Influence of Mn on the magnetocaloric effect of nanoperm-type alloys

Influence of Mn on the magnetocaloric effect of nanoperm-type alloys R. Caballero-Flores, V. Franco, A. Conde, and L. F. Kiss Citation: Journal of Applied Physics 108, 073921 (2010); doi: 10.1063/1.3489990 View online: http://dx.doi.org/10.1063/1.3489990 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/108/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Influence of copper substitution on the magnetic and magnetocaloric properties of NiMnInB alloys J. Appl. Phys. 117, 17A737 (2015); 10.1063/1.4916809 Influence of Ge addition on the magnetocaloric effect of a Co-containing Nanoperm-type alloy J. Appl. Phys. 103, 07B316 (2008); 10.1063/1.2835688 Magnetocaloric effect in Mn-containing Hitperm-type alloys J. Appl. Phys. 102, 013908 (2007); 10.1063/1.2751407 The influence of Co addition on the magnetocaloric effect of Nanoperm-type amorphous alloys J. Appl. 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Box 49, 1525 Budapest, Hungary 共Received 5 April 2010; accepted 15 August 2010; published online 12 October 2010兲 In this paper, the influence of the Mn content on the magnetocaloric response of ribbon-shaped amorphous samples of Fe80−xMnxB20 共x=10, 15, 18, 20, and 24兲, has been studied. For this purpose, the temperature and field dependence of the magnetic entropy change 共⌬SM兲have been obtained from magnetization curves. The partial substitution of Fe by Mn leads to a monotonous change in the Curie temperature 共TC兲of the alloys from 438 K for x=10 to 162 K for x=24, in agreement with the coherent-potential approximation. These Curie temperatures could make them good candidates to be used for magnetic refrigeration at room temperature. For an applied field of 1.5 T, the maximum entropy change 共⌬SM pk兲passes from 1 J K−1 kg−1 共x=10兲to 0.5 J K−1 kg−1 共x=24兲, and the refrigerant capacity varies between 117 J kg−1 共x=10兲and 68 J kg−1 共x=24兲. A linear relationship between ⌬SM pk and the average magnetic moment per transition metal atom 共具 ␮ 典Fe,Mn兲 has been presented. © 2010 American Institute of Physics.关doi:10.1063/1.3489990兴 I. INTRODUCTION Magnetic refrigeration based on the magnetocaloric effect 共MCE兲is currently gaining an increasing interest due to the discovery of materials with remarkable magnetocaloric response close to room temperature. Among others, its main advantages with respect to the systems based on the compression-expansion gas cycle are an improvement in the energetic efficiency and the avoidance of ozone depleting and green-house effect gases.1The MCE describes the reversible temperature change ⌬Tad due to the application of an external magnetic field change ⌬Hunder adiabatic conditions. Assumed an isobaric process at pressure P, as is usual in conventional magnetic refrigeration applications for solid state magnetic materials, the thermodynamic coefficient that controls the variation in the temperature Tin the MCE is 共 ⳵ T/ ⳵ H兲S,P, where Sis the total entropy of the magnetic solids defined as the sum of the magnetic SM, lattice SL, and electronic SEentropies.2Taking into account that Sremains constant in closed systems in an adiabatic process, when the entropy associated to magnetic degrees of freedom decreases 共increases兲the contribution to the entropy associated to non magnetic degrees of freedom increases 共decreases兲. In other words, the magnetic system experiments the aforementioned adiabatic temperature change ⌬Tad when the magnetic field changes ⌬Hin order to keep constant the total entropy S. Since the entropy is a state function, and considering the magnetic systems in which the SLand SEare field independent,2the magnetic entropy change ⌬SMexperimented in the MCE can be calculated in an isothermal process as follows: ⌬SM共T,⌬H兲= 冕 Ho Hf 冋 ⳵ ␮ 0M共T,H兲 ⳵ T 册 H dH,共1兲 where ⌬H=Hf−Hois the experimented magnetic field change, ␮ 0is the magnetic permeability of vacuum, and M共T,H兲is the magnetization of the magnetic material. The MCE characterization can be carried out through direct3measurements of ⌬Tad, or indirectly4by numerical approximation of Eq. 