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Magnetocaloric and critical behavior in the austenitic phase of Gd-doped Ni50Mn37Sn13 Heusler alloys
Journal of Alloys and Compounds xxx (2014) xxx–xxx
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Magnetocaloric and critical behavior in the austenitic phase of Gd-doped Ni50Mn37Sn13 Heusler alloys P. Zhang a, T.L. Phan a, N.H. Dan a, T.D. Thanh a,b, S.C. Yu a,⇑ a b
Department of Physics, Chungbuk National University, Cheongju 361-763, South Korea Institute of Materials Science, Vietnam Academy of Science and Technology, Hanoi, Viet Nam
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Magnetocaloric effect Ni–Mn–Sn Heusler alloys Critical behavior
a b s t r a c t The magnetic phase transition behavior were investigated in detail in Ni50yGdyMn37Sn13 (y = 1 and 3) alloys prepared by arc-melting method. The martensite phase was found to be strongly suppressed by a small amount of Gd doping. Based on isothermal magnetization curves around Curie temperature of the austenite (T AC ) phase, critical behavior in the austenite phases of both alloys were determined carefully by the Kouvel–Fisher method. The critical exponents were found to be b = 0.473 ± 0.020 and c = 1.141 ± 0.017 with T AC = 299.0 ± 0.2 K for y = 1, and b = 0.469 ± 0.068 and c = 1.214 ± 0.042 with T AC = 302.9 ± 0.7 K for y = 3, respectively. The values of the critical exponents for the ferromagnetic phase transition in the A phase of two alloys can be basically ascribed in the mean-field model (with b = 0.5, c = 1) with slightly deviation, revealing a long-range order of ferromagnetic interactions. Such critical behavior can be attributed to the magnetic inhomogeneities originated from the atomic disorder introduced by Gd doping. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction It was known that Ni–Mn-based Heusler alloys undergo a high symmetric L21-type austenite (A) to lattice-distorted (L10 tetragonal or 10M/14M modulated structures, etc.) martensite (M) phase transition if the temperature is lower than a certain point. The reduction of the structural symmetry affects the material’s magnetic behavior fundamentally. Due to the abrupt change of magnetization related to the structural phase transition, it often associates with an abnormal giant magnetocaloric effect (GMCE). However, different from the normal GMCE in Gd5Si2Ge2 [1], such GMCE is usually an inverse-type, which is resulted from considerable magnetization jump from lower magnetization for M phase to higher magnetization for A phase, caused by the change of the magnetocrystalline anisotropy due to the M–A phase structural phase transition [2]. As one of the typical Ni–Mn-based Heusler alloys, Ni–Mn–Sn based Heusler alloys with composition of Ni50Mn50xSnx (x = 13–15) show an inverse GMCE which was discovered by Krenke et al. [3] in 2005. This system has attracted intensive attention because of the inverse GMCE with a magnetic entropy change (DSM) of 18.5 J kg1 K1 for 50 kOe. Such inverse-type GMCE properties were reported for many Mn-rich compositions [4,5]. The influences of adding elements with small atomic radius such as Boron and Hydrogen in these Heusler alloy systems were also investigated [6,7]. Furthermore, the effects of ⇑ Corresponding author. E-mail address: [email protected] (S.C. Yu).
