A new criterion to distinguish the order of magnetic transitions by means of magnetic measurements

A new criterion to distinguish the order of magnetic transitions by means of magnetic measurements Claudia Marcela Bonilla,1,a兲Fernando Bartolomé,1Luis Miguel García,1 María Parra-Borderías,1Julia Herrero-Albillos,2and Victorino Franco3 1Departamento de Física de la Materia Condensada, Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain 2Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Albert-Einstein-Str. 15, 12489 Berlin, Germany 3Departamento de Física de la Materia Condensada, ICMSE-CSIC, Universidad de Sevilla, P.O. Box 1065,41080 Sevilla, Spain 共Presented 21 January 2010; received 3 November 2009; accepted 18 December 2009; published online 22 April 2010兲 A universal curve for the magnetic entropy change has been found to exist for a variety of materials with second order phase transitions. We have studied whether this universal behavior of the magnetocaloric effect is maintained in materials with first order phase transition, including RCo2 Laves phases and mixed La2/3共CaxSr1−x兲1/3MnO3manganites, which present both second order and first order magnetic ordering phase transitions. The rescaled magnetic entropy change curves for different applied fields collapse onto a single curve only for materials with second order phase transition. This universal curve may be used as a criterion for determining the order of magnetic phase transitions from purely magnetic measurements. © 2010 American Institute of Physics. 关doi:10.1063/1.3366614兴 Experimental distinction between first and second order phase transitions is usually relevant to test proposed models to describe the magnetism of materials, as it has been the case for colossal magnetoresistance in manganites,1or the cobalt Laves phases.2For magnetic cooling applications, the distinction of a first order transition 共FOT兲from a second order transition 共SOT兲is relevant when designing materials that optimize the magnetic entropy change ⌬SMand refrigerant capacity 共RC兲near room temperature. Large values of ⌬SMand large RC are needed to build magnetic refrigerators with commercial purposes. Both quantities are usually tied to the order of the transition phase. In one hand, large values of 兩⌬SM兩maximum at the transition 共⌬SM peak兲, are achieved in materials with first order magnetostructural phase transitions.3On the other hand, high RC values depend on both the height and the width of the ⌬SMcurve.4Although compounds with SOT show smaller 兩⌬SM peak兩than materials with FOT, the compromise between an optimal RC and the lack of hysteresis currently makes compounds with SOT better candidates for the development of magnetic cooling devices. It is relatively common to establish the order of a transition phase by calorimetric methods. However, these experiments typically involve long measurements with small variations around Tc. Besides, conventional calorimetric measurements for nanoscopic samples are not sensitive enough to follow the rapid changes in temperature for such sample sizes.5Even in bulk materials that show small latent heat, such as DyCo2, the identification of the order of the transition may not be straightforward.6Since in this compound the magnitude of the discontinuity in the derivative of the free energy at the transition temperature is small, their physical properties do not show steep features at the transition point. In consequence, to distinguish whether the transition has first or second order character, is not free from ambiguity. As an alternative to calorimetric methods, the order of magnetic transitions can be established from purely magnetic measurements by employing the Banerjee criterion.7This technique is specially interesting for samples of nanoscopic size. Under this criterion, the presence of a negative slope region on the isotherm plots of H/Mversus M2near the transition temperature region, indicate the first order character of the transition. However, for compounds near the critical point 共such as DyCo2兲, this criterion do not always work properly.6 A universal behavior for ⌬SM共T兲curves, for different applied fields, in materials