First-principles study of Zn-doping effects on phase stability and magnetic anisotropy of Ni-Mn-Ga alloys

The effect of Zn doping on Ni-Mn-Ga magnetic shape memory alloy was studied by the first-principles calculations using exact muffin-tin orbital method in combination with the coherent-potential approximation and projector augmented-wave method. Trends in martensitic transformation temperature TM and Curie temperature TC were predicted from calculated energy differences between austenite and nonmodulated martensite, ΔEA−NM, and energy differences between paramagnetic and ferromagnetic state, ΔEPM−FM. Doping upon the Ga-sublattice results in stabilization of martensitic phase which indicates the increase in TM. TC is affected only weakly or slightly decreases, because ΔEPM−FM of martensite does not change significantly with doping. The substitution of Mn atoms by Zn causes the decrease in both TM and TC. Comparing to Cu-doped Ni-Mn-Ga alloys, we predict that doping with Zn results in smaller decrease in TC but also in smaller increase in TM. Moreover, Cu doping upon the Ga-sublattice strongly decreases the magnetic anisotropy energy of martensite, whereas such strong effect was not observed for Zn doping. Based on the calculations of Zn-doped Ni-Mn-Ga alloys we suggest that simultaneous doping with Zn and an element increasing TC can result in significant increase in both transformation temperatures without strong decrease of magnetic anisotropy.


