III. RESULTS AND DISCUSSION

Temperature dependence of magnetization, M/M _5K, of the as-prepared samples exhibits small hysteresis in field cooling and field heating curves at about 100 K (Fig. 1). Magnetization, M/M _5K, rapidly drops with temperature (see Fig. 1) indicating that at nearly room temperature, the as-prepared samples are not ferromagnetic. Magnetization and M/M _5K(T) of the as-prepared samples considerably depend on applied magnetic field.

FIG. 1.

Temperature dependence of magnetization measured in the as-prepared NiMnGa microwire. The M/M _5K(T) dependencies measured at low field are presented in the inset.

Additionally M/M _5K(H) dependencies do not present saturation even at 5 K [Fig. 2(a)]. At temperatures above 5 K, the as-prepared samples do not present coercivity [Fig. 2(b)]. These features of the as-prepared sample can be attributed to the magnetic and atomic disorders.

FIG. 2.

Magnetization curves of the as-prepared NiMnGa microwire measured at maximum field 50 kOe (a) and 1 kOe (b).

After annealing of NiMnGa microwires (T _ann = 973 K for 2 h), we observed considerable change of magnetic properties. The character of M/M _5K(H) dependencies of annealed NiMnGa microwires becomes completely different from the as-prepared samples: all M/M _5K(H) curves present saturation at relatively low H-values up to 260 K (Fig. 3). At low temperatures, annealed samples present coercivity, H _c, of about 200 Oe (Fig. 4). Coercivity decrease is observed with temperature increasing. Finally considerable magnetic softening can be appreciated at about 260 K (see Fig. 4).

FIG. 3.

Magnetization curves of NiMnGa microwire annealed at 973 K (2 h).

FIG. 4.

Low field magnetization curves of NiMnGa microwire annealed at 973 K (2 h).

A ferromagnetic ordering with Curie temperature, T _C, near room temperature (T _C ≈ 300 K) is observed in the samples annealed at 923 and 973 K (Figs. 5 and 6). Similar to the previously reported results on Heusler-type microwires,^{Reference Aronin, Abrosimova, Kiselev, Zhukova, Varga and Zhukov20,Reference Zhukova, Ipatov, Granovsky and Zhukov21} an increasing of M/M _5K-values at heating for low H-values (H = 200 Oe) right below T _C (Fig. 6) can be seen. Such maximum on M/M _5K(T) dependences in some of previous publications has been discussed considering the Hopkinson effect^{Reference Zhukov, Rodionova, Ilyn, Aliev, Varga, Michalik, Aronin, Abrosimova, Kiselev, Ipatov and Zhukova5} since magnetic softening is usually observed at the same temperatures range (Fig. 4). However, in some cases, this maximum on M/M _5K(T) dependences can be observed even for high magnetic fields.^{Reference Zhukov, Ipatov, Talaat, Blanco, Hernando, Gonzalez-Legarreta, Suñol and Zhukova11} Therefore the origin of such maximum on M/M _5K(T) dependences is also discussed considering a structural transformation.^{Reference Zhukov, Rodionova, Ilyn, Aliev, Varga, Michalik, Aronin, Abrosimova, Kiselev, Ipatov and Zhukova5,Reference Zhukov, Ipatov, Talaat, Blanco, Hernando, Gonzalez-Legarreta, Suñol and Zhukova11}

FIG. 5.

M/M _5K(T) dependencies of NiMnGa glass-coated microwires annealed at T _ann = 923 K for 2 h.

FIG. 6.

M/M _5K(T) dependencies of NiMnGa glass-coated microwires annealed at T _ann = 973 K for 2 h.

The most relevant feature of observed M/M _5K(T) dependences for the NiMnGa microwire annealed at 923 and 974 K (for 2 h) is that they clearly show the hysteretic anomalies typical for the MT (see Figs. 5 and 6). This anomaly is more appreciable after annealing at 973 K (see Fig. 6). It is worth mentioning that at lower annealing temperatures (773 K), such hysteretic behavior was not observed.^{Reference Zhukov, Ipatov, del Val, Taskaev, Churyukanova and Zhukova18} Consequently, annealing conditions (temperature and time) are essentially important for realization of the MT.

