A first-principle assisted framework for designing high elastocaloric Ni-Mn-based magnetic shape memory alloy

doi:10.1016/j.jmst.2022.06.041

Abstract

Abstract:

A large adiabatic temperature change (∆T_ad) is a prerequisite for the application of elastocaloric refrigeration. Theoretically, a large volume change ratio (∆V/V₀) during martensitic transformation is favorable to enhance ∆T_ad. However, the design or prediction of ∆V/V₀ in experiments is a complex task because the structure of martensite changes simultaneously when the lattice parameter of austenite is tuned by modifying chemical composition. So far, the solid strategy to tailor ∆V/V₀ is still urgently desirable. In this work, a first-principles-based method was proposed to estimate ΔV/V₀ for Ni-Mn-based alloys. With this method, the substitution of Ga for In is found to be an effective method to increase the value of ΔV/V₀ for Ni-Mn-In alloys. Combined with the strategies of reducing the negative contribution of magnetic entropy change (via the substitution of Cu for Mn) and introducing strong crystallographic texture (through directional solidification), an outstanding elastocaloric prototype alloy of Ni₅₀(Mn_28.5Cu_4.5)(In₁₄Ga₃) was fabricated experimentally. At room temperature, a huge ∆T_ad of -19 K and a large specific adiabatic temperature change of 67.8 K/GPa are obtained. The proposed first-principle-assisted framework opens up the possibility of efficiently tailoring ∆V/V₀ to promote the design of advanced elastocaloric refrigerants.

Key words: Magnetic shape memory alloy, Elastocaloric effect, First-principles calculation, Martensitic transformation, Volume change ratio

Xiao-Ming Huang, Ying Zhao, Hai-Le Yan, Shuai Tang, Yiqiao Yang, Nan Jia, Bo Yang, Zongbin Li, Yudong Zhang, Claude Esling, Xiang Zhao, Liang Zuo. A first-principle assisted framework for designing high elastocaloric Ni-Mn-based magnetic shape memory alloy[J]. J. Mater. Sci. Technol., 2023, 134: 151-162.

Figures/Tables 11

Fig. 1. (a) Relation between ?M and ?Str of the Ni-Mn-Z (Z=In, Sn and Sb) alloys. The data cited is from the following literature: a, b [12], c [9], d [24], e [25], f [26], g [27], h, i, j [28], k [29], l [30], m [31], n [32], o [33], p, q [34], r [35], s [17], t, u [36] and v, w [37]. (b) Relation between ?V/V0 and ?Str of a series of reported magnetic phase transition materials. The data cited is from the following literature: 1 [42], 2 [24], 3 [43], 4 [25], 5 [26], 6 [44], 7 [45], 8 [40], 9 [46], 10 [47], 11 [48], 12 [49], 13 [50], 14 [51], 15 [52], 16 [53], 17 [56] and 18 [57].

Fig. 2. Adopted strategies to increase ?Tad in this work, i.e., increasing ΔV/V0 assisted by first-principles calculations, reducing the negative contribution of ΔSmag by decreasing ΔM, and introducing strong crystallographic texture by directional solidification technique.

Fig. 3. (a) Illustration of computational scheme for determining ΔV/V0. Distribution of total energy E against c/a and ΔV/V0 for (b1) Ni8Mn5In3, (b2) Ni8Mn5In2Ga1, and (b3) Ni8Mn5In1Ga2. Evolutions of (c) ΔV/V0 and (d) the energy difference ΔE between austenite and martensite against Ga content.

Fig. 4. (a) DSC curves measured in the temperature range of 200 to 325 K. (b) Enlarged figure in the dashed box in (a). The inset clearly shows the change in Curie temperature of Ga3Cu2.5, Ga3Cu4, and Ga3Cu4.5 samples. (c) Phase diagram and transformation entropy change of the prepared samples.

Fig. 5. (a) Macrophoto and (b1, b2) backscattered electron (BSE) images of the directionally solidified Ga3Cu4.5 sample. The inset in (b2) shows composition maps in the area near the grain boundary. (c) EBSD orientation micrograph and (d) {004} pole figure of austenite measured by XRD technique.

Fig. 6. XRD patterns of Ga3Cu4.5 measured at (a) 298 K and (b) 183 K. (c) Comparison of ΔV/V0 for Ga3Cu4.5 with some typical Ni?Mn-based alloys: a [40], b [46], c [48], d [47], e,f [44], g [76], h [45], i [43], j [42], k [77], l [24], m [25] and n [26].