Introduction
Numerous scientific investigations have been done in order to study Ni-Mn-Ga Heusler alloys mainly because they exhibit magnetic shape memory (MSM) behavior. The macroscopic deformation of such materials in an external magnetic field, so called Magnetic Field-Induced Strain (MFIS), is caused by the motion of highly mobile twin boundaries in magnetically ordered martensite [1,2]. Ni-Mn-Ga alloy is known for its 6 % MFIS in martensite with five-layered modulation (10M) [3,4]. Other martensitic phases observed experimentally in Ni-Mn-Ga systems are seven-layered martensite (14M) with MFIS up to 10 % [5] and nonmodulated martensite (NM), stable far from stoichiometric composition with no MFIS reported [6,7]. Recently the stability of fourlayered modulated martensite (4O) was predicted theoretically [8].
Practical usability of Ni-Mn-Ga is restricted by its low transformation temperature from cubic austenite with L2 1 structure to martensite which occurs at T M =202 K in stoichiometric Ni 2 MnGa alloy [9]. The Curie temperature is also relatively low, with T C =376K. For practical applications in small actuators [10] or energy harvesters [11], all relevant transformations should be at least several tens of kelvins above the room temperature. For more demanding applications e.g. for use in internal combustion engines, all transformation temperatures should be above 413K [12].
There are three ways to increase transformation temperatures: i) by finding an alternative alloy, ii) by changing the stoichiometry of known MSM alloy such as Ni-Mn-Ga, and iii) by doping or alloying the known alloy by additional elements. Simultaneously with improving T M and T C one may consider improvement of other application relevant properties such as saturation magnetization, magnetic anisotropy, or mobility of twin boundaries.
It has already been demonstrated experimentally that significant improvements can be achieved by doping and alloying [13,14]. For example, the alloy Ni 46 Co 4 Mn 24 Ga 22 Cu 4 shows 12 % MFIS in NM martensite and an increase in both T M and T C to 330 K and 393 K, respectively [15]. The increase in T M in this alloy is caused by the replacement of Cu upon the Ga sublattice, as this element independently can increase T M by 150 K if 3 at. % of Cu is substituted [16][17][18]. Increasing concentration of Cu on Ga sublattice is accompanied with a decrease in T C [17], which has to be compensated by substitution of Ni by Co as an element increasing T C [19]. However, magnetic anisotropy strongly decreases with increasing concentration of doping elements [20]. Promising results were also documented for alloys doped by Zn, since Ni 50 Mn 25 Ga 22 Zn 3 alloy exhibited T M increased by 114 K [21]. However, fabrication and consequently an experimental study of Ni-Mn-Ga-Zn systems with higher content of Zn are strongly limited due to intensive evaporation of Zn during alloying. Nevertheless, we believe that suitable experimental method, like sputtering or powder metallurgy will be found if Zn is beneficial for Ni-Mn-Ga system. Considering the difficulties in alloy preparation, employing of a computational approach is usefull to predict the properties relevant for MSM behavior such as martensitic transformation temperature T M , Curie temperature T C and magnetic anisotropy energy.
One of methods used for theoretical prediction of T M relates the transformation temperatures with the number of valence electrons per atom e/a [22,23] and concludes that higher e/a indicates higher T M . If we consider Mn having 7 valence electrons in d and s orbitals and Ga having 3 valence electrons in p and s orbitals, T M ∼e/a rule is very well applicable for off-stoichiometric alloys [23]. The same rule was applied also for alloys containing Cu. Considering its 11 valence electrons, the addition of Cu instead of Ga significantly increases the e/a ratio, which corresponds to a significant increase in T M [16,17,24,25]. Here we expand this approach further by selecting Zn-doping. One can expect that Zn, having 12 valence electrons, increases T M even more than Cu. Simultaneously, atomic radius of Zn is about the same as atomic radius of Ga atom (134 pm vs 135 pm) [26], hence in comparison with influence of Cu-doping (atomic radius of Cu is 128 pm) [26], we can expect small changes in Curie temperature due to lattice contraction [17,27].
Qualitative predictions of T M in the present study are based upon its correlation with energy difference between austenite and nonmodulated martensite, D -E A NM , taken from the energy profile along the tetragonal deformation path. The increase or decrease in T M is predicted by comparison of D -E A NM in a studied system with D -E A NM in a reference system of stoichiometric Ni 2 MnGa alloy. If D -E A NM for the modified alloy is greater than that for the referential one, an increase in T M is expected. Similarly, lowering of D -E A NM corresponds to the decrease in T M as was shown for offstoichiometric Ni 2 MnGa [28] and Ga 2 MnNi alloys [29].
All such predictions are based on an assumption that the entropy contributions to the Gibbs free energy lowers the free energy more or less equally in the systems with the same crystal structure for small concentrations of doping elements. Free energy profiles of corresponding phases in doped and non-doped systems are assumed to have very similar shape but are shifted with respect to each other, as is schematically shown in figure 1. With such assumption, a shift of intersection of austenite and martensite free energy profiles towards higher or lower temperature is directly dependent on the increase or decrease of D -E A NM at 0 K. This method, however, provides only qualitative predictions of changes in T M . For quantitative predictions, it is necessary to know the exact evolution of free energy.
The prediction of Curie temperature T C works similarly as described for T M , but here one has to consider not only the contribution of vibrational entropy but particularly the effect of magnetic entropy. In this case T C should correlate with the energy difference between paramagnetic (PM) and ferromagnetic (FM) state, D -E PM FM [30][31][32]. The validity of these approaches,~D - PM FM , has been established for Co and Cu-doping [24,33,34]. Both transformation temperatures can be theoretically predicted by more precise methods including phonon [35] or Monte Carlo [36] calculation, however, with much higher computational cost especially in the case of doped alloys. The less precise but computationaly less expensive approach presented in this paper can be used for fast preselection of alloy composition for further deeper investigation by more precise methods or for experimental preparation.
The purpose of this paper is to find how Zn-doping on both Ga or Mn sublattices affects the stability of austenite with respect to NM martensite. We present a detailed and comprehensive first-principles investigation of total-energy behavior along the tetragonal deformation path for PM and FM states for different compositions which allows us to predict trends in martensitic transformation temperatures T M and Curie temperature T C . Moreover, we also determine the heat of formation for studied systems, site preferences of doping atoms, and magnetic anisotropy of martensitic phase. The stability of cubic austenite and tetragonal martensite is evaluated using the density of states (DOS) analysis.

