The martensite transition temperature
Ni41Co9Mn31.5Ga18.5 is a magnetic Heusler alloy, which indicates metamagnetic transition at the reverse martensite transition. In this paper, caloric measurements were performed and discussed about magnetocaloric effect. We also performed magnetization measurements around Curie temperature TC in the martensite phase and analyzed by means of the spin fluctuation theory of itinerant electron magnetism. From the differential scanning calorimetry (DSC) measurements in zero fields, the value of the latent heat λ was obtained as 2.63 kJ/kg, and in magnetic fields the value was not changed. The entropy change ΔS was − 7.0 J/(kgK) in zero fields and gradually increases with increasing magnetic fields. The relative cooling power (RCP) was 104 J/kg at 2.0 T, which was comparable with In doped Ni41Co9Mn32Ga16In2 alloy.
- shape memory alloys
- differential scanning calorimetry
- magnetocaloric effect
- itinerant electron magnetism
Recently, ferromagnetic shape memory alloys (FSMA) have been studied extensively as candidates for highly functional materials. Between FSMA, Ni2MnGa is the most renowned alloy . The alloy has a cubic
New alloys in the Ni–Mn–In, Ni–Mn–Sn, and Ni–Mn–Sb Heusler alloy systems that are expected to be ferromagnetic shape memory alloys have been studied [7, 8]. A metamagnetic transition from paramagnetic martensite phase to ferromagnetic austenite phase was observed, and reverse martensite transition induced by magnetic fields was occurred under high magnetic fields [9, 10]. These alloys are promising as a metamagnetic shape memory alloys with a magnetic field‐induced shape memory effect (MSIF) and as magnetocaloric materials. Ni–Co–Mn–In alloys, in which Co is substituted for Ni in Ni–Mn–In alloys to increase the Curie temperature, indicate shape memory behaviors in compressive
The substitution of Co for Ni or Ga atoms in Ni2MnGa type alloys has turned the magnetic ordering of the parent phase from partially antiferromagnetic or paramagnetic to ferromagnetic, resulting in a large magnetization change across the transformation, which dramatically enhances the magnetic field driving force [12–40]. The phase diagram in the temperature‐concentration plane is determined on the basis of the experimental results. The determined phase diagram is spanned by a paramagnetic austenite (Para‐A) phase, paramagnetic martensite phase, ferromagnetic austenite phase, ferromagnetic martensite (Ferro‐M) phase of
We studied about the physical properties and magnetism of Ni50-
The effects of Co addition on the properties of Ni8-
In this paper, caloric measurements were performed. On the basis of the experimental results, magnetocaloric effect was discussed. We also studied about the itinerant electron magnetic properties of Ni41Co9Mn31.5Ga18.5. We performed the magnetization measurements by means of the pulsed magnetic fields. The
2. Experimental procedures
The sample used in this study was synthesized at Yamagata University. The Ni41Co9Mn31.5Ga18.5 alloy was prepared by arc melting 4N Ni, 4N Co, 4N Mn, and 6N Ga in an argon atmosphere. The sample annealed at 1123 K for three days to homogenize the sample in a double evacuated silica tube, and then quenched in cold water. The obtained sample was polycrystalline. DSC measurements were performed by means of Helium‐free magnet at High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University. The bore of this magnet is in the air and which installed the factory‐made DSC equipment.
Magnetization measurements were performed by means of the pulsed field magnet at Ryukoku University. The absolute value was adjusted by Ni. The diamagnetism of the sample was also concerned to analyze the field dependence of the magnetization.
3. Results and discussions
3.1. Crystallography of Ni41Co9Mn31.5Ga18.5
From X‐ray powder diffraction shown in Figure 1, the sample was confirmed as a single phase with a tetragonal
The final compositions of the grown sample were verified by energy dispersive spectroscopy and were close to the nominal values with a deviation of <1%.