Fig. 7. (a) Comparison of ?Str for the Ga3Cu4.5 sample with those of some reported Ni?Mn-based alloys with Af < 298 K: a [13], b [78], c [22], d [34], e [29], f [30], g [34], h [79], i [28], j [9], k [80] and l [12]. (b) Specific heat capacity at low temperature (2-21 K). (c) Variation of saturation magnetization of Ga3Cu4.5 against the reduced temperature τ near 0 K. The inset shows the differential of magnetization with temperature (dM/dT) under a magnetic field of 0.01 T.

Fig. 8. Comparison of ?Thys of the Ga3Cu4.5 sample with other reported typical Ni?Mn-based alloys: 1 [78], 2, 3 [89], 4 [13], 5 [22], 6, 7 [34], 8, 9 [79], 10, 11 [29], 12 [17], 13 [37], 14, 15 [90], 16 [91], 17 [92], 18 [93], 19 [94], 20-22 [28], 23 [23], 24-26 [96], 27 [95], 28 [97] and 29 [98].

Fig. 9. (a) Comparison of compressive fracture curves for the Ga3Cu4.5 sample and the reported Ni-Mn-based alloys: Ni51.5Mn33In15.5 [80], Ni45.7Co4.2Mn37.3Sb12.8 [17], Ni43Co6Mn40Sn11 [79], Ni45Mn37In13Co5 [74], Ni45Mn44Sn11 [101], Ni50Mn34.8In15.2 [9] and Ni50Mn31.75Ti18.25 [41]. DS and P stand for the directionally solidified and the cast samples, respectively. (b) Cyclic stress-strain curves at the maximum strains of 5%, 6%, 7% and 8%. (c) Comparison of stress hysteresis for the Ga3Cu4.5 sample and other elastocaloric materials reported in the literature: a, b [102], c [40], d [41], e [103], f [104,105], g [106], h [107], i [108], j, k [109,110], l [111], m [110], n, o [110,112], p [113], q [114], r [115], s [13], t [116], u [117], v [118], w, x [1,101], y [17], z, aa, ab, ac [2,6,9], ad [80], ae, af [12,18], ag, ah [14], ai, aj, ak [3,20,119] and al [74].

Fig. 10. (a) Temperature change of the Ga3Cu4.5 directionally solidified sample. (b) Comparison of the present ?Tad with other reported Ni?Mn-based alloys: 1 [2], 2 [9], 3 [3], 4 [119], 5 [18], 6 [80], 7 [14], 8 [4], 9 [75], 10 [12], 11 [101], 12 [15], 13 [121], 14 [79], 15 [17], 16 [22], 17 [78], 18 [13].

Fig. 11. (a) Strain and stress dependence of ?Tad. (b) Comparison of |?Tad/?εtr| and |?Tad/?σmax| for the Ga3Cu4.5 sample with the other reported eCE materials: a [105], b [104], c [122], d [106], e [123], f [108], g [109], h [124], i [112], j [110], k [124], l [113], m [114], n [125], o [40], p [41], q [2], r [9], s [6], t [3], u [20], v [119], w [74], x [80], y [18], z [12], aa [126], ab [17], ac [78], ad [13], ae [22], af [1] and ag [121]. Open symbols, symbols with grid lines, and solid symbols represent the non-textured polycrystalline, the textured polycrystalline and the single crystal, respectively.