Computational details
The ab initio calculations were performed using the exact muffin-tin orbital (EMTO) method [37,38] based on an improved Korringa-Kohn-Rostoker (KKR) approach [39]. In combination with the full charge density (FCD) technique [40], the EMTO is suitable to accurately describe the total energy with respect to anisotropic lattice distortions such as tetragonal deformation. The exchange-correlation term was described within the Perdew-Burke-Ernzerhof (PBE) parametrization of generalized gradient approximation [41]. In the self-consistent calculations, the one-electron equations were treated within the scalar-relativistic and soft-core approximations. The EMTO Green's function was calculated for 32 complex energy points distributed exponentially on a semicircular contour. In the EMTO basis set s, p, d and f orbitals were included and Ni 3d 8 4s 2 , Mn 3d 5 4s 2 , Ga 3d 10 4s 2 4p 1 and Zn 3d 10 4s 2 were considered as the valence orbitals. In order to get a better agreement with experiment for non-modulated martensitic structure, the muffin-tin potential on the Ni sublattice was optimized by choosing the atomic radius = R R 1.10 ws Ni ws [42] and the overlapping potential sphere radius = R R 0.95 mt Ni ws , [43] where R ws is the average Wigner-Seitz radius. In the one-center expansion of the full charge density, the number of components was truncated to eight. The Brillouin zone was defined on a 13×13×13 uniform k-point mesh without any smearing technique. The spin disordered magnetic structure of PM state was simulated using the disordered local moment (DLM) formalism, where the magnetic disorder was represented by randomly distributed Mn atoms with oppositely oriented magnetic moments [44]. Both chemical disorder caused by doping as well as magnetic disorder of PM state were included by using coherent potential approximation (CPA) [45,46]. The effect of the charge misfit on the spherical potential is taken into account using the screened impurity model in [47] and [48].
Considering previous theoretical and experimental studies, we have chosen doping with 2.5 at. % and 5 at. % of Zn on either the Mn or Ga sublattice. A series of total energies was calculated for each composition at constant volume of austenite in the range between c/a=0.9 and 1.4, which describes the tetragonal deformation of cubic L2 1 structure (c/a=1, see Supplementary material available online at stacks.iop.org/MRX/7/026101/mmedia for strucuture of austenite and tetragonaly distorted structure of NM marteniste). All calculated total energies along the deformation path were related to the energy of cubic structure in FM state for alloy with given composition. Magnetic anisotropy energy of NM martensite was computed with the help of force theorem from the energy difference between magnetization along [001] and [100] direction with spin-orbit coupling included in the Kohn-Sham equation while using the same self-consistent scalar-relativistic potential [49]. Thus, the negative MAE corresponds to preferred magnetization in easy plane given by equivalent directions [100] and [010], whereas positive MAE indicates preferred magnetization along easy axis parallel to [001] direction of tetragonal lattice. We used the Vienna Ab initio Simulation Package (VASP) [50,51] in which the electron-ion interaction was described by projector augmented-wave (PAW) potentials [52,53]. The electronic orbitals were expanded in terms of plane waves with a maximum kinetic energy of 600 eV. The doping by 6.25 at. % of Zn or Cu on either the Mn or Ga sublattice was modeled by replacement of single atom in 16 atom cell of tetragonally distorted L2 1 lattice (see Supplementary matrial). The Brillouin zone (BZ) was sampled using a 12×12×10 Γ-pointcentered mesh. The integration over the BZ used the Methfessel-Paxton smearing method [54] with a 0.02 eV smearing width. The total energy was calculated with high precision by convergence to 10 −7 eV per computational cell. The structural relaxation was stopped when all forces acting on the atoms converged to within 10 −3 eV/Åand all relevant components of the stress tensor converged to within 0.1 GPa.

Site preference and equilibrium volume of austenite
The first step in the theoretical investigation of alloys is to find their thermodynamic stability represented by the enthalpy of formation at equilibrium volume and the site preference of doping atoms. The standard enthalpy of formation was obtained from theoretical formula which is applicable for the Ni 50 Mn 25−y Ga 25−z X y+z system. Here E tot is the total energy of an alloy per atom in FM state and following energies represent total energies of corresponding elements in their standard forms per atom taken as follows: fcc nickel (ferromagnetic), manganese (antiferromagnetic), gallium and hcp zinc. The heat of formation of stoichiometric Ni 2 MnGa (or Ni 50 Mn 25 Ga 25 ) calculated in this work by EMTO-CPA is −0.3052 eV/atom, which agrees with other theoretical (−0.2993 eV/atom calculated by the projector augmented wave method [55]) and experimental results (−0.3089 eV/atom [56]). The site preference of substitutional atoms was determined by the lowest energy of formation. Normal site occupation was compared to anti-site occupancy, when dopant elements occupy other than deficient sublattice. The calculations were performed only for alloys with 5 at. % of doping element. Zinc shows tendency to always occupy sublattices of atoms in deficiency, which is in agreement with previous calculations for Zn-doping at the expense of Ga [57].
The results are summarized in table 1.
Calculations of standard enthalpy of formations as well as the following calculations of tetragonal deformation paths were performed at the equilibrium volume V 0A of the austenite L2 1 cell over the entire c/a range. The difference between the austenite and NM martensite equilibrium volumes is minimal, especially for low concentrations of dopants and therefore the energies along the deformation path are sufficiently accurate when using the austenite equilibrium volume for every c/a [33]. The results of calculations in FM state show that Zn substitution of Ga decreases V 0A and the Zn substitution of Mn does not have significant effect on V 0A . Equilibrium volumes in PM states are slightly larger than in FM states with the same effect of doping for all studied compositions. Results for all FM systems as well as for the most stable PM systems are summarized in table 1. The dependency of the equilibrium volume V 0A on the concentration of dopant is linear in all considered substitutions and can be described approximately as

