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Magnetocaloric effect and magnetic transition in bulk Mn1.1Fe0.9P0.8Ge0.2 compound
Journal of Alloys and Compounds 493 (2010) 22–25
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Magnetocaloric effect and magnetic transition in bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound M. Yue a,∗ , Z.Q. Li a , X.B. Liu b , H. Xu a , D.M. Liu a , J.X. Zhang a a b
College of Materials Science and Engineering, Beijing University of Technology, Beijing 100022, China Center for the Physics of Materials and Department of Physics, McGill University, 3600 University Street, Montreal, Quebec H3A 2T8, Canada
a r t i c l e
i n f o
Article history: Received 25 November 2009 Received in revised form 8 December 2009 Accepted 8 December 2009 Available online 14 December 2009 Keywords: Mn1.1 Fe0.9 P0.8 Ge0.2 compound Fe2 P-type structure Magnetocaloric effect First-order magnetic transition
a b s t r a c t Crystal structure, magnetocaloric effect and magnetic transition in bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound have been studied by X-ray diffraction, magnetic measurements and Landau–Ginzberg theory. Mn1.1 Fe0.9 P0.8 Ge0.2 compound crystallizes in a hexagonal Fe2 P-type structure with lattice constants of a = 6.0789(10) Å and c = 3.4674(9) Å. The compound exhibits giant magnetocaloric effect with maximum magnetic entropy change of 61.8 J/kg K in a field change from 0 to 5 T around its Curie temperature of 251 K. The temperature dependence of the Landau coefficients have been derived by fitting the magnetization with the Landau expansion of the magnetic free energy, indicating the first-order nature of the magnetic transition between ferromagnetic and paramagnetic states in the compound. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Recently, magnetic refrigeration based on the magnetocaloric effect (MCE) has drawn tremendous attention due to its good potential as an alternative to vapor-compression techniques around room temperature [1]. As a result, many new materials with room temperature giant MCE have been developed and broadly investigated like the Gd5 (Six Ge1−x )4 , La(Fe1−x Six )13 , MnFe(P1−x Mx ) with M = As, Si, or Ge, and the manganites [2–5]. Among these materials, MnFe(P1−x Gex ) is one of the most promising candidates for practical application with respect to its competitive advantages such as abundant raw materials, low fabrication costs, and addresses environmental concerns. In addition, by adjusting the P/Ge ratio in MnFe(P1−x Gex ) the Curie temperature (TC ) of the compound can be tuned over a large working temperature range for magnetic refrigeration application [6]. However, in the past, the compound was generally synthesized by a mechanically activated solid-diffusion method, which requires very long processing time and frequently involves the formation of undesirable inter-metallic impurities in the compound [7,8]. In this study, we report our results on bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound prepared by the new techniques of spark plasma sintering (SPS), a plasma-aid consolidating technique [9]. This SPS technique shortens considerably the diffusion paths of compound formation and homogenization and as
∗ Corresponding author. E-mail address: [email protected] (M. Yue). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.12.050
a result, the compound possesses homogeneous chemical composition and crystal structure as well as good magnetocaloric properties around room temperature. MCE is intimately related to the magnetic transition near TC . Generally, the temperature dependence of magnetization M(T) is described using a molecular field theory with Brillouin Function for the magnet with local moments [10]. If M(T) follows the Brillouin relationship around Tc, a second order magnetic transition occurs. On the other hand, if the change of M(T) is much sharper than that predicted by Brillouin function around Tc, a first-order magnetic transition takes place. For the weak itinerant magnet, a Landau–Ginzberg phase transition theory is often used to describe the field-induced magnetic transition [11]. Many 3d-based magnets are between the two extreme situations. For example, both Brillouin function and Landau expansion methods describe well the order of the magnetic transition in La(Fe,Co,Si)13 compounds [12]. The first-principles calculations indicate Mn (3g) has stable magnetic moment while the moment of Fe (3f) is metastable and at meta-magnetic state in the hexagonal MnFe(P1−x Mx ) (M = As, Si and Ge) with Fe2 P structure [13]. It is expected that the magnetic transition could be described by both Brillouin function and Landau expansion methods in Mn1.1 Fe0.9 P0.8 Ge0.2 . In fact, our previous Mössbauer spectroscopy data indicate that the temperature dependence of the hyperfine field changes more rapidly than that predicted by a simple molecular field Brillouin function, indicating the first-order nature of the magnetic transition in Mn1.1 Fe0.9 P0.8 Ge0.2 [14]. We, here, investigate the magnetic transition in Mn1.1 Fe0.9 P0.8 Ge0.2 using a Landau expansion.