References 133

[1]	W. Sun, J. Liu, B. Lu, Y. Li, A. Yan, Scr. Mater. 114 (2016) 1-4. DOI URL
[2]	Y.J. Huang, Q.D. Hu, N.M. Bruno, J.-H. Chen, I. Karaman, J.H. Ross, J.G. Li, Scr. Mater. 105 (2015) 42-45. DOI URL
[3]	B. Lu, F. Xiao, A. Yan, J. Liu, Appl. Phys. Lett. 105 (2014) 161905. DOI URL
[4]	J.P. Camarillo, C.O. Aguilarortiz, H. Floreszúñiga, D. Ríosjara, D.E. Sotoparra, E. Sterntaulats, L. Mañosa, A. Planes, Funct. Mater. Lett. 10 (2017) 1740007. DOI URL
[5]	T. Gottschall, A. Gracia-Condal, M. Fries, A. Taubel, L. Pfeuffer, L. Manosa, A. Planes, K.P. Skokov, O. Gutfleisch, Nat. Mater. 17 (2018) 929-934. DOI PMID
[6]	Z.Z. Li, Z.B. Li, D. Li, J.J. Yang, B. Yang, Y. Hu, D.H. Wang, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, Acta Mater. 192 (2020) 52-59. DOI URL
[7]	A. Gràcia-Condal, T. Gottschall, L. Pfeuffer, O. Gutfleisch, A. Planes, L. Mañosa, Appl. Phys. Rev. 7 (2020) 041406. DOI URL
[8]	G. Zhang, D. Li, C. Liu, Z. Li, B. Yang, H. Yan, X. Zhao, L. Zuo, Scr. Mater. 201 (2021) 113947. DOI URL
[9]	X.-M. Huang, L.-D. Wang, H.-X. Liu, H.-L. Yan, N. Jia, B. Yang, Z.-B. Li, Y.-D. Zhang, C. Esling, X. Zhao, L. Zuo, Intermetallics 113 (2019) 106579. DOI URL
[10]	X.-M. Huang, Y. Zhao, H.-L. Yan, N. Jia, B. Yang, Z. Li, Y. Zhang, C. Esling, X. Zhao, L. Zuo, J. Alloy. Compd. 889 (2021) 161652. DOI URL
[11]	L. Pfeuffer, J. Lemke, N. Shayanfar, S. Riegg, D. Koch, A. Taubel, F. Scheibel, N.A. Kani, E. Adabifiroozjaei, L. Molina-Luna, K.P. Skokov, O. Gutfleisch, Acta Mater. 221 (2021) 117390. DOI URL
[12]	X.-M. Huang, Y. Zhao, H.-L. Yan, N. Jia, S. Tang, J. Bai, B. Yang, Z.B. Li, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, Scr. Mater. 185 (2020) 94-99. DOI URL
[13]	D. Li, Z.B. Li, X.L. Zhang, B. Yang, D.H. Wang, X. Zhao, L. Zuo, Scr. Mater. 189 (2020) 78-83. DOI URL
[14]	D.W. Zhao, J. Liu, X. Chen, W. Sun, Y. Li, M.X. Zhang, Y.Y. Shao, H. Zhang, A. Yan, Acta Mater. 133 (2017) 217-223. DOI URL
[15]	Y. Shen, W. Sun, Z.Y. Wei, Q. Shen, Y.F. Zhang, J. Liu, Scr. Mater. 163 (2019) 14-18. DOI URL
[16]	Y.H. Qu, A. Gràcia-Condal, L. Mañosa, A. Planes, D.Y. Cong, Z.H. Nie, Y. Ren, Y.D. Wang, Acta Mater. 177 (2019) 46-55. DOI URL
[17]	Z.Z. Li, Z.B. Li, J.J. Yang, D. Li, B. Yang, H.L. Yan, Z.H. Nie, L. Hou, X. Li, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, Scr. Mater. 162 (2019) 486-491. DOI URL
[18]	X.H. Tang, Y. Feng, H.B. Wang, P. Wang, Appl. Phys. Lett. 114 (2019) 033901. DOI URL
[19]	T. Kihara, X. Xu, W. Ito, R. Kainuma, M. Tokunaga, Phys. Rev. B 90 (2014) 214409. DOI URL
[20]	D.W. Zhao, J. Liu, Y. Feng, W. Sun, A. Yan, Appl. Phys. Lett. 110 (2017) 021906. DOI URL
[21]	V. Recarte, J.I. Pérez-Landazábal, V. Sánchez-Alarcos, V. Zablotskii, E. Cesari, S. Kustov, Acta Mater. 60 (2012) 3168-3175. DOI URL