共1兲after measuring the temperature and field dependence of the magnetization. In this paper, only the latest method has been used to calculate ⌬SM. Taking into account that the heat transferred between the hot 共at temperature T=Thot兲and cold 共at temperature T=Tcold兲reservoirs in the implemented thermodynamic cycle is an intrinsic property of the MCE, this magnitude can be used to characterize it, instead of the adiabatic temperature change ⌬Tad. The refrigerant capacity RC, defined as the heat transferred mentioned above, can be calculated from ⌬SMas follows: RC共⌬H兲= 冕 Tcold Thot ⌬SM共T,⌬H兲dT.共2兲 From this expression, the hysteresis losses have to be subtracted.5However, for the studied alloys these losses are negligible. In accordance with that, the characterization of the magnetocaloric materials in which SLand SEare field independent is based on two parameters that can predict the goodness of a magnetic material to be used as magnetic refrigerant: the peak of the magnetic entropy change ⌬SM pk, and the refrigerant capacity RC. The study of amorphous materials to be used in magnetic refrigeration has been motivated by finding a compromise between the aforementioned parameters: a modest ⌬SM pk with a high RC. These quantities together with their reduced magnetic and thermal hysteresis, high electrical resistivity, a兲Electronic mail: [email protected]. JOURNAL OF APPLIED PHYSICS 108, 073921 共2010兲 0021-8979/2010/108共7兲/073921/5/$30.00 © 2010 American Institute of Physics108, 073921-1 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.182.17 On: Thu, 21 Jan 2016 14:35:41 good mechanical properties, and corrosion resistance, make these materials good candidates as magnetic refrigerators.6 Taking into account that a larger number of intermetallic Mn-based compounds present a great MCE response,7,8the aim of this work is to study the influence of the Mn content on the magnetocaloric behavior of the amorphous quasibinary ferromagnetic Fe80−xMnxB20 alloy series. II. EXPERIMENTAL Amorphous ribbons of Fe80−xMnxB20 共1 mm wide and ⬃12 ␮ m thick兲and compositional range x=10, 15, 18, 20, and 24, were obtained by a melt-spinning technique. The field and temperature dependence of magnetization M共T,H兲 of 3 mm long ribbon samples have been measured 共up to ␮ 0H=5 T and from 5 to 573 K兲in a superconducting quantum interference device and in a vibrating sample magnetometer, restricted in this case to ␮ 0Hⱕ1.5 T and T ⱖ303 K. Measurements of the ac susceptibility ␹ 共T兲in ac magnetic field of amplitude 10 mOe at frequency of 7 kHz have been obtained by a conventional induction technique. Microstructural analysis of the samples was performed by transmission electron microscopy 共TEM兲in a Philips CM200 operated at 200 kV. III. RESULTS AND DISCUSSION The amorphous character of the whole studied Fe80−xMnxB20 共x=10, 15, 18, 20, and 24兲alloy series was checked by TEM. The temperature dependence of the magnetization ␴ 共at ␮ 0H=10−3 T兲of these alloys is presented in Fig. 1, indicating that whole studied compositional range seems to be ferromagnetic at low T. The values of the Curie temperatures 共TC兲have been obtained from the inflection point of the experimental magnetization data 共x=10, 15, 18, 20, and 24兲at low field 共marked with crosses in Fig. 1兲, and also from the experimental ac susceptibility ␹ 共T兲data 共x =18, 20, and 24兲in ac magnetic field, obtaining a good agreement between both techniques. Figure 2shows the dependence of the experimental values of the Curie temperatures on the Mn content. Using the coherent-potential approximation 共CPA兲, the dependence of the TCof an amorphous quasibinary ferromagnetic alloy 共A1−yBy兲100−zCz共y=x/80, z=20 for the studied samples兲on the variable concentration y 共at a given value of the concentration z兲, is