The Scanning Electron Microscope (SEM) image of Ni41Co9Mn31.5Ga18.5 at 298 K by means of FE‐SEM (JSM6300F, JEOL Co. Ltd.) shown in Figure 3 indicates that there are macroscopic twin variants on a scale of a few micrometers. The twins were arranged neatly in the domains. A single martensite phase characterized by typical lamellar twin substructures was observed, agreeing well with the X‐ray diffraction results. This result is well agree with the optical micrographs of microstructure of Ni56-
The calorimetric measurements, which allowed for the estimation of the latent heat and magnetocaloric analysis, were performed with factory‐made differential scanning calorimeter able to work up to 6 T. This setup exploits Peltier cells in order to measure heat flow of the sample. Calorimetric measurements of Ni41Co9Mn31.5Ga18.5 polycrystalline ferromagnetic shape memory alloy (FSMA) were performed across the
3.2. Magnetocaloric effect of Ni41Co9Mn31.5Ga18.5
The thermodynamic properties of the presented sample in magnetic fields were studied experimentally by measuring the heat flow by means of the DSC equipment. The four panels of Figure 4 show the heat flow of Ni41Co9Mn31.5Ga18.5 in zero and magnetic fields. The endothermic reaction was occurred around the reverse martensite temperature
Figure 7 shows the entropy change
We also performed the DSC measurement of Ni52.5Mn24.5Ga23 in zero and magnetic fields by means of the water‐cooled electromagnet in Ryukoku University. Figure 9a shows the heat flow of Ni52.5Mn24.5Ga23 in a heating process. The endothermic reaction was occurred around
Table 1 shows the
||13.3 (5 T)||–||188 (5 T)|||
||17.8 (5 T)||12 (5 T)||156 (5 T)|||
The magnetostructural transformation in this system can be described, in the frame of a simple geometrical model, by a relation linking the field‐induced adiabatic temperature change Δ
In order to obtain an adiabatic temperature change Δ
Entel et al. studied about Ni50-
|Ni50Mn30Ga20||6.90||-3.7||+0.9||370||+0.8 (1.8 T)|||
|Ni52.5Mn24.5Ga23||6.78||-4.6||+1.5||348||+1.0 (1.5 T)||This work|
|Ni41Co9Mn32Ga16In2||2.30||4.5||-11.3||320||-2.3 (1.8 T)||[42, 47]|
|Ni41Co9Mn31.5Ga18.5||2.34||7.2||-8.6||348||-4.5 (2.0 T)||This work|
3.3. Itinerant electron magnetic properties of Ni41Co9Mn31.5Ga18.5
We performed the magnetization measurements by means of the pulsed magnetic fields in order to investigate the itinerant electron magnetic properties of Ni41Co9Mn31.5Ga18.5. Takahashi proposed a spin fluctuation theory of itinerant electron magnetism [44, 45]. The induced magnetization
where, is a spontaneous magnetization in a ground state.
In most cases, the critical temperature dependence was determined using the Arrott plot. The analysis is based on the implicit assumption that the linearity is always satisfied. Takahashi suggested that the Arrott plot is not applicable in much itinerant d‐electron ferromagnets and the revision is necessary in the itinerant electron magnetism .
Figure 11 shows the magnetization process of Ni41Co9Mn31.5Ga18.5 around the
Eq. (2) can be written as the formula of,
Figure 12 shows the logarithm plot of Eq. (5). The gradient of the X‐Y plots indicate the critical index
Figure 13 shows the
Table 4 indicates the values of
||Standard deviation (%)|
|Ni||0.6||623||1.76 × 104|||
|MnSi||0.4||30||2.18 × 103|||
|Co2CrGa||3.01||488||1.0 × 104|||
||4.63 × 102|||
||6.45 × 102||[6, 57]|
|URhGe||0.32||9.6||8.56 × 102|||
|UGe2||1.44||53.5||4.93 × 102|||
||7.03 × 102||This work|
We studied about the magnetocaloric properties of Ni41Co9Mn31.5Ga18.5 by means of differential scanning calorimetry (DSC) measurements. Magnetocalorimetric measurements and magnetization measurements of Ni41Co9Mn31.5Ga18.5 polycrystalline ferromagnetic shape memory alloy (FSMA) were performed across the TR, at atmospheric pressure. When heating from the martensite phase, a steep increase in the thermal expansion due to the reverse martensite transition at TR was observed by the thermal expansion measurements. These transition temperatures decreased gradually with increasing magnetic field. The field dependence of the reverse martensite transition temperature,
In order to investigate the itinerant electron magnetic properties of Ni41Co9Mn31.5Ga18.5, we performed the magnetization measurements by means of the pulsed magnetic fields. The
The authors thank to Dr. M. Mori for helping SEM microscope experiment. DSC measurements in steady magnetic fields were performed at High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University, Japan.
