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Magnetic properties of ferromagnetic Heusler alloy Co2NbGa
Journal Pre-proofs Magnetic properties of ferromagnetic Heusler alloy Co2NbGa T. Kanomata, H. Nishihara, T. Osaki, M. Doi, T. Sakon, Y. Adachi, T. Kihara, K. Obara, T. Shishido PII: DOI: Reference:
S0304-8853(19)33080-X https://doi.org/10.1016/j.jmmm.2020.166604 MAGMA 166604
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
3 September 2019 27 January 2020 9 February 2020
Please cite this article as: T. Kanomata, H. Nishihara, T. Osaki, M. Doi, T. Sakon, Y. Adachi, T. Kihara, K. Obara, T. Shishido, Magnetic properties of ferromagnetic Heusler alloy Co2NbGa, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/j.jmmm.2020.166604
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Magnetic properties of ferromagnetic Heusler alloy Co2NbGa
T. Kanomataa,b, H. Nishiharac, T. Osakib, M. Doia,b, T. Sakonc, Y. Adachid,*, T. Kiharae, K. Obarae, T. Shishidoe a
Research Institute for Engineering and Technology, Tohoku Gakuin University, Tagajo 985-8537,
Japan b
Graduate School of Engineering, Tohoku Gakuin University, Tagajo 985-8537, Japan
c
Faculty of Science and Technology, Ryukoku University, Otsu 520-2194, Japan
d
Gradual School of Science and Technology, Yamagata University, Yonezawa 992-8510, Japan
e
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
*
Correspondence author: Tel: +81-23-826-3381.
E-mail address: [email protected] (Y. Adachi)
1
ABSTRACT The compound Co2NbGa crystallizes in the Heusler-type structure. Magnetization measurements of Co2NbGa have been made under ambient pressure using a SQUID magnetometer. The spontaneous magnetic moment at 5 K and the Curie temperature are 1.81 μB/f.u. and 351 K, respectively. Many magnetic properties of the itinerant electron ferromagnets are explained by the Takahashi’s spin fluctuation theory. In the Takahashi’s spin fluctuation theory, spectral parameters of spin fluctuations, T0 and TA, are involved in various magnetic properties derived theoretically. In this work, we estimated T0 and TA of Co2NbGa by using the results of magnetization measurements at 5 K: T0 = 2.1 × 103 K and TA = 4.7 × 103 K. This experiment proved that the squared spontaneous magnetization Ms(T)2 is proportional to T2 at low temperature. The TA value estimated from the Ms(T)2 vs. T2 curve is 6.6 × 103 K. Furthermore, the field-induced magnetization M4 around TC is found to be proportional to H/M in the low magnetic field region.
Keywords: Magnetization Itinerant electron ferromagnet Spin fluctuation Magnetic transition
2
1. Introduction
Many of Co-based full Heusler alloys shows half-metallic behavior [1-3], and therefore, they have attracted much attention as potential applications for spintronic devices. These materials belong to a group of ternary intermetallic ordered alloys with the stoichiometric composition Co2MZ ordered in an L21-type structure where M is generally a transition metal atom, and Z is any one of the large number of s-p elements [4,5]. These alloys are broadly divided into two groups. In the first group containing Co2MZ (M = Mn and Fe, Z = Al, Si, and Ga), M atoms carry a magnetic moment. There have been many studies for the magnetic properties of this group of Co 2MZ alloys aiming at future spintronic devices [6-10]. The second group consists of those in which the magnetic moment is confined to Co atoms. Co-based full Heusler alloys Co2MZ (M = Ti, Nb, Zr and Hf) belong to this group. Contrary to the first group, there is little information concerning the magnetic properties of the second group, in particular those of Co2NbGa. Hereafter, we focus on the magnetism of Co2NbGa. Buschow and van Engen reported the basic magnetic properties of Co2MZ (M=Ti, V, Cr, Mn, Fe, Nb, Zr, Ta, and Hf, Z=Al and Ga) [11]. In their study, the saturation magnetic moment of Co2NbGa is estimated as 1.39 μB/f.u. from the magnetization measurement performed at 4.2 K. However, the temperature and the magnetic field dependences of the magnetization are not reported. Therefore, the detailed magnetic properties of Co 2NbGa are still unclear. In this study, we have carried out magnetization measurements on Co 2NbGa in wide range of temperature and magnetic field to obtain the comprehensive understanding of its magnetic properties. Through the careful analysis of the experimental data which are taken using the sample with high order parameter, we reveal that Co2NbGa exhibits itinerant electron magnetism. In this paper, we evaluate the itinerancy of Co2NbGa using the spin fluctuation theory developed by Takahashi [12,13].
3
2. Experimental
A polycrystalline sample of Co2NbGa was prepared by the repeated melting of appropriately composed mixtures of 99.9% pure Co, 99.96% pure Nb and 99.9999% pure Ga in an argon arc furnace. The weight loss (0.01%) after melting was negligible and so the sample was assumed to have the nominal composition. To achieve a homogenized sample, the reaction product was pulverized and annealed in vacuum at 900°C for 7 days after which it was quenched into cold water. Then, the pulverization and annealing process was repeated two times to ensure a well homogenized sample. The phase characterization of the sample was investigated by X-ray powder diffraction measurements using Cu-Kα radiation. The magnetization data were collected using a commercial superconducting quantum interference device (SQUID) magnetometer.
