Zero thermal expansion with high Curie temperature in Ho₂Fe₁₆Cr alloy

Abstract

We report the observation of zero thermal expansion with a high Curie temperature in a Ho₂Fe₁₆Cr alloy. Among the R₂Fe_17−xCr_x (R = rare earth elements) series of alloys, Ho₂Fe₁₆Cr shows not only enhancement of the Curie temperature (T_C) to 415 K in comparison with the parent compound Ho₂Fe₁₇ (330 K), but also shows zero thermal expansion (ZTE) in the wide temperature range 13–330 K due to reduction of the magneto-volume effect. We believe that such a single component ZTE magnetic material with a T_C higher than room temperature is of practical importance.

---

1 Introduction

Recently, ZTE materials with a very low coefficient of thermal expansion (α) have attracted considerable interest as a particular class of functional materials.^1–6 These materials appear to be of immense practical importance to improve the performance of various electronic and optical devices. Several materials: YbGaGe,¹ Fe[Co(CN)₆],² In(HfMg)_0.5Mo₃O₁₂,³ 0.8PbTiO₃–0.2Bi(Ni_0.5Ti_0.5)O₃,⁴ antiperovskite manganese nitride Mn₃AN (A = Cu/Sn, Zn/Sn),⁵ (Al_0.3(HfMg)_0.85)(WO₄)₃,⁶ Invar alloys,^7,8 Sc_0.05Ga_0.05Fe_0.1F₃,⁹ La(Fe,Si)₁₃,¹⁰ La(Fe,Al)₁₃,¹¹ carbon doped La(Fe,Si)₁₃ (ref. 12) etc. have been identified as ZTE materials, in different ranges of temperature.

Materials showing negative thermal expansion (NTE) play a key role in producing ZTE materials.^13,14 In general, to achieve ZTE materials, attempts have been made to form composites by dispersing particles of a NTE material like ZrW₂O₈ into an isotropic matrix of positive thermal expansion (PTE) material like copper (Cu) or aluminium (Al).^13,15,16 ZTE composites have also been synthesized using antiperovskite NTE materials like Mn₃Cu_0.5A_0.5N (A = Ni, Sn),¹⁷ Mn₃Zn_0.5Sn_0.5N¹⁸ and Cu by optimizing their mass ratios. LaFe_10.5Co_1.0Si_1.5/Cu¹⁹ has been recently found to show a tailoring thermal expansion property. In such composites, the NTE material is used to compensate for the thermal expansion of the matrix of PTE material to obtain a desired low α. However, the actual values of α do not match the desired values, as the effects of the interfaces could not be estimated in advance accurately.¹³ Among the composites, α as low as 3.5 × 10⁻⁶ K⁻¹ in the range of T = 320–355 K, has been obtained in the case of a metal matrix composite Mn₃Cu_0.5Sn_0.5N_1−δ/AC8A.¹³ In composites, the large difference in α between the matrix and the compensator causes a stress at the interfaces or grain boundaries, and thereby, may degrade the composite functionalities by forming micro-cracks.¹³ Therefore, as a functional material, a single-component ZTE material¹³ will be more effective than a composite one.

A single component ZTE material can be formed as a solid solution of a PTE material and a NTE material. In(HfMg)_0.5Mo₃O₁₂ ³ is such a solid solution of a PTE material HfMgMo₃O₁₂ and a NTE material In₂Mo₃O₁₂. It shows ZTE in the temperature range 500–900 K with an average linear intrinsic α = −0.4 × 10⁻⁶ K⁻¹, and an average bulk α = 0.4 × 10⁻⁶ K⁻¹. A similar single-phase ceramic material, (Al_2x(HfMg)_1−x) (WO₄)₃,⁶ formed by combining a NTE material (HfMg)(WO₄)₃ and a PTE material Al₂(WO₄)₃, behaves like a ZTE material for x = 0.15, between room temperature and 800 °C.