Tetragonal deformation in FM state
Results obtained for stoichiometric Ni 2 MnGa in both FM and PM states, are taken as reference values for all modified alloys. The tetragonal deformation path in FM state shows two energy minima and a barrier between them ( figure 2(a)). The minimum occurring at c/a=1 represents the L2 1 cubic austenite, the second minimum occurs at c/a≈1.25 and represents the NM tetragonal martensite. Experimentally observed tetragonality of NM martensite (c/a) NM ≈1.17-1.23 [23] is smaller than calculated value, however, all ab initio methods in general overestimate tetragonality [35,[59][60][61][62].
The development of energy profiles in figure 2(a) shows clearly that substitution of Mn by Zn leads to both destabilization of NM martensite as well as reduction of its tetragonality ( ) c a NM . Also, the energy barrier grows and moves towards higher c/a, which indicates additional stabilization of austenite phase. Notably Zn substitution instead of Ga has an opposite effect, as also shown in recent ab initio calculations of Zn doping on Ga sublattice with 6.25 and 12.5 at. % [57]. The total energy of NM martensite is lower for modified alloys and the energy barrier between austenite and martensite gets smaller. Both these factors are in favor of more stable NM martensite. The tetragonality changes only slightly.

Tetragonal deformation in PM state
In order to predict behavior of the Curie temperature, calculations of tetragonal deformation paths were performed in paramagnetic states employing the DLM approximation. Computed tetragonal deformation paths in both FM and PM states for alloys with 5 at. % of Zn are shown in figure 2(b), both magnetic states are related to the energy of the FM austenite of a given composition. The energy profile of Ni 2 MnGa in PM state exhibits a global minimum at c/a=1, whereas NM martensite is represented by a very shallow minimum with higher energy at (c/a) NM =1.14 in this magnetic state [34]. Doping on Mn sublattice has an even stronger suppressing effect on PM martensite and simultaneously lowers the austenite energy minimum, which predicts lower stability of FM states. On the contrary, doping on Ga sublattice strongly deepens the NM martensite minimum, which corresponds to similar stabilization effect of Zn on NM martensite found in the FM state.

Electronic structure
The effect of doping on electronic structure of Ni-Mn-Ga alloys was studied in order to explain observed behavior of total energy profiles and to examine the local stability of austenite. Majority density of states (DOS) channels do not play important role in the stability of Ni-Mn-Ga alloys due to their featureless character around the Fermi level. By analysis of minority spin channel of density of states, we can ascribe the stability of austenite in stoichiometric Ni 2 MnGa to formation of a pseudogap about 0.65 eV below the Fermi level, E f , and a Ni-Ni antibonding peak 0.2 eV below E f . A shallow and narrow pseudogap indicates weak covalent bonding [63]. Due to the Jahn-Teller effect a distortion of cubic lattice breaks the degeneracy of d bands near E f and thus causes a redistribution of electrons with resulting reduction of total energy [64][65][66]. The size and position of the antibonding peak is responsible for the instability of austenite, since high DOS near E f increases the total energy of the cubic phase. The tetragonal distortion is accompanied with shifting of the antibonding peak trough E f . The energy of the system first increases until the top of the peak reaches the Fermi level which creates an energy barrier in the tetragonal deformation path. Further tetragonal deformation results in further shifting of the peak and subsequently in decreasing of DOS at E f  as well as decreasing of total energy in martensite [33].
The total DOS of austenite phase for stoichiometric Ni 2 MnGa and doped alloys is compared in figure 3(a). In austenite, the substitution of Ga by Zn moves both the pseudogap and the antibonding peak closer to E f  and increases DOS at E f compared to the stoichiometric alloy. These effects are responsible for destabilization of the cubic austenite. On the contrary, substitution of Mn atoms by Zn fills the pseudogap and lowers the antibonding peak. This behavior is linked to the stabilization of austenite and consequently to the decrease in T M .
The stability of martensitic phase in the stoichiometric alloy is enhanced by the shift of the antibonding peak above the Fermi level as shown in figure 3(b). Similarly, the doping on Ga sublattice results in a shift of both pseudogap and antibonding peak towards higher energies. The pseudogap in DOS of the stoichiometric alloy is slightly deeper and the minimization of DOS of Ga deficient alloy on the Fermi level is not present. Hence an increase in T M is caused by destabilization of the austenitic phase.
On the other hand, doping on Mn sublattice affects neither pseudogap position nor its depth. A shift of the antibonding peak over E f is not as strong as for the Ga substitution and not even as in the Ni 2 MnGa alloy, hence stability of martensite is less resounding ( figure 3(b)).