Qualitatively, observed M/M _5K(T) dependences of annealed samples are similar to those observed in the bulk Heusler-type alloys.^{Reference Chernenko1,Reference Khovailo, Chernenko, Cherechukin, Takagi and Abe22,Reference Kazakov, Prudnikov, Granovsky, Perov, Dubenko, Pathak, Samanta, Stadler, Ali, Zhukov, Ilyin and Gonzalez23} Generally, the anomalies in the temperature dependences of the magnetization for the bulk NiMnGa alloys can be explained considering three phase transition temperatures: T _CM—Curie temperature of MP, T _M—temperature of MT, and T _C—Curie temperature of the high temperature (cubic) AP.^{Reference Khovailo, Chernenko, Cherechukin, Takagi and Abe22–Reference Sanchez-Alarcos, Perez-Landazabal, Recarte, Rodrıguez-Velamazan and Chernenko24} The sequence of these transitions is determined by the chemical composition of the Ni–Mn–Ga alloy which is very convenient to express via the valence electron concentration per atom, e/a.^{Reference Chernenko1,Reference Chernenko, L’vov, Zagorodnyuk and Takagi25,Reference Wu and Yang26}

The Curie temperature, T _C, of AP can be evaluated from M/M _5K(T) dependences as a temperature at which magnetization drops to zero. However, more precisely, T _C-value can be evaluated from the first derivative of the magnetization.^{Reference Shevyrtalov, Zhukov, Zhukova and Rodionova27}

The T _C-values evaluated from Figs. 5 and 6 are smaller than those reported for alloys presenting e/a ≈ 7.63 (calculated considering real chemical composition of studied microwire).^{Reference Chernenko1,Reference Sanchez-Alarcos, Perez-Landazabal, Recarte, Rodrıguez-Velamazan and Chernenko24–Reference Wu and Yang26}

The sharp change in magnetization at T _M can be associated with a MT from the magnetic state (MP) characterized by lower magnetic moment to a ferromagnetic AP state with higher magnetic moment (Figs. 5 and 6). This assumption is confirmed by the change of hysteresis loop character observed at around 260 K (Fig. 4).

Observed changes upon annealing can be related to stress relaxation as well as to the structural changes.

X-ray studies of the as-prepared and annealed samples have been performed at room temperature. The XRD peak shape and position are affected by various factors, such as internal stresses, chemical composition, phase separation, or instrument resolution. In the present case, the measurements have been performed in the same samples. Therefore observed evolution of XRD spectra must be attributed to the changes related to annealing.

The diffraction peaks of all crystalline phases observed in the XRD pattern are quite close to each other and even overlapped (see Fig. 7). However certain structural changes (i.e., intensity and positions of XRD peaks) can be appreciated after annealing [see Fig. 7(a)]. Most evident changes can be appreciated from the analysis of the first XRD peak [see Fig. 7(b)].

FIG. 7.

XRD (a) and first diffraction peak (b) of the as-prepared and annealed NiMnGa microwires at 973 K for different times.

Corresponding to each diffraction peak, phases are identified using the database (International Center for Diffraction Data, www.icdd.com).

The fitting of the diffractogram of the crystalline peak is performed using the Gaussian function.

Such fitting allows us to calculate the following:

1. (i) The area of the Gaussian that is proportional to the amount of the corresponding crystalline phase.

2. (ii) The width of the Gaussian half-height (subtracting the line corresponding to the amorphous background) with Scherrer formula gives us the average grain size, D _g.

The average crystalline grain size, D _g, can be evaluated from the analysis of the first crystalline peak position and width using the well-established Debye–Scherrer correlation^{Reference Zhukov, Ipatov, Talaat, Blanco, Hernando, Gonzalez-Legarreta, Suñol and Zhukova11,Reference Zhukov, Ipatov, del Val, Taskaev, Churyukanova and Zhukova18}

(1)$${D_{\rm{g}}} = {{K\lambda } \over {\varepsilon \cos 2\theta }}\quad ,$$

where K is a dimensionless shape coefficient of the order of 0.9 (that can vary with the actual shape of the crystallite), ε is the full width at half maximum of the first crystalline peak, and 2θ is the peak position.

The XRD pattern of the as-prepared sample (with broad peak) fits better to coexistence of the Ga₄Ni₃ bcc phase (interatomic distance a = 1.1411 nm, D _g ≈ 26 nm) and amorphous phase. XRD of annealed at 973 K (1 h) NiMnGa microwires fits better to the mixed structure consisting of 50% GaNi cubic (a = 0.2873 nm, D _g ≈ 27 nm) and 50% Ni₂GaMn fcc phases (a = 0.5805 nm, D _g ≈ 9 nm). Increasing annealing time, we observed further changes of XRD patterns. Thus, the further increasing of the content of the GaNi cubic phase is observed after annealing at 973 K (2 h). Finally the XRD pattern of the sample annealed at 973 K (4 h) fits better to increasing of Ni₂GaMn fcc phase content in expense of the GaNi cubic phase and D _g growing. In NiMnGa microwire annealed at 973 K for 4 h, the content of the Ni₂GaMn fcc phase is about 75% and D _g ≈ 29 nm (see Fig. 7).

