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Numerical simulation of magnetism and magnetocaloric effect of Mn-rich Ni-Mn-Ga alloy

WANG Bo ZHANG Yufen SHAO Hui ZHANG Zeyu HU Yong

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Numerical simulation of magnetism and magnetocaloric effect of Mn-rich Ni-Mn-Ga alloy

WANG Bo, ZHANG Yufen, SHAO Hui, ZHANG Zeyu, HU Yong
cstr: 32037.14.aps.75.20251394
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  • This work investigates the magnetocaloric effect-based green magnetic refrigeration technology, with a focus on Ni-Mn-Ga Heusler alloy as a promising magnetic refrigerant candidate. To elucidate the role of Mn-rich composition in regulating the magnetic and magnetocaloric properties, a multi-scale computational approach integrating first-principles calculations and Monte Carlo simulations is adopted. This method enables a detailed analysis of how Mn atoms occupying Ni and Ga sites influence the microstructure, atomic magnetic moments, exchange interactions, and macroscopic magnetocaloric response of the alloy. The results indicate that Mn site occupancy critically affects the magnetic performance: the occupation of Ni sites reduces the total magnetic moment and Curie temperature, thereby reducing the magnetic entropy change; in contrast, Mn occupying Ga sites significantly enhances both the total magnetic moment and the magnetic entropy change. Notably, the Ni8Mn7Ga1 alloy achieves a maximum magnetic entropy change of 2.32 J·kg–1·K–1 under a 2 T magnetic field, which significantly exceeds that of the stoichiometric Ni8Mn4Ga4 alloy. Further electronic structure analysis reveals that Mn content variation modulates the density of states near the Fermi level and optimizes orbital hybridization and ferromagnetic exchange interactions, thus adjusting the magnetic phase transition behavior. Critical exponent analysis confirms that the magnetic interactions are inherently long-range and tend toward mean-field behavior with compositional changes. By establishing a clear “composition-structure-magnetism-magnetocaloric performance” relationship on an atomic scale, this work provides theoretical foundations for designing high-performance, low-hysteresis magnetic refrigeration materials.
      Corresponding author: WANG Bo, 380678357@qq.com ; HU Yong, huyong@mail.neu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. U22A20117) and the Guangdong Provincial Basic and Applied Basic Research Foundation, China (Grant No. 2023A1515140171).
    [1]

    Dong Y, Coleman M, Miller S A 2021 Annu. Rev. Environ. Resour. 46 59Google Scholar

    [2]

    Zimm C, Jastrab A, Sternberg A, Pecharsky V, Gschneidner Jr K, Osborne M, Anderson I 1998 Advances in Cryogenic Engineering (Boston, MA: Springer) (Vol. 43) pp1759–1766Google Scholar

    [3]

    Pecharsky V K, Gschneidner Jr K A 1997 Phys. Rev. Lett. 78 4494Google Scholar

    [4]

    Provenzano V, Shapiro A J, Shull R D 2004 Nature (London) 429 853Google Scholar

    [5]

    Tegus O, Brück E, Buschow K H J, de Boer R D 2002 Nature (London) 415 150Google Scholar

    [6]

    郑新奇, 沈俊, 胡凤霞, 孙继荣, 沈保根 2016 物理学报 65 217502Google Scholar

    Zheng X Q, Shen J, Hu F X, Sun J R, Shen B G 2016 Acta Phys. Sin. 65 217502Google Scholar

    [7]

    李瑞, 沈俊, 张志鹏, 李振兴, 莫兆军, 高新强, 海鹏, 付琪 2024 物理学报 73 037501Google Scholar

    Li R, Shen J, Zhang Z P, Li Z X, Mo Z J, Gao X Q, Hai P, Fu Q 2024 Acta Phys. Sin. 73 037501Google Scholar

    [8]

    Tickle R, James R D 1999 J. Magn. Magn. Mater. 195 627Google Scholar

    [9]

    Chen J, Hana Z, Qiana B, Zhang P, Wang D, Duc Y 2011 J. Magn. Magn. Mater. 323 248Google Scholar

    [10]