annealing on the M–A transformation and the related MCE have been studied as well [8–11]. The structural and magnetic properties of Ni–Mn–Sn based Heusler alloys have been found to be strongly correlated with valence electron concentration of electrons per atom (e/a), which is the concentration-weighted sum of s, d, and p valence electrons of Ni (3d84s2), Mn (3d54s2), and Sn (5s25p2) [12]. It was found that the TC in M phase (T M C ) and M–A phase transition temperature (TM–A) is quite sensitive to the composition and the value of e/a. With such condition, only a narrow Sn content region x = 13–15 the alloy shows inverse MCE. By introducing small amount of transition metal like Co, Fe, Cu etc. [13–16], the structural and magnetic properties can be adjusted due to the variation in e/a. However, seldom work has performed on Ni–Mn–Sn alloys doped with 4f rare-earth metals. In this work, we have prepared rare-earth-doped Ni50yGdyMn37Sn13 (y = 1, 3) bulk alloys to study the influences of the rare-earth doping on their magnetocaloric properties. On the other hand, to understand ferromagnetism hidden inside, one powerful approach is the critical-exponent analysis of ferromagnetic (FM)–paramagnetic (PM) phase transitions. The critical exponents of these rare-earth-doped alloys were analysed as well. 2. Experimental In this work, the bulk alloys with composition of Ni50yGdyMn37Sn13 (y = 1, 3) were prepared by vacuum arc melting method with argon as the shielding gas, using Ni, Mn, Sn, and Gd powders (high purity of 99.99%) as precursors. investigations on the compensation of the elements with a low-melting point (such as Sn
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P. Zhang et al. / Journal of Alloys and Compounds xxx (2014) xxx–xxx
and Mn) were carried out carefully to achieve alloys with the expected compositions. The obtained ingots were annealed at 850 °C for 4 h to stabilize the crystal structure. The room-temperature structural analyses of the obtained samples were checked by an X-ray diffractometer (Siemens D5000), with a scanning step of 0.03°, using a radiation source of Cu Ka1 (with wave length of k = 1.5406 Å). The magnetic properties of the samples were measured mainly by using a SQUID magnetometer, where the temperature and applied magnetic field varied from 5 to 360 K and from 0 to 50 kOe, respectively. The temperature interval between magnetic field isotherms was 2 K near the phase transition temperatures for obtaining more accurately the MCE properties and the critical exponents, and the temperature interval in other regions was 5 K. Magnetic measurements were carried out using a warming protocol.
3. Results and discussion The XRD patterns of two Gd-doped bulk alloys (Ni50yGdyMn37Sn13 with y = 1 and 3) recorded at room temperature are shown in Fig. 1. The XRD pattern of parent alloy without Gd doping (y = 0) is plotted for comparison. It is clearly indicated that the main phase of both bulk alloys are L21-type A phase, without even trace amount of M phase which can be detected in the parent alloy (y = 0, as indicated). The result implies that M phase is strongly suppressed by the Gd doping, which is reasonable because TMA is quite sensitive with the value of e/a, which can be directly adjusted by the doping level. Fig. 2(a) and (b) gives the ZFC and FC magnetization curves with 100 Oe from 5 K to 360 K for the y = 1 and 3 bulk alloys. The Curie temperature of M phase (T M C ) is absent even with only 1 at.% Gd doping, which is quite different from the parent bulk alloy, as reported by Krenke et al. [12]. The MA phase transition temperature (TMA) can be indicated to be 190 K from the weak inflection point for the y = 1 bulk alloy shown in the inset of Fig. 2(a); whereas the M–A phase transition becomes unclear for the y = 3 bulk alloy. Such the features confirm that the M phase was largely suppressed by just a few percent of Gd doping, which is consistent with the structural analysis in Fig. 1. The T AC of y = 1 and 3 bulk alloys are obtained to be around 305 K and 315 K, respectively, which is almost independent with the value of e/a in correspondence with the doping level. The stable T AC and variable TM C in such system further confirmed the different nature of ferromagnetism in the two phases. The isothermal M–H curves with maximum applied field of 50 kOe in the vicinity of T AC for the two Gd-doped bulk alloys are shown in Fig. 3(a) and (b). With the strong suppression on the M phase from the Gd-doping, the field induced M–A phase transition cannot be observed in both alloys, which is different with the parent alloy of Ni50Mn37Sn13 reported before [3,12]. The magneti-
Fig. 2. Zero-field-cooled (ZFC) and field-cooled (FC) magnetizations of Ni50yGdyMn37Sn13 (y = 1, 3) with applied field of 100 Oe.