3. Results and discussion
The Heusler L21-type structure is composed of four interpenetrating fcc sublattices with A, B, C, and D sites. The A, B, C, and D sites are located at (0,0,0), (1/4,1/4,1/4), (1/2,1/2,1/2), and (3/4,3/4,3/4), respectively. In the stoichiometric Co2MZ Heusler alloys, the Co atoms occupy the A and C sites, and the M and Z atoms the B and D sites, respectively, as shown in Fig. 1. The upper part of Fig. 2 shows the X-ray powder diffraction pattern of Co2NbGa observed at room temperature. All of the experimentally obtained diffraction lines can be indexed using a fcc structure with a lattice parameter of 5.9579 ± 0.0007 Å at room temperature. This value is in good agreement with the lattice parameter reported by Buschow and van Engen [11]. The lattice parameter refinement in this study was performed using the program “CellCalc” developed by Miura [14]. The X-ray powder diffraction
4
pattern of Co2NbGa calculated using the Heusler L21-type structure (space group: Fm 3 m) is shown in the lower panel of Fig. 2. The good agreement between the experimentally obtained and calculated X-ray diffraction patterns indicates that the powder sample of Co2NbGa is ordered in the Heusler L21type structure. The upper panel of Fig. 3 shows the temperature dependence of the magnetization M(T, H) of Co2NbGa measured in a magnetic field of 100 Oe. The red and blue lines in this figure show the zerofield cooling (ZFC) and field cooling (FC) processes, respectively. As shown in the upper panel of Fig. 3, the magnetization abruptly increases at ~360 K with decreasing temperature. This corresponds to the transition from the paramagnetic to the ferromagnetic state. As described below, Co2NbGa has a feature of itinerant electron ferromagnet. For the itinerant electron ferromagnets, Arrott plots are not generally linear in the vicinity of the Curie temperature TC [13]. In fact, the magnetization curve at 350 K of Co2NbGa shows a convex-type behavior as shown in Fig.8, indicating that TC cannot be estimated from the Arrott plots of the M vs. T curves around TC. As shown in the lower panel of Fig. 3, the dM/dT vs. T curve of Co2NbGa shows a sharp dip. In this study, we defined the minimum point (inflection point) of the dM/dT vs. T curve as the Curie temperature (TC). TC of Co2NbGa is found to be 351 K. As far as we know, there is no information concerning TC for Co2NbGa in the literature. A characteristic feature of the present data is the bifurcation between ZFC and FC dependences as shown in the upper panel of Fig. 3. This may be due to the movement of magnetic domain walls existing in the ferromagnetic phase and/or due to magnetic anisotropy which aligns the spins in a preferred direction. Figure 4 shows the magnetic isotherms of Co2NbGa in magnetic fields up to 50 kOe for temperatures 5 K ≤ T ≤ 120 K (a) and 140 K ≤ T ≤ 300 K (b). As shown in Fig. 4(a), the magnetization of Co2NbGa at 5 K increases linearly with increasing magnetic field above ~20 kOe. The high field magnetic susceptibility χhf at 5 K of Co2NbGa is found to be ~0.01 emu/g·kOe, which was determined
5
from the linear part of high field magnetization curve. The magnetization at 5 K for the itinerant electron ferromagnets such as Co2TiGa, Co2ZrAl and Rh2NiGe with the Heusler-type structure also increases with increasing magnetic field above ~10 kOe [15-17]. The values of χhf for Co2TiGa, Co2ZrAl and Rh2NiGe were found to be ~0.01 emu/g·kOe, ~0.006 emu/g·kOe and ~0.01 emu/g·kOe, respectively. On the other hand, the magnetization at low temperature of the half-metallic Heusler alloys Co2VGa and Co2TiSn is saturated in the magnetic field above ~10 kOe [18, 19]. The large magnetic field susceptibility in high field region is a feature of the itinerant electron ferromagnets with the Heusler-type structure. Arrott plots of the data, isotherms of M2 vs. H/M, are shown in Figs. 5(a) and 5(b). As maybe seen, the Arrott plots give a series of almost parallel straight lines over a wide temperature range below TC. The spontaneous magnetization Ms(T) was determined by the linear extrapolation to H/M=0 of the M2 vs. H/M curves. The spontaneous magnetic moment per formula unit of Co2NbGa at 5 K was found to be 1.81 μB. Assuming that neither the Nb nor the Ga atoms carry a magnetic moment, the spontaneous magnetic moment ps(5 K) per Co atom in Co2NbGa is 0.91 μB. Buschow and van Engen reported that the saturation magnetic moment at 4.2 K of Co2NbGa is 1.39 μB/f.u. [11]. The magnetic moment of Co2NbGa determined in this study is ~30% larger than that reported by Buschow and van Engen. Buschow and van Engen [11] prepared the polycrystalline Co2NbGa by annealing the reaction product at 800°C for 14 days after arc melting the mixture of the constituent elements. As mentioned above, the sample in this study was prepared by repeating three times the pulverization and annealing at 900°C for 7 days of the sample to ensure a well homogenized sample. Therefore, the order parameter of crystal structure in this study should be higher than that of sample used in the experiments of Buschow and van Engen. Thus, it is considered that the high magnetic moment of Co2NbGa in this study than that reported by Buschow and van Engen [11] is attributed to the difference of the order parameter of crystal structure. The electronic and magnetic properties of a series of Co-based full Heusler alloys have been investigated by using the first-
6