given as a solution of the cubic equation9 ␣ 2tC 3+关 ␣ s− ␣ 共1+ ␣ 兲具j典兴tC 2+ 冋 共1+ ␣ 兲p具j−1典 − ␣ 冉 p jFe–Mn +p jMn–Mn +p jFe–Fe 冊 册 tC−p=0, 共3兲 where tCis the reduced TCof the system to the one in the pure binary compound Fe100−zBz共y=0兲, that is, tC=TC共y ⫽0兲/TC共y=0兲,z ⬘is the number of the average nearest neighbors in this pure binary amorphous compound 共y=0兲, ␣ =共z⬘/2兲−1, jik with i,k=Fe, Mn, are the exchange integrals confined to the nearest neighbors in the amorphous matrix Band reduced to the one in the pure binary crystal, i.e., jFe−Fe, and p,s, and involved mean values 共具 典兲 are given by p=jFe−FejMn−MnjFe−Mn, s=jFe−Fe +jMn−Mn +jFe−Mn, 具j典=共1−y兲2jFe−Fe +y2jMn−Mn +2y共1−y兲jFe−Mn, 具j−1典=共1−y兲2jFe−Fe −1 +y 2jMn−Mn −1 +2y共1−y兲jFe−Mn −1 .共4兲 Taking the values of TC共Ref. 10兲and z⬘共Ref. 11兲of Fe80B20 presented in the literature, TC=647 K and z⬘=12.4, and the values of the exchange integrals jFe–Fe=1,jMn–Mn=−0.25, and jFe–Mn=−0.1 共negative values of the exchange integrals indicate antiferromagnetic interactions兲, the coherent potential approximation gives values of tCin a good agreement with the experimental data, as it is presented in Fig. 2by the solid FIG. 1. 共Color online兲Temperature dependence of the magnetization ␴ of the studied amorphous quasibinary Fe80−xMnxB20 共x=10, 15, 18, 20, and 24兲 alloy series when a magnetic field of 10−3 T is applied. Crosses mark the Curie temperatures of the samples. FIG. 2. 共Color online兲Mn concentration dependence of the reduced Curie temperature tCof the amorphous quasibinary 共Fe1−yMny兲80B20 共y=0, 0.125, 0.1875, 0.225, 0.25, and 0.3兲alloy series. Solid line indicates the tCgiven by the CPA when jFe–Fe=1, jMn–Mn=−0.25, and jFe–Mn=−0.1. The critical Mn concentration of the studied alloys has been marked, being xC=80yC ⬇25 at. % Mn content. 073921-2 Caballero-Flores et al. J. Appl. Phys. 108, 073921 共2010兲 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.182.17 On: Thu, 21 Jan 2016 14:35:41 line. It should be marked that the critical concentration yC defined as the maximum concentration of Mn below which ferromagnetism exists, is an exchange integral dependent property. In this way, the temperature drop observed for the fitted experimental data indicates a critical Mn concentration yC=0.31, corresponding to xC⬇25 at. % Mn content. It is worth mentioning that the maximum Mn content in the amorphous quasibinary ferromagnetic alloy series is greater in 共Fe1−yMny兲100−zBz共Refs. 12 and 13兲than in 共Fe1−yMny兲100−zZrz.14 Therefore, the differences found for the critical concentration of the alloys studied in this paper with respect to mentioned literature data may be due to the different method to obtain the Curie temperature 共Mössbauer effect versus inflection point in M共T兲at low field兲,12 the different value of concentration z,13 and the different element in the amorphous phase Cused 共B versus Zr兲.14 The critical concentration could be even different in samples with the same composition made by different methods because of the non-uniqueness of the amorphous structure15 and the existence of inhomogeneities. Figure 3shows the field dependence of the magnetization at 5 K of the studied Fe80−xMnxB20 共x=10, 15, 20, and 24兲alloy series, and indicates that an increase in Mn content determines an increase in the magnetic field to get the saturating behavior. The Mn content dependence of the saturation magnetization extrapolated to ␮ 0H=0 T at T=5 K, ␴ 0, follows a nearly linear behavior. The extrapolated value for x=0 is in agreement with the result presented in literature.16 For the analysis of the field and Mn content dependence of the magnetization of the studied samples, the empirical law of the approach to ferromagnetic saturation17 can be used M共T,H兲=M共T,0兲 冋 1−a共T兲 Heff −b共T兲 Heff 2 册 +c共T兲Heff,共5兲 where Heff is the effective magnetic field 共applied field minus demagnetizing field兲, and a,b, and care temperaturedependent constants related to the presence of structural inhomogeneities, to the magnetic anisotropy, and to the socalled paraprocess,18 respectively. Since the ribbon-shaped samples have been magnetized in the plane of the ribbons, the influence of the demagnetizing factor Ncan be neglected due to the large aspect ratio. A non linear fit of the experimental data M共T,H兲have been carried out according to the Eq. 