Magnetic Moment of Cu-Modified Ni2MnGa Magnetic Shape Memory Alloys

The magnetization measurements at 5 K were carried out for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys. All of the magnetization curves are characteristic of ferromagnetism or ferrimagnetism. By using Arrott plot analysis the spontaneous magnetization of all samples was determined from the magnetization curves. The magnetic moment per formula unit, μs, at 5 K was estimated from the spontaneous magnetization. For Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys μs at 5 K decreases linearly with increasing x. On the other hand, the μs at 5 K for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys decreases more steeply with increasing x compared to the μs for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys. On the basis of the experimental results, the site-occupation configurations of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys are proposed.


Introduction
In recent years, Heusler alloys have become a subject of intensive experimental and theoretical investigations.Ferromagnetic shape memory alloys (FSMAs) with the Heusler-type structure (L2 1 -type structure), which exhibit both the ferromagnetic and structural transitions, have attracted much attention due to their potential application as smart materials [1,2].A large magnetic field-induced strain by the rearrangement of twin variants in the martensite phase was observed in the Ni-Mn-Ga FSMAs [3,4].Moreover, a large magnetocaloric effect (MCE) accompanied by a magnetostructural transition, where both the ferromagnetic and structural transitions occur together, has been expected to be useful for devices [5,6].Among FSMAs, the stoichiometric Heusler alloy Ni 2 MnGa has been the most studied.Ni 2 MnGa orders ferromagnetically with a Curie temperature of T C ≈ 365 K. On cooling below the martensitic transition temperature T M ≈ 200 K, a superstructure forms, and the ferromagnetic state remains below T M [7,8].The spontaneous magnetization M s just below T M is larger than the M s just above T M for Ni 2 MnGa.
Recently, Kataoka et al. [9] and Endo et al. [10] carried out magnetization, permeability and differential scanning calorimetric (DSC) measurements on the FMSAs Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) and Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys, respectively.It was found that for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys the magnetostructural transitions between the paramagnetic austenite phase (Para-A) and the ferromagnetic martensite phase (Ferro-M) occur in the concentration range of 0.23 ≤ x ≤ 0.30 [9].Similarly, the magnetostructural transitions between the Para-A and Ferro-M were observed in the concentration range of 0.12 ≤ y ≤ 0.14 for Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys [10].Furthermore, the characteristics of the phase diagrams of Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) and Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys were found to be very similar to those of Ni 2 + x Mn 1 − x Ga (0 ≤ x ≤ 0.36) alloys [11].Kataoka et al. explained the phase diagram of Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys using the Landau-type phenomenological free energy as a function of the martensitic distortion and the magnetization [9].Their analysis showed that the biquadratic coupling term, together with a higher order term, of the martensitic distortion and the magnetization plays an important role in the interplay between the martensite phase and the ferromagnetic phase.As the result, Kataoka et al. could obtain the satisfactory agreement between the calculated and observed phase diagrams for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys.Also the phase diagram of Ni 2 − z Cu z MnGa (0 ≤ z ≤ 0.8) alloys was determined from the results of the temperature dependence of the initial permeability [12].The T C of Ni 2 − z Cu z MnGa (0 ≤ z ≤ 0.8) alloys increased with the Cu concentration z.While, the T M decreased abruptly with z.
In this paper, the concentration dependence of the magnetic moment for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) and Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys is examined to gain deeper insight for the magnetic properties of these FSMAs.On the basis of the experimental results, the site occupancy and the magnetic structure of Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) and Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys are presented.Furthermore, the site occupancy of Ni 2 − z Cu z MnGa (0 ≤ z ≤ 0.4) alloys is also presented.

Experimental Section
The Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) and Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys were prepared by repeated arc melting of the constituent elements, namely 99.99% pure Ni, 99.99% pure Mn, 99.99% pure Cu and 99.9999% pure Ga in argon atmosphere.The heat treatments of all reaction products after the arc melting were reported in the references [9,10].Weight loss between before and after the arc melting is within 0.5%, thus the composition of the specimens is seen to be the same with the nominal ones.By using X-ray powder diffraction measurements all samples were confirmed to be of single phase at room temperature.Magnetization measurements on prepared samples were carried out in magnetic fields up to 50 kOe using a superconducting quantum interference device (SQUID) magnetometer.