[22]	J.M. Wang, Q. Yu, K.Y. Xu, C. Zhang, Y.Y. Wu, C.B. Jiang, Scr. Mater. 130 (2017) 148-151. DOI URL
[23]	Z.Z. Li, Z.B. Li, D. Li, J.J. Yang, B. Yang, D.H. Wang, L. Hou, X. Li, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, Appl. Phys. Lett. 115 (2019) 083903. DOI URL
[24]	L. Pfeuffer, T. Gottschall, T. Faske, A. Taubel, F. Scheibel, A.Y. Karpenkov, S. Ener, K.P. Skokov, O. Gutfleisch, Phys. Rev. Mater. 4 (2020) 111401.
[25]	L.M. Wang, Z.B. Li, J.J. Yang, B. Yang, X. Zhao, L. Zuo, Intermetallics 125 (2020) 106888. DOI URL
[26]	H.-L. Yan, X.-M. Huang, J.-H. Yang, Y. Zhao, F. Fang, N. Jia, J. Bai, B. Yang, Z.B. Li, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, Intermetallics 130 (2021) 107063. DOI URL
[27]	V. Recarte, J.I. Pérez-Landazábal, S. Kustov, E. Cesari, J. Appl. Phys. 107 (2010) 053501. DOI URL
[28]	Z.B. Li, J.J. Yang, D. Li, Z.Z. Li, B. Yang, H.L. Yan, C.F. Sánchez-Valdés, J.L.S. Lla-mazares, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, Adv. Electron. Mater. 5 (2019) 1800845.
[29]	Y.H. Qu, D.Y. Cong, X.M. Sun, Z.H. Nie, W.Y. Gui, R.G. Li, Y. Ren, Y.D. Wang, Acta Mater. 134 (2017) 236-248. DOI URL
[30]	Z.B. Li, Y.W. Jiang, Z.Z. Li, C.F. Sanchez Valdes, J.L. Sanchez Llamazares, B. Yang, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, IUCrJ 5 (2018) 54-66. DOI URL
[31]	L. Huang, D.Y. Cong, H.L. Suo, Y.D. Wang, Appl. Phys. Lett. 104 (2014) 132407. DOI URL
[32]	H. Zhang, X. Zhang, M. Qian, Z. Yao, L. Wei, L. Geng, J. Magn. Magn. Mater. 500 (2020) 166359. DOI URL
[33]	H. Zhang, X. Zhang, M. Qian, L. Yin, L. Wei, D. Xing, J. Sun, L. Geng, Appl. Phys. Lett. 116 (2020) 063904. DOI URL
[34]	M.N. Inallu, P. Kameli, A.G. Varzaneh, I.A. Sarsari, D. Salazar, I. Orue, V.A. Cher-nenko, J. Phys. D 52 (2019) 235001. DOI URL
[35]	A.K. Nayak, K.G. Suresh, A.K. Nigam, A.A. Coelho, S. Gama, J. Appl. Phys. 106 (2009) 053901. DOI URL
[36]	R. Sahoo, D.M. Raj Kumar, D. Arvindha Babu, K.G. Suresh, A.K. Nigam, M. Manivel Raja, J. Magn. Magn. Mater. 347 (2013) 95-100. DOI URL
[37]	C. Salazar-Mejia, V. Kumar, C. Felser, Y. Skourski, J. Wosnitza, A.K. Nayak, Phys. Rev. Appl. 11 (2019) 054006. DOI URL
[38]	K.A. Gschneidner, Y. Mudryk, V.K. Pecharsky, Scr. Mater. 67 (2012) 572- 577. DOI URL
[39]	T. Samanta, D.L. Lepkowski, A.U. Saleheen, A. Shankar, J. Prestigiacomo, I. Dubenko, A. Quetz, I.W.H. Oswald, G.T. McCandless, J.Y. Chan, P.W. Adams, D.P. Young, N. Ali, S. Stadler, Phys. Rev. B 91 (2015) 020401. DOI URL
[40]	D. Cong, W. Xiong, A. Planes, Y. Ren, L. Mañosa, P. Cao, Z. Nie, X. Sun, Z. Yang, X. Hong, Y. Wang, Phys. Rev. Lett. 122 (2019) 255703. DOI URL
[41]	H.-L. Yan, L.-D. Wang, H.-X. Liu, X.-M. Huang, N. Jia, Z.-B. Li, B. Yang, Y.-D. Zhang, C. Esling, X. Zhao, L. Zuo, Mater. Des. 184 (2019) 108180. DOI URL