M. Yue et al. / Journal of Alloys and Compounds 493 (2010) 22–25
Fig. 1. Observed and calculated XRD patterns of bulk Mn1.1 Fe0.9 P0.8 Ge0.2 alloy. The bottom curve is the difference between the observed and the calculated intensities. The upper and lower rows of vertical bars indicate the Bragg reflection positions of MnFePGe and MnO compounds, respectively.
2. Experimental procedure Mn powder (>99.99 wt.%), Fe powder (>99.99 wt.%), red P powder (>99.3 wt.%) and Ge powder (>99.9999 wt.%) were mixed together in quantities corresponding to the nominal chemical composition of Mn1.1 Fe0.9 P0.8 Ge0.2 . The mixed powders were then ball milled under an argon atmosphere for 1.5 h in a high energy Pulverisette 4 mill. The above milled powders were collected into a graphite mold and consolidated into a Ф20 mm × 5 mm wafer sample at 1183 K under 30 MPa by the SPS technique. The density of the sample was examined by the Archimedes method to be over 95% of the density of the as-cast ingot. The crystal structure of the bulk sample was measured by powder X-ray diffraction techniques (Rigaku, Cu K␣ radiation) and analyzed by the Rietveld method using the general structure analysis system (GSAS) code [15]. Magnetic measurements were carried out in a 5 T Quantum Design physical properties measurement system (PPMS) magnetometer.
3. Results and discussion 3.1. Structure and magnetocaloric effect in bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound Powder X-ray diffraction results show that the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 sample has a hexagonal Fe2 P-type crystal ¯ structure with space group P 62m. Fig. 1 displays the observed and calculated XRD patterns for the Mn1.1 Fe0.9 P0.8 Ge0.2 compound. The crystallographic data are derived from Rietveld fitting for the MnFePGe hexagonal phase. The hexagonal phase has lattice constants of a = 6.07789(10) Å and c = 3.4674(9)Å. The Mn atoms occupy exclusively the 3 g (0.9505(15), 0, 0.5) site and part of the 3f (0.2540(17), 0, 0) site; the Fe atoms occupy the rest of the 3f site, while P and the Ge atoms randomly occupy the 2c and 1b sites. These results are qualitatively in agreement with our previous neutron diffraction results [16]. It is worth mentioning that some secondary phases such as (Mn, Fe)5 Ge3 or (Mn1−x Fex )3+ı Ge, which persist in conventionally sintered and cast samples even after long time annealing [8,17], are not present in the present bulk sample prepared by the SPS technique. In addition, a minor impurity phase of MnO, which probably originated from the starting materials or from the oxidation of Mn during the preparation process, accounts for less than 2 wt.% in the sample according to the refinement results. Fig. 2 shows the temperature dependence of magnetization of bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound measured in a magnetic field of 0.05 T. It should be noted that the virgin effect, which had been found in first time cooling of as-prepared MnFePGe alloy by some previous investigations [6–8], does exist in our sample. The heating and cooling curves shown in Fig. 2 are for the sample that has experienced thermal cycling. A large thermal hysteresis of about
23
Fig. 2. Temperature dependence of magnetization of bulk Mn1.1 Fe0.9 P0.8 Ge0.2 alloy measured in a magnetic field of 0.05 T.