principles calculations. It was predicted that many Co2MZ alloys are half-metallic [1-3]. Half-metallic full Heusler alloys follow a Slater-Pauling (SP) behavior [20], i.e., the total magnetic moment per formula unit, pstot, in μB scales with the total number of valence electrons, Zt, following the rule: pstot = Zt – 24. If Co2NbGa is a half-metallic, the SP rule predicts that pstot value should be 2.0 μB/f.u. The total magnetic moment at 5 K of Co2NbGa determined in this study does not follow the SP rule, suggesting that Co2NbGa is not a half-metallic ferromagnet, which always has an energy gap for one of the spin directions at the Fermi level. The temperature dependence of the spontaneous magnetization Ms(T) of Co2NbGa is shown in Fig. 6 in which the open circles indicate the experimental values determined by the Arrott plot analysis in this study. The solid line in Fig. 6 was calculated using the mean field theory on the basis of the localized electron model [21], where we used the values of TC = 351 K and spin s = 1/2 because the magnetic moment per Co atom at 5 K of Co2NbGa is 0.91 μB. As shown in Fig. 6, the values of Ms(T) determined in this study fall below the solid line. This means that the Ms (T) vs. T curve of Co2NbGa is not explained by the mean field theory on the basis of the localized electron model, and indicates the existence of the special modulation of the local magnetic field caused by the spin fluctuation effect. Similar temperature dependence of Ms(T) is observed in FeNi binary alloy system [22]. The self-consistent renormalization (SCR) spin fluctuation theory by Moriya and Kawabata has been successful in explaining the various interesting properties of itinerant electron magnets [23, 24]. Subsequently, Takahashi has reported a new spin fluctuation theory [12, 13] for itinerant electron ferromagnets, in which quantum spin fluctuations (zero-point spin fluctuation) are also considered in addition to thermal spin fluctuations. The magnetic properties of a number of itinerant electron ferromagnets such as (Fe, Co)Si [25], MnSi [26], Ni-Pt alloy [27, 28], CrAlGe [29, 30], Co2TiGa [15], Co2ZrAl [16], CoVSb [31], and Rh2NiGe [17] have been successfully discussed using Takahashi’s spin fluctuation theory. Recently, the magnetic properties of pure Ni [32], the ferromagnetic shape
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memory alloy Ni2MnGa [32, 33], and actinide 5f-electron system [34] have been explained using the spin fluctuation theory [12, 13] developed by Takahashi. According to the Takahashi’s spin fluctuation theory [12, 13], the fourth order expansion coefficient F1 of magnetic free energy and the spontaneous magnetic moment ps(0) are expressed by the following equations: 𝐹1 =
4 𝑘B 𝑇A2 15 𝑇0
(1)
𝑝s (0)2 15𝑇0 4 = 𝑐𝜂 , 4 𝑇A 𝑝s (0) =
c = 0.3353 ,
(2)
𝑀s (0) 𝑇C , 𝜂3 = , 𝑁0 𝜇B 𝑇0
where kB is the Boltzmann constant, μB the Bohr magneton, N0 the number of magnetic sites, and Ms(0) the spontaneous magnetization at 0 K. The spectral parameters TA and T0 represent the spectral widths of the spin fluctuation spectra in wave vector and frequency spaces, respectively. In the spin fluctuation theories [12, 13, 24], the parameters T0 and TA characterize various magnetic properties derived theoretically. The values of F1 and ps(0) of Co2NbGa are obtained experimentally from the analysis of the Arrott plots in this study. As the Curie temperature is 351 K, the spontaneous magnetization Ms(0) at 0 K was approximated by that measured at 5 K. The parameter T0 can be expressed by eliminating TA from eqs. (1) and (2) as follows: 5⁄ 6
𝑇0
=
8√15𝑐 𝑘B 4⁄3 √ 𝑇 . 𝑝s (0)2 𝐹1 C
(3)
From the above expression, quantitative values for the energy scale of spin fluctuation spectrum can be obtained. The values obtained are T0 = 2.1 × 103 K, TA = 4.7 × 103 K, and η = 0.55. Characteristic parameters for the spin fluctuations in some itinerant electron ferromagnets with the Heusler-type structure are summarized in Table 1. All values summarized in Table 1 were estimated using eqs. (1)(3) from the results of macroscopic magnetization measurements. As seen in Table 1, the value of T0 for Co2NbGa is comparable to those of Co2TiGa, Co2ZrAl, CoVSb and Rh2NiGa Heusler alloys. The
8
value of η (= 0.55) for Co2NbGa is also almost same to those of Co2TiGa, Co2ZrAl, and Rh2NiGe Heusler alloys. On the other hand, the values of η for weak itinerant ferromagnets such as ZrZn2 and Ni3Al are small (η ~ 0.25) [13]. Figure 7 shows the Ms(T)2 vs. T2 plot at low temperature for Co2NbGa. Takahashi’s spin fluctuation theory gives the following relation for the temperature dependence of the spontaneous magnetization at low temperature: 2
𝑝s (𝑇) 112.1 𝑇 2 [ ] =1− ( ) , 𝑝s (0) 𝑝s (0)4 𝑇A
(4)
where the effect of the spin wave was neglected [13]. As shown in Fig. 7, the experimental results in this study are consistent of the prediction of Takahashi’s spin fluctuation theory mentioned above. From eq. (4) by using the data at 5 K ≤ T ≤ 80 K, TA is estimated to be 6.6 × 103 K, which is consistent with the value (4.7 × 103 K) determined by the magnetization process at 5 K. Lonzarich and Taillefer [35] also gave the quadratic temperature dependence of Ms(T)2 over a wide range well below TC for itinerant electron ferromagnetic metals in their model, taking account of both longitudinal and transverse spin fluctuations. Figure 8 shows the M4 versus H/M curve at 350 K of Co2NbGa. The value of TC for Co2NbGa is 351 K as mentioned above. As seen in Fig. 8, M4 of Co2NbGa is proportional to H/M at 350 K. Takahashi’s spin fluctuation theory gives the following relation for the magnetic field dependence of the magnetization at TC [13]. 𝐻 𝑘B 𝑇A3 𝑀4 = ∙ 5 6, 2 𝑀 2[3𝜋𝑇 (2 + √5)] 𝑁0 𝜇B
(5)
C
We estimated the TA value from eq. (5) using the data in the low magnetic field region of the M4 vs. H/M curve. The TA value is estimated to be 6.4 × 103 K. This value is also consistent with the value (4.7 × 103) estimated by the magnetization process at 5 K. It should be noted that the measurement temperature (350 K) of the magnetization process shown in Fig. 8 is very close to TC (351 K). However, as shown in Fig. 8, in the high magnetic field region the values of M4 deviate from a straight line. The reason for this deviation is not clear.
