Compositional Dependence of Magnetocrystalline Anisotropy in Fe-, Co-, and Cu-Alloyed Ni-Mn-Ga

: The key for the existence of magnetic induced reorientation is strong magnetocrystalline anisotropy, i.e., the coupling between ferroelastic and ferromagnetic ordering. To increase the transformation temperatures and thus functionality, various elemental alloying in Ni-Mn-Ga is tried. We analyzed more than twenty polycrystalline alloys alloyed by small amount (up to 5atom%) of transitional metals Co, Fe, Ni, and Cu for the value of magnetic anisotropy in search of general trends with alloying. In agreement with previous reports, we found that maximum anisotropy occurs at stoichiometric Ni 2 MnGa and any alloying decreases its value. The strongest decrease of the anisotropy is observed in the case where the alloyed elements substitute Ga.


Introduction
Magnetocrystalline anisotropy is a key parameter for existence of magnetically induced reorientation (MIR) [1], i.e., giant magnetic field induced strain enabled by twin boundary motion and consequent lattice reorientation [2]. The magnetocrystalline anisotropy represents a coupling between ferroelastic and ferromagnetic ordering or between magnetization and lattice. If the anisotropy, i.e., the coupling, is weak, the magnetization vector rotates toward the direction of external magnetic field and no reorientation occurs. If, on the other hand, the coupling is strong, crystal lattice follows the magnetization and structural reorientation takes place.
Such structural reorientation was observed already some time ago in Dy and Tb compounds [3] at low temperatures and a very high magnetic field of tens of Tesla. In these compounds, the anisotropy is very large ≈ 10 7 J/m 3 . Apart from the observed peculiar magnetization loops, now recognized as a result of the structural reorientation and the observation of emerging structural twinning, the effect was not fully understood and investigated further. A new impetus was provided by discovery of giant magnetic field induced strain (MFIS) in Ni-Mn-Ga in relatively modest field below 1 T close to room temperature [4].
The importance of magnetocrystalline anisotropy for MIR as one of the magnetic shape memory (MSM) effects [1] was recognized from the onset [5,6] and its magnitude was established for several compositions of Ni-Mn-Ga [7][8][9]. It was shown that the anisotropy is larger for the stoichiometry alloy and it decreases with increasing Mn content [9]. Although the large MSM effect is possible only in single crystal, the extensive search for improved performance of MSM alloys was done mostly on polycrystalline alloys [10][11][12]. The main focus is usually on transformation behavior and search for increasing transformation temperatures, i.e., ferromagnetic and martensitic transformation temperatures with various elemental alloying of parent Ni-Mn-Ga compound [13][14][15][16][17]. Such an investigation usually leaves the magnetic anisotropy untouched.
The omission is understandable as the absolute value of the anisotropy can be correctly evaluated only in single crystals [18] and in the case of ferroelastic materials, even the  [19] and in materials alloyed by Cu and Co [20]. The preparation of a single crystal would be quite ineffective for each tried composition, hence the other method is needed in order to provide at least approximate values and to catch the anisotropy trend with various alloying.
Albertini et al. used a method based on singular point detection [21]. However, the magnetic curve measurements may not be always susceptible to this analysis. It can be difficult to locate the expected minimum on second derivative. The anisotropy was also investigated by ferromagnetic resonance (FMR) method [22,23], but again, the polycrystalline and polytwinned martensite can result in a much lower anisotropy value [24] compared to single crystal due to averaging. Another method is to use magnetization approach to saturation [3]. Using this method, the magnetocrystalline anisotropy of polycrystalline Ni 2 MnGa was determined to be much higher [25] compared to the anisotropy obtained from the measurement of single crystal [26]. The ab initio computation provides a way to determine magnetocrystalline anisotropy theoretically but their results when compared with the available experiment are not persuasive [20,27]. This is mostly due to fact that a relatively small anisotropy term is determined from the difference of two large numbers, which is prone to significant error.
In summary, all methods can have some merit but in general the value of magnetocrystalline anisotropy determined from polycrystalline materials can exhibit large error and comparison between methods can be questionable. Moreover, other effects contributing to anisotropy measurement (demagnetization, internal stress) are often not considered. Although the absolute value of the anisotropy in polycrystalline materials can be difficult to determine, the comparison of the samples with various alloying but prepared and measured by the same methods can provide good measure of anisotropy trends if not precise quantitative values.