25 K upon heating and cooling indicates the first-order nature of the ferromagnetic ↔ paramagnetic transition. In addition, the Curie temperature (TC ) of the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound was determined as 251 K from the heating curve where the first temperature derivative of the magnetization has its highest value. The isothermal magnetization curves for the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound around its Tc in external magnetic field up to 5 T are shown in Fig. 3. A magnetic transition in the compound from the paramagnetic state to the ferromagnetic state was observed above its TC . In addition, the large magnetic hysteresis during the increase and decrease of the magnetic field in the vicinity of TC indicates that the transition is a first-order magnetic phase transition, consistent to our observation from the M(T) data in Fig. 2. The magnetic entropy change derived from the magnetization data using the Maxwell relation is shown in Fig. 4 for the magnetic field changes from 0 to 1, 2, 3, 4, and 5 T. The compound exhibits large MCE and the values of the magnetic entropy change are 20.6 and 61.8 J/kg K for field changes of 2 and 5 T at 251 K, respectively. These values are superior to those in MnFePGe compound in previous studies [6–8,17], and are amongst the highest reported magnetic entropy changes around room temperature.
Fig. 3. Isothermal magnetization of the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound as a function of applied magnetic field up to 5 T.
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M. Yue et al. / Journal of Alloys and Compounds 493 (2010) 22–25
Fig. 4. Temperature dependence of the magnetic entropy change of the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound measured in a magnetic field change from 0 to 1, 2, 3, 4, and 5 T.
3.2. Landau phenomenological description of the magnetic transition The order of the phase transition is determined by the temperature dependence of the magnetic free energy. The Landau–Ginzberg phenomenological description can be given by the Landau expansion of the magnetic free energy with the total magnetization M: F(M, T ) =
c1 (T ) 2 c3 (T ) 4 c5 (T ) 6 M + M + M + · · · + −0 HM 2 4 6
(1)
and the temperature and magnetic field dependence of F(M, T) determines the nature of the magnetic transition. For the Landau expansion up to forth order, the Arrott plots relationship is obtained [18]: 0 H = c1 (T ) + c3 (T )M 2 M
Fig. 6. Temperature dependence of landau coefficients for the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound. (The units for c1 (T), c3 (T), and c5 (T) are T2 (kg/J), T4 (kg/J), and T6 (kg/J), respectively.)
(2)
Above Tc, a linear relationship is expected for the Arrott plots. However, if there is field-induced magnetic transition from paramagnetic to ferromagnetic states, the inflection points and the negative slope will appear in the plots. Fig. 5 shows the Arrott plots near the Tc for the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound. The inflection points and the negative slope in the plots above Tc clearly
Fig. 5. Arrott plots in the vicinity of TC for the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound.
indicate the occurrence of the field-induced magnetic transition in the compound. To gain more insights on the magnetic transition, F(M, T) is expanded up to six power and the Inoue–Shimizu model is obtained [19,20]. The Landau coefficients are accessible through the equation of state linking M and the magnetic field, 0 H: 0 H = c1 (T )M + c3 (T )M 3 + c5 M 5
(3)
The Landau coefficient at TC , c1 (TC ) and c5 (TC ) are positive. However, c3 (TC ) may be positive, zero or negative. For a positive or zero value of c3 (TC ), the magnetic free energy has only one minima at M = 0, which corresponds to the paramagnetic state, so a second magnetic transition is expected. On the other hand, for a negative c3 (TC ), the magnetic free energy has two minima at M = 0 and M = / 0 which, respectively, corresponds to the paramagnetic and ferromagnetic state. In this case, a first-order magnetic transition occurs. The Landau coefficients c1 (TC ), c3 (TC ), and c5 (TC ) were determined by fitting the magnetic field, 0 H against magnetization, M(0 H), using Eq. (2). The detail fitting method has been reported elsewhere [12]. The temperature dependence of the Landau coefficients derived from these fitting results is shown in Fig. 6 for the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound. As expected, c1 (TC ) is positive with a minimum at TCc1 (T ) , and the derived magnetic transition temperature TCc1 (T ) is, within error, the same as TC , determined from the heating curve of temperature dependence of magnetization of bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound (Fig. 2). The value of c3 (TC ) at TC is negative, indicating the first-order magnetic transition at TC . Such calculation agrees well with the aforementioned experimental results, which indicates that the zero field magnetic transition at TC is first-order in the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound.