[42]	L. Mañosa, D. González-Alonso, A. Planes, E. Bonnot, M. Barrio, J.-L. Tamarit, S. Aksoy, M. Acet, Nat. Mater. 9 (2010) 478-481. DOI PMID
[43]	M.K. Chattopadhyay, V.K. Sharma, A. Chouhan, P. Arora, S.B. Roy, Phys. Rev. B 84 (2011) 064417. DOI URL
[44]	C.O. Aguilar-Ortiz, D. Soto-Parra, P. Álvarez-Alonso, P. Lázpita, D. Salazar, P.O. Castillo-Villa, H. Flores-Zúñiga, V.A. Chernenko, Acta Mater. 107 (2016) 9-16. DOI URL
[45]	S. Aksoy, M. Acet, E.F. Wassermann, T. Krenke, X. Moya, L. Mañosa, A. Planes, P.P. Deen, Philos. Mag. 89 (2009) 2093-2109. DOI URL
[46]	S.Y. Yu, Z.X. Cao, L. Ma, G.D. Liu, J.L. Chen, G.H. Wu, B. Zhang, X.X. Zhang, Appl. Phys. Lett. 91 (2007) 102507. DOI URL
[47]	F. Albertini, S. Fabbrici, A. Paoluzi, J. Kamarad, Z. Arnold, L. Righi, M. Solzi, G. Porcari, C. Pernechele, D. Serrate, P. Algarabel, Mater. Sci. Forum 684 (2011) 151-163. DOI URL
[48]	L. Mañosa, E. Stern-Taulats, A. Planes, P. Lloveras, M. Barrio, J.-L. Tamarit, B. Emre, S. Yüce, S. Fabbrici, F. Albertini, Phys. Status Solidi B 251 (2014) 2114-2119. DOI URL
[49]	R.R. Wu, L.F. Bao, F.X. Hu, H. Wu, Q.Z. Huang, J. Wang, X.L. Dong, G.N. Li, J.R. Sun, F.R. Shen, T.Y. Zhao, X.Q. Zheng, L.C. Wang, Y. Liu, W.L. Zuo, Y.Y. Zhao, M. Zhang, X.C. Wang, C.Q. Jin, G.H. Rao, X.F. Han, B.G. Shen, Sci. Rep. 5 (2015) 18027. DOI URL
[50]	T. Samanta, P. Lloveras, A.U. Saleheen, D.L. Lepkowski, E. Kramer, I. Dubenko, P.W. Adams, D.P. Young, M. Barrio, J.L. Tamarit, N. Ali, S. Stadler, Appl. Phys. Lett. 112 (2018) 021907. DOI URL
[51]	A. Aznar, P. Lloveras, J.Y. Kim, E. Stern-Taulats, M. Barrio, J.L. Tamarit, C.F. Sánchez-Valdés, J.L. Sánchez Llamazares, N.D. Mathur, X. Moya, Adv. Mater. 31 (2019) 1903577. DOI URL
[52]	Y.F. Kuang, B. Yang, H.J. Xu, X.W. Hao, Z.B. Li, H.L. Yan, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, J. Alloy. Compd. 835 (2020) 155313. DOI URL
[53]	E. Stern-Taulats, A. Gràcia-Condal, A. Planes, P. Lloveras, M. Barrio, J.-L. Tamarit, S. Pramanick, S. Majumdar, L. Mañosa, Appl. Phys. Lett. 107 (2015) 152409. DOI URL
[54]	C.F. Sánchez-Valdés, R.R. Gimaev, M. López-Cruz, J.L. Sánchez Llamazares, V.I. Zverev, A.M. Tishin, A.M.G. Carvalho, D.J.M. Aguiar, Y. Mudryk, V.K. Pecharsky, J. Magn. Magn. Mater. 498 (2020) 166130. DOI URL
[55]	M.L. Arreguín-Hernández, C.F. Sánchez-Valdés, J.L.S. Llamazares, D. Ríos- Jara, V.K. Pecharsky, M.I. Blinov, V.N. Prudnikov, B.B. Kovalev, V.I. Zverev, A.M. Tishin, J. Alloy. Compd. 871 (2021) 159586. DOI URL
[56]	L. Mañosa, D. Gonzalez-Alonso, A. Planes, M. Barrio, J.L. Tamarit, I.S. Titov, M. Acet, A. Bhattacharyya, S. Majumdar, Nat. Commun. 2 (2011) 595. DOI PMID
[57]	S. Yuce, M. Barrio, B. Emre, E. Stern-Taulats, A. Planes, J.L. Tamarit, Y. Mudryk, K.A. Gschneidner, V.K. Pecharsky, L. Manosa, Appl. Phys. Lett. 101 (2012) 071906. DOI URL