K. Ullakko, J. K. Huang, C. Kantner, R. C. O'Handley and V. V. Kokorin, Large magnetic‐field‐induced strains in Ni2MnGa single crystals. Appl. Phys. Lett. 69(1996) 1966.
P. J. Webster, K. R. A. Ziebeck, S. L. Town and M. S. Peak, Magnetic order and phase transformation in Ni2MnGa. Philos. Mag. B. 49(1984) 295.
P. J. Brown, J. Crangle, T. Kanomata, M. Matsumoto, K‐. U. Neumann, B. Ouladdiaf and K. R. A. Ziebeck, The crystal structure and phase transitions of the magnetic shape memory compound Ni2MnGa. J. Phys. Condens. Matter. 14(2002) 10159.
J. Pons, R. Santamarta, V. A. Chernenko and E. Cesari, Long‐period martensitic structures of Ni‐Mn‐Ga alloys studied by high‐resolution transmission electron microscopy. J. Appl. Phys. 97(2005) 083516.
R. Ranjan, S. Banik, S. R. Barman, U. Kumar, P. K. Mukhopadhyay and D. Pandey, Powder X‐ray diffraction study of the thermoelastic martensitic transition in Ni2Mn1.05Ga0.95. Phys. Rev. B. 74(2006) 224443.
T. Sakon, K. Otsuka, J. Matsubayashi, Y. Watanabe, H. Nishihara, K. Sasaki, S. Yamashita, R. Y. Umetsu, H. Nojiri and T. Kanomata, Magnetic properties of the ferromagnetic shape memory alloy Ni50+ xMn27- xGa23 in magnetic fields. Materials 7(2014) 3715.
Y. Sutou, Y. Imano, N. Koeda, T. Omori, R. Kainuma, K. Ishida and K. Oikawa, Magnetic and martensitic transformations of NiMnX (X=In,Sn,Sb) ferromagnetic shape memory alloys. Appl. Phys. Lett. 85(2004) 4358.
K. Oikawa, W. Ito, Y. Imano, Y. Sutou, R. Kainuma, K. Ishida, S. Okamoto, O. Kitakami and T Kanomata, Effect of magnetic field on martensitic transition of Ni46Mn41In13 Heusler alloy. Appl. Phys. Lett. 88(2006) 122507.
R. Y. Umetsu, R. Kainuma, Y. Amako, Y. Taniguchi, T. Kanomata, K. Fukushima, A. Fujita, K. Oikawa and K. Ishida, Mössbauer study on martensite phase in Ni50Mn36.557Fe0.5Sn13 metamagnetic shape memory alloy. Appl. Phys. Lett. 93(2008) 042509.
V. V. Khovaylo, T. Kanomata, T. Tanaka, M. Nakashima, Y. Amako, R. Kainuma, R. Y. Umetsu, H. Morito and H. Miki, Magnetic properties of Ni50Mn34.8In15.2 probed by Mössbauer spectroscopy. Phys. Rev. B 80(2009) 144409.
R. Kainuma, Y. Imano, W. Ito, Y. Sutou. H. Morino, S. Okamoto, O. Kitakami, K. Oikawa, A. Fujita, T. Kanomata and K. Ishida, Magnetic‐field‐induced shape recovery by reverse phase transformation. Nature 439(2006) 957.
F. Albertini, S. Fabbrici, A. Paoluzi, J. Kamarad, Z. Arnold, L. Righi, M. Solzi, G. Porcari, C. Pernechele, D. Serrate and P. Algarabel, Reverse magnetostructural transitions by Co and In doping NiMnGa alloys: Structural, magnetic, and magnetoelastic properties mater. Sci. Forum 684(2011) 151.
C. Seguí, E. Cesari and P. Lázpita, Magnetic properties of martensite in metamagnetic Ni–Co–Mn–Ga alloys. J. Phys. D: Appl. Phys. 49(2016) 165007.
J. Kamarád, J. Kaštil, Y. Skourski, F. Albertini, S. Fabbrici and Z. Arnold, Magneto‐structural transitions induced at 1.2 K in Ni2MnGa‐based Heusler alloys by high magnetic field up to 60 T. Mater. Res. Express 1(2014) 016109.