The aforementioned analysis involving the Debye–Scherrer correlation allows estimation of the average grain size. More detailed information can be provided using direct structural methods like transmission electron microscopy or atomic force microscopy (AFM). Recently the nanocrystalline structure of both as-prepared and annealed microwires with the same nominal composition (Ni₂GaMn) prepared using the same technique has been confirmed by the AFM studies. In particular, the annealed samples present grain size distribution ranging from 20 to 60 nm.^{Reference Shevyrtalov, Zhukov, Zhukova and Rodionova27}

It is worth mentioning that the as-prepared samples present mixed nanocrystalline–amorphous structure.

Additionally, amorphous glass coating contributes with a broad halo at small angles (2θ ≈ 15–20°). This part of spectra is not presented in Fig. 7.

It is worth mentioning that the magnetic ordering of the samples with the nanocrystalline structure can be different from the sample with larger grain size. This difference can be related to a larger contribution of the grain boundaries in nanocrystalline structures.^{Reference Tietze, Audehm, Chen, Schutz, Straumal, Protasova, Mazilkin, Straumal, Prokscha, Luetkens, Salman, Suter, Baretzky, Fink, Wenzel, Danilov and Goering28} Indeed the structure of grain boundaries is considered as consisting of flat (faceted) and curved (rough) portions. In most cases, facets are parallel to the most densely packed planes of coincidence site lattice formed by two lattices of abutting grains.

For the nanocrystalline materials, the specific grain boundary area increases with decreasing of the average grain size.^{Reference Tietze, Audehm, Chen, Schutz, Straumal, Protasova, Mazilkin, Straumal, Prokscha, Luetkens, Salman, Suter, Baretzky, Fink, Wenzel, Danilov and Goering28} Therefore, consideration of the intergranular regions’ contribution in nanocrystalline materials allows better understanding of properties.^{Reference Hernando, Navarro, Hadjipanayis and Siegel29} Additionally, increasing of stresses with increasing of the specific grain boundary area in nanocrystalline Heusler alloys can affect magnetic properties.

Consequently the magnetic ordering of nanocrystalline materials even presenting the same crystalline phases can be different from the bulk alloys.^{Reference Hernando, Navarro, Hadjipanayis and Siegel29,Reference Zhukov, Ipatov, Talaat, Aronin, Abrosimova, del Val and Zhukova30}

On the other hand, observed peculiarities in magnetic properties of studied NiMnGa microwires can be related to the evolution of the phase content upon annealing.

Usually the paramagnetic ordering is reported for the GaNi phase.^{Reference Hsu, Wang and Guo31} Additionally, paramagnetic ordering is reported for the Ga₄Ni₃ phase observed in the as-prepared microwires and also previously observed for NiGa thin films.^{Reference Aurongzeb, Song, Kipshidze, Yavich, Nyakiti, Lee, Chaudhuri, Temkin and Holtz32} Therefore the origin of ferromagnetic ordering of studied microwires can be related to either amorphous phase observed in the as-prepared microwires or Ni₂MnGa phase observed after long annealing.

It is worth mentioning that in NiMnGa thin films deposited on the cold substrate, the paramagnetic behavior in a wide temperature range has been previously observed.^{Reference Besseghini, Gambardella, Chernenko, Hagler, Pohl, Mullner, Ohtsuka and Doyle8} Similar to the studied NiMnGa microwires after annealing of NiMnGa thin films, a restoring of a ferromagnetic state has been reported.^{Reference Besseghini, Gambardella, Chernenko, Hagler, Pohl, Mullner, Ohtsuka and Doyle8} Such a difference of NiMnGa thin films with respect to bulk NiMnGa materials was explained considering internal stresses related to the preparation method.