[58]	L. Righi, F. Albertini, L. Pareti, A. Paoluzi, G. Calestani, Acta Mater. 55 (2007) 5237-5245. DOI URL
[59]	H.L. Yan, Y.D. Zhang, N. Xu, A. Senyshyn, H.-G. Brokmeier, C. Esling, X. Zhao, L. Zuo, Acta Mater. 88 (2015) 375-388. DOI URL
[60]	L. Righi, F. Albertini, E. Villa, A. Paoluzi, G. Calestani, V. Chernenko, S. Bessegh-ini, C. Ritter, F. Passaretti, Acta Mater. 56 (2008) 4529-4535. DOI URL
[61]	J. Hafner, J. Comput. Chem. 29 (2008) 2044-2078. DOI URL
[62]	G.G. Kresse, J.J. Furthmüller, Phys. Rev. B 54 (1996) 11169. DOI PMID
[63]	J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865-3868. DOI PMID
[64]	H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188-5192. DOI URL
[65]	S. Kaufmann, U.K. Rößler, O. Heczko, M. Wuttig, J. Buschbeck, L. Schultz, S. Fähler, Phys. Rev. Lett. 104 (2010) 145702. DOI URL
[66]	P. Entel, M. Siewert, M.E. Gruner, A. Chakrabarti, S.R. Barman, V.V. Sokolovskiy, V.D. Buchelnikov, J. Alloy. Compd. 577 (2013) S107-S112. DOI URL
[67]	H.-L. Yan, Y. Zhang, C. Esling, X. Zhao, L. Zuo, Acta Mater. 202 (2021) 112-123. DOI URL
[68]	K. Bhattacharya, Microstructure of Martensite: Why It Forms And How It Gives Rise to The Shape-Memory Effect, Oxford University Press, 2003.
[69]	H.-L. Yan, Y. Zhao, H.-X. Liu, M.-J. Zhang, H.-F. Zhang, J. Bai, N. Jia, B. Yang, Z.-B. Li, Y.-D. Zhang, C. Esling, X. Zhao, L. Zuo, J. Alloy. Compd. 821 (2020) 153481. DOI URL
[70]	E. Şaşıoğlu, L.M. Sandratskii, P. Bruno, Phys. Rev. B 70 (2004) 024427. DOI URL
[71]	E. Şaşıoğlu, L.M. Sandratskii, P. Bruno, Phys. Rev. B 71 (2005) 214412. DOI URL
[72]	E. Şaşıoğlu, L.M. Sandratskii, P. Bruno, Phys. Rev. B 77 (2008) 064417. DOI URL
[73]	W. Ito, Y. Imano, R. Kainuma, Y. Sutou, K. Oikawa, K. Ishida, Metall. Mater. Trans. A 38 (2007) 759-766. DOI URL
[74]	A. Shen, W. Sun, D. Zhao, J. Liu, Phys. Lett. A 382 (2018) 2876-2879. DOI URL
[75]	F. Henández-Navarro, J.P. Camarillo-Garcia, C.O. Aguilar-Ortiz, H. Flo-res-Zúñiga, D. Ríos, J.G. González, P. Álvarez-Alonso, Appl. Phys. Lett. 112 (2018) 164101. DOI URL
[76]	V. Recarte, M. Zbiri, M. Jimenez-Ruiz, V. Sanchez-Alarcos, J.I. Perez-Landaza-bal, J. Phys. Condes. Matter 28 (2016) 205402. DOI URL
[77]	L. Mañosa, X. Moya, A. Planes, O. Gutfleisch, J. Lyubina, M. Barrio, J.-L.s. Tamarit, S. Aksoy, T. Krenke, M. Acet, Appl. Phys. Lett. 92 (2008) 012515. DOI URL
[78]	D. Li, Z.B. Li, J.J. Yang, Z.Z. Li, B. Yang, H. Yan, D.H. Wang, L. Hou, X. Li, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, Scr. Mater. 163 (2019) 116-120. DOI URL
[79]	Y.H. Qu, D.Y. Cong, S.H. Li, W.Y. Gui, Z.H. Nie, M.H. Zhang, Y. Ren, Y.D. Wang, Acta Mater. 151 (2018) 41-55. DOI URL
[80]	Z. Yang, D.Y. Cong, X.M. Sun, Z.H. Nie, Y.D. Wang, Acta Mater. 127 (2017) 33-42. DOI URL
[81]	B. Li, W.J. Ren, Q. Zhang, X.K. Lv, X.G. Liu, H. Meng, J. Li, D. Li, Z.D. Zhang, Appl. Phys. Lett. 95 (2009) 172506. DOI URL