which present SOT has been recently proposed by Franco and co-workers.8–10 The phenomenological universal curve 共that can be calculated from purely magnetic measurements兲consists in the collapse of entropy change curves after a scaling process, regardless the applied magnetic field. In principle, with this curve, it is possible to predict the field dependence of ⌬SM共T兲even in those materials that do not follow a mean field approach. It can be used to make extrapolations in temperature or field close to the entropy change peak as well. The existence of this universal curve for the magnetocaloric effect is based on the assumption of scaling near a second-order phase transition.11,12 As the underlying cause for the collapse of the scaled ⌬SM共T兲curves is the universal behavior from critical phenomena theory, it is natural to expect a breakdown of the universal curve for compounds with a FOT. a兲Electronic mail: [email protected]. JOURNAL OF APPLIED PHYSICS 107, 09E131 共2010兲 0021-8979/2010/107共9兲/09E131/3/$30.00 © 2010 American Institute of Physics107, 09E131-1 Downloaded 03 Apr 2012 to 161.111.180.191. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions Within this scenario, whether or not a breakdown of the universal behavior of ⌬SMimplies that the compound goes through a transition of first or second order, respectively. This assumption allows us to use this method to distinguish the order of the transition. In order to observe the validity of our statement, we have applied this method to the RCo2 Laves phases which present both second order 共TbCo2and PrCo2兲and first order magnetic ordering phase transitions 共DyCo2兲as well as mixed La2/3共Ca,Sr兲1/3MnO3manganites. The structural, electronic, and magnetic properties of these families of compounds have been well studied.2,3,6,13–16 The intermetallic RCo2samples with R=Tb, Pr, and Dy were prepared by using an induction furnace under Ar atmosphere. The alloys were later annealed under Ar atmosphere at 850 °C for 8–12 days depending on the sample. Powder samples of manganites La2/3Ca1/3MnO3,La 2/3Sr1/3MnO3, and La2/3共Ca0.5Sr0.5兲1/3MnO3were obtained using La2O3, CaCo3,Mn 2O3, and Sr2Co3as precursors. The starting powders were ground, pelleted, and sintered following a standard ceramic method. Magnetization measurements were carried out in a Quantum Design MPMS-5S superconducting quantum interference device magnetometer. M共H兲isotherms, for each sample, were obtained for applied magnetic fields between 0 to 5 T and the temperatures varying in a range from 6 to 400 K depending on the ordering temperature of the sample. According to the previously reported results,16,17 the magnetic ordering for PrCo2, DyCo2, and TbCo2at zero field occurs at 40, 138, and 231 K, respectively. The critical temperatures for manganites La2/3共CaxSr1−x兲1/3MnO3have been determined to be 260, 340, and 370 K for x=1, 0.5, and 0, respectively. The manganite La2/3Ca1/3MnO3, present a FOT, while La2/3Sr1/3MnO3and La2/3共Ca0.5Sr0.5兲1/3MnO3present a SOT. The magnetic entropy change ⌬SM共T兲can be evaluated from M共H兲curves, as those shown in Fig. 1, by using a numerical approximation to the equation ⌬SM= 冕 0 H 冉 ⳵ M ⳵ T 冊 H dH,共1兲 where the partial derivative is replaced by finite differences and the integrals are solved numerically. The construction of the phenomenological universal curve requires to normalize each isofield ⌬SM共T兲to its maximum value ⌬SM peak and then rescaling the temperature axis defining a new variable ␪ , ␪ = 再 −共T−Tc兲/共Tr1−Tc兲,TⱕTc, 共T−Tc兲/共Tr2−Tc兲,T⬎Tc, 冎 共2兲 The two reference temperatures Tr1and Tr2satisfy Tr1⬍Tc ⬍Tr2. These temperatures are selected for each curve in such way that for an arbitrary value h⬍1 such that, ⌬SM共T兲/⌬SM peak=h, the reference points in the new curve correspond to ⌬SM共 ␪ =⫾1兲=h. Although the universal curve can be built with only one reference temperature,12 it has been shown that the effect of the demagnetization factor18 or the presence of a minority magnetic phase19 can lead to a breakdown of the ⌬SMcurve collapse. Two reference temperatures are used in the data treatment in order to avoid the effect of these extrinsic factors. In consequence any observed