Magnetocaloric effect and critical behavior in ternary equiatomic magnesium compounds REPtMg (RE = Tb, Dy and Ho)

Intermetallics 109 (2019) 24–29

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Magnetocaloric effect and critical behavior in ternary equiatomic magnesium compounds REPtMg (RE = Tb, Dy and Ho)

T

Zhenqian Zhanga, Sebastian Steinb, Lingwei Lia,∗, Rainer Pöttgenb a b

Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, Shenyang, 110819, China Institut für Anorganische und Analytische Chemie, Universität Münster, Corrensstrasse 30, D-48149, Münster, Germany

A R T I C LE I N FO

A B S T R A C T

Keywords: REPtMg (RE = Tb, Dy and Ho) compounds Magnetocaloric effect (MCE) Magnetic properties Critical behavior Magnetic phase transition

The magnetocaloric effect (MCE) and critical behavior in the REPtMg (RE = Tb, Dy and Ho) intermetallic compounds around Curie temperatures TC were investigated by magnetization measurements. All the REPtMg compounds exhibit pronounced MCE performance with the maximum magnetic entropy change (− ΔSMmax ) values up to 5.1, 7.2, 10.2 J/kg K under the magnetic field change (ΔH ) of 0–5 T around TC of 58, 29, and 20 K for RE = Tb, Dy and Ho, respectively. The reasonable and accurate critical exponents for the present REPtMg series compounds for RE = Tb, Dy and Ho obtained by the ΔH dependence of ΔSM method are evaluated to be β= 0.4691, 0.4681, 0.4141, γ = 1.0412, 1.0482, 1.1067 and δ = 3.2196, 3.2393, 3.6728 around TC, which are verified by the Widom scaling law and scaling equations, respectively.

1. Introduction Magnetic cooling (MC) technology based on the application of the magnetocaloric effect (MCE) has received wide attention in last several decades. Compared with the traditional gas compression refrigeration technology which consumes a large amount of fuel, it has the advantages of environmental friendly, higher energy efficiency as well as mute [1–4]. The configurational entropy of the spin structure during isothermal magnetization process and absorption of heat energy of the spin rearrangement during adiabatic demagnetization process can be defined as the intrinsic thermal reaction of MCE. To satisfy practical application, exploring and developing for magnetic materials with the optimal MCE performance have been considered as the main mission [5–8]. In recent years, not only the large reversible MCEs, but also a small hysteresis loss has been found in many heavy rare-earth (RE) based oxides and intermetallic compounds, which plays a key step in the development of MC materials [9–16]. Recently, the precipitation hardening caused by the addition of magnesium based alloys has been concerned with for the significant optimization of microstructure and the mechanical properties in the alloys composed of RE and certain transition metals (T) [17–20]. The ternary RE-T-Mg compounds exhibit a rich variety of crystallographic structures and a wide range of physical properties [21–24]. Recently, a series new equiatomic magnesium compounds of REPtMg (RE = Y, Eu, Tb-Tm, Lu) have been fabricated and characterized with respect of the

∗

crystal structure and some primary magnetic properties [25,26]. Among these compounds, ferromagnetic ordering phase transition are observed for RE = Tb, Dy and Ho. As we all know, the critical behavior analysis of magnetic materials can reflect some important information for the magnetic phase transition as well as the magnetocaloric performances, which will help us to further understand the magnetic characterization of the materials. Thus, the MCE and the critical behavior of the REPtMg (RE = Tb, Dy and Ho) compounds were further systematically studied in this article. 2. Experimental details Polycrystalline samples of the REPtMg (RE = Tb, Dy and Ho) were synthesised by induction melting of the high purity raw materials in sealed Niobium ampoules in a water cooled sample chamber. All the samples are confirmed to be singled with the ZrNiAl-type hexagonal structure (space group P6¯ 2m) by powder X-ray diffraction (XRD) and Energy Dispersive X-Ray Spectroscopy (EDX) analyses. Detail description of sample preparation and phase analysis can be found in Ref. 26. The magnetic data of REPtMg compounds were measured with the magnetic field up to 7 T using the commercial vibrating sample magnetometer by Lakeshore which is added at a high field measurement system by Cryogenic.