Here we present the evaluation of magnetization energy obtained from magnetization curves of polycrystalline Ni-Mn-Ga alloyed with various content of Fe, Cu, and to smaller extent of Co, covering the area explored in the search to increase the transformation temperatures [28,29]. We assume that the magnetization energy corresponds to effective magnetocrystalline anisotropy. We evaluate the anisotropy energy at 10 K to obtain fundamental value independent from Curie transformation temperature. Although the method does not provide precise values of the anisotropy, it supplies the useful comparative values and helps to evaluate anisotropy trend with elemental alloying. Such knowledge has a practical impact for the MIR effect, in particular alloys and for theoretical investigation, to guide their calculation being able to predict new magnetic shape memory (MSM) materials.

Materials and Methods
We prepared two sets of doped materials starting with stoichiometric Ni 2 MnGa. The first group contains nine alloys with the substitutions by transitional metals Ni, Co and Fe as in [28]. The second group contains 12 Ni-Mn-Ga-Fe-Cu alloys with varied composition around reference slightly off-stoichiometric ratio Ni 50 Mn 28 Ga 22 . The alloys were designed to follow constraints predicted to be important for MSM effect: keeping Ni (Mn) concentration near 50% (28.5%), altering the Fe/Cu ratio. The effort to keep 50% of Ni was not fully successful and some deviations were detected. All alloys were prepared by arc-melting of pure metals under 4 × 10 −4 mbar argon atmosphere with Edmund Bühler MAM-1 arc furnace in a water-cooled copper crucible. Ingots were re-melted at least three times to improve homogeneity.
Several samples were annealed in an alumina crucible within a tube-furnace under argon gas flow at 1273 K for 72 h and ordered at 1073 K for 24 h, then left in the furnace to cool slowly. This treatment resulted in 3% Mn loss compared to nominal composition. To keep the composition closer to a nominal one, the majority of samples were annealed in argon-backfilled quartz ampoules. These experienced less than 0.5% Mn loss. Wire electric discharge machining (ZAP BP) was used for sample cutting to obtain samples suitable for magnetic measurement. These samples were cut from the central part of the ingot and have the same shape with dimension approximately 5 × 3 × 1 mm 3 .
The surfaces of all samples were ground with progressively finer grit SiC papers to remove kerfs formed during discharge cutting and brass contamination from cutting wire. To determine precise elemental compositions, all samples were measured by X-ray fluorescent spectroscopy (XRF) with an Eagle III EDAX µProbe (Roentgenanalytik Systeme GmbH & Co., Taunusstein, Germany). The measurement error of the XRF was highest for Mn and Ga, reaching ±0.5 at. %. The experimentally determined compositions of these alloys are reported in Table 1. We were not able to determine the precise structure of martensite at 10 K due to experimental method limitation. The structure of the samples at 250 K or room temperature are listed in [28,29]. Magnetization loops were measured using a vibrating sample magnetometer in PPMS, (Quantum Design, Inc., San Diego, CA, USA). For representation of the ground state of the martensite in our alloys the magnetic hysteresis loops were measured up to 9 T at temperature T = 10 K. The measured curves were corrected for demagnetization using slope determined from the curve of cubic austenite measured below T C , since in (cubic) ferromagnetic austenite the anisotropy is expected to be negligible [7]. The correction is demonstrated in Figure 1. Then descending branches of the corrected curves were numerically integrated with respect to magnetization from remnant magnetization up to saturation magnetization M s . We put M s as magnetization at field µ 0 H = 3 T. We marked the calculated magnetic energy as effective anisotropy K eff . Assuming that no other anisotropies are present and after the correction for demagnetization we obtained value comparable to magnetocrystalline anisotropy.
In addition, we try to use singular point detection method for comparison. The minimum in second derivative of the magnetization curve should occur at the anisotropy field. Most of the curves did not, however, exhibit expected minimum, and the anisotropy field could not be determined. In a few available cases, the anisotropy determined by this method was somehow higher than the values determined using magnetic energy. This is to be expected as the singular point detection method should identify the anisotropy field directly. demonstrated in Figure 1. Then descending branches of the corrected curves were numerically integrated with respect to magnetization from remnant magnetization up to saturation magnetization Ms. We put Ms as magnetization at field μ0H = 3 T. We marked the calculated magnetic energy as effective anisotropy Keff. Assuming that no other anisotropies are present and after the correction for demagnetization we obtained value comparable to magnetocrystalline anisotropy. Measured magnetization loops of austenite (black) and martensite (dashed blue) measured at 300 K and 10 K, respectively. Demagnetization field μ0HD at Ms of martensite determined from the initial slope of the austenite loop is shown. Work done by internal magnetic field, equal to anisotropy energy, is given by the area above the magnetization curve corrected for demagnetization (red).