    Sharma V K, Chattopadhyay M K, Kumar R, Ganguli T, Tiwari P, Roy S B 2007 J. Phys. Condens. Matter 19 496207Google Scholar

    [11]

    Hu F X, Shen B G, Sun J R, Cheng Z H, Rao G H, Zhang X X 2001 Appl. Phys. Lett. 78 3675Google Scholar

    [12]

    Fujieda S, Fujita A, Fukamichi K 2002 Appl. Phys. Lett. 81 1276Google Scholar

    [13]

    Shen Q, van Rooij F, Zhang Z, Hao W, Dugulan A I, van Dijk N, Brück E, Li L 2026 J. Mater. Sci. Technol. 254 196Google Scholar

    [14]

    Na Y Z, Wang Z X, Kong Z, Xie Y, Zhang Y K 2025 J. Rare Earth https://doi.org/10.1016/j.jre.2025.09.044

    [15]

    Campos A, Rocco D, Carvalho A, Caron L, Coelho A, Gama S, Silva L, Gandra F, Santos A, Cardoso L, von Ranke P J, Oliveira N A 2006 Nat. Mater. 5 802Google Scholar

    [16]

    Gschneidner Jr K A, Pecharsky V V, Tsokol A O 2005 Rep. Prog. Phys. 68 1479Google Scholar

    [17]

    Gshneidner Jr K A, Pecharsky V V 2008 Int. J. Refrig. 31 945Google Scholar

    [18]

    Planes A, Mañosa L, Acet M 2009 J. Phys. Condens. Matter 21 233201Google Scholar

    [19]

    Franco V, Blázquez J S, Ingalge B, Conde A 2012 Ann. Rev. Mater. Res. 42 305Google Scholar

    [20]

    de Oliveira N A, von Ranke P J, Troper A 2014 Int. J. Refrig. 37 237Google Scholar

    [21]

    Dunand D C, Mullner P 2011 Adv. Mater. 23 216Google Scholar

    [22]

    Webster P J, Ziebeck K R A, Town S L, Peak M S 1984 Philos. Magn. 49 295Google Scholar

    [23]

    Entel P, Dannenberg A, Siewert M, Herper H C, Gruner M E, Buchelnikov V D, Chernenko V A 2011 Mater. Sci. Forum 684 1Google Scholar

    [24]

    Datta S, Dheke S S, Panda S K, Rout S N, Das T, Kar M 2023 J. Alloys Compd. 968 172251Google Scholar

    [25]

    Fabbrici S, Porcari G, Cugini F, Solzi M, Kamarad J, Arnold Z, Cabassi R, Albertini F 2014 Entropy 16 2204Google Scholar

    [26]

    Schleicher B, Klar D, Ollefs K, Diestel A, Walecki D, Weschke E, Schultz L, Nielsch K, Fähler S, Wende H, Gruner M E 2017 J. Phys. D: Appl. Phys. 50 465005Google Scholar

    [27]

    Diestel A, Niemann R, Schleicher B, Nielsch K, Fähler S 2018 Energy Technol. 6 1463Google Scholar

    [28]

    Schröter M, Herper H C, Grünebohm A 2022 J. Phys. D: Appl. Phys. 55 025002Google Scholar

    [29]

    Fu S, Gao J, Wang K, Ma L, Zhu J 2024 Intermetallics 169 108276Google Scholar

    [30]

    Mendonça A A, Ghivelder L, Bernardo P L, Cohen L F, Gomes A M 2023 J. Alloys Compd. 938 168444Google Scholar

    [31]

    Sarkar S K, Babu P D, Biswas A, Siruguri V, Krishnan M 2016 J. Alloys Compd. 670 281Google Scholar

    [32]

    Zhang X, Qian M, Zhang Z, Wei L, Geng L, Sun J 2016 Appl. Phys. Lett. 108 052401Google Scholar

    [33]

    Gràcia-Condal A, Planes A, Mañosa L, Wei Z, Guo J, Soto-Parra D, Liu J 2022 Phys. Rev. Mater. 6 084403Google Scholar

    [34]