The fabrication method of the glass-coated microwires involves simultaneous rapid solidification from the melt of metallic alloy and glass-coating with quite different thermal expansion coefficients.^{Reference Antonov, Borisov, Borisov, Prokoshin and Usov33–Reference Zhukov, Gonzalez, Torcunov, Pina, Prieto, Cobeño, Blanco, Larin and Baranov35} Both rapid solidification itself and presence of glass coating with different thermal expansion coefficients are the main factors responsible for the appearance of strong internal stresses distributed in a complex way within the microwires. According to all theoretical calculations and indirect experiments, the axial internal stresses in glass-coated microwires arising during the preparation process are the highest within the most part of the metallic nucleus.^{Reference Zhukov, Ipatov, Churyukanova, Talaat, Blanco and Zhukova36} The estimated value of internal stresses in microwires is between 100 and 1000 MPa.^{Reference Zhukov, Vázquez, Velázqez, Hernando and Larin37} The stress induced by the magnetic field in NiMnGa bulk alloys is between 1 and 7 MPa, i.e., much lower than the stress induced by the glass coating. Therefore the stresses induced by the glass coating can impede the first-order phase transition and hence internal stresses relaxation is needed.^{Reference Dunand and Müllner2}

Consequently after high temperature annealing (923–973 K), studied microwires present M/M _5K(T) dependencies more similar to that reported for bulk Heusler alloys exhibiting the hysteresis on the temperature dependence of magnetization attributed to the MT as well as a drastic change of magnetization at the Curie temperature, T _C, around 300 K, as a result of the improved structural order and precipitation of the Ni₂MnGa phase. The T _C values observed in Figs. 5 and 6 are still smaller than those evaluated from the phase diagram for e/a ≈ 7.63 (calculated considering real chemical composition of studied microwire).^{Reference Chernenko1}

As discussed elsewhere, the alloys with e/a ≈ 7.55–7.7 must display the high sensitivity of their crystalline structure on mechanical stress and magnetic field.^{Reference Chernenko1} As mentioned above, M/M _5K(T) dependences of the as-prepared microwires considerably affected by applied magnetic field. Although similar to thin films,^{Reference Besseghini, Gambardella, Chernenko, Hagler, Pohl, Mullner, Ohtsuka and Doyle8} these features of the as-prepared sample have been attributed to the magnetic and atomic disorder in part considerable influence of M/M _5K(T) dependences on magnetic field can be related to e/a-values.

As mentioned in Sec. I, one of the peculiarities of glass-coated NiMnGa microwires is the existence of insulating biocompatible glass coating additionally allowing improvement of mechanical properties especially in the case of fragile metallic wires (as the case of studied NiMnGa) surrounded by flexible glass coating.^{Reference Zhukova, Cobeño, Zhukov, de Arellano Lopez, López-Pombero, Blanco, Larin and Gonzalez38}

On the other hand, as shown above, the presence of the glass coating considerably affects magnetic properties of glass-coated microwires because of additional internal stresses. Therefore most previous attempts on preparation of thin glass-coated microwires presenting MT have not been completely successful.^{Reference Zhukov, Rodionova, Ilyn, Aliev, Varga, Michalik, Aronin, Abrosimova, Kiselev, Ipatov and Zhukova5–Reference Zhukov, Ipatov, del Val, Zhukova and Chernenko7,Reference Wang, Zheng, Nie, Ren, Wang, Müllner and Dunand10,Reference Zhukov, Ipatov, Talaat, Blanco, Hernando, Gonzalez-Legarreta, Suñol and Zhukova11} In the present study, we used higher annealing temperature that allowed us to achieve better internal stresses relaxation, disorder reduction, and precipitation of the Ni₂GaMn fcc phase. Consequently, the structure of both as-prepared and annealed NiMnGa microwires looks rather different from bulk NiMnGa materials.

Finally the composition of metallic nucleus is different from the stoichiometric one (Ni₂MnGa). This difference is related to the peculiarities of the preparation method involving alloy melting and casting. As discussed above, the sequence of phase transitions of the Ni–Mn–Ga alloy and hence phase composition and Curie temperature of studied microwire are determined by the chemical composition (usually expressed via e/a ratio).

Consequently, the structure of both the as-prepared and annealed Ni_2.52Mn_0.54Ga_0.94 microwires is rather different from Ni₂MnGa bulk materials.

Therefore additional efforts like preparation of the ingot for microwire casting with excess of Mn are needed to achieve the versatile properties reported for the stoichiometric (Ni₂MnGa) alloy. However, although microwires prepared from the Ni₂Mn₂Ga ingot present some interesting features (i.e., exchange bias and enhanced coercivity),^{Reference Zhukov, Ipatov, del Val, Churyukanova and Zhukova39} the MT was not realized in microwires with Ni₂Mn₂Ga nominal composition.