin structure completely recovers after a heating–cooling cycle across the structural transition with only minor changes. These changes can be explained considering dislocations (e.g. Fe precipitates, etc) located at the substrate side of the thin film. During thermally induced structural phase transitions, local relaxation processes due to generation and relaxation of biaxial in-plane stresses are most probably correlated to a change in defect configuration. The surface roughness of the substrate and associated local stress gradients may also generate varying twin nucleation seeds. Furthermore, the temperature interval of the phase transition of a few tens of kelvins can be at least partially attributed to stress gradients correlated to substrate constraints, defects and roughness.

As we know from a comparison of freestanding and as-deposited austenitic films, the formation of magnetic domains can be traced back to magnetocrystalline anisotropy due to thermal stresses. Considering the thermally induced austenite transition, an interesting point is the fact that only minor changes in the magnetic stripe domain pattern occur. These minor alignment tendencies are probably connected to local stress relaxations during heating. After cooling across the martensite transition, the slightly modified domain configuration remains, which is probably due to the non-elastic nature of local stress relaxations. Furthermore, a wider hysteresis—associated with this first-order phase transition—may have an additional influence. Further cooling would thus be necessary to obtain a (partial) recovery. However, in the case of as-deposited twinned Ni–Mn–Ga thin films, a well-pronounced drop in MFM phase contrast as well as a significant change in domain stripe width are reported at the phase transition [17]. The comparably low MFM phase drop and the absence of a similar domain width reduction in our Fe–Pd films might be associated with a simultaneous change of several competing material properties. For instance, the effectively reduced average easy axis normal to the surface plane—associated with regular twinned fct martensite (one easy a-axis alternates directions and the other easy axis always lies in-plane as addressed in finding (i))—could be close to the estimated value of stress-induced uniaxial anisotropy in as-deposited austenite. Moreover, the saturation magnetization in austenite of M_s,fcc ≈ 0.89M_s,fct [3] leads to a lower influence of the shape anisotropy energy contribution in the parental phase and promotes a more pronounced M_z component of the domain stripe pattern. These assumptions are strengthened by temperature-dependent MFM measurements on freestanding films. Magnetic domains become blurred and less pronounced in the MFM phase shift, as it would be expected for transition to a magnetocrystalline cubic phase.

It is, however, questionable whether the microvariant structure and domain pattern would vanish completely at even higher temperatures. On the one hand, observed microvariant superstructures do not yield a twin structure in the common sense, but a plateau-like topography as schematically shown in figure 5(b). It is not yet clear whether the hierarchical structure is completely decoupled from typical martensitic twinning. On the other hand, the existence of lattice dislocations at the film back side could be the cause for a partial austenite transition during heating. They may induce the hierarchical structure by pinning and hinder the phase transition as well. Furthermore, a change in crystalline structure, due to the lift-off process, might be a reason for this phenomenon. Measuring the c/a ratio of the surface corrugation pattern, partially occurring in LM (see figure 5(a)), does not only yield a clear identification of fct structure but also between fct and bct martensite. The latter is thermally stable [3, 24] and could hinder the complete martensite–austenite transition.