Magnetic anisotropy energy
Magnetic anisotropy energies (MAE) for different alloy compositions with 6.25 at. % of doping element calculated using PAW method are summarized in table 2 together with magnetic moment and c/a of NM martensite. We calculated also Cu doping for the sake of comparison. Equilibrium c/a of doped alloys calculated by PAW method agree well with those provided by EMTO-CPA method (see table 1 for Zn-doping and figure 4 in [33] for Cu-doping). The only difference is that PAW method predicts small increase of c/a for Zn-doping on the Ga-sublattice (Zn  Ga), whereas EMTO-CPA predicts small decrease. However, the deviation from c/a of stoichiometric alloy is very small in both methods and this difference can be neglected. All studied compositions exhibit negative MAE, which indicates preferred magnetisation in (001) plane. MAE of NM martensite with  stoichiometric composition is equal to −0.074 meV/atom which is in good agreement with other calculated values −0.08 meV/atom reported in previous works [67][68][69].
Both Zn-doping and Cu-doping have a similar effect on magnetic moments and they decrease the anisotropy. However, the anisotropy decrease depends strongly on doping element and doped sublattice. The Zn-doping on the Ga sublattice results in about 30% decrease of MAE in comparison to the stoichiometric alloy but the MAE is still nearly twice larger than for the case of Cu doping on the Ga sublattice. On the other hand the Zn-and Cu-doping on Mn sublattice results in about 50% drop in MAE in comparison to stoichiometric alloy, with the Cu doping exhibiting MAE slightly larger than Zn doping. Such behaviour indicates, that Cu is responsible for significant decrease of magnetic anisotropy in Co-and Cu-doped alloy [20]. Thus, the replacement of Cu by Zn could result in higher magnetic anisotropy of the modified alloy.
The different effect of Cu and Zn doping on MAE originates in different localization of Cu and Zn atomic orbital in Ni-Mn-Ga alloy. Whereas the Cu d states exhibit wide bands lying approximately from −5 to −1 eV bellow Fermi level (see [33] and

Discussion
To predict the behavior of T M in doped alloys the energy differences D -E A NM are plotted in figure 4(a) as a function of concentration of doping elements. The onset of plotted lines at concentration equal to zero represents the austenite-martensite total energy difference for stoichiometric Ni 2 MnGa. The assumption is that all the ascending lines represent alloys with higher T M compared to the unmodified alloy. In particular, the line representing Zn-doping on the Ga-sublattice (Zn  Ga) indicate that this doping should increase T M whereas doping on Mn-sublattice (Zn  Mn) is expected to decrease T M . Results computed in this work are compared with Cu-doping [33]. For Cu-doping on both Ga and Mn sublattices (Cu  Ga and Cu  Mn) D -E A NM dependencies ascend, predicting the increase in T M . Theoretical predictions may be compared with available experimental results summarized in figure 4(b).
In all cases, theoretically obtained ascending lines correlate with experimentally observed increase in T M . Moreover, the steepness of theoretical lines predicts the rate of growth of T M as follows from the comparison of theoretical and experimental results. It predicts the weaker effect for Zn-doping than Cu-doping on Ga sublattice but stronger than Cu-doping on Mn sublattice [25,70]. As can be also seen from figure 4(b), the effect of doping can be further enhanced when used in combination with off-stoichiometric Ni-Mn-Ga composition [17,71].
Predictions of T C are based on the study of energy differences between FM and PM states, D -E PM FM . Since all structures were calculted at 0 K, we cannot say whether martensitic transformation takes place at lower temperature than magnetic transformation or if the Curie temperature of martensite T C M equals T C A of austenite. Hence, we focus on both~D