共5兲at temperature T=5 K, showing that the term b共T兲/H2plays a negligible role, and that an increase in the Mn content produces an increase in the coefficient M共T,0兲 a共T兲. Therefore, an increase in Mn content determines an increase in the required field to get the saturating behavior 共Fig. 3兲, which, according to the usual interpretation,17 should be ascribed to structural inhomogeneities. To characterize the MCE in the studied system, the ⌬SM pk and RC have been measured. The temperature dependence of the ⌬SMobtained according to the thermodynamic Eq. 共1兲, and caused by the variation in a external magnetic field from 0 to 1.5 T, has been plotted in Fig. 4for the studied alloy series in the compositional range x=10, 15, 20, and 24. The field dependence of the ⌬SMhas been obtained at the temperature of the peak of the magnetic entropy change ⌬SM pk and is presented in Fig. 5for the studied compositional range. This field dependence of the ⌬SMhas been proposed in several works19,20 as ⌬SM pk共H兲⬀Hn, where the exponent n is field independent at the temperature of ⌬SM pk.21 Although the variation in ⌬SMin the close proximity of the temperature of the peak is small, the field dependence of the exponent nis very sensitive to the temperature. However, at high fields it tends asymptotically to a constant value npk when the temperature is close to the temperature of the peak. The experimental n共H兲curves for x=15 共Fig. 6兲are not field independent because the temperature is not exactly that of the peak, but npk can always be extracted as the asymptotic value of n共H兲. Although the ⌬SMin the x=10 studied alloy has been measured only for a variation in an external magnetic field from 0 to 1.5 T 共solid symbols 䊏for x=10 in Fig. 5兲, its ⌬SM pk values can be extrapolated through the abovementioned power law for the field dependence of the exponent nto a range of higher values of field 共open symbols 䊐for x=10 in Fig. 5兲. For x=15, the ⌬SM pk data can be fitted from 0 to 1.5 T FIG. 3. 共Color online兲Field dependence, at 5 K, of the magnetization of the amorphous quasibinary Fe80−xMnxB20 共x=10, 15, 20, and 24兲alloy series. FIG. 4. 共Color online兲Temperature dependence of the magnetic entropy change corresponding to an applied field ␮ 0H=1.5 T of the amorphous quasibinary Fe80−xMnxB20 共x=10, 15, 20, and 24兲alloy series. The maximum of the magnetic entropy change and the values of the temperatures determined at half maximum of the peak are presented for the x=10 composition. 073921-3 Caballero-Flores et al. J. Appl. Phys. 108, 073921 共2010兲 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.182.17 On: Thu, 21 Jan 2016 14:35:41 according to the expression ⌬SM pk共Tpk,H兲=c15共Tpk兲Hn15 and, in order to check the goodness of this expression, the fitted data for x=15 can be compared to the experimentally known ⌬SM pk data from 1.5 to 5 T. This comparison is presented in Fig. 7and shows a good agreement between both extrapolated and experimentally known data. In accordance with this fitting procedure for x=10, cross sections of Fig. 5at magnetic field ␮ 0H=1.5 T and 5 T has been obtained, showing a nearly linear behavior as a function of the Mn content. On the other hand, a proportional relationship between the average magnetic moment per transition metal atom 共具 ␮ 典Fe,Mn兲and the magnetic entropy change has been recently proposed.22,23 Therefore, there should be a relationship between ⌬SM pk and ␴ 0. Figure 8confirms the validity of this relationship for ⌬SM pk measured at ␮ 0H=1.5 and 5 T. Considering that SEand SLare field independent in the system under study, and that the hysteresis losses are negligible for these alloys, an estimation of the RC given from Eq. 