C. Seguí, Effects of the interplay between atomic and magnetic order on the properties of metamagnetic Ni‐Co‐Mn‐Ga shape memory alloys. J. Appl. Phys. 115(2014) 113903.
P. Entel, M. E. Gruner, D. Comtesse, V. V. Sokolovskiy and V. D. Buchelnikov, Interacting magnetic cluster‐spin glasses and strain glasses in Ni–Mn based Heusler structured intermetallics, Phys. Stat. Sol. B 251(2014) 2135.
J. Kamarád, S. Fabbrici, J. Kasštil, F. Albertini, Z. Arnold and L. Righi, Pressure dependence of magneto‐structural properties of Co‐doped off stoichiometric Ni2MnGa alloys. EPJ Web Conf. 40(2013) 11002.
J. Kasštil, J. Kamarád, K. Knížek, Z. Arnold and P. Javorský, Peculiar magnetic properties of Er conditioned Ni43Co7Mn31Ga19 at ambient and hydrostatic pressures. J. Alloys Compd. 565(2013) 134.
G. Porcari S. Fabbrici, C. Pernechele, F. Albertini, M. Buzzi, A. Paoluzi, J. Kamarad, Z. Arnold and M. Solzi, Reverse magnetostructural transformation and adiabatic temperature change in Co‐ and In‐substituted Ni‐Mn‐Ga alloys. Phys. Rev. B. 85(2012) 024414.
C. Segui and E. Cesari, Composition and atomic order effects on the structural and magnetic transformations in ferromagnetic Ni–Co–Mn–Ga shape memory alloys. J. Appl. Phys. 111(2012) 043914.
T. Kanomata, S. Nunoki, K. Endo, M. Kataoka, H. Nishihara, V. V. Khovaylo, R. Y. Umetsu, T. Shishido, M. Nagasako, R. Kainuma and K. R. A. Ziebeck, Phase diagram of the ferromagnetic shape memory alloys Ni2MnGa1- xCo x. Phys. Rev. B. 85(2012) 134421.
Y. Wang, C. Huang, J. Gao, S. Yang, X. Ding, X. Song and X. Ren, Evidence for ferromagnetic strain glass in Ni‐Co‐Mn‐Ga Heusler alloy system. Appl. Phys. Lett. 101(2012) 101913.
S. K. Ayila, R. Machavarapu and S. Vummethala, Site preference of magnetic atoms in Ni–Mn–Ga–M (M = Co, Fe) ferromagnetic shape memory alloys. Phys. Stat. Sol. B 249(2012) 620.
S. Fabbrici, J. Kamarad, Z. Arnold, F. Casoli, A. Paoluzi, F. Bolzoni, R. Cabassi, M. Solzi, G. Porcari, C. Pernechele and F. Albertini, From direct to inverse giant magnetocaloric effect in Co‐doped NiMnGa multifunctional alloys. Acta Mater. 59(2011) 412.
P. O. Castillo‐Villa, D. E. Soto‐Parra, J. A. Matutes‐Aquino, R. A. Ochoa‐Gamboa, A. Planes, L. Mañosa, D. González‐Alonso, M. Stipcich, R. Romero, D. Ríos‐Jara and H. Flores‐Zúñiga, Caloric effects induced by magnetic and mechanical fields in a Ni50Mn25- xGa25Co xmagnetic shape memory alloy. Phys. Rev. B. 83(2011) 174109.
J. Bai, J. M. Raulot, Y. Zhang, C. Esling, X. Zhao and L. Zuo, The effects of alloying element Co on Ni–Mn–Ga ferromagnetic shape memory alloys from first‐principles calculations. Appl. Phys. Lett. 98(2011) 164103.
D. E. Soto‐Para, X. Moya, L. Mañosa, A. Planes, H. Flores‐ Zúñiga, F. Alvarado‐Hernández, R. A. Ochoa‐Gamboa, J. A. Matutes‐Aquino and D. Ríos‐Jara, Fe and Co selective substitution in Ni2MnGa: effect of magnetism on relative phase stability. Philos. Mag. 90(2010) 2771.
X. Xu, W. Ito, R. Y. Umetsu, K. Koyama, R. Kainuma, K. Ishida, Kinetic Arrest of Martensitic Transformation in Ni33.0Co13.4Mn39.7Ga13.9 Metamagnetic Shape Memory Alloy. Mater. Trans. 51(2010) 469.