E A
PM FM , is smaller for Zn-doped alloys than for the unmodified alloy, which can be related to reduction of magnetic moments (see table 1) in modified alloys. The same decrease of D -E PM FM can be seen also for tetragonal phase. This predicts the decrease in Curie temperature in both phases. Since NM martensite in PM state is unstable with respect to tetragonal deformation for doping with Zn as can be seen in figure 2(b), we used the total energy corresponding to the structure of stoichiometric NM martensite in FM state with c/a=1.14 for estimation of D Our results show that doping of Ni-Mn-Ga alloys by Zn exhibits effects comparable to Cu doping. Simultaneous doping with Zn and an element increasing T C (Co [72] or Fe [73,74] on Ni sublattice) may result in similar enhancement of properties as in the case of Ni-Mn-Ga-Cu-Co alloy, with significant increase in both T M and T C [15], where Co compensates negative effect of Cu on T C . Further improvement of MFIS can be expected if we consider also significantly higher magnetic anisotropy predicted for Zn-doped alloy. Zn-doping on Ga sublattice decreases the MAE much less than Cu-doping.
The calculated behavior can be compared with theT e a M phenomenological rule. If we assume Zn having 12 valence electrons, which is more than number of valence electrons in Ga or Mn, doping by Zn on both sublattices should should raise T M . This prediction is qualitatively correct for substitution of Ga atoms. As Zn has more valence electron than Cu, the effect of Zn should be even stronger and T M should grow more steeply than in Cu-doped alloys. This, however, does not agree with our theoretical prediction based on D -E A NM and experimental results ( figure 4). Moreover, the e/a rule fails completely for doping on Mn sublattice, where T M drops with growing concentration of Zn. On the other hand, if we consider that Zn has only 2 valence s-electrons, the decrease in T M is expected for doping on both Mn and Ga sublattice, which is also not seen. Apparently the simple rule of valence electron concentration is not applicable to Zn-doped alloys and alternative methods such as ab initio calculations are needed.

Conclusions
The development of martensitic transformation temperature, T M , and Curie temperature, T C , in Zn-doped Ni-Mn-Ga magnetic shape memory alloys was predicted with the help of first-principles calculation employing EMTO-CPA method. The prediction of trends in T M as a function of concentration of doping element is based upon calculated energy differences between the cubic structure of austenite and the tetragonal structure of NM martensite, D -E A NM , whereas the energy difference between paramagnetic and ferromagnetic states D -E PM FM serves for estimation of trends in T C . Although used calculations can be considered rudimentary the calculated trends for T M and T C provide important guide for experimentalist and theorist alike. For more quantitative calculation of T M , more detailed method based on lattice dynamics should be used. The same is valid for T C where the mean field approximation or Monte Carlo method can be used.
The alloys with Zn substituted on Ga-sublattice exhibit stabilization of NM martensite compared to austenite, which results in the increase in T M . In contrast, if Mn-sublattice is occupied by Zn then NM martensite is destabilized and its equilibrium (c/a) NM decreases and the decrease in T M can be expected. This finding is not in agreement with the empirical rule found e.g. for Cu-doping that T M should increase with increasing concentration of valence electron per atom, e/a, and it casts doubt upon general validity of thẽ T e a M rule for Ni-Mn-Ga system, as indicated also before [21]. Substitution of Ga by Zn does not have significant effect on D -E PM FM in austenite hence a very small effect on T C can be expected. In martensite, D -E PM FM decreases only slightly. Calculated D -E PM FM in NM martensite is smaller than for Cu-doped alloys, thus Zn on Ga sublattice decreases T C less significantly than Cu on the same sublattice. A much stronger decrease of D -E PM FM in both phases was observed when Zn was substituted for Mn, which suggests stronger decrease in T C .
Moreover, a beneficial effect of Zn can be expected for magnetic anisotropy of NM martensite. Whereas Cu on Ga sublattice significantly decreases MAE, the decrease is only moderate in case of Zn doping on Ga sublattice. Zn thus seems to be a suitable candidate to replace Cu in Ni-Mn-Ga-Co-Cu alloys.