In addition, we try to use singular point detection method for comparison. The minimum in second derivative of the magnetization curve should occur at the anisotropy field. Most of the curves did not, however, exhibit expected minimum, and the anisotropy Figure 1. Measured magnetization loops of austenite (black) and martensite (dashed blue) measured at 300 K and 10 K, respectively. Demagnetization field µ 0 H D at M s of martensite determined from the initial slope of the austenite loop is shown. Work done by internal magnetic field, equal to anisotropy energy, is given by the area above the magnetization curve corrected for demagnetization (red).

Results and Discussion
Before investigation of the compositional variation of the effective magnetocrystalline anisotropy K eff , we checked the microstructure of the prepared polycrystalline bulk. By arc-melting method, the resulting small ingots were textured with relatively large grains. The grains grow further after annealing. An example of grain orientation determined by EBSD is shown in Figure 2 together with sample cut. The prepared small ingots were heavily textured with [001] preferential columnar orientation from the ingot bottom. The orientation of magnetic field in magnetic measurement was approximately perpendicular to the texture. The samples with large preferentially oriented grains are not very suitable for the singular point detection and approach to saturation methods. Instead, we used evaluation of magnetic energy assuming that the distribution of the grains was similar in all samples.
In addition, after martensitic transformation from cubic to lower symmetry phase the crystal became twinned. Assuming the simplest (pseudo)tetragonal structure, there are three structural variants with c-axis approximately along axes of cubic parent phase connected by twinning. To keep structural compatibility and the same shape, the distribution of twin domains is expected to be about equal, i.e., each orientation of structural or ferroelastic variant occupies one third of the volume. Thus, we can expect that maximum one third of the volume has easy magnetization axis along the field but as the orientation in perpendicular texture direction is random, the probability of easy axis along field is even less. The unknown orientation of easy axes in individual grains is the main source of the error in determining the anisotropy from the curve. It is, however, clear from the sample textured state and nature of the measurement that the determined value of the anisotropy must be smaller than value of a single crystal. Importantly, the Ni-Mn-Ga martensites exhibit very low magnetic hysteresis, therefore the domain wall motion takes place in low field and does not affect strongly the calculated anisotropy. mined by EBSD is shown in Figure 2 together with sample cut. The prepared small ingots were heavily textured with [001] preferential columnar orientation from the ingot bottom. The orientation of magnetic field in magnetic measurement was approximately perpendicular to the texture. The samples with large preferentially oriented grains are not very suitable for the singular point detection and approach to saturation methods. Instead, we used evaluation of magnetic energy assuming that the distribution of the grains was similar in all samples. As the feasibility check we measured stoichiometric Ni 2 MnGa. The magnetic energy determined from magnetization curve of polycrystalline material gives 2.8 × 10 5 J/m 3 comparable with the magnetocrystalline anisotropy of a single crystalline bulk 3.4-3.8 × 10 5 J/m 3 [9,30]. The measured value was smaller as expected from above discussion. The reasonable agreement, however, demonstrates that the method is applicable for the textured samples. In contrast, very low magnetocrystalline anisotropy of cubic austenite cannot be determined precisely and measured value is higher due to the effect of grains, imprecise correction for demagnetization field and other irregularities of polycrystals. Using our method, we determined the magnetic anisotropy of cubic stoichiometric Ni 2 MnGa at room temperature to be about 20 kJ/m 3 which was an order of magnitude lower than for the martensite but somehow higher than value determined from single crystal [7,31].
Two groups of alloyed Ni-Mn-Ga were measured. To evaluate the effect of transitional metal alloying in a systematic way, we substituted 5% of each element in stoichiometric alloy with transitional metal Ni, Fe or Co [28]. Nine compositions were prepared in which one was stoichiometric. The anisotropy values for all compositions are summarized in Figure 3. The maximum anisotropy appeared for stoichiometric alloy and the anisotropy strongly depended not only on substituting element but also what element was substituted. The substitution of Ni by Fe resulted in cubic (austenite) structure down to at least 10 K. In this case, the determined magnetic energy was the order of magnitude smaller and comparable to stoichiometric Ni 2 MnGa. In martensites, the differences in the anisotropy were significant, well above the expected error. It is apparent that adding Co to the alloy strongly decreases the magnetocrystalline anisotropy and more so if Ga is substituted. The decrease of anisotropy by Co alloying is in line with theoretical prediction [20] and experiment [30]. The decrease of anisotropy agreed with [25] which shows that anisotropy decreases more than twice for 5 at. % Gd or Ti substitution of Ga.