A single component ZTE material can also be achieved by lowering the NTE coefficient of a NTE material, by weakening the inherent mechanism responsible for NTE. The underlying mechanism responsible for the observed NTE in different reported materials is not unique; rather, they are widely different.^13,20 For example, a flexible network causes NTE in ZrW₂O₈,²¹ LiAlSiO₄,²² Cd(CN)₂,²³ ReO₃,²⁴ siliceous faujasite,²⁵ metal nitroprussides,²⁶ HfScMo₂VO₁₂ (ref. 27) etc. whereas atomic radius contraction is responsible for NTE in Bi_0.95La_0.05NiO₃.²⁸ The site anisotropy results in NTE in GdPd₃B_0.25C_0.75,²⁹ and tetragonality introduces NTE in PbTiO₃.⁴ The magneto-volume effect (MVE) causes NTE in different magnetic materials like Invar alloys,^30,31 YMn₂,³² pure³³ and substituted R₂Fe₁₇ (R = rare earth element) compounds,^34–36 manganese antiperovskites.³⁷ A ZTE multiferroic compound 0.8PbTiO₃–0.2Bi(Ni_0.5Ti_0.5)O₃ (ref. 4) with α = 0.4 × 10⁻⁷ K⁻¹ between room temperature and 500 °C has been achieved by weakening the tetragonality of the parent compound PbTiO₃, by using the dopant Bi(Ni_0.5Ti_0.5)O₃. A similar study has also been done on Nd/Sm substituted 0.5PbTiO₃–0.5BiFeO₃.³⁸ Optimization of the heat treatment and the chemical composition lowers the NTE coefficient of antiperovskite Mn₃AN(A = Cu/Sn, Zn/Sn).⁵ ZTE can be achieved by weakening the MVE in magnetic materials showing NTE. R₂Fe₁₇ compounds are such magnetic materials, where on increasing the temperature, the lattice parameter c decreases faster than the lattice parameter a due to MVE, and thereby, results in NTE.

R₂Fe₁₇ compounds with a hexagonal Th₂Ni₁₇ structure for heavy rare earths (rhombohedral Th₂Zn₁₇ structure for light rare earths) show NTE due to MVE. Cr-substitution in R₂Fe₁₇ compounds can weaken the NTE behavior as well as increase T_C.^34–36 Thus, the study of Cr-substitution in R₂Fe₁₇ compounds is important in searching for ZTE magnetic materials with a high T_C, although previous studies in Cr-substituted R₂Fe₁₇ compounds (R = Tb, Tm, Gd) do not show the existence of ZTE in their studied range of temperature. Such studies are restricted only in a temperature range above room temperature. Tm₂Fe_17−xCr_x (x > 0) shows NTE near the T_C (around 430 K) with a minimum NTE coefficient of volume expansion, α_ν = −9.15 × 10⁻⁶ K⁻¹ for the x = 0.5 compound.³⁶ Tb₂Fe₁₆Cr possesses a minimum value of α_ν = −5.28 × 10⁻⁶ K⁻¹ in the temperature range 292–511 K,³⁵ whereas Gd₂Fe₁₆Cr has minimum α_ν = −7.03 × 10⁻⁶ K⁻¹ in the temperature range 294–454 K.³⁴ Possessing a lower NTE coefficient³³ and having T_C (330 K) higher than the room temperature among the R₂Fe₁₇ compounds, Ho₂Fe₁₇ may be a good starting material for finding a magnetic ZTE material operative at room temperature. In this paper, we study the effect of Cr-substitution on the NTE and the magnetic behavior of a R₂Fe₁₇-type compound, Ho₂Fe₁₇. Our study suggests that Ho₂Fe₁₆Cr, with a high T_C, is a ZTE material having a low coefficient of thermal expansion (α_ν = 1.3 × 10⁻⁶ K⁻¹) over a wide range of temperature (13–330 K).