    Liu Y, Zhang X, Xing D, Shen H, Chen D, Liu J, Sun J 2014 J. Alloys Compd. 616 184Google Scholar

    [35]

    Liu Y, Luo L, Zhang X, Shen H, Liu J, Sun J, Zu N 2019 Intermetallics 112 106538Google Scholar

    [36]

    Qian M, Zhang X, Wei L, Martin P, Sun J, Geng L, Scott T B, Peng H X 2018 Sci. Rep. 8 16574Google Scholar

    [37]

    Qian M, Zhang X, Jia Z, Wan, X, Geng L 2018 Mater. Des. 148 115Google Scholar

    [38]

    Zhang Y C, Franco V, Wang Y F, Peng H X, Qin F X 2022 J. Alloys Compd. 918 165664Google Scholar

    [39]

    Chiu W T, Sratong-on P, Chang T F M, Tahara M, Sone M, Chernenko V, Hosoda H 2023 J. Mater. Res. Technol. 23 131Google Scholar

    [40]

    Zhang Y C, Gao Y, Franco V, Yin H B C, Peng H X, Qin F X 2023 Sci. Chin. -Mater. 66 3670Google Scholar

    [41]

    Hu F X, Shen B G, Sun J R 2000 Appl. Phys. Lett. 76 3460Google Scholar

    [42]

    Pasquale M, Sasso C P, Lewis L H, Giudici L, Lograsso T, Schlagel D 2005 Phys. Rev. B 72 094435Google Scholar

    [43]

    Miroshkina O N, Sokolovskiy V V, Zagrebin M A, Taskaev S V, Buchelnikov V D 2020 Phys. Solid State 62 785Google Scholar

    [44]

    Brown P J, Crangle J, Kanomata T, Matsumoto M, Neumann K U, Ouladdiaf B, Ziebeck K R A 2002 J. Phys. Condens. Matter 14 10159Google Scholar

    [45]

    Hafner J 2000 Acta Mater. 48 71Google Scholar

    [46]

    Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169Google Scholar

    [47]

    Kresse G, Hafner J 1993 Phys. Rev. B 47 558Google Scholar

    [48]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [49]

    Perdew J P, Wang Y 1992 Phys. Rev. B 45 13244Google Scholar

    [50]

    Blöchl P E 1994 Phys. Rev. B 50 17953Google Scholar

    [51]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188Google Scholar

    [52]

    Ebert H, Dreysee H 1999 The Use of the LMTO Method (Lecture Notes in Physics) (Berlin: Springer) (Vol. 535) pp191–246

    [53]

    Ebert H 2005 The Munich SPR-KKR Package (Version 8.6) SPRKKR 8.6 Manual

    [54]

    Minár J, Perlov A, Ebert H, Hashizume H 2005 J. Phys. Condens. Matter 17 5785Google Scholar

    [55]

    Zhang C, Zhang Z, Wang D, Hu Y 2024 Appl. Phys. Lett. 124 082407Google Scholar

    [56]

    Liechtenstein A I, Katsnelson M I, Antropov V P, Gubanov V A 1987 J. Magn. Magn. Mater. 67 65Google Scholar

    [57]

    Phan M H, Yu S C 2007 J. Magn. Magn. Mater. 308 325Google Scholar

    [58]

    Pecharsky V K, Gschneidner K A 2000 Annu. Rev. Mater. Sci. 30 387Google Scholar

    [59]

    Hu Y, Wang Y, Li Z, Chi X, Lu Q, Hu T, Liu Y, Du A, Shi F 2018 Appl. Phys. Lett. 113 133902Google Scholar

    [60]

    Hu Y, Hu T, Chi X, Wang Y, Lu Q, Yu L, Li R, Liu Y, Du A, Li Z, Shi F 2019 Appl. Phys. Lett. 114 023903Google Scholar

    [61]

    Hao F, Hu Y 2020 Appl. Phys. Lett. 117 063902Google Scholar

    [62]

    Zhang J, Hu Y 2021 Appl. Phys. Lett. 119 213903Google Scholar

    [63]

    Oesterreicher H, Parker F T 1984 J. Appl. Phys. 55 4334Google Scholar

    [64]