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4. Conclusion
The compound Co2NbGa crystallizes in the normal Heusler-type structure. The lattice parameter is found to be 5.9579 ± 0.0007 Å at room temperature. Co2NbGa undergoes a magnetic transition at 351 K from the paramagnetic state to the ferromagnetic one with decreasing temperature. The spontaneous magnetic moment at 5 K is found to be 1.81 μB/f.u. The magnetization at 5 K increases linearly with increasing magnetic field above ~20 kOe. The high field magnetic susceptibility at 5 K is ~0.01 emu/g·kOe. On the basis of the experimental results of the magnetization process at 5 K, the spectral parameters T0 and TA characterizing spin fluctuations in Co2NbGa are estimated by using the spin fluctuation theory developed by Takahashi. The values of T0 and TA are 2.1 × 103 K and 4.7 × 103 K, respectively. The squared spontaneous magnetization of Co 2NbGa is proportional to T2 at low temperature. The TA value estimated from Ms (T)2 vs. T2 curve is 6.6 × 103 K, which is consistent with the TA value determined by the magnetization process at 5 K. According to the prediction of Takahashi’s spin fluctuation theory, the field-induced magnetization M4 at TC is proportional to H/M. In this study, it was confirmed that M4 of Co2NbGa is proportional to H/M at 350 K in the low magnetic field region. Thus, the magnetic properties of Co2NbGa observed in this study can be analyzed consistently by the Takahashi’s spin fluctuation theory.
Acknowledgements
The authors would like to express our sincere thanks to Professor K.R.A. Ziebeck for reading the manuscript. This work was partly supported by a grant based on the High-Tech Research Center Program for private universities from the Japan Ministry of Education, Culture, Sports, Science and
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Technology.
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References
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Figure captions Fig. 1. The crystal structure of Co2MZ Heusler alloys. The sites are presented by A, B, C, and D. Fig. 2. The upper part shows the experimental X-ray powder diffraction pattern of Co2NbGa at room temperature. The lower part is the calculated X-ray powder diffraction pattern of Co2NbGa. Fig. 3. The temperature dependence of the magnetization M (upper panel) and dM/dT (lower panel) of Co2NbGa in a field of 100 Oe. The red and blue lines show the zero-field-cooling (ZFC) and fieldcooling (FC) processes, respectively. Fig. 4. The magnetization curves of Co2NbGa at various temperatures in magnetic fields up to 50 kOe: (a) 5 K ≤ T ≤ 120 K and (b) 140 K ≤ T ≤ 300 K. Fig. 5. Magnetic isotherms of Co2NbGa in the form of Arrott plots: (a) 5 K ≤ T ≤ 120 K, (b) 140 K ≤ T ≤ 300 K. Fig. 6. The temperature dependence of the spontaneous magnetization Ms (T) for Co2NbGa. The open circles indicate the experimental values and the solid line was calculated using the mean field theory on the basis of the localized electron model. Fig. 7. Ms (T)2 vs. T2 plots of Co2NbGa, where Ms (T) represents the spontaneous magnetization. Fig. 8. M4 vs. H/M plots at 350 K for Co2NbGa.
15
Table 1. Spectral parameters T0, TA estimated from magnetization measurements.
T0 (K)
TA (K)
η
351
2.1×103
4.7×103
0.55
128
0.834×103
8.00×103
0.54
[15]
4
0.52
[16]
Substance
TC (K)
Co2NbGa Co2TiGa
1.38×10 4.7×104
0.33
[31]
3
0.47
[17]
180
1.28×10
CoVSb
45
1.21×103
113
1.1×10
this work
3
Co2ZrAl Rh2NiGe
Reference
3
3.3×10
16
Highlights Article: “Magnetic properties of ferromagnetic Heusler alloy Co 2NbGa” • The stoichiometric compound Co2NbGa crystallizes in the Heusler-type structure. • Co2NbGa is ferromagnetic below the Curie temperature of 351 K. • The spontaneous magnetic moment at 5 K of Co 2NbGa is 1.81 μB/f.u. • The spectral parameters T0 and TA of the spin fluctuation for Co2NbGa are estimated to be 2.1 x 103 K and 4.7 x 103 K by using the results of magnetization measurements at 5 K, respectively. • The TA value estimated from the Ms(T)2 vs. T2 curve is 6.6 × 103 K. • The field-induced magnetization M4 around TC is found to be proportional to H/M in the low magnetic field region.