Corresponding author. E-mail address: [email protected] (L. Li).

https://doi.org/10.1016/j.intermet.2019.03.003 Received 17 January 2019; Received in revised form 16 February 2019; Accepted 1 March 2019 0966-9795/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. The X-ray diffraction patterns for the REPtMg (RE = Tb, Dy and Ho) compounds, respectively.

3. Results and discussion Room temperature X-ray diffraction patterns of the REPtMg (RE = Tb, Dy and Ho) compounds are illustrated in Fig. 1(a), (b) and (c), respectively. All peaks can be indexed to the ZrNiAl-type hexagonal structure (space group P6¯ 2m), with lattice parameters consistent with the results reported in previous literatures [26]. The magnetization (M) together with the reciprocal susceptibility (1/χ) represented by the left and right coordinate axes as a function of temperature for the present REPtMg series compounds measured in the ΔH = 1 T for RE = Tb, Dy and Ho are illustrated in Fig. 2(a), (b) and (c), respectively. The corresponding M(T) curves in the ΔH = 0.2 T under the zero field cooling (ZFC) mode as well as field cooling (FC) mode are illustrated in the insets of Fig. 2(a), (b) and (c), respectively. The Cuire-Weiss paramagnetism of the REPtMg (RE = Tb, Dy and Ho) compounds is fitted in the linear regions with the temperature range of 150 K–300 K. The effective magnetic moments are calculated to be 9.75, 10.61 and 10.21 μB, respectively, which are close to the corresponding values for free

Fig. 3. Isothermal field dependence of the magnetization at various temperatures in the vicinity of the Curie temperatures for the REPtMg (RE = Tb, Dy and Ho) compounds, respectively.

Fig. 2. The magnetization (M, left side) together with the reciprocal susceptibility (1/χ, right side) as a function of temperature for TbPtMg (a) DyPtMg (b) and HoPtMg (c) compounds measured in an external magnetic field of 1 T. Insets are the corresponding ZFC and FC M(T) curves at 0.2 T. 25

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Fig. 4. Temperature dependence of the magnetic entropy change (− ΔSM , left side) and the overlapped curves with the transformed ΔS (θ ) (ΔSM/ΔSMmax , right side) for the TbPtMg compound with various magnetic field changes ΔH up to 0–7 T.

Fig. 6. Temperature dependence of the magnetic entropy change (− ΔSM , left side) and the overlapped curves with the transformed ΔS (θ ) (ΔSM/ΔSMmax , right side) for the HoPtMg compound with various magnetic field changes ΔH up to 0–7 T.

RE3+ ion values. Except slight differences in values, all the primary magnetic properties are consistent very well with previous reported results. To evaluate the MCE of REPtMg compounds, the magnetization isotherm curves (M-H) of the present REPtMg series compounds collect various temperatures in the vicinity of the Curie temperatures with H up to 7 T and the results for RE = Tb, Dy and Ho are shown in Fig. 3(a), (b) and (c), respectively. The magnetization of all compounds shows a saturation trends at a high values and changes fast around the transition which may result large values of magnetic entropy change (ΔSM ) at low temperatures. The ΔSM (T ) data under the magnetic field change (ΔH ) up to 0–7 T are calculated from the M(H, T) results by the Maxwell's thermodynamic equation,

estimate the performance of refrigerant material, named refrigerant capacity (RC) and relative cooling power (RCP). According to the ΔSM (T ) curves, the relation between them are related as,

ΔSM ⎛⎜T , ΔH ⎞⎟ = ⎝ ⎠

∫0

H max

⎛ ∂M ⎞ dH ⎝ ∂T ⎠ H

RC =

∫T

T1

2

ΔSM dT

(2)