共2兲has been obtained from the product of ⌬SM pk times the full temperature width at half maximum of the peak: RCFWHM=⌬SM pk⫻⌬TFWHM=⌬SM pk⫻共T2−T1兲, as is indicated in Fig. 4for the composition with x=10. Other estimations of the RC calculated by the Wood and Potter definition24 共RCWP兲, and by the numerical integration of the area under the ⌬SMversus Tcurves 共RCAREA兲, using the full temperature width at half maximum of the peak as the integration limits, have been obtained and the results indicate approximately the same dependence on the applied field. Figure 9 presents the Mn content dependence of the different RCs for a magnetic field of ␮ 0H=1.5 T of the Fe80−xMnxB20 共x =10, 15, 20, and 24兲alloy series showing a nearly linear behavior. However, as RC depends not only on the magnetization at TCbut also on that at other temperatures, it is not easy to give a theoretical justification for this phenomenological result. FIG. 5. 共Color online兲Field dependence of the maximum entropy change in the studied Fe80−xMnxB20 共x=10, 15, 20, and 24兲alloy series. Open symbols indicate the non linear fit corresponding to experimental data of the x=10 composition sample. FIG. 6. Field dependence of the exponent nin the x=15 studied sample at the temperatures of the peaks of ⌬SMfrom ␮ 0H=0 to 5 T. FIG. 7. 共Color online兲Extrapolation of the fitted data from 0 to 1.5 T for x=15 according to the expression ⌬SM pk共Tpk,H兲=c15共Tpk兲Hn15, and comparison with the experimentally known ⌬SM pk data from 1.5 to 5 T. FIG. 8. 共Color online兲Dependence of the ⌬SM pk on the saturation magnetization extrapolated to ␮ 0H=0 T at T=5 K, ␴ 0. 073921-4 Caballero-Flores et al. J. Appl. Phys. 108, 073921 共2010兲 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.182.17 On: Thu, 21 Jan 2016 14:35:41 IV. CONCLUSIONS In conclusion, the Mn content dependence of the thermomagnetic properties of the amorphous quasibinary ferromagnetic Fe80−xMnxB20 共x=10, 15, 20, and 24兲alloy series have been shown. The Mn addition can be used to tune TC close to room temperature, but at the expense of reducing ⌬SM pk and RC. The dependence of the Curie temperature of the studied alloys on the Mn concentration is in agreement with the CPA, and a linear relationship between the ⌬SM pk at ␮ 0H=1.5 and 5 T of the studied alloys and the saturation magnetization extrapolated to ␮ 0H=0 T at T=5 K, ␴ 0, has been shown. The results indicate a nearly linear dependence on the Mn content x of the Curie temperature TC, the maximum magnetic entropy change ⌬SM pk, and the refrigerant capacity RCFWHM, with approximate slopes of −20 K/at. % Mn, −0.04 J K−1 kg−1/at. % Mn, and −3.5 J kg−1/at. % Mn, respectively. ACKNOWLEDGMENTS This work was supported by the Spanish Ministry of Science and Innovation and EU FEDER 共Projects MAT 2007-65227 and MAT 2010-20537兲, the PAI of the Regional Government of Andalucia, the Hispano-Hungarian bilateral cooperation Project 共No. 2006HU0015兲and the Hungarian Scientific Research Fund 共Grant No. OTKA 68612兲. RCF acknowledges a research fellowship from the Regional Government of Andalucia. 1B. F. Yu, Q. Gao, B. Zhang, X. Z. Meng, and Z. Chen, Int. J. Refrig. 26, 622 共2003兲. 2V. K. Pecharsky and K. A. Gschneidner, Jr., J. Appl. Phys. 90, 4614 共2001兲. 3A. M. Tishin, A. V. Derkach, Y. I. Spichkin, M. D. Kuz’min, A. S. Chernyshow, K. A. Gschneidner, and V. K. Pecharsky, J. Magn. Magn. Mater. 310, 2800 共2007兲. 4V. K. Pecharsky and K. A. Gschneidner, Jr., J. Appl. Phys. 86,565共1999兲. 5J. Du, Q. Zheng, E. Bruck, K. H. J. Buschow, W. B. Cui, W. J. Feng, and Z. D. Zhang, J. Magn. Magn. Mater. 321, 413 共2009兲. 6V. Franco, J. S. Blázquez, C. F. Conde, and A. Conde, Appl. 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Phys. 108, 073921 共2010兲 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.182.17 On: Thu, 21 Jan 2016 14:35:41