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S0304-8853(19)33080-X https://doi.org/10.1016/j.jmmm.2020.166604 MAGMA 166604
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
3 September 2019 27 January 2020 9 February 2020
Please cite this article as: T. Kanomata, H. Nishihara, T. Osaki, M. Doi, T. Sakon, Y. Adachi, T. Kihara, K. Obara, T. Shishido, Magnetic properties of ferromagnetic Heusler alloy Co2NbGa, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/j.jmmm.2020.166604
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Magnetic properties of ferromagnetic Heusler alloy Co2NbGa
T. Kanomataa,b, H. Nishiharac, T. Osakib, M. Doia,b, T. Sakonc, Y. Adachid,*, T. Kiharae, K. Obarae, T. Shishidoe a
Research Institute for Engineering and Technology, Tohoku Gakuin University, Tagajo 985-8537,
Japan b
Graduate School of Engineering, Tohoku Gakuin University, Tagajo 985-8537, Japan
c
Faculty of Science and Technology, Ryukoku University, Otsu 520-2194, Japan
d
Gradual School of Science and Technology, Yamagata University, Yonezawa 992-8510, Japan
e
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
*
Correspondence author: Tel: +81-23-826-3381.
E-mail address: [email protected] (Y. Adachi)
1
ABSTRACT The compound Co2NbGa crystallizes in the Heusler-type structure. Magnetization measurements of Co2NbGa have been made under ambient pressure using a SQUID magnetometer. The spontaneous magnetic moment at 5 K and the Curie temperature are 1.81 μB/f.u. and 351 K, respectively. Many magnetic properties of the itinerant electron ferromagnets are explained by the Takahashi’s spin fluctuation theory. In the Takahashi’s spin fluctuation theory, spectral parameters of spin fluctuations, T0 and TA, are involved in various magnetic properties derived theoretically. In this work, we estimated T0 and TA of Co2NbGa by using the results of magnetization measurements at 5 K: T0 = 2.1 × 103 K and TA = 4.7 × 103 K. This experiment proved that the squared spontaneous magnetization Ms(T)2 is proportional to T2 at low temperature. The TA value estimated from the Ms(T)2 vs. T2 curve is 6.6 × 103 K. Furthermore, the field-induced magnetization M4 around TC is found to be proportional to H/M in the low magnetic field region.
Keywords: Magnetization Itinerant electron ferromagnet Spin fluctuation Magnetic transition
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1. Introduction
Many of Co-based full Heusler alloys shows half-metallic behavior [1-3], and therefore, they have attracted much attention as potential applications for spintronic devices. These materials belong to a group of ternary intermetallic ordered alloys with the stoichiometric composition Co2MZ ordered in an L21-type structure where M is generally a transition metal atom, and Z is any one of the large number of s-p elements [4,5]. These alloys are broadly divided into two groups. In the first group containing Co2MZ (M = Mn and Fe, Z = Al, Si, and Ga), M atoms carry a magnetic moment. There have been many studies for the magnetic properties of this group of Co 2MZ alloys aiming at future spintronic devices [6-10]. The second group consists of those in which the magnetic moment is confined to Co atoms. Co-based full Heusler alloys Co2MZ (M = Ti, Nb, Zr and Hf) belong to this group. Contrary to the first group, there is little information concerning the magnetic properties of the second group, in particular those of Co2NbGa. Hereafter, we focus on the magnetism of Co2NbGa. Buschow and van Engen reported the basic magnetic properties of Co2MZ (M=Ti, V, Cr, Mn, Fe, Nb, Zr, Ta, and Hf, Z=Al and Ga) [11]. In their study, the saturation magnetic moment of Co2NbGa is estimated as 1.39 μB/f.u. from the magnetization measurement performed at 4.2 K. However, the temperature and the magnetic field dependences of the magnetization are not reported. Therefore, the detailed magnetic properties of Co 2NbGa are still unclear. In this study, we have carried out magnetization measurements on Co 2NbGa in wide range of temperature and magnetic field to obtain the comprehensive understanding of its magnetic properties. Through the careful analysis of the experimental data which are taken using the sample with high order parameter, we reveal that Co2NbGa exhibits itinerant electron magnetism. In this paper, we evaluate the itinerancy of Co2NbGa using the spin fluctuation theory developed by Takahashi [12,13].
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2. Experimental
A polycrystalline sample of Co2NbGa was prepared by the repeated melting of appropriately composed mixtures of 99.9% pure Co, 99.96% pure Nb and 99.9999% pure Ga in an argon arc furnace. The weight loss (0.01%) after melting was negligible and so the sample was assumed to have the nominal composition. To achieve a homogenized sample, the reaction product was pulverized and annealed in vacuum at 900°C for 7 days after which it was quenched into cold water. Then, the pulverization and annealing process was repeated two times to ensure a well homogenized sample. The phase characterization of the sample was investigated by X-ray powder diffraction measurements using Cu-Kα radiation. The magnetization data were collected using a commercial superconducting quantum interference device (SQUID) magnetometer.