Results and Discussion
Figures 1 and 2 show the phase diagrams of Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) and Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys reported by Kataoka et al. [9] and Endo et al. [10], respectively.The phase diagrams shown in Figures 1 and 2 have characteristics very similar to that [11] of Ni 2 + x Mn 1 − x Ga (0 ≤ x ≤ 0.36) alloys.As shown in Figure 1, the samples with x ≤ 0.20 of Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys crystallize in the L2 1 -type structure at room temperature.However, the details of the crystal structure in the martensite phase for the samples with x ≤ 0.20 are not clear.It was confirmed by the low temperature X-ray powder diffraction measurements that the sample with x = 0.23 for Ni 2 Mn 1-x Cu x Ga alloy crystallizes in a 14-layered monoclinic (14M) structure (space group: C2/m) well below the martensitic transition temperature [9].The X-ray powder diffraction pattern of the sample with x = 0.23 at room temperature shows that the cubic phase with the L2 1 -type structure and the monoclinic phase with the 14M structure coexist.Similarly, the X-ray powder diffraction patterns at room temperature of the samples with x = 0.25 and 0.27 indicated that the L2 1 phase and the 14M phase coexist although the fraction of the 14M phase increases with increasing the concentration     Recently, Li et al. investigated theoretically the site preference and elastic properties of Fe-, Coand Cu-doped Ni 2 MnGa alloys by using the first-principles exact muffin-tin orbital method in combination with the coherent-potential approximation [14].According to the results of the calculation by Li et al. [14], Cu atoms for Ni 2 Mn 0.95 Cu 0.05 Ga occupy the vacant Mn sublattice and the magnetic moments of the Ni, Mn, Cu and Ga atoms, μ Ni , μ Mn , μ Cu and μ Ga , in Ni 2 Mn 0.95 Cu 0.05 Ga are 0.32 μ B , 3.37 μ B , −0.03 μ B and −0.05 μ B , respectively.The values of μ Ni , μ Mn and μ Ga calculated by Li et al. [14] are in good agreement with those reported earlier for the stoichiometric Heusler alloy Ni 2 MnGa [15][16][17][18][19][20][21][22].In order to explain the observed concentration dependence of the magnetic moment for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys we present a simple model in which the following assumptions are made.Cu atoms for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys always occupy the vacant Mn sublattice.The magnetic moments of the Ni, Mn, Cu and Ga atoms in Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys are collinear and have Li et al.'s values independent of x.The magnetic moments of the Mn atoms are ferromagnetically coupled to the magnetic moments of the Ni atoms.Then, the total magnetic moment per formula unit, μ s (cal), of Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys is given by μ s (cal) = 2μ Ni + (1 − x)μ Mn + xμ Cu + μ Ga .The solid line in Figure 5 is the one calculated by using this equation.As seen in Figure 5, the experimental values are in good agreement with those calculated.5, the experimental μ s at 5 K for Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys decreases steeply with increasing y.We, therefore, suggest a different site-occupation configuration i.e., Ni 2 (Mn 1 − y Cu y )(Ga 1 − y Mn y ) with the Cu atoms occupying the Mn sublattice, for Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys, where some of the Mn atoms move on to the Ga sublattice.Here, we assume that the magnetic moment of the Mn atoms substituted on to the Ga sites in Ni 2 (Mn 1 − y Cu y )(Ga 1 − y Mn y ) alloys is antiferomagnetically coupled to the magnetic moment of the Mn atoms on the Mn sublattice.The values of the magnetic moments of the Mn atoms on the Mn and Ga sublattices, respectively, are assumed to be 3.37 μ B and −3.43 μ B , which remain constant with increasing y from y = 0.The other magnetic moments μ Ni , μ Cu and μ Ga in the Ni 2 (Mn 1 − y Cu y )(Ga 1 − y Mn y ) alloys are the constant values 0.32 μ B , −0.03 μ B and −0.05 μ B , respectively, as in Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys.A value of −3.43 μ B was calculated by Li et al. [14] for the magnetic moment of the Mn atoms on the Ga sublattice.The antiferromagnetic coupling between nearest-neighbor Mn atoms in Ni 2 (Mn 1 − y Cu y )(Ga 1 − y Mn y ) alloys is due to the variation of the exchange interaction that becomes antiferromagnetic for small Mn-Mn interatomic distances.This antiferromagnetic coupling was already proved experimentally and theoretically in many Mn-rich Ni-Mn-Ga Heusler alloys [14,[23][24][25][26][27].Then, the μ s of Ni 2 (Mn 1 − y Cu y )(Ga 1 − y Mn y ) alloys is given by μ s (cal) = 2μ Ni + (1 − y)μ MnI + yμ Cu + (1 − y)μ Ga + yμ MnII , where μ MnI and μ MnII mean the values of the magnetic moment of the Mn atoms on the Mn sublattice and the Ga sublattice, respectively.The broken line in Figure 5 is the one calculated by using the above equation.As seen in Figure 5, the experimental values are in agreement with those calculated for low y concentrations.For samples with high y concentrations, however, the experimental values of μ s deviate from the broken line in Figure 5.This may be attributed to any concentration dependence of the μ MnI , μ MnII and μ Ni values or occurrence of disorder of the constituent elements associated with the increase of y.
In the above considerations on Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys, we excluded the site-occupation configurations of (Ni 2 − y Cu y )(Mn 1 − y Ni y )(Ga 1 − y Mn y ) and (Ni 2 − y Mn y )(Mn 1 − y Cu y )(Ga 1 − y Ni y ) by taking into account the theoretical result that the formation energies of the site-occupations in Ni 2 Mn(Ga 0.95 Cu 0.05 ) and Ni 2 (Mn 0.95 Cu 0.05 )(Ga 0.95 Mn 0.05 ) are much smaller than those of (Ni 1.95 Cu 0.05 )(Mn 0.95 Ni 0.05 )(Ga 0.95 Mn 0.05 ) and (Ni 1.95 Mn 0.05 )(Mn 0.95 Cu 0.05 )(Ga 0.95 Ni 0.05 ) [14].Unfortunately, the calculations in [14] were made for the site occupation of Cu-doped Ni 2 MnGa with the L2 1 -type structure, instead of the one with the observed martensitic structure at 5 K. Nevertheless, the above satisfactory agreements between the experimental and calculated concentration dependence of the magnetic moment μ s may rather confirm that the site-occupation configurations in the present analyses exist also in the martensite phase.Lastly, we consider the concentration dependence of μ s for Ni 2 − z Cu z MnGa (0 ≤ z ≤ 0.40) alloys.As shown in Figure 5, the experimental values of μ s for Ni 2 − z Cu z MnGa (0 ≤ z ≤ 0.40) alloys are almost independent of concentration z [12].We assume that Cu atoms for Ni 2 − z Cu z MnGa (0 ≤ z ≤ 0.40) alloys occupy the vacant Ni sublattice according to the results of the calculation by Li et al. [14].Furthermore, we assume that μ Ni , μ Cu , μ Mn and μ Ga in Ni 2 − z Cu z MnGa (0 ≤ z ≤ 0.40) alloys, respectively, are the constant values 0.32 μ B , 0.04 μ B , 3.37 μ B and −0.05 μ B , which are the magnetic moments calculated by Li et al. [14] for Ni 1.95 Cu 0.05 MnGa.Then, the concentration dependence of μ s (cal) for FSMAs Ni 2 − z Cu z MnGa (0 ≤ z ≤ 0.40) alloys is given by μ s (cal) = (2 − z)μ Ni + zμ Cu + μ Mn + μ Ga , which is shown by the dot dash line in Figure 5.As seen in Figure 5, the experimental values are in good agreement with those calculated.