    Franco V, Blázquez J S, Conde A 2006 Appl. Phys. Lett. 89 222512Google Scholar

    [65]

    Franco V, Conde A, Sidhaye D, Prasad B L V, Poddar P, Srinath S, Phan M H, Srikanth H 2010 J. Appl. Phys. 107 09A902Google Scholar

    [66]

    Liu Y, Petrovic C 2018 Phys. Rev. B 97 174418Google Scholar

  • 图 1  带有特定成分占比的Ni-Mn-Ga三元合金的晶体结构模型, 其中Mn1和Mn2分别代表原位和占据Ni或Ga位的Mn原子

    Figure 1.  Crystal structure models of Ni-Mn-Ga ternary alloys with specific composition ratios, where Mn1 and Mn2 represent Mn atoms of original sites and those occupying Ni or Ga sites, respectively.

    图 2  奥氏体相和马氏体相Ni8–xMn4+xGa4 (x = 0, 1, 2)和Ni8Mn4+yGa4–y (y = 0, 1, 2, 3)合金总磁矩和Mn, Ni原子磁矩随成分的变化趋势

    Figure 2.  Total magnetic moment of alloy and magnetic moments of Mn and Ni atoms as a function of composition in austenitic and martensitic Ni8–xMn4+xGa4 (x = 0, 1, 2) and Ni8Mn4+yGa4–y (y = 0, 1, 2, 3) alloys.

    图 3  不同成分配比的奥氏体相Ni-Mn-Ga合金的总态密度和各元素态密度随能量的变化关系

    Figure 3.  Total density of states and partial density of states of each elements as a function of energy in austenitic Ni-Mn-Ga alloys.

    图 4  不同成分配比的马氏体相Ni-Mn-Ga合金的总态密度和各元素态密度随能量的变化关系

    Figure 4.  Total density of states and partial density of states of each elements as a function of energy in martensitic Ni-Mn-Ga alloys.

    图 5  在奥氏体相Ni8–xMn4+xGa4(x = 0, 1, 2)和Ni8Mn4+yGa4–y(y = 0, 1, 2, 3)合金中, Mn-Mn和Mn-Ni交换作用常数随原子间距的变化关系, 其中Mn1和Mn2分别代表原位和占据Ni或Ga位的Mn原子, 原子间距以晶格常数a为单位

    Figure 5.  Exchange coupling constants between Mn-Mn and Mn-Ni as a function of distance in austenitic Ni8–xMn4+xGa4 (x = 0, 1, 2)和Ni8Mn4+yGa4–y (y = 0, 1, 2, 3) alloys, where Mn1 and Mn2 represent Mn atoms of original sites and those occupying Ni or Ga sites, respectively, and distance is given in units of lattice constant a.

    图 6  在零外磁场作用下, 奥氏体相Ni8–xMn4+xGa4(x = 0, 1, 2)和Ni8Mn4+yGa4–y(y = 0, 1, 2, 3)合金的磁化强度和磁化率随温度的变化关系, 其中MS为饱和磁化强度值; 居里温度随富Mn成分的变化关系

    Figure 6.  Magnetization and magnetic susceptibility as a function of temperature in austenitic Ni8–xMn4+xGa (x = 0, 1, 2) and Ni8Mn4+yGa4–y (y = 0, 1, 2, 3) alloys under zero magnetic field, where MS is the value of saturated magnetization; Curie temperature as a function of composition of excess Mn.

    图 7  在选定的外磁场作用下, 不同成分的奥氏体相Ni-Mn-Ga合金的磁化强度随温度的变化关系, 其中MS为饱和磁化强度值

    Figure 7.  Magnetization of austenitic Ni-Mn-Ga alloys with different compositions as a function of temperature under selected magnetic fields, where MS is the value of saturated magnetization.

    图 8  在选定的外磁场作用下, 不同成分的奥氏体相Ni-Mn-Ga合金的磁熵变随温度的变化关系

    Figure 8.  Magnetic entropy change of austenitic Ni-Mn-Ga alloys with different compositions as a function of temperature under selected magnetic fields.