3. Results and discussion
The Heusler L21-type structure is composed of four interpenetrating fcc sublattices with A, B, C, and D sites. The A, B, C, and D sites are located at (0,0,0), (1/4,1/4,1/4), (1/2,1/2,1/2), and (3/4,3/4,3/4), respectively. In the stoichiometric Co2MZ Heusler alloys, the Co atoms occupy the A and C sites, and the M and Z atoms the B and D sites, respectively, as shown in Fig. 1. The upper part of Fig. 2 shows the X-ray powder diffraction pattern of Co2NbGa observed at room temperature. All of the experimentally obtained diffraction lines can be indexed using a fcc structure with a lattice parameter of 5.9579 ± 0.0007 Å at room temperature. This value is in good agreement with the lattice parameter reported by Buschow and van Engen [11]. The lattice parameter refinement in this study was performed using the program “CellCalc” developed by Miura [14]. The X-ray powder diffraction
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pattern of Co2NbGa calculated using the Heusler L21-type structure (space group: Fm 3 m) is shown in the lower panel of Fig. 2. The good agreement between the experimentally obtained and calculated X-ray diffraction patterns indicates that the powder sample of Co2NbGa is ordered in the Heusler L21type structure. The upper panel of Fig. 3 shows the temperature dependence of the magnetization M(T, H) of Co2NbGa measured in a magnetic field of 100 Oe. The red and blue lines in this figure show the zerofield cooling (ZFC) and field cooling (FC) processes, respectively. As shown in the upper panel of Fig. 3, the magnetization abruptly increases at ~360 K with decreasing temperature. This corresponds to the transition from the paramagnetic to the ferromagnetic state. As described below, Co2NbGa has a feature of itinerant electron ferromagnet. For the itinerant electron ferromagnets, Arrott plots are not generally linear in the vicinity of the Curie temperature TC [13]. In fact, the magnetization curve at 350 K of Co2NbGa shows a convex-type behavior as shown in Fig.8, indicating that TC cannot be estimated from the Arrott plots of the M vs. T curves around TC. As shown in the lower panel of Fig. 3, the dM/dT vs. T curve of Co2NbGa shows a sharp dip. In this study, we defined the minimum point (inflection point) of the dM/dT vs. T curve as the Curie temperature (TC). TC of Co2NbGa is found to be 351 K. As far as we know, there is no information concerning TC for Co2NbGa in the literature. A characteristic feature of the present data is the bifurcation between ZFC and FC dependences as shown in the upper panel of Fig. 3. This may be due to the movement of magnetic domain walls existing in the ferromagnetic phase and/or due to magnetic anisotropy which aligns the spins in a preferred direction. Figure 4 shows the magnetic isotherms of Co2NbGa in magnetic fields up to 50 kOe for temperatures 5 K ≤ T ≤ 120 K (a) and 140 K ≤ T ≤ 300 K (b). As shown in Fig. 4(a), the magnetization of Co2NbGa at 5 K increases linearly with increasing magnetic field above ~20 kOe. The high field magnetic susceptibility χhf at 5 K of Co2NbGa is found to be ~0.01 emu/g·kOe, which was determined
5
from the linear part of high field magnetization curve. The magnetization at 5 K for the itinerant electron ferromagnets such as Co2TiGa, Co2ZrAl and Rh2NiGe with the Heusler-type structure also increases with increasing magnetic field above ~10 kOe [15-17]. The values of χhf for Co2TiGa, Co2ZrAl and Rh2NiGe were found to be ~0.01 emu/g·kOe, ~0.006 emu/g·kOe and ~0.01 emu/g·kOe, respectively. On the other hand, the magnetization at low temperature of the half-metallic Heusler alloys Co2VGa and Co2TiSn is saturated in the magnetic field above ~10 kOe [18, 19]. The large magnetic field susceptibility in high field region is a feature of the itinerant electron ferromagnets with the Heusler-type structure. Arrott plots of the data, isotherms of M2 vs. H/M, are shown in Figs. 5(a) and 5(b). As maybe seen, the Arrott plots give a series of almost parallel straight lines over a wide temperature range below TC. The spontaneous magnetization Ms(T) was determined by the linear extrapolation to H/M=0 of the M2 vs. H/M curves. The spontaneous magnetic moment per formula unit of Co2NbGa at 5 K was found to be 1.81 μB. Assuming that neither the Nb nor the Ga atoms carry a magnetic moment, the spontaneous magnetic moment ps(5 K) per Co atom in Co2NbGa is 0.91 μB. Buschow and van Engen reported that the saturation magnetic moment at 4.2 K of Co2NbGa is 1.39 μB/f.u. [11]. The magnetic moment of Co2NbGa determined in this study is ~30% larger than that reported by Buschow and van Engen. Buschow and van Engen [11] prepared the polycrystalline Co2NbGa by annealing the reaction product at 800°C for 14 days after arc melting the mixture of the constituent elements. As mentioned above, the sample in this study was prepared by repeating three times the pulverization and annealing at 900°C for 7 days of the sample to ensure a well homogenized sample. Therefore, the order parameter of crystal structure in this study should be higher than that of sample used in the experiments of Buschow and van Engen. Thus, it is considered that the high magnetic moment of Co2NbGa in this study than that reported by Buschow and van Engen [11] is attributed to the difference of the order parameter of crystal structure. The electronic and magnetic properties of a series of Co-based full Heusler alloys have been investigated by using the first-