Summary
The magnetization measurements at 5 K of FSMAs Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) and Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys have been carried out.The μ s at 5 K for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys decreases linearly with increasing concentration x.On the other hand, the μ s at 5 K for Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys decreases steeply with increasing y compared to the μ s for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys.To explain the concentration dependence of μ s for the Cu-modified Ni 2 MnGa alloys, we suggested the site-occupation configurations, Ni x.The sample with x = 0.35 crystallizes in a tetragonal D0 22 -like crystal structure with no lattice modulation at room temperature.The crystal structures of the 14M and the D0 22 -like also appear in the martensite phase of Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys depending on the Cu concentration, being similar to that of Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys[10].The magnetization curves at 5 K for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys with various concentrations x are shown in Figure3.All of the magnetization curves are characteristic of ferromagnetism or ferrimagnetism.The magnetization M at 5 K for all samples is saturated in a field of about 20 kOe.The magnetization curves at 5 K for Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys with various concentrations y are shown in Figure 4.The spontaneous magnetization at 5 K for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) and Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys was determined by the linear extrapolation to H/M = 0 of the M 2 versus H/M curves (Arrott plot).The magnetic moments per formula unit, μ s , at 5 K for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) and Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys were estimated from the values of the spontaneous magnetization and are plotted against concentrations x and y as shown in Figure 5.The concentration dependence of μ s at 5 K for Ni 2 − z Cu z MnGa (0 ≤ z ≤ 0.40) alloys is also shown in Figure 5 [12], where the values of μ s for Ni 2 − z Cu z MnGa (0 ≤ z ≤ 0.40) alloys were determined at 4.2 K.The μ s at 5 K of the stoichiometric Ni 2 MnGa is estimated to be about 4 μ B /f.u. by extrapolations of the μ s versus x curve for Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.40) alloys to x = 0 and of the μ s versus y curve for Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys to y = 0. Recently, Ahuja et al. carried out a magnetic Compton scattering study of the near-stoichiometric Heusler alloy Ni 2.03 Mn 0.97 Ga[13].For Ni 2.03 Mn 0.97 Ga, they found the value of μ s to be 4.01 μ B /f.u. at 110 K in a field of 2 T. The value of μ s at 5 K for Ni 2 MnGa in the present study is in good agreement with the value reported by Ahuja et al.[13].

Figure 1 .
Figure 1.Phase diagram of Ni 2 Mn 1 − x Cu x Ga (0 ≤ x ≤ 0.4) alloys [9].Para and Ferro mean the paramagnetic and ferromagnetic state, respectively.A and M represent the austenite and martensite phases, respectively.T p is the premartensitic transition temperature.T C and T M are the Curie temperature and the martensitic transition temperature, respectively.

Figure 2 .
Figure 2. Phase diagram of Ni 2 MnGa 1 − y Cu y (0 ≤ y ≤ 0.25) alloys [10].Para and Ferro mean the paramagnetic state and ferromagnetic one, respectively.A and M represent the austenitic and martensitic phases, respectively.T C , T M and T p are the Curie temperature, the martensitic transition temperature, and premartensitic transition temperature, respectively.