[82]	P. Debye, Ann. Phys. (Leipzig) 344 (1912) 789-839. DOI URL
[83]	P.J.V. Ranke, N.A. de Oliveira, C. Mello, A.M.G. Carvalho, S. Gama, Phys. Rev. B 71 (2005) 054410. DOI URL
[84]	G.J. Liu, J.R. Sun, J. Lin, Y.W. Xie, T.Y. Zhao, H.W. Zhang, B.G. Shen, Appl. Phys. Lett. 88 (2006) 212505. DOI URL
[85]	J. Xia, Y. Noguchi, X. Xu, T. Odaira, Y. Kimura, M. Nagasako, T. Omori, R. Kainuma, Science 369 (2020) 855-858. DOI PMID
[86]	P.M. Chaikin, T.C. Lubensky, in: Principles of Condensed Matter Physics, Cam-bridge University Press, Cambridge, 1995, pp. 1-28.
[87]	V. Recarte, J.I. Perez-Landazabal, C. Gomez-Polo, V. Sanchez-Alarcos, E. Cesari, J. Pons, J. Phys.: Condens. Matter 22 (2010) 416001. DOI URL
[88]	T. Gottschall, K.P. Skokov, D. Benke, M.E. Gruner, O. Gutfleisch, Phys. Rev. B 93 (2016) 184431. DOI URL
[89]	Z. Li, Z. Li, B. Yang, Y. Yang, Y. Zhang, C. Esling, X. Zhao, L. Zuo, J. Magn. Magn. Mater. 445 (2018) 71-76. DOI URL
[90]	W.J. Feng, L. Zuo, Y.B. Li, Y.D. Wang, M. Gao, G.L. Fang, Mater. Sci. Eng. B 176 (2011) 621-625. DOI URL
[91]	F. Luo, X. He, S. Rauf, C.P. Yang, Z.G. Sun, Z. Tayyab, R.L. Wang, S.H. Liang, K.B. Zhang, G.Q. Liu, H.B. Xiao, V.V. Marchenkov, J. Magn. Magn. Mater. 502 (2020) 166277. DOI URL
[92]	R. Sahoo, A.K. Nayak, K.G. Suresh, A.K. Nigam, J. Appl. Phys. 109 (2011) 123904. DOI URL
[93]	S. Pandey, A. Quetz, A. Aryal, I. Dubenko, M. Blinov, I. Rodionov, V. Prudnikov, D. Mazumdar, A. Granovsky, S. Stadler, N. Ali, J. Appl. Phys. 121 (2017) 133901. DOI URL
[94]	Z.Z. Li, Z.B. Li, B. Yang, X. Zhao, L. Zuo, Scr. Mater. 151 (2018) 61-65. DOI URL
[95]	J. Liu, T. Gottschall, K.P. Skokov, J.D. Moore, O. Gutfleisch, Nat. Mater. 11 (2012) 620-626. DOI URL
[96]	Z.B. Li, S.Y. Dong, Z.Z. Li, B. Yang, F. Liu, C.F. Sánchez-Valdés, J.L. Sánchez Lla-mazares, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, Scr. Mater. 159 (2019) 113-118. DOI URL
[97]	E. Stern-Taulats, P.O. Castillo-Villa, L. Mañosa, C. Frontera, S. Pramanick, S. Ma-jumdar, A. Planes, J. Appl. Phys. 115 (2014) 173907. DOI URL
[98]	J.-P. Camarillo, E. Stern-Taulats, L. Mañosa, H. Flores-Zúñiga, D. Ríos-Jara, A. Planes, J. Phys. D-Appl. Phys. 49 (2016) 125006. DOI URL
[99]	Y. Song, X. Chen, V. Dabade, T.W. Shield, R.D. James, Nature 502 (2013) 85-88. DOI URL
[100]	K. Bhattacharya, S. Conti, G. Zanzotto, J. Zimmer, Nature 428 (2004) 55-59. DOI URL
[101]	W. Sun, J. Liu, D.W. Zhao, M.X. Zhang, J. Phys. D-Appl. Phys. 50 (2017) 444001. DOI URL
[102]	Y. Shen, Z. Wei, W. Sun, Y. Zhang, E. Liu, J. Liu, Acta Mater. 188 (2020) 677-685. DOI URL
[103]	F. Xiao, M. Jin, J. Liu, X. Jin, Acta Mater. 96 (2015) 292-300. DOI URL
[104]	Y. Xu, B.F. Lu, W. Sun, A. Yan, J. Liu, Appl. Phys. Lett. 106 (2015) 201903. DOI URL
[105]	Y. Li, D. Zhao, J. Liu, Sci. Rep. 6 (2016) 25500. DOI URL