2 Experimental procedure

Ho₂Fe_17–xCr_x (x = 0, 1, 2) compounds were prepared by the method of arc-melting (in an argon atmosphere) with at least 99.9% pure starting materials. The ingots were re-melted five to six times to ensure homogeneity. The samples were annealed in a vacuum sealed quartz tube at 1173 K for 7 days, followed by quenching in ice water. The room temperature powder X-ray diffraction (XRD) patterns of the samples were taken using CuK_α radiation in a TTRAX III diffractometer (M/S Rigaku Corp., Japan). The XRD patterns at different temperatures (13–515 K) were recorded using the same instrument, with a very low scan speed (0.01° steps, and 0.4° min⁻¹) for a better statistical average. This is necessary in our case as our sample contains more than 85% Fe and the Cu K_α radiation is in the absorption edge of Fe. The magnetization was measured using SQUID VSM and PPMS evercool-II (M/S Quantum Design, Inc., USA) from 4–380 K. High temperature VSM (Model EV9, M/S MicroSense, LLC Corp., USA) was employed to measure the magnetization from 300–550 K.

3 Results and discussion

Fig. 1 [left panel] shows the room temperature XRD data of the Ho₂Fe_17−xCr_x compounds. The data show that all the samples form in a single phase with a hexagonal Th₂Ni₁₇-type structure (space group: P6₃/mmc). Miller indices (hkl) for the major set of crystallographic planes have been shown in the figure. Fig. 1 [right panel] shows the XRD pattern of Ho₂Fe₁₆Cr at three temperatures, namely, 13 K, 300 K, and 453 K. The XRD data suggest that the compound remains in a single phase with the Th₂Ni₁₇-type structure in the temperature range of measurement. This is consistent for other Ho₂Fe_17−xCr_x compounds (x = 0, 2). Lattice parameters (a, c) of each sample at different temperatures have been estimated by analyzing XRD patterns.

Fig. 1 [Left panel] Room temperature XRD pattern of Ho₂Fe_17−xCr_x (x = 0, 1, 2) compounds. [Right panel] XRD patterns of Ho₂Fe₁₆Cr at T = 13 K, 300 K and 453 K. Red circles depict the experimentally observed data points, the black lines are data generated using FullProf software, and the blue lines are the differences between the estimated and experimentally observed data points. The olive bars are the Bragg positions allowed by the space group.

Fig. 2 [left panel] shows the effect of Cr substitution on the lattice parameters (a, c) and [right panel] the lattice volume v of the Ho₂Fe_17−xCr_x (x = 0, 1, 2) compounds. We observe that the thermal expansion of any of the Ho₂Fe_17−xCr_x compounds is anisotropic like the parent R₂Fe₁₇ compounds³³ and their derivatives,^34–36 i.e., a increases while c decreases with increasing temperature. The decrease in c with increasing temperature results from MVE. In R₂Fe₁₇ compounds, with a hexagonal Th₂Ni₁₇ structure for heavy rare earths (rhombohedral Th₂Zn₁₇ structure for light rare earths), the crystallographic sites for the Fe atoms are 4f(6c), 6g(9d), 12j(18f), and 12k(18h) sites.³⁹ As the distance between the Fe atoms at 4f(6c) sites is very short (<0.244 nm)³⁶ (Fig. 3), the direct exchange between these atoms gives rise to antiferromagnetic (AFM) coupling, while the rest of the atoms are coupled ferromagnetically. Therefore, a large amount of magnetic energy is stored along the Fe–Fe distance between the atoms at 4f(6c) sites, and this magnetic energy can be reduced by increasing said distance, which is dependent only on the parameter c.⁴⁰ Finally, a compromise is obtained between the magnetic energy and the elastic energy by increasing the lattice volume for the magnetic state at a lower temperature. If Cr atoms are substituted for Fe atoms in R₂Fe₁₇ compounds, Cr atoms prefer to occupy 4f(6c) sites.³⁶ As the magnetic moment of a Cr atom is less than that of an Fe atom, such substitution will reduce the effective MVE, and consequently weaken the NTE below T_C.

Fig. 2 [Left panel] Lattice parameters a and c and [Right panel] unit cell volume v of Ho₂Fe_17−xCr_x (x = 0, 1, 2) compounds (vertical line in both left and right panel corresponds to T/T_C = 1). Data for the parent compound (x = 0) has been taken from ref. 41.