B. M. Wang, P. Ren, Y. Liu and L. Wang, Enhanced magnetoresistance through magnetic‐field‐induced phase transition in Ni2MnGa co‐doped with Co and Mn. J. Magn. Magn. Mater. 322(2010) 715.
S. Yan, J. Pu, B. Chi and L. Jian, Estimation of driving force for martensitic transformation in (Ni52.5Mn23.5Ga24)100- xCo xalloys. J. Alloys Compd. 507(2010) 331.
S. Fabbrici, F. Albertini, A. Paoluzi, F. Bolzoni, R. Cabassi, M. Solzi, L. Righi and G. Calestani, Reverse magnetostructural transformation in Co‐doped NiMnGa multifunctional alloys. Appl. Phys. Lett. 95(2009) 022508.
Y. Ma, S. Yang, Y. Liu and X. Liu, The ductility and shape‐memory properties of Ni–Mn–Co–Ga high‐temperature shape‐memory alloys. Acta Mater. 57(2009) 3232.
L. Ma, H. W. Zhang, S. Y. Yu, Z. Y. Zhu, J. L. Chen, G. H. Wu, H. Y. Liu, J. P. Qu and Y. X. Li, Magnetic‐field‐induced martensitic transformation in MnNiGa:Co alloys. Appl. Phys. Lett. 92(2008) 032509.
V. Sánchez‐Alarcos, J. I. Pérez‐Landazábal, V. Recarte, C. Gómez‐Polo and J. A. Rodríguez‐Velamazán, Correlation between composition and phase transformation temperatures in Ni–Mn–Ga–Co ferromagnetic shape memory alloys. Acta Mater. 56(2008) 5370.
D. Y. Cong, S. Wang, Y. D. Wang, Y. Ren, L. Zuo and C. Esling, Martensitic and magnetic transformation in Ni–Mn–Ga–Co ferromagnetic shape memory alloys. Mater. Sci. Eng. A 473(2008) 213–218.
X. Q. Chen, X. Lu, D. Y. Wang and Z. X. Qin, The effect of Co‐doping on martensitic transformation temperatures in Ni–Mn–Ga Heusler alloys. Smart Mater. Struct. 17(2008) 065030.
P. Entel, M. E. Gruner, W. A. Adeagbo and A. T. Zayak, Magnetic‐field‐induced changes in magnetic shape memory alloys. Mater. Sci. Eng. A 481–482 (2008) 258–261.
Y. Ma, S. Yang, C. Wang and X. Liu, Tensile characteristics and shape memory effect of Ni56Mn21Co4Ga19 high‐temperature shape memory alloy. Scr. Mater. 58(2008) 918–921.
S. Y. Yu, Z. X. Cao, L. Ma, G. D. Liu, J. L. Chen, G. H. Wu, B. Zhang and X. X. Zhang, Realization of magnetic field‐induced reversible martensitic transformation in NiCoMnGa alloys. Appl. Phys. Lett. 91(2007) 102507.
I. Glavatskyy, N. Glavatska, O. Söderberg, S.‐P. Hannula and J.‐U. Hoffmann, Transformation temperatures and magnetoplasticity of Ni–Mn–Ga alloyed with Si, In, Co or Fe. Scr. Mater. 54(2006) 1891–1895.
T. Sakon, Y. Adachi, R. Y. Umetsu, H. Nojiri, H. Nishihara and T. Kanomata, Crystallography and Magnetic Field‐Induced Strain by Co Doping NiCoMnGa Heusler Alloy, TMS2013 Supplemental Proceeding, pp. 967–974, 2013, Wiley, USA.
C. Seguí and E. Cesari, Contributions to the transformation entropy change and influencing factors in metamagnetic Ni‐Co‐Mn‐Ga shape memory alloys. Entropy 16(2014) 5560.
A, E. Clark, J. D. Verhoeven, O. D. McMasters and E. D. Gibson, Magnetostriction in twinned  crystals of Tb0.27Dy0.73Fe2. IEEE Trans. Magn. Mag. 22(1986) 973.
Y. Takahashi, Quantum spin fluctuation theory of the magnetic equation of state of weak itinerant‐electron ferromagnets. J. Phys.: Condens. Matter. 13(2001) 6323–6358.