[106]	A. Shen, D. Zhao, W. Sun, J. Liu, C. Li, Scr. Mater. 127 (2017) 1-5. DOI URL
[107]	G.J. Pataky, E. Ertekin, H. Sehitoglu, Acta Mater. 96 (2015) 420-427. DOI URL
[108]	S. Xu, H.Y. Huang, J.X. Xie, S. Takekawa, X. Xu, T. Omori, R. Kainuma, APL Mater. 4 (2016) 106106. DOI URL
[109]	L. Manosa, S. Jarque-Farnos, E. Vives, A. Planes, Appl. Phys. Lett. 103 (2013) 211904. DOI URL
[110]	Y. Wu, E. Ertekin, H. Sehitoglu, Acta Mater. 135 (2017) 158-176. DOI URL
[111]	L.C. Brown, Metall. Trans. A 12 (1981) 1491-1494. DOI URL
[112]	J. Cui, Y. Wu, J. Muehlbauer, Y. Hwang, R. Radermacher, S. Fackler, M. Wuttig, I. Takeuchi, Appl. Phys. Lett. 101 (2012) 073904. DOI URL
[113]	H. Chen, F. Xiao, X. Liang, Z. Li, X. Jin, T. Fukuda, Acta Mater. 158 (2018) 330-339. DOI URL
[114]	Y. Kim, M.G. Jo, J.W. Park, H.K. Park, H.N. Han, Scr. Mater. 144 (2018) 48-51. DOI URL
[115]	C. Bechtold, C. Chluba, R. Lima de Miranda, E. Quandt, Appl. Phys. Lett. 101 (2012) 091903. DOI URL
[116]	J. Guo, Z. Wei, Y. Shen, Y. Zhang, J. Li, X. Hou, J. Liu, Scr. Mater. 185 (2020) 56-60. DOI URL
[117]	L. Wei, X. Zhang, J. Liu, L. Geng, AIP Adv. 8 (2018) 055312. DOI URL
[118]	D. Zhao, T. Castán, A. Planes, Z. Li, W. Sun, J. Liu, Phys. Rev. B 96 (2017) 224105. DOI URL
[119]	B. Lu, P. Zhang, Y. Xu, W. Sun, J. Liu, Mater. Lett. 148 (2015) 110-113. DOI URL
[120]	Z. Zhang, R.D. James, S. Müller, Acta Mater. 57 (2009) 4332-4352. DOI URL
[121]	Y. Li, W. Sun, D. Zhao, H. Xu, J. Liu, Scr. Mater. 130 (2017) 278-282. DOI URL
[122]	D. Zhao, F. Xiao, Z. Nie, D. Cong, W. Sun, J. Liu, Scr. Mater. 149 (2018) 6-10. DOI URL
[123]	F. Xiao, T. Fukuda, T. Kakeshita, Appl. Phys. Lett. 102 (2013) 161914. DOI URL
[124]	J. Tušek, K. Engelbrecht, R. Millán-Solsona, L. Mañosa, E. Vives, L.P. Mikkelsen, N. Pryds, Adv. Energy Mater. 5 (2015) 1500361. DOI URL
[125]	Z.Y. Wei, W. Sun, Q. Shen, Y. Shen, Y.F. Zhang, E.K. Liu, J. Liu, Appl. Phys. Lett. 114 (2019) 101903. DOI URL
[126]	Q. Shen, D.W. Zhao, W. Sun, Y. Li, J. Liu, J. Alloy. Compd. 696 (2017) 538-542. DOI URL
[127]	J. Hao, F. Hu, J.-T. Wang, F.-R. Shen, Z. Yu, H. Zhou, H. Wu, Q. Huang, K. Qiao, J. Wang, J. He, L. He, J.-R. Sun, B. Shen, Chem. Mater. 32 (2020) 1807-1818. DOI URL
[128]	B. Emre, I. Dincer, Y. Elerman, Intermetallics 31 (2012) 16-20. DOI URL
[129]	N.J. Ghimire, S.K. Cary, S. Eley, N.A. Wakeham, P.F.S. Rosa, T. Albrecht-Schmitt, Y. Lee, M. Janoschek, C.M. Brown, L. Civale, J.D. Thompson, F. Ronning, E.D. Bauer, Phys. Rev. B 93 (20) (2016).
[130]	I. Dincer, E. Yüzüak, G. Durak, Y. Elerman, J. Alloy. Compd. 588 (2014) 332-336. DOI URL
[131]	G.A. Slack, Solid State Phys. 34 (1979) 1-71.
[132]	M. Pugaczowa-Michalska, Solid State Commun. 140 (2006) 251-255. DOI URL
[133]	M.D. Kuz’min, Phys. Rev. Lett. 94 (2005) 107204. DOI URL