Fig. 3 Th₂Ni₁₇ – type crystal structure (space group: P6₃/mmc) of Ho₂Fe₁₇ compound. Short distances between Fe atoms at 4f sites (highlighted by red boxes) are responsible for the magneto-volume effect.

The Curie temperature (T_C) for each of the Ho₂Fe_17−xCr_x (x = 0, 1, 2) compounds has been determined from the magnetization (M) curve plotted as a function of temperature at a magnetic field of H = 0.05 T (Fig. 4 [left panel]). The data shows that the T_C of Ho₂Fe₁₆Cr is 415 K, higher than that (326 K) of the parent compound, whereas the T_C (402 K) of Ho₂Fe₁₅Cr₂ is lower than that of Ho₂Fe₁₆Cr. The Cr-substitution enhances T_C substantially for a lower concentration of Cr, and then T_C decreases at higher concentrations. Similar behavior has also been observed for other Cr-substituted R₂Fe₁₇ compounds.^34–36 The modification of T_C due to Cr substitution has been explained by the preference of the magnetically weaker Cr atoms to replace Fe atoms at 4f(6c) sites.³⁶ The strength of the Fe(Cr)–Fe(Cr) interactions in the 3d-sublattice determines the value of T_C in the R₂Fe_17−xCr_x compounds.³⁶ In the parent compound R₂Fe₁₇, the Fe atoms at the 4f(6c) sites are coupled antiferromagnetically, while the rest of the atoms are coupled ferromagnetically. The Cr atoms at 4f(6c) sites reduce the interactions between 4f(6c) and other crystal sites (4f(6c), 6g(9d), 12j(18f), and 12k(18h)). At lower concentrations of Cr, the strength of the AFM interactions between 4f(6c)–4f(6c) sites reduces much more strongly than the ferromagnetic (FM) interactions between 4f(6c)-other sites.³⁶ This results in an enhancement in the total FM interactions in the 3d-sublattice and a subsequent increase in T_C. For higher concentrations of Cr, the reduction of FM interactions has been argued to surpass that of AFM interactions causing a decrease in total FM strength of the 3d-sublattice, and an associated lowering of T_C. A similar feature of T_C dependence on the Cr-concentration has also been observed in Fe–Cr alloys,⁴² where through experimental as well as computational studies, it was shown that the T_C of the Fe–Cr alloy (up to 6 at% Cr-substitution) is higher than that of pure Fe. The coercive field (H_c) also increases with increasing Cr concentration. Materials with a high coercive field possess a high value of maximum energy product (BH_max), a necessary criterion for permanent magnetic materials. The values of T_C, M_S and H_c of Ho₂Fe_17−xCr_x (x = 0, 1, 2) are shown in Table 1.

Fig. 4 [Left panel] Magnetization as a function of temperature at a magnetic field of H = 0.05 T, [Right panel] magnetization as a function of magnetic field at T = 5 K for Ho₂Fe_17−xCr_x (x = 0, 1, 2) compounds. The lower inset of [Right panel] shows the virgin curves with the fit of eqn (3), and the upper inset of [Right panel] shows the central part of each M–H curve.

Table 1 T_C, M_S and H_c of Ho₂Fe_17−xCr_x (x = 0, 1, 2)

Sample name	TC (in K)	MS (in μB per f.u)	Hc (in Oe)
Ho2Fe17	330	23.5	175
Ho2Fe16Cr	415	16.4	720
Ho2Fe15Cr2	402	10.8	2300

---

According to the Stoner–Edwards–Wohlfarth (SEW) theory,⁴³ in the absence of any external magnetic field, the volume strain (ω_S) arising from MVE at a temperature T is

where M₀ is the spontaneous magnetic moment, κ is the compressibility, and C is the magneto-volume coupling constant. Moriya and Usami modified eqn (1) by including the contribution of spin fluctuations to the free energy as⁴³where ξ²(T) represents the average of the squared thermal spin fluctuation amplitude. The volume strain due to MVE is proportional to the square of M₀. The Cr-substitution reduces the value of M₀. This is evident from Fig. 4 [right panel], where we observe that the saturation magnetization (M_S), which is a measure of M₀, decreases with increasing Cr-concentration. M_S has been estimated by fitting the virgin M–H curve of each sample with the expression⁴⁴that describes the law of approach to saturation (where A, B and χ are constants). As M₀ decreases with increasing Cr-concentration, so also ω_S decreases.