    图 9  不同成分的Ni-Mn-Ga合金的最大磁熵变和相对冷却能力随外磁场的变化关系

    Figure 9.  Maximum magnetic entropy change and relative cooling power as a function of magnetic field in Ni-Mn-Ga alloys with different compositions.

    图 10  在Ni8–xMn4+xGa4 (x = 0, 1, 2)和Ni8Mn4+yGa4–y (y = 0, 1, 2, 3)合金中, 计算的参数随成分的变化关系

    Figure 10.  Calculated parameters as a function of composition in Ni8–xMn4+xGa4 (x = 0, 1, 2) and Ni8Mn4+yGa4–y (y = 0, 1, 2, 3) alloys.

    表 1  不同富Mn成分下的奥氏体相和马氏体相Ni-Mn-Ga合金的晶格常数

    Table 1.  Crystal lattice constants of austenitic and martensitic Ni-Mn-Ga alloys with different Mn-rich compositions.

    AusteniteMartensite
    abcabc
    Ni8Mn4Ga4 (x/y = 0)5.8095.8095.8095.3225.3226.919
    Ni7Mn5Ga4 (x = 1)5.8005.8005.8005.3145.3146.908
    Ni6Mn6Ga4 (x = 2)5.7855.7855.7855.3005.3006.891
    Ni8Mn5Ga3 (y = 1)5.8185.8185.8185.3315.3316.931
    Ni8Mn6Ga2 (y = 2)5.8285.8285.8285.3405.3406.942
    Ni8Mn7Ga1 (y = 3)5.8345.8345.8345.3465.3466.949
    DownLoad: CSV
  • [1]

    Dong Y, Coleman M, Miller S A 2021 Annu. Rev. Environ. Resour. 46 59Google Scholar

    [2]

    Zimm C, Jastrab A, Sternberg A, Pecharsky V, Gschneidner Jr K, Osborne M, Anderson I 1998 Advances in Cryogenic Engineering (Boston, MA: Springer) (Vol. 43) pp1759–1766Google Scholar

    [3]

    Pecharsky V K, Gschneidner Jr K A 1997 Phys. Rev. Lett. 78 4494Google Scholar

    [4]

    Provenzano V, Shapiro A J, Shull R D 2004 Nature (London) 429 853Google Scholar

    [5]

    Tegus O, Brück E, Buschow K H J, de Boer R D 2002 Nature (London) 415 150Google Scholar

    [6]

    郑新奇, 沈俊, 胡凤霞, 孙继荣, 沈保根 2016 物理学报 65 217502Google Scholar

    Zheng X Q, Shen J, Hu F X, Sun J R, Shen B G 2016 Acta Phys. Sin. 65 217502Google Scholar

    [7]

    李瑞, 沈俊, 张志鹏, 李振兴, 莫兆军, 高新强, 海鹏, 付琪 2024 物理学报 73 037501Google Scholar

    Li R, Shen J, Zhang Z P, Li Z X, Mo Z J, Gao X Q, Hai P, Fu Q 2024 Acta Phys. Sin. 73 037501Google Scholar

    [8]

    Tickle R, James R D 1999 J. Magn. Magn. Mater. 195 627Google Scholar

    [9]

    Chen J, Hana Z, Qiana B, Zhang P, Wang D, Duc Y 2011 J. Magn. Magn. Mater. 323 248Google Scholar

    [10]

    Sharma V K, Chattopadhyay M K, Kumar R, Ganguli T, Tiwari P, Roy S B 2007 J. Phys. Condens. Matter 19 496207Google Scholar

    [11]

    Hu F X, Shen B G, Sun J R, Cheng Z H, Rao G H, Zhang X X 2001 Appl. Phys. Lett. 78 3675Google Scholar

    [12]

    Fujieda S, Fujita A, Fukamichi K 2002 Appl. Phys. Lett. 81 1276Google Scholar

    [13]

    Shen Q, van Rooij F, Zhang Z, Hao W, Dugulan A I, van Dijk N, Brück E, Li L 2026 J. Mater. Sci. Technol. 254 196Google Scholar