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principles calculations. It was predicted that many Co2MZ alloys are half-metallic [1-3]. Half-metallic full Heusler alloys follow a Slater-Pauling (SP) behavior [20], i.e., the total magnetic moment per formula unit, pstot, in μB scales with the total number of valence electrons, Zt, following the rule: pstot = Zt – 24. If Co2NbGa is a half-metallic, the SP rule predicts that pstot value should be 2.0 μB/f.u. The total magnetic moment at 5 K of Co2NbGa determined in this study does not follow the SP rule, suggesting that Co2NbGa is not a half-metallic ferromagnet, which always has an energy gap for one of the spin directions at the Fermi level. The temperature dependence of the spontaneous magnetization Ms(T) of Co2NbGa is shown in Fig. 6 in which the open circles indicate the experimental values determined by the Arrott plot analysis in this study. The solid line in Fig. 6 was calculated using the mean field theory on the basis of the localized electron model [21], where we used the values of TC = 351 K and spin s = 1/2 because the magnetic moment per Co atom at 5 K of Co2NbGa is 0.91 μB. As shown in Fig. 6, the values of Ms(T) determined in this study fall below the solid line. This means that the Ms (T) vs. T curve of Co2NbGa is not explained by the mean field theory on the basis of the localized electron model, and indicates the existence of the special modulation of the local magnetic field caused by the spin fluctuation effect. Similar temperature dependence of Ms(T) is observed in FeNi binary alloy system [22]. The self-consistent renormalization (SCR) spin fluctuation theory by Moriya and Kawabata has been successful in explaining the various interesting properties of itinerant electron magnets [23, 24]. Subsequently, Takahashi has reported a new spin fluctuation theory [12, 13] for itinerant electron ferromagnets, in which quantum spin fluctuations (zero-point spin fluctuation) are also considered in addition to thermal spin fluctuations. The magnetic properties of a number of itinerant electron ferromagnets such as (Fe, Co)Si [25], MnSi [26], Ni-Pt alloy [27, 28], CrAlGe [29, 30], Co2TiGa [15], Co2ZrAl [16], CoVSb [31], and Rh2NiGe [17] have been successfully discussed using Takahashi’s spin fluctuation theory. Recently, the magnetic properties of pure Ni [32], the ferromagnetic shape
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memory alloy Ni2MnGa [32, 33], and actinide 5f-electron system [34] have been explained using the spin fluctuation theory [12, 13] developed by Takahashi. According to the Takahashi’s spin fluctuation theory [12, 13], the fourth order expansion coefficient F1 of magnetic free energy and the spontaneous magnetic moment ps(0) are expressed by the following equations: 𝐹1 =
4 𝑘B 𝑇A2 15 𝑇0
(1)
𝑝s (0)2 15𝑇0 4 = 𝑐𝜂 , 4 𝑇A 𝑝s (0) =
c = 0.3353 ,
(2)
𝑀s (0) 𝑇C , 𝜂3 = , 𝑁0 𝜇B 𝑇0
where kB is the Boltzmann constant, μB the Bohr magneton, N0 the number of magnetic sites, and Ms(0) the spontaneous magnetization at 0 K. The spectral parameters TA and T0 represent the spectral widths of the spin fluctuation spectra in wave vector and frequency spaces, respectively. In the spin fluctuation theories [12, 13, 24], the parameters T0 and TA characterize various magnetic properties derived theoretically. The values of F1 and ps(0) of Co2NbGa are obtained experimentally from the analysis of the Arrott plots in this study. As the Curie temperature is 351 K, the spontaneous magnetization Ms(0) at 0 K was approximated by that measured at 5 K. The parameter T0 can be expressed by eliminating TA from eqs. (1) and (2) as follows: 5⁄ 6
𝑇0
=
8√15𝑐 𝑘B 4⁄3 √ 𝑇 . 𝑝s (0)2 𝐹1 C
(3)
From the above expression, quantitative values for the energy scale of spin fluctuation spectrum can be obtained. The values obtained are T0 = 2.1 × 103 K, TA = 4.7 × 103 K, and η = 0.55. Characteristic parameters for the spin fluctuations in some itinerant electron ferromagnets with the Heusler-type structure are summarized in Table 1. All values summarized in Table 1 were estimated using eqs. (1)(3) from the results of macroscopic magnetization measurements. As seen in Table 1, the value of T0 for Co2NbGa is comparable to those of Co2TiGa, Co2ZrAl, CoVSb and Rh2NiGa Heusler alloys. The
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value of η (= 0.55) for Co2NbGa is also almost same to those of Co2TiGa, Co2ZrAl, and Rh2NiGe Heusler alloys. On the other hand, the values of η for weak itinerant ferromagnets such as ZrZn2 and Ni3Al are small (η ~ 0.25) [13]. Figure 7 shows the Ms(T)2 vs. T2 plot at low temperature for Co2NbGa. Takahashi’s spin fluctuation theory gives the following relation for the temperature dependence of the spontaneous magnetization at low temperature: 2
𝑝s (𝑇) 112.1 𝑇 2 [ ] =1− ( ) , 𝑝s (0) 𝑝s (0)4 𝑇A
(4)
where the effect of the spin wave was neglected [13]. As shown in Fig. 7, the experimental results in this study are consistent of the prediction of Takahashi’s spin fluctuation theory mentioned above. From eq. (4) by using the data at 5 K ≤ T ≤ 80 K, TA is estimated to be 6.6 × 103 K, which is consistent with the value (4.7 × 103 K) determined by the magnetization process at 5 K. Lonzarich and Taillefer [35] also gave the quadratic temperature dependence of Ms(T)2 over a wide range well below TC for itinerant electron ferromagnetic metals in their model, taking account of both longitudinal and transverse spin fluctuations. Figure 8 shows the M4 versus H/M curve at 350 K of Co2NbGa. The value of TC for Co2NbGa is 351 K as mentioned above. As seen in Fig. 8, M4 of Co2NbGa is proportional to H/M at 350 K. Takahashi’s spin fluctuation theory gives the following relation for the magnetic field dependence of the magnetization at TC [13]. 𝐻 𝑘B 𝑇A3 𝑀4 = ∙ 5 6, 2 𝑀 2[3𝜋𝑇 (2 + √5)] 𝑁0 𝜇B
(5)
C
We estimated the TA value from eq. (5) using the data in the low magnetic field region of the M4 vs. H/M curve. The TA value is estimated to be 6.4 × 103 K. This value is also consistent with the value (4.7 × 103) estimated by the magnetization process at 5 K. It should be noted that the measurement temperature (350 K) of the magnetization process shown in Fig. 8 is very close to TC (351 K). However, as shown in Fig. 8, in the high magnetic field region the values of M4 deviate from a straight line. The reason for this deviation is not clear.