Fig. 2 [left panel] shows that a(T) is lower for a higher concentration (x) of Cr. This observation can be explained by the smaller ionic size of Cr than Fe,³⁶ and the fact that MVE does not alter a much. However, Cr is positioned in the left side of the same row of Fe in the periodic table, and it suggests that Cr possesses a larger crystal or ionic radius than that of Fe.⁴⁵ It may be pointed out that such understanding holds well when both the ions possess the same valence as well as identical spin state (high-spin or low-spin).⁴⁵ Moreover, in two different crystal environments, if the site coordination numbers differ, the same element in a particular valence state may assume two different ionic radii.⁴⁵ Reduction of the lattice parameter a has also been found for other members of the R₂Fe_17−xCr_x series.^{34–36,46–48} Even for Mn, placed also like Cr on the left side of Fe in the periodic table, similar reduction in a has been found with increasing x, in R₂Fe_17−xMn_x.^49,50 A better understanding of the fact can be obtained from the neutron diffraction study of Nd₂Fe_17−δCr_δ (δ = 0, 0.5, 1, 1.9).⁴⁷ The study suggests that Cr prefers to occupy 6c, and with the introduction of Cr, 6c–6c, 6c–18h, and 6c–18f bond lengths reduce continuously with increasing δ, while 6c–9d bond length remains almost constant. Considering such reduction in different bond lengths with the introduction of Cr, one may conclude that the ionic size of Cr is less than Fe in the same site of the R₂Fe_17−xCr_x lattice. The reduction of the mentioned bond lengths is an experimental observation, but the underlying reason lies within the valence as well as the spin states of two (Fe, Cr) ions and finally the crystalline environment. Here, MVE does not alter a much. The lattice parameter c(T) for Ho₂Fe₁₆Cr is higher than that of the parent compound even above T_C. This occurs because the strain along the c-axis arising from MVE is not only higher in the parent compound than Ho₂Fe₁₆Cr, but also more than the change in the c parameter obtained by just replacing one Fe atom by a Cr atom in Ho₂Fe₁₇. The higher value of c(T) for Ho₂Fe₁₆Cr, even above T_C, suggests that the effect of spin fluctuation is important in this system. A similar conclusion can also be drawn from the observation of NTE in the parent compound below 365 K,⁴¹ which is higher than T_C = 330 K (Fig. 2 [right panel]). For Ho₂Fe₁₅Cr₂, the reduction of c(T) due to further replacement of one more Fe atom by a Cr atom overcompensates the change in the same due to reduction of MVE, and therefore, c(T) reduces compared to Ho₂Fe₁₆Cr.

Fig. 2 [right panel] shows the unit cell volume v(T) of Ho₂Fe_17−xCr_x (x = 0, 1, 2). The parent compound Ho₂Fe₁₇ shows NTE in the temperature range 295–365 K with α_ν lying in the range (1.3–3.7) × 10⁻⁵ K⁻¹.⁴¹ The parent compound appears to be a strong magnetostrictive material. In comparison with the parent compound, in Ho₂Fe₁₆Cr, Cr-substitution increases T_C and weakens NTE. For Ho₂Fe₁₆Cr, NTE is observed in the range T = 330–425 K with α_ν = −4.3 × 10⁻⁶ K⁻¹. However, the most interesting feature of Ho₂Fe₁₆Cr is the negligible thermal expansion of the unit cell over a wide range of temperature (13–330 K) including room temperature. In this temperature range, the magneto-volume strain compensates for the lattice volume strain, and Ho₂Fe₁₆Cr behaves as a single component ZTE material with α_ν = 1.3 × 10⁻⁶ K⁻¹. By further increasing the Cr concentration NTE disappears, i.e., we do not observe any NTE for Ho₂Fe₁₅Cr₂.