    [14]

    Na Y Z, Wang Z X, Kong Z, Xie Y, Zhang Y K 2025 J. Rare Earth https://doi.org/10.1016/j.jre.2025.09.044

    [15]

    Campos A, Rocco D, Carvalho A, Caron L, Coelho A, Gama S, Silva L, Gandra F, Santos A, Cardoso L, von Ranke P J, Oliveira N A 2006 Nat. Mater. 5 802Google Scholar

    [16]

    Gschneidner Jr K A, Pecharsky V V, Tsokol A O 2005 Rep. Prog. Phys. 68 1479Google Scholar

    [17]

    Gshneidner Jr K A, Pecharsky V V 2008 Int. J. Refrig. 31 945Google Scholar

    [18]

    Planes A, Mañosa L, Acet M 2009 J. Phys. Condens. Matter 21 233201Google Scholar

    [19]

    Franco V, Blázquez J S, Ingalge B, Conde A 2012 Ann. Rev. Mater. Res. 42 305Google Scholar

    [20]

    de Oliveira N A, von Ranke P J, Troper A 2014 Int. J. Refrig. 37 237Google Scholar

    [21]

    Dunand D C, Mullner P 2011 Adv. Mater. 23 216Google Scholar

    [22]

    Webster P J, Ziebeck K R A, Town S L, Peak M S 1984 Philos. Magn. 49 295Google Scholar

    [23]

    Entel P, Dannenberg A, Siewert M, Herper H C, Gruner M E, Buchelnikov V D, Chernenko V A 2011 Mater. Sci. Forum 684 1Google Scholar

    [24]

    Datta S, Dheke S S, Panda S K, Rout S N, Das T, Kar M 2023 J. Alloys Compd. 968 172251Google Scholar

    [25]

    Fabbrici S, Porcari G, Cugini F, Solzi M, Kamarad J, Arnold Z, Cabassi R, Albertini F 2014 Entropy 16 2204Google Scholar

    [26]

    Schleicher B, Klar D, Ollefs K, Diestel A, Walecki D, Weschke E, Schultz L, Nielsch K, Fähler S, Wende H, Gruner M E 2017 J. Phys. D: Appl. Phys. 50 465005Google Scholar

    [27]

    Diestel A, Niemann R, Schleicher B, Nielsch K, Fähler S 2018 Energy Technol. 6 1463Google Scholar

    [28]

    Schröter M, Herper H C, Grünebohm A 2022 J. Phys. D: Appl. Phys. 55 025002Google Scholar

    [29]

    Fu S, Gao J, Wang K, Ma L, Zhu J 2024 Intermetallics 169 108276Google Scholar

    [30]

    Mendonça A A, Ghivelder L, Bernardo P L, Cohen L F, Gomes A M 2023 J. Alloys Compd. 938 168444Google Scholar

    [31]

    Sarkar S K, Babu P D, Biswas A, Siruguri V, Krishnan M 2016 J. Alloys Compd. 670 281Google Scholar

    [32]

    Zhang X, Qian M, Zhang Z, Wei L, Geng L, Sun J 2016 Appl. Phys. Lett. 108 052401Google Scholar

    [33]

    Gràcia-Condal A, Planes A, Mañosa L, Wei Z, Guo J, Soto-Parra D, Liu J 2022 Phys. Rev. Mater. 6 084403Google Scholar

    [34]

    Liu Y, Zhang X, Xing D, Shen H, Chen D, Liu J, Sun J 2014 J. Alloys Compd. 616 184Google Scholar

    [35]

    Liu Y, Luo L, Zhang X, Shen H, Liu J, Sun J, Zu N 2019 Intermetallics 112 106538Google Scholar

    [36]

    Qian M, Zhang X, Wei L, Martin P, Sun J, Geng L, Scott T B, Peng H X 2018 Sci. Rep. 8 16574Google Scholar

    [37]

    Qian M, Zhang X, Jia Z, Wan, X, Geng L 2018 Mater. Des. 148 115Google Scholar

    [38]