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4. Conclusion
The compound Co2NbGa crystallizes in the normal Heusler-type structure. The lattice parameter is found to be 5.9579 ± 0.0007 Å at room temperature. Co2NbGa undergoes a magnetic transition at 351 K from the paramagnetic state to the ferromagnetic one with decreasing temperature. The spontaneous magnetic moment at 5 K is found to be 1.81 μB/f.u. The magnetization at 5 K increases linearly with increasing magnetic field above ~20 kOe. The high field magnetic susceptibility at 5 K is ~0.01 emu/g·kOe. On the basis of the experimental results of the magnetization process at 5 K, the spectral parameters T0 and TA characterizing spin fluctuations in Co2NbGa are estimated by using the spin fluctuation theory developed by Takahashi. The values of T0 and TA are 2.1 × 103 K and 4.7 × 103 K, respectively. The squared spontaneous magnetization of Co 2NbGa is proportional to T2 at low temperature. The TA value estimated from Ms (T)2 vs. T2 curve is 6.6 × 103 K, which is consistent with the TA value determined by the magnetization process at 5 K. According to the prediction of Takahashi’s spin fluctuation theory, the field-induced magnetization M4 at TC is proportional to H/M. In this study, it was confirmed that M4 of Co2NbGa is proportional to H/M at 350 K in the low magnetic field region. Thus, the magnetic properties of Co2NbGa observed in this study can be analyzed consistently by the Takahashi’s spin fluctuation theory.
Acknowledgements
The authors would like to express our sincere thanks to Professor K.R.A. Ziebeck for reading the manuscript. This work was partly supported by a grant based on the High-Tech Research Center Program for private universities from the Japan Ministry of Education, Culture, Sports, Science and
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Technology.
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Figure captions Fig. 1. The crystal structure of Co2MZ Heusler alloys. The sites are presented by A, B, C, and D. Fig. 2. The upper part shows the experimental X-ray powder diffraction pattern of Co2NbGa at room temperature. The lower part is the calculated X-ray powder diffraction pattern of Co2NbGa. Fig. 3. The temperature dependence of the magnetization M (upper panel) and dM/dT (lower panel) of Co2NbGa in a field of 100 Oe. The red and blue lines show the zero-field-cooling (ZFC) and fieldcooling (FC) processes, respectively. Fig. 4. The magnetization curves of Co2NbGa at various temperatures in magnetic fields up to 50 kOe: (a) 5 K ≤ T ≤ 120 K and (b) 140 K ≤ T ≤ 300 K. Fig. 5. Magnetic isotherms of Co2NbGa in the form of Arrott plots: (a) 5 K ≤ T ≤ 120 K, (b) 140 K ≤ T ≤ 300 K. Fig. 6. The temperature dependence of the spontaneous magnetization Ms (T) for Co2NbGa. The open circles indicate the experimental values and the solid line was calculated using the mean field theory on the basis of the localized electron model. Fig. 7. Ms (T)2 vs. T2 plots of Co2NbGa, where Ms (T) represents the spontaneous magnetization. Fig. 8. M4 vs. H/M plots at 350 K for Co2NbGa.
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Table 1. Spectral parameters T0, TA estimated from magnetization measurements.
T0 (K)
TA (K)
η
351
2.1×103
4.7×103
0.55
128
0.834×103
8.00×103
0.54
[15]
4
0.52
[16]
Substance
TC (K)
Co2NbGa Co2TiGa
1.38×10 4.7×104
0.33
[31]
3
0.47
[17]
180
1.28×10
CoVSb
45
1.21×103
113
1.1×10
this work
3
Co2ZrAl Rh2NiGe
Reference
3
3.3×10
16
Highlights Article: “Magnetic properties of ferromagnetic Heusler alloy Co 2NbGa” • The stoichiometric compound Co2NbGa crystallizes in the Heusler-type structure. • Co2NbGa is ferromagnetic below the Curie temperature of 351 K. • The spontaneous magnetic moment at 5 K of Co 2NbGa is 1.81 μB/f.u. • The spectral parameters T0 and TA of the spin fluctuation for Co2NbGa are estimated to be 2.1 x 103 K and 4.7 x 103 K by using the results of magnetization measurements at 5 K, respectively. • The TA value estimated from the Ms(T)2 vs. T2 curve is 6.6 × 103 K. • The field-induced magnetization M4 around TC is found to be proportional to H/M in the low magnetic field region.
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