The temperature dependence of the spontaneous linear magnetostrictive deformation in the basal plane, λ_a = (a_m − a_p)/a_p, that along the c-axis λ_c = (c_m − c_p)/c_p, and the spontaneous volume magnetostrictive deformation ω_S = (v_m − v_p)/v_p³⁶ are important parameters for identifying the strength and the nature of magnetoelastic coupling. a_m, c_m, and v_m are the experimentally measured values of a, c and v, whereas a_p, c_p, and v_p are the corresponding values obtained by extrapolation³⁶ from the paramagnetic state using the Grüneisen relation, , , where θ_D is the Debye temperature and [scr R, script letter R] is the molar gas constant. The value of θ_D has been taken as 400 K, estimated earlier⁵¹ for R₂Fe₁₇ compounds other than Y₂Fe₁₇. The parameters a_m, c_m, and v_m along with a_p, c_p, and v_p are presented in Fig. 5 for the compound Ho₂Fe₁₆Cr. λ_a, λ_c and ω_S have been plotted as a function of temperature in Fig. 6(a)–(c) respectively.

Fig. 5 Temperature dependent lattice parameters a, c and unit cell volume v of the compound Ho₂Fe₁₆Cr, extracted from the fitted temperature dependent XRD patterns (denoted by suffix m), and the same parameters extrapolated from the paramagnetic region (denoted by suffix p).

Fig. 6 (a and b) Linear magnetostrictive deformations λ_a, and λ_c, (c) spontaneous volume magnetostrictive deformation ω_S as a function of temperature (T) for the Ho₂Fe_17−xCr_x (x = 1, 2) compounds. (d) ω_S as a function of M_S² for the compound Ho₂Fe₁₆Cr.

Although it has been suggested that the free energy in the magnetic state can be reduced by changing the dimension along the c-axis only,⁵² our experimental data show a finite λ_a for both the samples Ho₂Fe_17−xCr_x (x = 1 or 2) i.e., the magneto-elastic effect also changes a. Moreover, the larger value of λ_c than λ_a in each case suggests that the magnetoelastic effect along the c-axis is stronger than that in the basal plane. As evident from Fig. 6(c), the value of ω_S is considerably high at low temperatures, and it is non-zero above T_C. Thus Ho₂Fe_17−xCr_x is a strong magnetostrictive material in which spin fluctuation plays an important role. Fig. 6(d) shows that ω_S varies linearly with the square of M_S. This is in accordance with eqn (1) and (2), and has been suggested to be a direct experimental proof of the fact that ω_S is related to the MVE.⁵³

4 Conclusion

In the search for magnetic ZTE materials, our study shows that Cr-substitution for Fe atoms in Ho₂Fe₁₇ weakens the NTE of the parent compound and alters the T_C. Ho₂Fe₁₆Cr behaves as a single component ZTE material in the temperature range 13–330 K. Moreover, the T_C of Ho₂Fe₁₆Cr is 415 K, considerably higher than room temperature. Cr-substitution also increases the coercivity compared to that of the parent compound. Therefore, Ho₂Fe₁₆Cr with a high T_C, moderate coercivity and very low thermal expansion is a potential material for a permanent magnet.

Acknowledgements

Shovan Dan and S. Mukherjee thank UGC for financial support in the form of major project (MRP-MAJOR-PHYS-2013-16282). The work at SINP was carried out under CMPID-DAE Project.

