Magnetic shape memory effect

The mechanism behind the MSM effect and the large MFIS observed in Ni-Mn-Ga is the magnetically induced reorientation of the crystal lattice through TB motion (Ullakko et al., 1996; Heczko et al., 2009). Figure 2.2 schematically illustrates the MSM effect, wherein the TBs separate the twin variants with a different – by around 86° – orientation of the c-axis. When the field reaches the minimum value, the martensitic twin variants

2.1 Ni-Mn-Ga-based magnetic shape memory alloys 21

with the shorter crystallographic c-axis, which is the axis of easy magnetization, oriented along the applied magnetic field (H) grow at the expense of other variants with different orientations. The reorientation of the c-axis along the applied field and the subsequent

‘expansion’ of the corresponding twin variant cause the sample to physically contract along the field direction; see Figure 2.2b.

The minimum field value depends on multiple factors, including chemical composition, crystal quality and TB type (Straka et al., 2012). The maximum strain, which ideally results in a single variant structure, is achieved when the applied magnetic field saturates the material. During saturation, all magnetic moments in each twin variant are aligned with the applied magnetic field, and the corresponding magnetic field-induced stress for TB motion reaches its maximum value. As a result, any increase in the applied magnetic field beyond the saturation field value provides no further increase in the magnetic driving force for TB motion (Saren et al., 2016). The sample retains its shape after the magnetic field is removed. A reverse transformation can be induced by applying a transverse magnetic field or by mechanical force.

Figure 2.2: A schematic illustration of the magnetic shape memory effect in a single crystalline Ni-Mn-Ga sample exhibiting a microstructure with two parallel TBs: Yellow variants with the c-axis in the horizontal direction, and an orange variant with the c-c-axis in a vertical direction. The b-axis is oriented normal to the plane of view. The inset contains a magnified image showing the orientation of the unit cell on each side of the TB. (a) The sample before applying the magnetic field. (b) The same sample after magnetic field (H) application in the direction pointed by the arrow.

Multiple factors determine whether a Ni-Mn-Ga alloy can exhibit large MFIS. The foremost requirement is the crystal structure, which must be martensitic at the intended actuation temperature – typically ambient temperature. Additionally, to exhibit the MSM effect, the alloy must have high magnetic anisotropy compared to the energy needed to move the TBs – the magnetic-field-induced stress should be higher than the twinning stress, which defines the minimum stress needed to move an existing TB.

The theoretical maximum strain (ε) for the martensitic crystal lattice can be calculated using the following equation:

𝜀 = 1 −𝑐

𝑎 (2.1)

where c (Å) and a (Å) correspond to the lattice parameters of the martensite unit cell (Söderberg et al., 2005).

The largest MFIS at ambient temperature was observed in oriented Ni-Mn-Ga single crystals exhibiting modulated martensite structures: up to 6% for 10M martensite (Murray et al., 2000) and up to 9.5% for 14M martensite (Sozinov et al., 2002). Among the modulated Ni-Mn-Ga martensites, the 10M is the most studied structure, mostly because it has relatively low twinning stress and high work output while still maintaining a large MFIS. Overall, the observed maximum strains are approximately two orders of magnitude larger than the ~0.1 % strains obtained in competing giant magnetostrictive materials (Engdahl, 2000). Additionally, Ni-Mn-Ga can exhibit high strain accelerations of up to 1.6×10⁶ m/s² (Smith et al., 2014), and its fatigue life can exceed 2×10⁹ cycles (Aaltio et al., 2010). Although 12% MFIS has been obtained in a doped alloy exhibiting an NM structure (Sozinov et al., 2013), a typical non-doped alloy with an NM martensite structure has a twinning stress that is much greater than its maximum magnetic-field-induced stress; therefore, it does not typically exhibit large MFIS (Likhachev et al., 2006;

Chernenko et al., 2009).

The twinning stresses (in 10M martensite) of TB type 1 have been experimentally determined as ~1 MPa at ambient temperature, whereas TB type 2 exhibits a drastically different value of ~0.05-0.3 MPa (Sozinov et al., 2011; Straka et al., 2011). Additionally, TB type 1 exhibits a large increase in twinning stress when temperature is decreased (Straka et al., 2012), which is the reason why most functional Ni-Mn-Ga compositions have been tailored to start the martensite to austenite transformation at ~40-50 °C.

However, TB type 2 shows considerably lower twinning stress temperature dependency (Heczko et al., 2013). The stress required for the nucleation of another variant and the formation of a completely new TB is typically higher than the twinning stress (Aaltio et al., 2010b). There is also the concept of dynamic twinning stress, which describes the twinning stress of the TB as a function of TB velocity (Saren & Ullakko, 2017).

Crystal quality is also a limiting factor in the MSM effect because TB mobility can be affected by internal defects (e.g. crystal defects or particle/phase inclusions) and surface

2.1 Ni-Mn-Ga-based magnetic shape memory alloys 23

defects (Chmielus et al., 2011). These defects can result in the formation of pinning obstacles and residual twin variants, which restrict TB motion. For example, the motion of TBs is significantly hindered by the grain boundaries, which is the major reason why large MFIS in Ni-Mn-Ga is almost exclusively observed in oriented single crystals, while polycrystalline alloys typically do not exhibit large strains. In polycrystalline Ni-Mn-Ga, some of these constraints can be removed by increasing the grain size and applying training (Gaitzsch et al., 2011; Hürrich et al., 2011) or by inducing a ‘bamboo-grained’

structure with a crystallographic texture (Chmielus et al., 2009). Additionally, applying a magnetic field and/or mechanical stress can help remove the complex self-accommodated twin microstructure, composed of multiple twin variants, which appears during cooling from austenite into martensite.