Y. Takahashi, Spin Fluctuation Theory of Itinerant Electron Magnetism;Springer‐Verlag: Berlin/Heidelberg, Germany, 2013.
T. Sakon, K. Sasaki, D. Numakura, M. Abe, H. Nojiri, Y. Adachi and T. Kanomata, Magnetic field‐induced transition in Co‐doped Ni41Co9Mn31.5Ga18.5 Heusler Alloy. Mater. Trans. 54(2013) 9–13.
S. Fabbrici, G. Porcari, F. Cugini, M. Solzi, J. Kamarad, Z. Arnold, R. Cabassi and F. Albertini, Co and In doped Ni‐Mn‐Ga magnetic shape memory alloys: a thorough structural, magnetic and magnetocaloric study. Entropy 16(2014) 2204–2222.
F. ‐X. Hu, B‐G. Shen, J. ‐O. Sun and G. ‐H. Wu, Large magnetic entropy change in a Heusler alloy Ni52.6Mn23.1Ga24.3 single crystal. Phys. Rev. B 64(2001) 132412.
M. Pasquale, C. P. Sasso, L. H. Lewis, L. Giudici, T. Lograsso and D. Schlagel, Magnetostructural transition and magnetocaloric effect in Ni55Mn20Ga25 single crystals. Phys. Rev. B. 72(2005) 094435.
A. K. Nayak, K. G. Suresh and A. K. Nigam, Magnetic, electrical, and magnetothermal properties in Ni–Co–Mn–Sb Heusler alloys. J. Appl. Phys. 107(2010) 09A927.
A. K. Pathak, I. Dubenko, J. C. Mabon, S. Stadler and N. Ali, The effect of partial substitution of In by X= Si, Ge and Al on the crystal structure, magnetic properties and resistivity of Ni50Mn35In15 Heusler alloys. J. Phys. D: Appl. Phys. 42(2009) 045004.
D. Bourgault, J. Tillier, P. Courtois, D. Maillard and X. Chaud, Large inverse magnetocaloric effect in Ni45Co5Mn37.5In12.5 single crystal above 300 K. Appl. Phys. Lett. 96(2010) 132501.
G. Porcari, F. Cugini, S. Fabbrici, C. Pernechele, F. Albertini, M. Buzzi, M. Mangia and M. Solzi, Convergence of direct and indirect methods in the magnetocaloric study of first order transformations: The case of Ni‐Co‐Mn‐Ga Heusler alloys. Phys. Rev. B. 86(2012) 104432.
V. Sokolovskiy, A. Gruünebohm, V. Buchelnikov and P. Entel, Ab Initioand Monte Carlo approaches for the magnetocaloric effect in Co‐ and In‐doped Ni‐Mn‐Ga Heusler alloys. Entropy 16(2014) 4992.
H. Nishihara, K. Komiyama, I. Oguro, T. Kanomata and V. Chernenko, Magnetization processes near the Curie temperatures of the itinerant ferromagnets. Ni2MnGa and pure nickel. J. Alloys. Compd. 442(2007) 191.
M. Seeger, S. N. Kaul, H. Kronmüller and R. Reisser, Asymptotic critical behavior of Ni. Phys. Rev. B. 51(1995) 12585.
In Ref.  (Sakon et al., Materials 2014), The calculated result of TA was incorrect. From the experimental results of the magnetic moment and the gradient of M4 vs. H/ M, which are shown in Ref. , the calculated spin fluctuation parameter TA is 645 K.
T. Sakon, S. Saito, K. Koyama, S. Awaji, I. Sato, T. Nojima, K. Watanabe and N. K. Sato, Experimental investigation of giant magnetocrystalline anisotropy of UGe2. Phys. Scr. 75(2007) 546–550.
V. G. Storchak, J. H. Brewer, D. G. Eshchenko, P. W. Mengyan, O. E. Parfenov and D. Sokolov, Spin‐polaron band in the ferromagnetic heavy‐fermion superconductor UGe2. J. Phys.: Conf. Ser. 551(2014) 012016.
F. Hardy, D. Aoki, C. Meingast, P. Schweiss, P. Burger, H. V. Löhneysen and J. Flouquet, Transverse and longitudinal magnetic‐field responses in the Ising ferromagnets URhGe, UCoGe, and UGe2. Phys. Rev. B. 83(2011) 195107.