References

1. J. R. Salvador, F. Guo, T. Hogan and M. G. Kanatzidis, Nature, 2003, 425, 702–705.
2. S. Margadonna, K. Prassides and A. N. Fitch, J. Am. Chem. Soc., 2004, 126, 15390–15391.
3. K. J. Miller, C. P. Romao, M. Bieringer, B. A. Marinkovic, L. Prisco and M. A. White, J. Am. Ceram. Soc., 2013, 96, 561–566.
4. P. Hu, J. Chen, J. Deng and X. Xing, J. Am. Chem. Soc., 2010, 132, 1925–1928.
5. K. Takenaka and H. Takagi, Appl. Phys. Lett., 2009, 94, 131904.
6. T. Suzuki and A. Omote, J. Am. Ceram. Soc., 2006, 89, 691–693.
7. M. van Schilfgaarde, I. A. Abrikosov and B. Johansson, Nature, 1999, 400, 46–49.
8. M. Shiga, Curr. Opin. Solid State Mater. Sci., 1996, 1, 340–348.
9. L. Hu, J. Chen, L. Fan, Y. Ren, Y. Rong, Z. Pan, J. Deng, R. Yu and X. Xing, J. Am. Chem. Soc., 2014, 136, 13566–13569.
10. W. Wang, R. Huang, W. Li, J. Tan, Y. Zhao, S. Li, C. Huang and L. Li, Phys. Chem. Chem. Phys., 2015, 17, 2352–2356.
11. W. Li, R. Huang, W. Wang, Y. Zhao, S. Li, C. Huanga and L. Li, Phys. Chem. Chem. Phys., 2015, 17, 5556–5560.
12. S. Li, R. Huang, Y. Zhao, W. Wanga and L. Li, Phys. Chem. Chem. Phys., 2015, 17, 30999–31003.
13. K. Takenaka, Sci. Technol. Adv. Mater., 2012, 13, 013001–013012.
14. H. Li, S. Liu, L. Chen, J. Zhao, B. Chen, Z. Wang, J. Meng and X. Liu, RSC Adv., 2015, 5, 1801–1807.
15. C. Verdon and D. C. Dunand, Scr. Mater., 1997, 36, 1075–1080.
16. A. Matsumoto, K. Kobayashi, T. Nishio and K. Ozaki, Mater. Sci. Forum, 2003, 426–432, 2279–2284.
17. L. Ding, C. Wang, Y. Na, L. Chu and J. Yan, Scr. Mater., 2011, 65, 687–690.
18. X. Yan, J. Miao, J. Liu, X. Wu, H. Zou, D. Sha, J. Ren, Y. Dai, J. Wang and X. Cheng, J. Alloys Compd., 2016, 677, 52–56.
19. X. Shan, R. Huang, Y. Han, C. Huang, X. Liu, Z. Lu and L. Li, J. Alloys Compd., 2016, 662, 505–509.
20. G. D. Barrera, J. A. O. Bruno, T. H. K. Barron and N. L. Allan, J. Phys.: Condens. Matter, 2005, 17, R217–R252.
21. T. A. Mary, J. S. O. Evans, T. Vogt and A. W. Sleight, Science, 1996, 272, 90–92.
22. F. H. Gillery and E. A. Bush, J. Am. Ceram. Soc., 1959, 42, 175–177.
23. A. E. Phillips, A. L. Goodwin, G. J. Halder, P. D. Southon and C. J. Kepert, Angew. Chem., Int. Ed., 2008, 47, 1396–1399.
24. T. Chatterji, T. C. Hansen, M. Brunelli and P. F. Henry, Appl. Phys. Lett., 2009, 94, 241902.
25. M. P. Attfield, M. Feygenson, J. C. Neuefeind, T. E. Proffen, T. C. A. Lucas and J. A. Hriljac, RSC Adv., 2016, 6, 19903–19909.
26. T. Matsuda, J. Kimb and Y. Moritomo, RSC Adv., 2011, 1, 1716–1720.
27. Y. Cheng, Y. Liang, X. Ge, X. Liu, B. Yuan, J. Guo, M. Chao and E. Lianga, RSC Adv., 2016, 6, 53657–53661.
28. M. Azuma, W. Chen, H. Seki, M. Czapski, S. Olga, K. Oka, M. Mizumaki, T. Watanuki, N. Ishimatsu, N. Kawamura, S. Ishiwata, M. G. Tucker, Y. Shimakawa and J. P. Attfield, Nat. Commun., 2011, 2, 347.