RCP = −ΔSMmax × δTFWHM

(3)

where T1, T2 and δTFWHM represent two endpoints corresponding to temperature point at half-maximun in the ΔSM (T ) curve and the value of half-maximun of the ΔSM (T ) curves, respectively. The RCP (RC) values are 278 (211), 331 (253) and 400 (298) J/kg of the present REPtMg series compounds with the ΔH up to 0–7 T for RE = Tb, Dy and Ho, respectively. For comparison, the parameters of − ΔSMmax and RCP of the present REPtMg series compounds and some other compounds with the magnetocaloric properties at the similar magnetic ordering temperature are given in Table 1. We can note that present REPtMg series compounds would be competitive cryogenic MC materials. Moreover, the ΔSM (T ) curves can be simply collapsed into a single curve by ignoring the magnetic field change, which indicates that the materials have the characteristics of second order phase transition (SOPT) materials [4,37]. The Y-axis shows that all the ΔSM (T ) curves with their own ΔSMmax are normalized, ΔS ΄ = ΔSM (T )/ΔSMmax . Then, the X-axis is the reconditioned temperature θ can be expressed as,

(1)

The − ΔSM (T ) curves of the present REPtMg series compounds are given in Figs. 4(a), 5(a) and 6(a) for RE = Tb, Dy and Ho, respectively. Around TC of 58, 29, and 20 K for the present REPtMg series compounds, the resulting maximum values of − ΔSM are determined to be 6.3, 8.9 and 12.2 J/kg K with ΔH up to 0–7 T, respectively. Moreover, two peaks corresponding to the two magnetic phase transitions around TC and TSR (spin-reorientation) in the − ΔSM (T ) curves of the HoPtMg compound, which leads to the widening of the temperature range. Similar behaviors in − ΔSM (T ) curves have also been observed in the compounds that undergoes two magnetic phase transition, such as, Ho2Co2Al, Dy2Cu2Cd, TbMn2Si2 etc. [27–29]. Besides the magnetic entropy change, another two parameters could

− (T − TC )/(Tr1 − TC ); T ≤ TC θ=⎧ ⎨ ⎩ (T − TC )/(Tr 2 − TC ); T > TC

(4)

Table 1 The transition temperature (TC), the maximum values of − ΔSMmax and RCP with the magnetic field changes ΔH = 0–2 T and 0–5 T for the REPtMg (RE = Tb, Dy and Ho) compounds and some other compounds with the MCE. Material

Fig. 5. Temperature dependence of the magnetic entropy change (− ΔSM , left side) and the overlapped curves with the transformed ΔS (θ ) (ΔSM/ΔSMmax , right side) for the DyPtMg compound with various magnetic field changes ΔH up to 0–7 T.

TC [K]

max − ΔSM [J/kg K]

RCP [J/kg]

2T

5T

2T

5T

Ref.

TbPtMg DyPtMg HoPtMg

58 29 20

2.6 3.7 5.2

5.1 7.2 10.2

68 70 114

192 220 283

present present present

PrNi HoPdIn Er5Ni2In4 TbCo3B2 NdCo2B2 ErFeAl EuAuZn

20 23 21 28 27 55 51

2.4 7.9 3.3 4.9 4.5 2.4 4.8

6.1 14.6 7.7 8.7 7.1 6.1 9.1

15a 125a 71 41a 35a 77 105

61a 496 248 215a 93a 311 318

[30] [31] [32] [33] [34] [35] [36]

a

The values were estimated from the magnetic entropy ΔSM (T ) curves in the relevant literatures. 26

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where Tr1 and Tr2 are the temperatures equal to 0. 6 × ΔSMmax . The transformed ΔS ΄ versus θ curves for the present REPtMg series compounds for RE = Tb, Dy and Ho are shown in Figs. 4(b), 5(b) and 6(b), respectively. Except the deviation around and below TSR (θ ≈ −2 ) for the HoPtMg compound which is due to fact of the existence of spin reorientation transition. All the normalized ΔS ΄(θ) curves are falling into a single curve which indicating the SOPT for the present REPtMg series compounds around TC. The critical behavior in the vicinity of TC for the SOPT materials can be identified by a series independent and correlated critical exponents of β , γ and δ . Above TC, critical exponent β and the spontaneous magnetization, MS (T ) = lim M can be expressed as [38,39]: H→0

MS (T ) = M0 (−ε ) β , ε < 0

(5)

below TC, the critical exponent γ and the initial magnetic susceptibility χ0−1 (T ) = lim (H / M ) can be expressed as H→0

χ −0 1 (T ) = (h 0 / M0), ε > 0

(6)

and at TC, the critical exponent δ can be given as: 1

M = XH δ , ε = 0, T = TC

(7)

where the reduced temperature ε = (T − TC )/ TC and M0 , h 0 / M0 , and X are defined as the critical amplitudes. In addition, the critical exponents satisfy with the Widom scaling relation [40]:

δ=1+

γ β

(8)

According to Eq. (7), to obtain the value of δ for the present REPtMg series compounds, the magnetization curves of M (TC , H ) for RE = Tb, Dy and Ho are illustrated in Fig. 7(a), (b) and (c), respectively. The linear behavior at high field region is obtained by taking the logarithm of the same curves which is illustrated in the insets of Fig. 7. The values of δ for the present REPtMg series compounds for RE = Tb, Dy and Ho are obtained to be 3.2196, 3.2393 and 3.6728, respectively. According to the ΔH dependence of − ΔSM reported in the previous literature [4,37,41], which could be defined as, ΔSM = A × ΔH n , where A is a constant and n is determined by the temperature. T < TC and T > TC for n∼1 and 2, T = TC , n could be calculated by a universal relation corresponding to − ΔSMmax written as follows,

n=1+

β−1 β+γ

Fig. 7. Magnetic isothermal M(H) curves of the REPtMg (RE = Tb, Dy and Ho) compounds at the Curie temperatures. Insets are the same plots in a ln-ln scale.

(9)

Thus, the ΔH dependence of ΔSM method could be explained that the use of Eqs. (8) and (9) to deduce the values of β , γ and n . This method has been successfully applied to the materials, such as, RECo3B2, La1-xCexMn2Si2 etc [33,42]. The exponent n as a function of temperature for the present REPtMg series compounds are illustrated in Fig. 8. The values of n for the present REPtMg series compounds at the temperature corresponding to − ΔSMmax are found to be 0.6485, 0.6492 and 0.61468 for RE = Tb, Dy and Ho, respectively. The values of β , γ and n determined by using Eqs. (8) and (9) together with those from various theoretical models are given in Table 2. As on can see, all the values of β and for the present REPtMg series compounds are close to those of mean field theory, indicating that the long-range magnetic interaction. In addition, the obtained critical exponents can be verified by the scaling equations, which are related to the three variables, M (H , ε ) , H and T can be expressed as [39]:

M (H , ε ) = ε β f± (H / ε β + γ )

Fig. 8. Temperature dependence of the exponent n for the REPtMg (RE = Tb, Dy and Ho) compounds, respectively.

(10)

compounds are plotted in Fig. 9(a), (b) and (c), respectively. Except the deviation of HoPtMg for the curves with T < TC which is due to the additional SR transition happens. All experimental data coincide to two single curves basically for above and below TC, coinciding well with the scaling theory. The reasonably and accurate values of the critical

where f± are defined as f+ (T > TC ) and f− (T < TC ) as a regular functions, respectively. According to Eq. (10), the plots of ln(M / ε β ) vs. ln(H / ε β + γ ) should correspond to two separate lines for the temperature above and below TC, respectively. The transferred curves by using the obtained critical exponents for the present REPtMg series 27

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RE = Tb, Dy and Ho, respectively, the corresponding RCP (RC) values are 278 (211), 331 (253) and 400 (298) J/kg. The critical exponents of the present REPtMg series compounds obtained by the field dependence of ΔSM are close to those of predicted values by the Mean-field model, indicating the long-range magnetic interaction.

Table 2 The values of critical exponents β , γ , δ and n for the REPtMg (RE = Tb, Dy and Ho) compounds and various theoretical models. Materials

β

γ

δ

n

Ref.

TbPtMg DyPtMg HoPtMg

0.4691 0.4681 0.4141

1.0412 1.0482 1.1067

3.2196 3.2393 3.6728

0.6485 0.6492 0.61468

present present present

Mean-field model 3D Heisenberg model 3D Ising model Tricritical mean-field model

0.5 0.365 0.325 0.25

1.0 1.336 1.24 1.0

3 4.8 4.82 5.0

0.667 0.627 0.569 0.4

[43,44] [43,44] [43,44] [43,44]

Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51671048), the Fundamental Research Funds for the Central Universities (Grant Nos. N170904001 and N170908001), and the Research Funds for Innovation Talents in Universities and Colleges of Liaoning Province (Grant No. LR2016003). References [1] K.A. Gschneidner Jr., V.K. Pecharsky, A.O. Tsokol, Recent developments in magnetocaloric materials, Rep. Prog. Phys. 68 (2005) 1479–1539. [2] B.G. Shen, J.R. Sun, F.X. Hu, H.W. Zhang, Z.H. Cheng, Recent progress in exploring magnetocaloric materials, Adv. Mater. 21 (2009) 4545–4564. [3] V. Franco, J.S. Blazquez, B. Ingale, A. Conde, The magnetocaloric effect and magnetic refrigeration near room temperature: materials and models, Annu. Rev. Mater. Res. 42 (2012) 305–342. [4] L.W. Li, Review of magnetic properties and magnetocaloric effect in the intermetallic compounds of rare earth with low boiling point metals, Chin. Phys. B 25 (2016) 037502. [5] V. Franco, J.S. Blázquez, J.J. Ipus, J.Y. Law, L.M. Moreno-Ramírez, A. Conde, Magnetocaloric effect: from materials research to refrigeration devices, Prog. Mater. Sci. 93 (2018) 112–232. [6] L. Li, C. Xu, Y. Yuan, S.Q. Zhou, Large refrigerant capacity induced by table-like magnetocaloric effect in amorphous Er0.2Gd0.2Ho0.2Co0.2Cu0.2 ribbons, Mater. Res. Lett. 6 (2018) 413–418. [7] Y. Zhang, D. Guo, S. Geng, X. Lu, G. Wilde, Structure, magnetic and cryogenic magneto-caloric properties in intermetallic gallium compounds RE2Co2Ga (RE = Dy, Ho, Er and Tm), J. Appl. Phys. 124 (2018) 043903. [8] V.K. Pecharsky, K.A. Gschneidner Jr., Magnetocaloric effect from indirect measurements: magnetization and heat capacity, J. Appl. Phys. 86 (1999) 565–575. [9] Y.K. Zhang, Y. Yang, C.J. Hou, D. Guo, X. Li, Z.M. Ren, G. Wilde, Metamagnetic transition and magnetocaloric properties in antiferromagnetic Ho2Ni2Ga and Tm2Ni2Ga compounds, Intermetalics 94 (2018) 17–21. [10] L.W. Li, K. Nishimura, W.D. Hutchison, Z. Qian, D. Huo, T. Namiki, Giant reversible magnetocaloric effect in ErMn2Si2 compound with a second order magnetic phase transition, Appl. Phys. Lett. 100 (2012) 152403. [11] Y. Zhang, H. Li, S. Geng, X. Lu, G. Wilde, Microstructure and cryogenic magnetic properties in amorphousized RE57Cu25Al18 (RE = Ho and Tm) ribbons, J. Alloy. Comp. 770 (2019) 849–853. [12] Y.K. Zhang, D. Guo, H.D. Li, S.H. Geng, J. Wang, X. Li, H. Xu, Z.M. Ren, G. Wilde, Low field induced large magnetic entropy change in the amorphousized Tm60Co20Ni20 ribbon, J. Alloy. Comp. 733 (2018) 40–44. [13] D. Guo, H. Li, Y. Zhang, Magnetic phase transition and magnetocaloric effect in Er2Ni2Ga compound, IEEE Trans. Magn. 55 (2019) 2500204. [14] L.W. Li, Y. Yuan, Y. Qi, Q. Wang, S.Q. Zhou, Achievement of a table-like magnetocaloric effect in the dual-phase ErZn2/ErZn composite, Mater. Res. Lett. 6 (2018) 67–71. [15] Y.K. Zhang, Review of the structural, magnetic and magnetocaloric properties in ternary rare earth RE2T2X type intermetallic compounds, J. Alloy. Comp. 787 (2019) 1173–1186. [16] D. Guo, Y. Zhang, S. Geng, H. Xu, Z. Ren, G. Wilde, Structure, glass forming ability, magnetic and cryogenic magneto-caloric properties in the amorphous Ni30Co10RE60 (RE = Ho and Tm) ribbons, J. Mater. Sci. 53 (2018) 9816–9822. [17] B.L. Mordike, T. Ebert, Magnesium: properties-applications-potential, Mater. Sci. Eng. A 302 (2001) 37–45. [18] L. Bao, Q. Le, Z.Q. Zhang, Strengthening effect and texture of Mg-3Li alloys strengthened by various rare-earth elements, Adv. Eng. Mater. 20 (2018) 1700491. [19] N. Hort, Y. Huang, K.U. Kainer, Intermetallics in magnesium alloys, Adv. Eng. Mater. 8 (2010) 235–240. [20] R. Pöttgen, R.D. Hoffmann, The role of magnesium in intermetallics and related compounds, Metall 58 (2004) 557–561. [21] R. Pöttgen, A. Fugmann, R.D. Hoffmann, U.C. Rodewald, D. Niepmann, Intermetallic cerium compounds with ordered U3Si2 type structure, Z. Naturforsch. B Chem. Sci. 55 (2000) 155–161. [22] T. Fickenscher, R.D. Hoffmann, R. Kraft, R. Pöttgen, Syntheses and crystal structures of LaRhMg, CeRhMg, PrRhMg, and NdRhMg, Z. Anorg. Allg. Chem. 628 (2002) 667–672. [23] U.C. Rodewald, B. Chevalier, R. Pöttgen, Rare earth-transition metal-magnesium compounds-An overview, J. Solid State Chem. 180 (2007) 1720–1736. [24] S. Tuncel, B. Chevalier, S.F. Matar, R. Pöttgen, Synthesis, structure and chemical bonding of RE4RuMg (RE = La-Nd, Sm, Gd-Ho), Z. Anorg. Allg. Chem. 633 (2007) 2019–2024. [25] K. Latka, Z. Tomkowicz, R. Kmiec, A.W. Pacyna, R. Mishra, T. Fickenscher, R.D. Hoffmann, R. Pöttgen, H. Piotrowski, Structure and properties of GdTMg (T =

Fig. 9. Scaling plots of ln(M / ε β ) vs. ln(H / ε β + γ ) below and above the critical temperatures for the REPtMg (RE = Tb, Dy and Ho) compounds, respectively.

exponents for REPtMg compounds could be deduced from the method of ΔH dependence of ΔSM . 4. Conclusions In conclusion, the REPtMg (RE = Tb, Dy and Ho) compounds with the ZrNiAl-type hexagonal structure (space group P 62m ) were systematically investigated with respect to its magnetocaloric and magnetic transition properties. Around the Curie temperatures TC of 58, 29, and 20 K for the present REPtMg series compounds, the − ΔSMmax values are determined to be 6.3, 8.9 and 12.2 J/kg K with the ΔH up to 0–7 T for 28

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