    Zhang Y C, Franco V, Wang Y F, Peng H X, Qin F X 2022 J. Alloys Compd. 918 165664Google Scholar

    [39]

    Chiu W T, Sratong-on P, Chang T F M, Tahara M, Sone M, Chernenko V, Hosoda H 2023 J. Mater. Res. Technol. 23 131Google Scholar

    [40]

    Zhang Y C, Gao Y, Franco V, Yin H B C, Peng H X, Qin F X 2023 Sci. Chin. -Mater. 66 3670Google Scholar

    [41]

    Hu F X, Shen B G, Sun J R 2000 Appl. Phys. Lett. 76 3460Google Scholar

    [42]

    Pasquale M, Sasso C P, Lewis L H, Giudici L, Lograsso T, Schlagel D 2005 Phys. Rev. B 72 094435Google Scholar

    [43]

    Miroshkina O N, Sokolovskiy V V, Zagrebin M A, Taskaev S V, Buchelnikov V D 2020 Phys. Solid State 62 785Google Scholar

    [44]

    Brown P J, Crangle J, Kanomata T, Matsumoto M, Neumann K U, Ouladdiaf B, Ziebeck K R A 2002 J. Phys. Condens. Matter 14 10159Google Scholar

    [45]

    Hafner J 2000 Acta Mater. 48 71Google Scholar

    [46]

    Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169Google Scholar

    [47]

    Kresse G, Hafner J 1993 Phys. Rev. B 47 558Google Scholar

    [48]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [49]

    Perdew J P, Wang Y 1992 Phys. Rev. B 45 13244Google Scholar

    [50]

    Blöchl P E 1994 Phys. Rev. B 50 17953Google Scholar

    [51]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188Google Scholar

    [52]

    Ebert H, Dreysee H 1999 The Use of the LMTO Method (Lecture Notes in Physics) (Berlin: Springer) (Vol. 535) pp191–246

    [53]

    Ebert H 2005 The Munich SPR-KKR Package (Version 8.6) SPRKKR 8.6 Manual

    [54]

    Minár J, Perlov A, Ebert H, Hashizume H 2005 J. Phys. Condens. Matter 17 5785Google Scholar

    [55]

    Zhang C, Zhang Z, Wang D, Hu Y 2024 Appl. Phys. Lett. 124 082407Google Scholar

    [56]

    Liechtenstein A I, Katsnelson M I, Antropov V P, Gubanov V A 1987 J. Magn. Magn. Mater. 67 65Google Scholar

    [57]

    Phan M H, Yu S C 2007 J. Magn. Magn. Mater. 308 325Google Scholar

    [58]

    Pecharsky V K, Gschneidner K A 2000 Annu. Rev. Mater. Sci. 30 387Google Scholar

    [59]

    Hu Y, Wang Y, Li Z, Chi X, Lu Q, Hu T, Liu Y, Du A, Shi F 2018 Appl. Phys. Lett. 113 133902Google Scholar

    [60]

    Hu Y, Hu T, Chi X, Wang Y, Lu Q, Yu L, Li R, Liu Y, Du A, Li Z, Shi F 2019 Appl. Phys. Lett. 114 023903Google Scholar

    [61]

    Hao F, Hu Y 2020 Appl. Phys. Lett. 117 063902Google Scholar

    [62]

    Zhang J, Hu Y 2021 Appl. Phys. Lett. 119 213903Google Scholar

    [63]

    Oesterreicher H, Parker F T 1984 J. Appl. Phys. 55 4334Google Scholar

    [64]

    Franco V, Blázquez J S, Conde A 2006 Appl. Phys. Lett. 89 222512Google Scholar

    [65]

    Franco V, Conde A, Sidhaye D, Prasad B L V, Poddar P, Srinath S, Phan M H, Srikanth H 2010 J. Appl. Phys. 107 09A902Google Scholar

    [66]

    Liu Y, Petrovic C 2018 Phys. Rev. B 97 174418Google Scholar

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Publishing process
  • Received Date:  15 October 2025
  • Accepted Date:  28 October 2025
  • Available Online:  01 November 2025
  • Published Online:  05 January 2026
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