The other set is concerning with small amount of alloying by Fe and Cu to slightly offstoichiometric alloys in attempt to further increase transformation temperatures [29]. For all these alloys, Table 1 summarizes the effective magnetocrystalline anisotropy determined from the magnetization loops. The anisotropy, as a function of the alloying Fe and Cu elements, is also drawn in Figure 4. Apparently, there is no correlation between amount of alloying and anisotropy. Although the small amount of Fe and Cu have a significant effect on martensite transformation temperature, it does not affect the magnetocrystalline anisotropy in any systematic way. From our data, it is difficult to judge the effect of small Cu and Fe alloying. For Mn = 25 at. %, the anisotropy slightly increases with increasing Cu content; however, for 27.5 at% of Mn the tendency is just the opposite (Table 1) The other set is concerning with small amount of alloying by Fe and Cu to slightly off-stoichiometric alloys in attempt to further increase transformation temperatures [29]. For all these alloys, Table 1 summarizes the effective magnetocrystalline anisotropy determined from the magnetization loops. The anisotropy, as a function of the alloying Fe and Cu elements, is also drawn in Figure 4. Apparently, there is no correlation between amount of alloying and anisotropy. Although the small amount of Fe and Cu have a significant effect on martensite transformation temperature, it does not affect the magnetocrystalline anisotropy in any systematic way. From our data, it is difficult to judge the effect of small Cu and Fe alloying. For Mn = 25 at. %, the anisotropy slightly increases with increasing Cu content; however, for 27.5 at% of Mn the tendency is just the opposite (Table  1). In general, the alloying by Fe and Cu resulted in the anisotropy decrease in agreement with 5% set. As demonstrated in Figure 5, the anisotropy slightly decreased with The other set is concerning with small amount of alloying by Fe and Cu to s off-stoichiometric alloys in attempt to further increase transformation temperatur For all these alloys, Table 1 summarizes the effective magnetocrystalline anisotro termined from the magnetization loops. The anisotropy, as a function of the alloy and Cu elements, is also drawn in Figure 4. Apparently, there is no correlation b amount of alloying and anisotropy. Although the small amount of Fe and Cu hav nificant effect on martensite transformation temperature, it does not affect the ma crystalline anisotropy in any systematic way. From our data, it is difficult to jud effect of small Cu and Fe alloying. For Mn = 25 at. %, the anisotropy slightly increas increasing Cu content; however, for 27.5 at% of Mn the tendency is just the opposite 1). In general, the alloying by Fe and Cu resulted in the anisotropy decrease in ment with 5% set. As demonstrated in Figure 5, the anisotropy slightly decrease In general, the alloying by Fe and Cu resulted in the anisotropy decrease in agreement with 5% set. As demonstrated in Figure 5, the anisotropy slightly decreased with increasing Mn content in agreement with Albertini [9] but there were analyzed only three compositions. Surprisingly, the slight decrease of Ni from stoichiometric 50% resulted mostly in the magnetic anisotropy increase. In agreement with the first set, the decrease of anisotropy occurred when Ga content decreased ( Figure 5), i.e., when an alloying element substituted Ga.
These inconclusive results are difficult to interpret. The anisotropy fluctuation and missing expected trends may be ascribed to the imperfect ordering or disordering of the structure by alloyed elements. It is not known to which atomic positions the alloyed elements settle which can strongly affect the anisotropy values. In addition, possible different martensite structures appearing at 10 K can contribute to the scatter.
Despite unclear trends and tendencies, the findings have a practical impact for estimation of MIR effect in given alloys. The presented experimental results can also guide theoretical computation being able to predict new MSM materials, but it is also clear that further experimental investigation is needed. martensite structures appearing at 10 K can contribute to the scatter.
Despite unclear trends and tendencies, the findings have a practical impact for estimation of MIR effect in given alloys. The presented experimental results can also guide theoretical computation being able to predict new MSM materials, but it is also clear that further experimental investigation is needed.

Conclusions
In Ni2MnGa alloyed with 3d transition metals (Ni, Fe, Co) the magnetic anisotropy decreases. The maximum value of anisotropy is in stoichiometry. The strongest decrease is observed when alloyed element substitutes Ga.
Magnetocrystalline anisotropy in non-stoichiometric Ni-Mn-Ga decreases with several percent Fe and Cu alloying but no clear trend with increasing alloying is observed.
The decrease of anisotropy with alloying is weaker in contrast to calculations, which predicts even zero anisotropy for larger Cu and Co alloying.

Conclusions
In Ni 2 MnGa alloyed with 3d transition metals (Ni, Fe, Co) the magnetic anisotropy decreases. The maximum value of anisotropy is in stoichiometry. The strongest decrease is observed when alloyed element substitutes Ga.
Magnetocrystalline anisotropy in non-stoichiometric Ni-Mn-Ga decreases with several percent Fe and Cu alloying but no clear trend with increasing alloying is observed.
The decrease of anisotropy with alloying is weaker in contrast to calculations, which predicts even zero anisotropy for larger Cu and Co alloying.