zation always decreases with increasing temperature for the both alloys. The variation of M–H curves around 190 K is small for y = 1, which is the only indication of weak M–A phase transition. As expected, the positive slopes in M2 vs. H/M plots confirmed the second-order-type magnetic phase transition around T AC , (not shown). The temperature dependent isothermal DSM curves for both bulk alloys are calculated with the M–H data recorded and given in Fig. 3(c) and (d). The weak inverse MCE was found in y = 1 bulk alloy with DSmax about only 0.6 J kg1 K1 with maximum field of 50 kOe around TM–A. For the normal MCE region near T AC , DSmin of both alloys are determined to be 3.5 J kg1 K1 for y = 1 and 2.9 J kg1 K1 for y = 3 with the field of 50 kOe. The mean-field type long-range FM interaction in the A phase of the both Gd-doped bulk alloys can be indicated from the invariable peak temperature of the DSM curves [17]. In a magnetic system showing continuous phase transition, the critical behavior can be characterized by three important critical exponents of b, c, and d, which describe the ordered phase, disordered phase and critical temperature phase, separately. They are associated with the spontaneous magnetization MS(T), inversely initial susceptibility v01(T), and critical isotherm M at TC, respectively. These critical exponents can be defined by the following power-law relations [18].
Ms ðTÞ ¼ M 0 ðeÞb H ¼ DM d Fig. 1. XRD pattern at room temperature for Ni50yGdyMn37Sn13 bulk alloys (y = 1, 3) compared with Ni50Mn37Sn13 bulk alloy (y = 0).
e < 0;
e ¼ 0;
c v1 e > 0; 0 ¼ ðH 0 =M 0 Þe
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Fig. 3. (a) and (b) M–H curves, (c) and (d) DSM vs. T curves for Ni50yGdyMn37Sn13 (a) y = 1, (b) y = 3 with different field in the range of 5–50 kOe.
where e is the reduced temperature e ¼ ðT T C Þ=T C ; M0, H0 and D are the critical amplitudes. These three critical exponents are in the Widom scaling relation [19]: d ¼ 1 þ c=b. Based on the Arrott– Noakes equation of state [20] given by
ðH=MÞ1=c ¼ ðT T C Þ=T 1 þ ðM=M 1 Þ1=b :
ð4Þ
To obtain the critical exponents more accurately, the Kouvel– Fisher (K–F) method [21] is frequently-used. The K–F linear relations can be easily derived from Eqs. (1) and (3).
M S ðTÞ½dMS ðTÞ=dT
1
1 v1 0 ðTÞ dv0 ðTÞ=dT
¼ ðT T C Þ=b;
1
¼ ðT T C Þ=c;
ð5Þ ð6Þ
The optimal values of critical exponents can be thusly obtained by the iterative fitting process. To ensure the reliability of obtained critical-exponents, the scaling hypothesis can be further checked, which is described by
Mjejb ¼ f HjejðbþcÞ ;
Fig. 4. Kouvel–Fisher plots the MS (T) and v01(T) data of Ni50yGdyMn37Sn13 (y = 1, 3).
ð7Þ
where f+ for T > TC and f for T < TC are regular analytical functions. This equation implies that for true scaling relations and right choice of b and c values, scaled M plotted as a function of scaled H will fall on two universal curves: one above TC and another below TC. In this case, by using the K–F method, the critical exponents for the FM phase transition in A phase of y = 1 and 3 bulk alloys were analyzed carefully. The K–F plots with perfect linear fitting after iteration process for the both alloys are shown in Fig. 4. The critical exponents were found to be b = 0.471 ± 0.020 and c = 1.141 ± 0.017 with T AC = 299.0 ± 0.2 K for y = 1, and b = 0.469 ± 0.068 and c = 1.214 ± 0.042 with T AC = 302.9 ± 0.7 K for y = 3, respectively. Fig. 5(a) and (b) shows the linear fitting with good parallelity for the high field region for the both Gd-doped bulk alloys. The scaling plots on the log–log scale were shown in Fig. 5(c) and (d), respectively. Hence, the critical exponents obtained for the both alloys are fairly reliable. The values of the critical exponents for the FM in A phase of two alloys are close to the standard mean-field model (with b = 0.5, c = 1), revealing a dominated long-range order of FM interactions. Such critical phenomenon is completely different from the parent
compound (x = 0), which shows short-range order type of FM interactions [22]. This implies that the Gd doping tends to drive in the system, the austenitic FM phase, from the short-range to longrange order. As indicated in Fig. 1, the modulated martensitic phase was strongly suppressed by the tiny amount of Gd doping. Therefore, the intrinsic long-range RKKY-type FM interactions, can be reestablished in the high symmetric austenitic phase and resulted in a mean-field-like critical behavior. However, there is an obvious deviation from theoretical values as the Gd doping content increases. The value of b for the FM state decreases to 0.471 and 0.469 as the Gd doping amount increasing, which is slightly lower than 0.5. On the other hand, the values of c represent for the PM state increases to 1.141 and 1.214 for y = 1 and 3 bulk alloys. Such critical behavior can be attributed to the magnetic inhomogeneities directly introduced by the Gd doping. It has been clarified that the DSM for the system showing second-order magnetic phase transition can be expressed by the power law relation with the applied field.
DSM / H n
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Fig. 5. (a) and (b) MAPs; (c) and (d) scaling plots on the log–log scale for Ni50yGdyMn37Sn13 (y = 1, 3).
When T TC, n 1 due to the field-independent magnetization; when T TC, n 2 based on the Curie–Weiss relation. For the system near TC, it was proven that the power n is related to the critical exponent b and c in the form of n ¼ 1 þ ðb 1Þ=ðb þ cÞ [23]. From the critical exponents for the bulk alloys and ribbons, the power exponent n values are determined and used to verify the linear relation by plotting the DSTMC vs. Hn, as shown in Fig. 6(a) for the M phase and (b) for the A phase. The good linear relations confirmed again the reliability of the obtained critical exponents. Obviously, the n values for the A phase dominated samples are found to be close to 0.667 for the mean-field case, except for the x = 13 ribbons of which the critical behavior is disturbed by the M–A phase transition. On the other hand, the n values for the M phase dominated samples are not in the universal classes.
4. Conclusions The martensitic phase can be strongly suppressed by Gd doping, resulting in absence of inverse giant magnetocaloric effect. The ferromagnetism in the austenitic phase basically belongs to the mean-field type for the long-range ferromagnetic order. However, such the long-range ferromagnetic order of austenitic phase can be easily influenced by the magnetically inhomogeneity in the austenitic phase, which was directly generated by such exotic atomic disorder. Such magnetically inhomogeneity can be clearly indicated from the deviated mean-field-like critical behavior. Acknowledgement This research was supported by the Converging Research Center Program through the Ministry of Science, ICT and Future Planning, Korea(2013K000405). References
Fig. 6. The relation between critical exponents and DSM for Gd-doped Ni50Mn37Sn13.
[1] V.K. Pecharsky, J.K.A. Gschneidner, Phys. Rev. Lett. 78 (1997) 4494–4497. [2] V.A.L. Vov, E.V. Gomonaj, V.A. Chernenko, J. Phys. Condensed Matter 10 (1998) 4587. [3] T. Krenke, E. Duman, M. Acet, E.F. Wassermann, X. Moya, L. Manosa, A. Planes, Nat. Mater. 4 (2005) 450–454. [4] Z.D. Han, D.H. Wang, C.L. Zhang, S.L. Tang, B.X. Gu, Y.W. Du, Appl. Phys. Lett. 89 (2006) 182503–182507. [5] Z.D. Han, D.H. Wang, C.L. Zhang, H.C. Xuan, B.X. Gu, Y.W. Du, Appl. Phys. Lett. 90 (2007) 042503–042507. [6] H.C. Xuan, D.H. Wang, C.L. Zhang, Z.D. Han, B.X. Gu, Y.W. Du, Appl. Phys. Lett. 92 (2008) 102503. [7] F.X. Hu, J. Wang, L. Chen, J.L. Zhao, J.R. Sun, B.G. Shen, Appl. Phys. Lett. 95 (2009) 112503. [8] S. Kustov, M.L. Corro, J. Pons, E. Cesari, Appl. Phys. Lett. 94 (2009) (1903) 191901–191903. [9] L. Chen, F.X. Hu, J. Wang, J. Shen, J.R. Sun, B.G. Shen, J.H. Yin, L.Q. Pan, Q.Z. Huang, J. Appl. Phys. 109 (2011) 07A939-933. [10] L. Chen, F.X. Hu, J. Wang, J.L. Zhao, J.R. Sun, B.G. Shen, J.H. Yin, L.Q. Pan, J. Phys. D: Appl. Phys. 44 (2011) 085002. [11] W. Ito, M. Nagasako, R.Y. Umetsu, R. Kainuma, T. Kanomata, K. Ishida, Appl. Phys. Lett. 93 (2008) 232503-1–232503-3. [12] T. Krenke, M. Acet, E.F. Wassermann, X. Moya, L. Mañosa, A. Planes, Phys. Rev. B 72 (2005) 014412.
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P. Zhang et al. / Journal of Alloys and Compounds xxx (2014) xxx–xxx [13] T. Krenke, E. Duman, M. Acet, X. Moya, L. Manosa, A. Planes, J. Appl. Phys. 102 (2007) 033903–033905. [14] B. Gao, F.X. Hu, J. Shen, J. Wang, J.R. Sun, B.G. Shen, J. Magn. Magn. Mater. 321 (2009) 2571–2574. [15] J.L. Yan, Z.Z. Li, X. Chen, K.W. Zhou, S.X. Shen, H.B. Zhou, J. Alloy. Comp. 506 (2010) 516–519. [16] B.M. Wang, L. Wang, Y. Liu, B.C. Zhao, J. Appl. Phys. 105 (2009) 023913– 023915. [17] V. Franco, A. Conde, M.D. Kuz’min, J.M. Romero-Enrique, J. Appl. Phys. 105 (2009) 07A917-913.
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[18] H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, London, 1971. [19] B. Widom, J. Chem. Phys. 41 (1964) 1633–1634. [20] A. Arrott, J. Noakes, Phys. Rev. Lett. 19 (1967) 786–789. [21] J. Kouvel, M. Fisher, Phys. Rev. 136 (1964) A1626–A1632. [22] T.-L. Phan, P. Zhang, N.H. Dan, N.H. Yen, P.T. Thanh, T.D. Thanh, M.H. Phan, S.C. Yu, Appl. Phys. Lett. 101 (2012) 212403–212405. [23] V. Franco, J.S. Blazquez, A. Conde, Appl. Phys. Lett. 89 (2006) 222512–222513.
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Magnetocaloric and critical behavior in the austenitic phase of Gd-doped Ni50Mn37Sn13 Heusler alloys P. Zhang a, T.L. Phan a, N.H. Dan a, T.D. Thanh a,b, S.C. Yu a,⇑ a b
Department of Physics, Chungbuk National University, Cheongju 361-763, South Korea Institute of Materials Science, Vietnam Academy of Science and Technology, Hanoi, Viet Nam
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Magnetocaloric effect Ni–Mn–Sn Heusler alloys Critical behavior
a b s t r a c t The magnetic phase transition behavior were investigated in detail in Ni50yGdyMn37Sn13 (y = 1 and 3) alloys prepared by arc-melting method. The martensite phase was found to be strongly suppressed by a small amount of Gd doping. Based on isothermal magnetization curves around Curie temperature of the austenite (T AC ) phase, critical behavior in the austenite phases of both alloys were determined carefully by the Kouvel–Fisher method. The critical exponents were found to be b = 0.473 ± 0.020 and c = 1.141 ± 0.017 with T AC = 299.0 ± 0.2 K for y = 1, and b = 0.469 ± 0.068 and c = 1.214 ± 0.042 with T AC = 302.9 ± 0.7 K for y = 3, respectively. The values of the critical exponents for the ferromagnetic phase transition in the A phase of two alloys can be basically ascribed in the mean-field model (with b = 0.5, c = 1) with slightly deviation, revealing a long-range order of ferromagnetic interactions. Such critical behavior can be attributed to the magnetic inhomogeneities originated from the atomic disorder introduced by Gd doping. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction It was known that Ni–Mn-based Heusler alloys undergo a high symmetric L21-type austenite (A) to lattice-distorted (L10 tetragonal or 10M/14M modulated structures, etc.) martensite (M) phase transition if the temperature is lower than a certain point. The reduction of the structural symmetry affects the material’s magnetic behavior fundamentally. Due to the abrupt change of magnetization related to the structural phase transition, it often associates with an abnormal giant magnetocaloric effect (GMCE). However, different from the normal GMCE in Gd5Si2Ge2 [1], such GMCE is usually an inverse-type, which is resulted from considerable magnetization jump from lower magnetization for M phase to higher magnetization for A phase, caused by the change of the magnetocrystalline anisotropy due to the M–A phase structural phase transition [2]. As one of the typical Ni–Mn-based Heusler alloys, Ni–Mn–Sn based Heusler alloys with composition of Ni50Mn50xSnx (x = 13–15) show an inverse GMCE which was discovered by Krenke et al. [3] in 2005. This system has attracted intensive attention because of the inverse GMCE with a magnetic entropy change (DSM) of 18.5 J kg1 K1 for 50 kOe. Such inverse-type GMCE properties were reported for many Mn-rich compositions [4,5]. The influences of adding elements with small atomic radius such as Boron and Hydrogen in these Heusler alloy systems were also investigated [6,7]. Furthermore, the effects of ⇑ Corresponding author. E-mail address: [email protected] (S.C. Yu).
annealing on the M–A transformation and the related MCE have been studied as well [8–11]. The structural and magnetic properties of Ni–Mn–Sn based Heusler alloys have been found to be strongly correlated with valence electron concentration of electrons per atom (e/a), which is the concentration-weighted sum of s, d, and p valence electrons of Ni (3d84s2), Mn (3d54s2), and Sn (5s25p2) [12]. It was found that the TC in M phase (T M C ) and M–A phase transition temperature (TM–A) is quite sensitive to the composition and the value of e/a. With such condition, only a narrow Sn content region x = 13–15 the alloy shows inverse MCE. By introducing small amount of transition metal like Co, Fe, Cu etc. [13–16], the structural and magnetic properties can be adjusted due to the variation in e/a. However, seldom work has performed on Ni–Mn–Sn alloys doped with 4f rare-earth metals. In this work, we have prepared rare-earth-doped Ni50yGdyMn37Sn13 (y = 1, 3) bulk alloys to study the influences of the rare-earth doping on their magnetocaloric properties. On the other hand, to understand ferromagnetism hidden inside, one powerful approach is the critical-exponent analysis of ferromagnetic (FM)–paramagnetic (PM) phase transitions. The critical exponents of these rare-earth-doped alloys were analysed as well. 2. Experimental In this work, the bulk alloys with composition of Ni50yGdyMn37Sn13 (y = 1, 3) were prepared by vacuum arc melting method with argon as the shielding gas, using Ni, Mn, Sn, and Gd powders (high purity of 99.99%) as precursors. investigations on the compensation of the elements with a low-melting point (such as Sn
0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.12.072
Please cite this article in press as: P. Zhang et al., J. Alloys Comp. (2014), http://dx.doi.org/10.1016/j.jallcom.2013.12.072
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and Mn) were carried out carefully to achieve alloys with the expected compositions. The obtained ingots were annealed at 850 °C for 4 h to stabilize the crystal structure. The room-temperature structural analyses of the obtained samples were checked by an X-ray diffractometer (Siemens D5000), with a scanning step of 0.03°, using a radiation source of Cu Ka1 (with wave length of k = 1.5406 Å). The magnetic properties of the samples were measured mainly by using a SQUID magnetometer, where the temperature and applied magnetic field varied from 5 to 360 K and from 0 to 50 kOe, respectively. The temperature interval between magnetic field isotherms was 2 K near the phase transition temperatures for obtaining more accurately the MCE properties and the critical exponents, and the temperature interval in other regions was 5 K. Magnetic measurements were carried out using a warming protocol.
3. Results and discussion The XRD patterns of two Gd-doped bulk alloys (Ni50yGdyMn37Sn13 with y = 1 and 3) recorded at room temperature are shown in Fig. 1. The XRD pattern of parent alloy without Gd doping (y = 0) is plotted for comparison. It is clearly indicated that the main phase of both bulk alloys are L21-type A phase, without even trace amount of M phase which can be detected in the parent alloy (y = 0, as indicated). The result implies that M phase is strongly suppressed by the Gd doping, which is reasonable because TMA is quite sensitive with the value of e/a, which can be directly adjusted by the doping level. Fig. 2(a) and (b) gives the ZFC and FC magnetization curves with 100 Oe from 5 K to 360 K for the y = 1 and 3 bulk alloys. The Curie temperature of M phase (T M C ) is absent even with only 1 at.% Gd doping, which is quite different from the parent bulk alloy, as reported by Krenke et al. [12]. The MA phase transition temperature (TMA) can be indicated to be 190 K from the weak inflection point for the y = 1 bulk alloy shown in the inset of Fig. 2(a); whereas the M–A phase transition becomes unclear for the y = 3 bulk alloy. Such the features confirm that the M phase was largely suppressed by just a few percent of Gd doping, which is consistent with the structural analysis in Fig. 1. The T AC of y = 1 and 3 bulk alloys are obtained to be around 305 K and 315 K, respectively, which is almost independent with the value of e/a in correspondence with the doping level. The stable T AC and variable TM C in such system further confirmed the different nature of ferromagnetism in the two phases. The isothermal M–H curves with maximum applied field of 50 kOe in the vicinity of T AC for the two Gd-doped bulk alloys are shown in Fig. 3(a) and (b). With the strong suppression on the M phase from the Gd-doping, the field induced M–A phase transition cannot be observed in both alloys, which is different with the parent alloy of Ni50Mn37Sn13 reported before [3,12]. The magneti-
Fig. 2. Zero-field-cooled (ZFC) and field-cooled (FC) magnetizations of Ni50yGdyMn37Sn13 (y = 1, 3) with applied field of 100 Oe.
zation always decreases with increasing temperature for the both alloys. The variation of M–H curves around 190 K is small for y = 1, which is the only indication of weak M–A phase transition. As expected, the positive slopes in M2 vs. H/M plots confirmed the second-order-type magnetic phase transition around T AC , (not shown). The temperature dependent isothermal DSM curves for both bulk alloys are calculated with the M–H data recorded and given in Fig. 3(c) and (d). The weak inverse MCE was found in y = 1 bulk alloy with DSmax about only 0.6 J kg1 K1 with maximum field of 50 kOe around TM–A. For the normal MCE region near T AC , DSmin of both alloys are determined to be 3.5 J kg1 K1 for y = 1 and 2.9 J kg1 K1 for y = 3 with the field of 50 kOe. The mean-field type long-range FM interaction in the A phase of the both Gd-doped bulk alloys can be indicated from the invariable peak temperature of the DSM curves [17]. In a magnetic system showing continuous phase transition, the critical behavior can be characterized by three important critical exponents of b, c, and d, which describe the ordered phase, disordered phase and critical temperature phase, separately. They are associated with the spontaneous magnetization MS(T), inversely initial susceptibility v01(T), and critical isotherm M at TC, respectively. These critical exponents can be defined by the following power-law relations [18].
Ms ðTÞ ¼ M 0 ðeÞb H ¼ DM d Fig. 1. XRD pattern at room temperature for Ni50yGdyMn37Sn13 bulk alloys (y = 1, 3) compared with Ni50Mn37Sn13 bulk alloy (y = 0).
e < 0;
e ¼ 0;
c v1 e > 0; 0 ¼ ðH 0 =M 0 Þe
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3
Fig. 3. (a) and (b) M–H curves, (c) and (d) DSM vs. T curves for Ni50yGdyMn37Sn13 (a) y = 1, (b) y = 3 with different field in the range of 5–50 kOe.
where e is the reduced temperature e ¼ ðT T C Þ=T C ; M0, H0 and D are the critical amplitudes. These three critical exponents are in the Widom scaling relation [19]: d ¼ 1 þ c=b. Based on the Arrott– Noakes equation of state [20] given by
ðH=MÞ1=c ¼ ðT T C Þ=T 1 þ ðM=M 1 Þ1=b :
ð4Þ
To obtain the critical exponents more accurately, the Kouvel– Fisher (K–F) method [21] is frequently-used. The K–F linear relations can be easily derived from Eqs. (1) and (3).
M S ðTÞ½dMS ðTÞ=dT
1
1 v1 0 ðTÞ dv0 ðTÞ=dT
¼ ðT T C Þ=b;
1
¼ ðT T C Þ=c;
ð5Þ ð6Þ
The optimal values of critical exponents can be thusly obtained by the iterative fitting process. To ensure the reliability of obtained critical-exponents, the scaling hypothesis can be further checked, which is described by
Mjejb ¼ f HjejðbþcÞ ;
Fig. 4. Kouvel–Fisher plots the MS (T) and v01(T) data of Ni50yGdyMn37Sn13 (y = 1, 3).