29. A. Pandey, C. Mazumdar, R. Ranganathan, S. Tripathi, D. Pandey and S. Dattagupta, Appl. Phys. Lett., 2008, 92, 261913.
30. M. Hayase, M. Shiga and Y. Nakamura, J. Phys. Soc. Jpn., 1973, 34, 925–933.
31. K. Sumiyama, M. Shiga, M. Morioka and Y. Nakamura, J. Phys. F: Met. Phys., 1979, 9, 1665–1677.
32. H. Nakamura, H. Wada, K. Yoshimura, M. Shiga, Y. Nakamura, J. Sakurai and Y. Komura, J. Phys. F: Met. Phys., 1988, 18, 981–991.
33. P. A. Alanso, Doctoral Thesis, University of Oviedo, Spain, 2011.
34. H. Yan-Ming, T. Ming, W. Wei and W. Fang, Chin. Phys. B, 2010, 19, 067502.
35. Y. Hao, M. Zhao, Y. Zhou and J. Hu, Scr. Mater., 2005, 53, 357–360.
36. Y. Hao, X. Zhang, B. Wang, Y. Yuang and F. Wang, J. Appl. Phys., 2010, 108, 023915.
37. K. Takenaka and H. Takagi, Appl. Phys. Lett., 2005, 87, 261902.
38. X. Peng, J. Chen, K. Lin, L. Fan, Y. Rong, J. Deng and X. Xing, RSC Adv., 2016, 6, 32979–32982.
39. J. L. Wang, S. J. Campbell, O. Tegus, C. Marquina and M. R. Ibarra, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 75, 174423.
40. D. Givord and R. Lemaire, IEEE Trans. Magn., 1974, 10, 109–113.
41. J. L. Wang, A. J. Studer, S. J. Kennedy, R. Zeng, S. X. Dou and S. J. Campbell, J. Appl. Phys., 2012, 111, 07A911.
42. M. Y. Lavrentiev, K. Mergia, M. Gjoka, D. Nguyen-Manh, G. Apostolopoulos and S. L. Dudarev, J. Phys.: Condens. Matter, 2012, 24, 326001.
43. Y. Takahashi, Spin Fluctuation Theory of Itinerant Electron Magnetism, Springer Tracts in Modern Physics, Springer-Verlag, Berlin Heidelberg, 2013, p. 253.
44. B. D. Cullity and C. D. Graham, Introduction to Magnetic Materials, IEEE Press, Wiley, 2008.
45. R. D. Shannon, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr., 1976, 32, 751–767.
46. X. C. Kou, F. R. de Boer, R. Grssinger, G. Wiesinger, H. Suzuki, H. Kitazawa, T. Takamasu and G. Kido, J. Magn. Magn. Mater., 1998, 177–181, 1002–1007.
47. E. Girt, Z. Altounian and J. Yang, J. Appl. Phys., 1997, 81, 5118–5120.
48. I. Nehdi, L. Bessais, C. D. -Mariadassou, M. Abdellaoui and H. Zarrouk, J. Alloys Compd., 2003, 351, 24–30.
49. P. C. Ezekwenna, G. K. Marasinghe, W. J. James, O. A. Pringle, G. J. Long, H. Luo, Z. Hu, W. B. Yelon and P. I. Hritier, J. Appl. Phys., 1997, 81, 4533.
50. Y. Wang, F. Yang, C. Chen, N. Tang, P. Lin and Q. Wang, J. Appl. Phys., 1998, 84, 6229–6232.
51. A. V. Andreev, A. V. Deryagin, S. M. Zadvorkin, N. V. Kudrevatykh, R. H. Levitin, V. N. Moskalev, Y. F. Popov and R. Y. Yumaguzhin, Fizika Magnitnykh Materialov, Physics of Magnetic Materials, ed. D. D. Mishin, Kalinin University, Kalinin, USSR, 1985, p. 21, in Russian.
52. D. Givord, R. Lemaire, W. J. James, J.-M. Moreau and J. S. Shah, IEEE Trans. Magn., 1971, 7, 657–659.
53. J. Chen, L. Hu, J. Deng and X. Xing, Chem. Soc. Rev., 2015, 44, 3522–3567.

---