M. Yue et al. / Journal of Alloys and Compounds 493 (2010) 22–25
4. Conclusions A preparation route of ball milling and subsequent spark plasma sintering has been applied to prepare bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound. The crystal structure and magnetocaloric properties of the compound were investigated. It is found that the compound possesses a hexagonal Fe2 P-type crystal structure, in which the Mn atoms occupy the total 3g sites and part of the 3f sites; the Fe atoms occupy the rest of the 3f sites, while P and the Ge atoms randomly occupy the 2c and 1b sites. The compound exhibits giant magnetocaloric effect with maximum magnetic entropy change of 61.8 J/kg K in a field change from 0 to 5 T at 251 K. Arrott plots and the temperature dependence of landau expansion coefficients of magnetic free energy near TC indicate that the magnetic transition between ferromagnetic and paramagnetic states in the compound shows typical first-order character. Acknowledgement This work was supported by the National High Technology Research and Development Program of China (2002AA324010). References [1] J. Glanz, Science 279 (1998) 2045.
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[2] V.K. Pecharsky, K.A. Gschneidner, Phys. Rev. Lett. 78 (1997) 4494. [3] F.X. Hu, B.G. Shen, J.R. Sun, Z.H. Cheng, Appl. Phys. Lett. 78 (2001) 3675. [4] O. Tegus, E. Brück, K.H.J. Buschow, F.R. de. Boer, Nature 415 (2002) 150. [5] Z.B. Guo, Y.W. Du, J.S. Zhu, H. Huang, W.P. Ding, D. Feng, Phys. Rev. Lett. 78 (1997) 1142. [6] W. Dagula, O. Tegus, B. Fuquan, L. Zhang, P.Z. Si, M. Zhang, W.S. Zhang, E. Brück, F.R. de. Boer, K.H.J. Buschow, IEEE Trans. Magn. 41 (2005) 2778. [7] D.T. Cam Thanh, E. Brück, O. Tegus, J.C.P. Klaasse, T.J. Gortenmulder, K.H.J. Buschow, J. Appl. Phys. 99 (2006), 08Q107. [8] Z.Q. Ou, G.F. Wang, O. Lin Song, E. Tegus, K.H.J. Brück, Buschow, J. Phys. Condens. Matter 18 (2006) 11577. [9] N. Tamari, T. Tanaka, K. Tanaka, I. Kondoh, M. Kawahara, M. Tokita, J. Ceram. Soc. Jpn. 103 (1995) 740. [10] A. Aharoni, Introduction to the Theory of Ferromagnetism, Oxford University Press, New York, 1996. [11] H. Yamada, Phys. Rev. B 47 (1991) 11211. [12] X.B. Liu, D.H. Ryan, Z. Altounian, J. Magn. Magn. Mater. 270 (2004) 305. [13] X.B. Liu, Z. Altounian, J. Magn. Magn. Mater. 321 (2009) 2005. [14] X.B. Liu, Z. Altounian, D.H. Ryan, M. Yue, Z.Q. Li, D.M. Liu, J.X. Zhang, J. Appl. Phys. 105 (2009), 07A920. [15] A.C. Larson, R.B. Von Dreele, General Structure Analysis System GSAS, Los Alamos National Laboratory, Report No: LAUR 86-748. [16] D.M. Liu, M. Yue, J.X. Zhang, T.M. McQueen, J.W. Lynn, X. Wang, Y. Chen, J. Li, R.J. Cava, X.B. Liu, Z. Altounian, Q. Huang, Phys. Rev. B 79 (2009) 014435. [17] A. Yan, K.H. Müller, L. Schultz, O. Gutfleisch, J. Appl. Phys. 99 (2006), 08K903. [18] A. Arrott, Phys. Rev. 108 (1957) 1394. [19] J. Inoue, M. Shimizu, J. Phys. F 12 (1982) 1811. [20] P.E. Brommer, Physica B 154 (1989) 197.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Magnetocaloric effect and magnetic transition in bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound M. Yue a,∗ , Z.Q. Li a , X.B. Liu b , H. Xu a , D.M. Liu a , J.X. Zhang a a b
College of Materials Science and Engineering, Beijing University of Technology, Beijing 100022, China Center for the Physics of Materials and Department of Physics, McGill University, 3600 University Street, Montreal, Quebec H3A 2T8, Canada
a r t i c l e
i n f o
Article history: Received 25 November 2009 Received in revised form 8 December 2009 Accepted 8 December 2009 Available online 14 December 2009 Keywords: Mn1.1 Fe0.9 P0.8 Ge0.2 compound Fe2 P-type structure Magnetocaloric effect First-order magnetic transition
a b s t r a c t Crystal structure, magnetocaloric effect and magnetic transition in bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound have been studied by X-ray diffraction, magnetic measurements and Landau–Ginzberg theory. Mn1.1 Fe0.9 P0.8 Ge0.2 compound crystallizes in a hexagonal Fe2 P-type structure with lattice constants of a = 6.0789(10) Å and c = 3.4674(9) Å. The compound exhibits giant magnetocaloric effect with maximum magnetic entropy change of 61.8 J/kg K in a field change from 0 to 5 T around its Curie temperature of 251 K. The temperature dependence of the Landau coefficients have been derived by fitting the magnetization with the Landau expansion of the magnetic free energy, indicating the first-order nature of the magnetic transition between ferromagnetic and paramagnetic states in the compound. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Recently, magnetic refrigeration based on the magnetocaloric effect (MCE) has drawn tremendous attention due to its good potential as an alternative to vapor-compression techniques around room temperature [1]. As a result, many new materials with room temperature giant MCE have been developed and broadly investigated like the Gd5 (Six Ge1−x )4 , La(Fe1−x Six )13 , MnFe(P1−x Mx ) with M = As, Si, or Ge, and the manganites [2–5]. Among these materials, MnFe(P1−x Gex ) is one of the most promising candidates for practical application with respect to its competitive advantages such as abundant raw materials, low fabrication costs, and addresses environmental concerns. In addition, by adjusting the P/Ge ratio in MnFe(P1−x Gex ) the Curie temperature (TC ) of the compound can be tuned over a large working temperature range for magnetic refrigeration application [6]. However, in the past, the compound was generally synthesized by a mechanically activated solid-diffusion method, which requires very long processing time and frequently involves the formation of undesirable inter-metallic impurities in the compound [7,8]. In this study, we report our results on bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound prepared by the new techniques of spark plasma sintering (SPS), a plasma-aid consolidating technique [9]. This SPS technique shortens considerably the diffusion paths of compound formation and homogenization and as
∗ Corresponding author. E-mail address: [email protected] (M. Yue). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.12.050
a result, the compound possesses homogeneous chemical composition and crystal structure as well as good magnetocaloric properties around room temperature. MCE is intimately related to the magnetic transition near TC . Generally, the temperature dependence of magnetization M(T) is described using a molecular field theory with Brillouin Function for the magnet with local moments [10]. If M(T) follows the Brillouin relationship around Tc, a second order magnetic transition occurs. On the other hand, if the change of M(T) is much sharper than that predicted by Brillouin function around Tc, a first-order magnetic transition takes place. For the weak itinerant magnet, a Landau–Ginzberg phase transition theory is often used to describe the field-induced magnetic transition [11]. Many 3d-based magnets are between the two extreme situations. For example, both Brillouin function and Landau expansion methods describe well the order of the magnetic transition in La(Fe,Co,Si)13 compounds [12]. The first-principles calculations indicate Mn (3g) has stable magnetic moment while the moment of Fe (3f) is metastable and at meta-magnetic state in the hexagonal MnFe(P1−x Mx ) (M = As, Si and Ge) with Fe2 P structure [13]. It is expected that the magnetic transition could be described by both Brillouin function and Landau expansion methods in Mn1.1 Fe0.9 P0.8 Ge0.2 . In fact, our previous Mössbauer spectroscopy data indicate that the temperature dependence of the hyperfine field changes more rapidly than that predicted by a simple molecular field Brillouin function, indicating the first-order nature of the magnetic transition in Mn1.1 Fe0.9 P0.8 Ge0.2 [14]. We, here, investigate the magnetic transition in Mn1.1 Fe0.9 P0.8 Ge0.2 using a Landau expansion.
M. Yue et al. / Journal of Alloys and Compounds 493 (2010) 22–25
Fig. 1. Observed and calculated XRD patterns of bulk Mn1.1 Fe0.9 P0.8 Ge0.2 alloy. The bottom curve is the difference between the observed and the calculated intensities. The upper and lower rows of vertical bars indicate the Bragg reflection positions of MnFePGe and MnO compounds, respectively.
2. Experimental procedure Mn powder (>99.99 wt.%), Fe powder (>99.99 wt.%), red P powder (>99.3 wt.%) and Ge powder (>99.9999 wt.%) were mixed together in quantities corresponding to the nominal chemical composition of Mn1.1 Fe0.9 P0.8 Ge0.2 . The mixed powders were then ball milled under an argon atmosphere for 1.5 h in a high energy Pulverisette 4 mill. The above milled powders were collected into a graphite mold and consolidated into a Ф20 mm × 5 mm wafer sample at 1183 K under 30 MPa by the SPS technique. The density of the sample was examined by the Archimedes method to be over 95% of the density of the as-cast ingot. The crystal structure of the bulk sample was measured by powder X-ray diffraction techniques (Rigaku, Cu K␣ radiation) and analyzed by the Rietveld method using the general structure analysis system (GSAS) code [15]. Magnetic measurements were carried out in a 5 T Quantum Design physical properties measurement system (PPMS) magnetometer.
3. Results and discussion 3.1. Structure and magnetocaloric effect in bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound Powder X-ray diffraction results show that the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 sample has a hexagonal Fe2 P-type crystal ¯ structure with space group P 62m. Fig. 1 displays the observed and calculated XRD patterns for the Mn1.1 Fe0.9 P0.8 Ge0.2 compound. The crystallographic data are derived from Rietveld fitting for the MnFePGe hexagonal phase. The hexagonal phase has lattice constants of a = 6.07789(10) Å and c = 3.4674(9)Å. The Mn atoms occupy exclusively the 3 g (0.9505(15), 0, 0.5) site and part of the 3f (0.2540(17), 0, 0) site; the Fe atoms occupy the rest of the 3f site, while P and the Ge atoms randomly occupy the 2c and 1b sites. These results are qualitatively in agreement with our previous neutron diffraction results [16]. It is worth mentioning that some secondary phases such as (Mn, Fe)5 Ge3 or (Mn1−x Fex )3+ı Ge, which persist in conventionally sintered and cast samples even after long time annealing [8,17], are not present in the present bulk sample prepared by the SPS technique. In addition, a minor impurity phase of MnO, which probably originated from the starting materials or from the oxidation of Mn during the preparation process, accounts for less than 2 wt.% in the sample according to the refinement results. Fig. 2 shows the temperature dependence of magnetization of bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound measured in a magnetic field of 0.05 T. It should be noted that the virgin effect, which had been found in first time cooling of as-prepared MnFePGe alloy by some previous investigations [6–8], does exist in our sample. The heating and cooling curves shown in Fig. 2 are for the sample that has experienced thermal cycling. A large thermal hysteresis of about
23
Fig. 2. Temperature dependence of magnetization of bulk Mn1.1 Fe0.9 P0.8 Ge0.2 alloy measured in a magnetic field of 0.05 T.
25 K upon heating and cooling indicates the first-order nature of the ferromagnetic ↔ paramagnetic transition. In addition, the Curie temperature (TC ) of the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound was determined as 251 K from the heating curve where the first temperature derivative of the magnetization has its highest value. The isothermal magnetization curves for the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound around its Tc in external magnetic field up to 5 T are shown in Fig. 3. A magnetic transition in the compound from the paramagnetic state to the ferromagnetic state was observed above its TC . In addition, the large magnetic hysteresis during the increase and decrease of the magnetic field in the vicinity of TC indicates that the transition is a first-order magnetic phase transition, consistent to our observation from the M(T) data in Fig. 2. The magnetic entropy change derived from the magnetization data using the Maxwell relation is shown in Fig. 4 for the magnetic field changes from 0 to 1, 2, 3, 4, and 5 T. The compound exhibits large MCE and the values of the magnetic entropy change are 20.6 and 61.8 J/kg K for field changes of 2 and 5 T at 251 K, respectively. These values are superior to those in MnFePGe compound in previous studies [6–8,17], and are amongst the highest reported magnetic entropy changes around room temperature.
Fig. 3. Isothermal magnetization of the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound as a function of applied magnetic field up to 5 T.
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M. Yue et al. / Journal of Alloys and Compounds 493 (2010) 22–25
Fig. 4. Temperature dependence of the magnetic entropy change of the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound measured in a magnetic field change from 0 to 1, 2, 3, 4, and 5 T.
3.2. Landau phenomenological description of the magnetic transition The order of the phase transition is determined by the temperature dependence of the magnetic free energy. The Landau–Ginzberg phenomenological description can be given by the Landau expansion of the magnetic free energy with the total magnetization M: F(M, T ) =
c1 (T ) 2 c3 (T ) 4 c5 (T ) 6 M + M + M + · · · + −0 HM 2 4 6
(1)
and the temperature and magnetic field dependence of F(M, T) determines the nature of the magnetic transition. For the Landau expansion up to forth order, the Arrott plots relationship is obtained [18]: 0 H = c1 (T ) + c3 (T )M 2 M
Fig. 6. Temperature dependence of landau coefficients for the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound. (The units for c1 (T), c3 (T), and c5 (T) are T2 (kg/J), T4 (kg/J), and T6 (kg/J), respectively.)
(2)
Above Tc, a linear relationship is expected for the Arrott plots. However, if there is field-induced magnetic transition from paramagnetic to ferromagnetic states, the inflection points and the negative slope will appear in the plots. Fig. 5 shows the Arrott plots near the Tc for the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound. The inflection points and the negative slope in the plots above Tc clearly
Fig. 5. Arrott plots in the vicinity of TC for the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound.
indicate the occurrence of the field-induced magnetic transition in the compound. To gain more insights on the magnetic transition, F(M, T) is expanded up to six power and the Inoue–Shimizu model is obtained [19,20]. The Landau coefficients are accessible through the equation of state linking M and the magnetic field, 0 H: 0 H = c1 (T )M + c3 (T )M 3 + c5 M 5
(3)
The Landau coefficient at TC , c1 (TC ) and c5 (TC ) are positive. However, c3 (TC ) may be positive, zero or negative. For a positive or zero value of c3 (TC ), the magnetic free energy has only one minima at M = 0, which corresponds to the paramagnetic state, so a second magnetic transition is expected. On the other hand, for a negative c3 (TC ), the magnetic free energy has two minima at M = 0 and M = / 0 which, respectively, corresponds to the paramagnetic and ferromagnetic state. In this case, a first-order magnetic transition occurs. The Landau coefficients c1 (TC ), c3 (TC ), and c5 (TC ) were determined by fitting the magnetic field, 0 H against magnetization, M(0 H), using Eq. (2). The detail fitting method has been reported elsewhere [12]. The temperature dependence of the Landau coefficients derived from these fitting results is shown in Fig. 6 for the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound. As expected, c1 (TC ) is positive with a minimum at TCc1 (T ) , and the derived magnetic transition temperature TCc1 (T ) is, within error, the same as TC , determined from the heating curve of temperature dependence of magnetization of bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound (Fig. 2). The value of c3 (TC ) at TC is negative, indicating the first-order magnetic transition at TC . Such calculation agrees well with the aforementioned experimental results, which indicates that the zero field magnetic transition at TC is first-order in the bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound.
M. Yue et al. / Journal of Alloys and Compounds 493 (2010) 22–25
4. Conclusions A preparation route of ball milling and subsequent spark plasma sintering has been applied to prepare bulk Mn1.1 Fe0.9 P0.8 Ge0.2 compound. The crystal structure and magnetocaloric properties of the compound were investigated. It is found that the compound possesses a hexagonal Fe2 P-type crystal structure, in which the Mn atoms occupy the total 3g sites and part of the 3f sites; the Fe atoms occupy the rest of the 3f sites, while P and the Ge atoms randomly occupy the 2c and 1b sites. The compound exhibits giant magnetocaloric effect with maximum magnetic entropy change of 61.8 J/kg K in a field change from 0 to 5 T at 251 K. Arrott plots and the temperature dependence of landau expansion coefficients of magnetic free energy near TC indicate that the magnetic transition between ferromagnetic and paramagnetic states in the compound shows typical first-order character. Acknowledgement This work was supported by the National High Technology Research and Development Program of China (2002AA324010). References [1] J. Glanz, Science 279 (1998) 2045.
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