ð7Þ
where f+ for T > TC and f for T < TC are regular analytical functions. This equation implies that for true scaling relations and right choice of b and c values, scaled M plotted as a function of scaled H will fall on two universal curves: one above TC and another below TC. In this case, by using the K–F method, the critical exponents for the FM phase transition in A phase of y = 1 and 3 bulk alloys were analyzed carefully. The K–F plots with perfect linear fitting after iteration process for the both alloys are shown in Fig. 4. The critical exponents were found to be b = 0.471 ± 0.020 and c = 1.141 ± 0.017 with T AC = 299.0 ± 0.2 K for y = 1, and b = 0.469 ± 0.068 and c = 1.214 ± 0.042 with T AC = 302.9 ± 0.7 K for y = 3, respectively. Fig. 5(a) and (b) shows the linear fitting with good parallelity for the high field region for the both Gd-doped bulk alloys. The scaling plots on the log–log scale were shown in Fig. 5(c) and (d), respectively. Hence, the critical exponents obtained for the both alloys are fairly reliable. The values of the critical exponents for the FM in A phase of two alloys are close to the standard mean-field model (with b = 0.5, c = 1), revealing a dominated long-range order of FM interactions. Such critical phenomenon is completely different from the parent
compound (x = 0), which shows short-range order type of FM interactions [22]. This implies that the Gd doping tends to drive in the system, the austenitic FM phase, from the short-range to longrange order. As indicated in Fig. 1, the modulated martensitic phase was strongly suppressed by the tiny amount of Gd doping. Therefore, the intrinsic long-range RKKY-type FM interactions, can be reestablished in the high symmetric austenitic phase and resulted in a mean-field-like critical behavior. However, there is an obvious deviation from theoretical values as the Gd doping content increases. The value of b for the FM state decreases to 0.471 and 0.469 as the Gd doping amount increasing, which is slightly lower than 0.5. On the other hand, the values of c represent for the PM state increases to 1.141 and 1.214 for y = 1 and 3 bulk alloys. Such critical behavior can be attributed to the magnetic inhomogeneities directly introduced by the Gd doping. It has been clarified that the DSM for the system showing second-order magnetic phase transition can be expressed by the power law relation with the applied field.
DSM / H n
Please cite this article in press as: P. Zhang et al., J. Alloys Comp. (2014), http://dx.doi.org/10.1016/j.jallcom.2013.12.072
ð8Þ
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P. Zhang et al. / Journal of Alloys and Compounds xxx (2014) xxx–xxx
Fig. 5. (a) and (b) MAPs; (c) and (d) scaling plots on the log–log scale for Ni50yGdyMn37Sn13 (y = 1, 3).
When T TC, n 1 due to the field-independent magnetization; when T TC, n 2 based on the Curie–Weiss relation. For the system near TC, it was proven that the power n is related to the critical exponent b and c in the form of n ¼ 1 þ ðb 1Þ=ðb þ cÞ [23]. From the critical exponents for the bulk alloys and ribbons, the power exponent n values are determined and used to verify the linear relation by plotting the DSTMC vs. Hn, as shown in Fig. 6(a) for the M phase and (b) for the A phase. The good linear relations confirmed again the reliability of the obtained critical exponents. Obviously, the n values for the A phase dominated samples are found to be close to 0.667 for the mean-field case, except for the x = 13 ribbons of which the critical behavior is disturbed by the M–A phase transition. On the other hand, the n values for the M phase dominated samples are not in the universal classes.
4. Conclusions The martensitic phase can be strongly suppressed by Gd doping, resulting in absence of inverse giant magnetocaloric effect. The ferromagnetism in the austenitic phase basically belongs to the mean-field type for the long-range ferromagnetic order. However, such the long-range ferromagnetic order of austenitic phase can be easily influenced by the magnetically inhomogeneity in the austenitic phase, which was directly generated by such exotic atomic disorder. Such magnetically inhomogeneity can be clearly indicated from the deviated mean-field-like critical behavior. Acknowledgement This research was supported by the Converging Research Center Program through the Ministry of Science, ICT and Future Planning, Korea(2013K000405). References
Fig. 6. The relation between critical exponents and DSM for Gd-doped Ni50Mn37Sn13.
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