lack of the universal character in our work will not be related to them. The normalized entropy change curves as a function of the rescaled temperature ␪ for compounds with magnetic SOT are shown in Fig. 2. The universal behavior for TbCo2 and PrCo2can be observed in panel a, while the universal behavior for La2/3Sr1/3MnO3and La2/3共Ca0.5Sr0.5兲1/3MnO3is shown in panel b. From these results, we can notice two interesting features. First, all normalized entropy change curves collapse onto a single curve for each compound. This result implies the validity of our data treatment for compounds with SOT in both families. Second, as it had been pointed out before, if the compounds belong to the same universality class, one can assume the magnetization curves scaling near a secondorder phase transition,11,12 i.e., the materials have the same critical exponents and in consequence their entropy change curves scale. Indeed this is observed for both ferromagnets La2/3Sr1/3MnO3and La2/3共Ca0.5Sr0.5兲1/3MnO3in Fig. 2, panel b. Correspondingly the deviation from a common universal behavior at lower theta for the TbCo2and PrCo2may be due to the fact that TbCo2is a ferrimagnet while PrCo2is a ferromagnet, therefore belonging to different universality classes. Besides, for values far from TCthe collapse does not need to hold, because in general, the scaling is satisfied close FIG. 1. 共Color online兲Magnetization vs field isoterms for different temperatures for La2/3Ca1/3MnO3. FIG. 2. 共Color online兲Panel a: universal behavior of the scaled entropy change curves in cobalt Laves phases compounds: TbCo2共blue dots兲and PrCo2共green dots兲. Panel b: universal behavior of the entropy change in manganites La2/3Sr1/3MnO3共green dots兲and La2/3共Ca0.5Sr0.5兲1/3MnO3共blue dots兲. 09E131-2 Bonilla et al. J. Appl. Phys. 107, 09E131 共2010兲 Downloaded 03 Apr 2012 to 161.111.180.191. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions to the critical temperature 共near ␪ =0兲. The collapse holds disregarding the material family. This suggest that this universal behavior always takes place for compounds with SOT. Figure 3permits the comparison of results between compounds with FOT and SOT. Panel a shows the scaled entropy change curves for DyCo2and PrCo2in semilogarithmic axes. The difference between both behaviors is clear. Below ␪ =0 there is no collapse for DyCo2. As it was mentioned before, the first order character of the transition in DyCo2is not evident from purely magnetic measurements.6Nevertheless, our method allows the discrimination of the order of DyCo2 transition from mere inspection of Fig. 3. The use of two reference temperatures prevents the influence of any extrinsic factor that can alter the result for in DyCo2. Panel b shows the comparison between the three manganites La2/3共CaxSr1−x兲1/3MnO3with x=0, 0.5, and 1. The universal behavior for SOT and its breakdown in FOT is evident also in manganites, suggesting that the breakdown of the universal behavior for the entropy change scaled curves in compounds with FOT is a general result. In summary, the scaling of the entropy change curves leads to such different results for compounds with FOT and SOT that we can propose this construction to discriminate the order of magnetic phase transitions, as an alternative to the Banerjee criterion. The financial support of MAT08/1077, DECRYPT and CAMRADS is acknowledged. The authors are thankful to Dr. J. Bartolomé for fruitful discussions. C.M. Bonilla acknowledges a Banco Santander grant and a Ministerio de Ciencia e Innovación grant. Victorino Franco acknowledges the Spanish Ministry of Science and Innovation and EU FEDER 共Project No. MAT 2007-65227兲, and the PAI of the Regional Government of Andalucía 共Project No. P06-FQM- 01823兲. 1J. L. Alonso, L. A. Fernández, F. Guinea, V. Laliena, and V. 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For the sake of clarity DyCo2and La2/3Ca1/3MnO3have been vertically shifted by a factor of 5 and La2/3Sr1/3MnO3have been vertically shifted by a factor of 1/5. 09E131-3 Bonilla et al. J. Appl. Phys. 107, 09E131 共2010兲 Downloaded 03 Apr 2012 to 161.111.180.191. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions