Ames Laboratory Publications Ames Laboratory 2015 Gd5(Si,Ge)4 thin film displaying large magnetocaloric and strain effects due to magnetostructural transition Ravi L. Hadimani Iowa State University, hadimani@iastate.edu Joao H. B. Silva Universidade do Porto Andre M. Pereira Imperial College Devo L. Schlagel Iowa State University, schlagel@iastate.edu Thomas A. Lograsso Follow and additional works at: http://lib.dr.iastate.edu/ameslab_pubs Iowa Statethis University, lograsso@ameslab.gov Part of the Electromagnetics and Photonics Commons, Engineering Physics Commons, and the Metallurgy Commons See next page for additional authors The complete bibliographic information for this item can be found at http://lib.dr.iastate.edu/ ameslab_pubs/258. For information on how to cite this item, please visit http://lib.dr.iastate.edu/ howtocite.html. This Article is brought to you for free and open access by the Ames Laboratory at Digital Repository @ Iowa State University. It has been accepted for inclusion in Ames Laboratory Publications by an authorized administrator of Digital Repository @ Iowa State University. For more information, please contact digirep@iastate.edu. Authors Ravi L. Hadimani, Joao H. B. Silva, Andre M. Pereira, Devo L. Schlagel, Thomas A. Lograsso, Yang Ren, David C. Jiles, and Joao P. Araújo This article is available at Digital Repository @ Iowa State University: http://lib.dr.iastate.edu/ameslab_pubs/258 Gd5(Si,Ge)4 thin film displaying large magnetocaloric and strain effects due to magnetostructural transition Ravi L. Hadimani, Joao H. B. Silva, Andre M. Pereira, Devo L. Schlagel, Thomas A. Lograsso, Yang Ren, Xiaoyi Zhang, David C. Jiles, and Joao P. Araújo Citation: Applied Physics Letters 106, 032402 (2015); doi: 10.1063/1.4906056 View online: http://dx.doi.org/10.1063/1.4906056 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/106/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Large magnetocaloric effect and refrigerant capacity near room temperature in as-cast Gd5Ge2Si2−xSnx compounds Appl. Phys. Lett. 102, 192410 (2013); 10.1063/1.4806971 Low hysteresis and large room temperature magnetocaloric effect of Gd5Si2.05− x Ge1.95− x Ni2 x (2x = 0.08, 0.1) alloys J. Appl. Phys. 113, 17A916 (2013); 10.1063/1.4795434 Exchange coupling in pure hcp Gd and magnetostructural transition in Gd 5 ( Si 2 Ge 2 ) J. Appl. Phys. 97, 10A310 (2005); 10.1063/1.1851693 Thermal Property of DyxEr1−xAl2 and Gd5(SixGe1−x)4 for Hydrogen Magnetic Refrigeration AIP Conf. Proc. 711, 11 (2004); 10.1063/1.1774546 Thermal expansion studies on the unusual first order transition of Gd 5 Si 2.09 Ge 1.91 : effects of purity of Gd J. Appl. Phys. 93, 8486 (2003); 10.1063/1.1540060 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: 129.186.176.91 On: Tue, 02 Jun 2015 21:19:45 APPLIED PHYSICS LETTERS 106, 032402 (2015) Gd5(Si,Ge)4 thin film displaying large magnetocaloric and strain effects due to magnetostructural transition Ravi L. Hadimani,1,a) Joao H. B. Silva,2,a) Andre M. Pereira,3 Devo L. Schlagel,4 jo2,b) Thomas A. Lograsso,5 Yang Ren,6 Xiaoyi Zhang,6 David C. Jiles,1 and Joao P. Arau 1 Department of Electrical and Computer Engineering, Iowa State University, Ames, Iowa 50011, USA and Ames Laboratory, US Department of Energy, Iowa State University, Ames, Iowa 50011, USA 2 IFIMUP and IN-Institute of Nanoscience and Nanotechnology, Departamento de Fısica e Astronomia, da Faculdade de Ci^ encias, da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal 3 Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom 4 Ames Laboratory, US Department of Energy, Iowa State University, Ames, Iowa 50011, USA 5 Ames Laboratory, US Department of Energy, Iowa State University, Ames, Iowa 50011, USA, Division of Materials Science and Engineering, Ames Laboratory, Ames, Iowa 50011, USA 6 X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA (Received 4 November 2014; accepted 3 January 2015; published online 20 January 2015) Magnetic refrigeration based on the magnetocaloric effect is one of the best alternatives to compete with vapor-compression technology. Despite being already in its technology transfer stage, there is still room for optimization, namely, on the magnetic responses of the magnetocaloric material. In parallel, the demand for different magnetostrictive materials has been greatly enhanced due to the wide and innovative range of technologies that emerged in the last years (from structural evaluation to straintronics fields). In particular, the Gd5(SixGe1x)4 compounds are a family of well-known alloys that present both giant magnetocaloric and colossal magnetostriction effects. Despite their remarkable properties, very few reports have been dedicated to the nanostructuring of these materials: here, we report a 800 nm Gd5Si2.7Ge1.3 thin film. The magnetic and structural investigation revealed that the film undergoes a first order magnetostructural transition and as a consequence exhibits large magnetocaloric effect (DSmMAX 8.83 J kg1 K1, DH ¼ 5T) and giant thermal expansion (12000 p.p.m). The thin film presents a broader magnetic response in comparison with the bulk compound, which results in a beneficial magnetic hysteresis reduction. The DSmMAX exhibited by the Gd5(Si,Ge)4 thin film makes it a promising candidate for micro/nano magnetic C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4906056] refrigeration area. V The magnetic materials presenting strong spin-lattice coupling are a powerful set of candidates for multifunctional applications because of their multiferroism, magnetocaloric (MCE), magnetostrictive (MSE), and magnetoresistance (MRE) effects. This coupling is particularly influent on the magnitude of the MCE and MSE. The Gd5(SixGe1x)4 family of compounds is a fruitful example of a strongly coupled system that was responsible for the boost in the magnetic refrigeration research at room temperature in 1997.1 Since then, other material families presenting the Giant MCE (GMCE) were discovered, such as La-Fe-Si2,3 and its hydrides4 Mn-Fe-P-(As, Ge)5,6 and the Heusler alloys based in Ni–Mn–(In, Sn, Sb) compounds.7–10 Nowadays, the Gd5(SixGe1x)4 compounds exhibit one of the highest MCE for the broadest temperature range.10–13 Besides the GMCE, these materials show colossal magnetostriction,14 giant magnetoresistance,15 and also spontaneous generation of voltage16—their main feature is their multifunctionality. The agile interplay between magnetic and atomic lattice degrees of freedom makes them sensitive materials, capable of undergoing magnetostructural transitions by the variation of external magnetic fields,17 pressure,18 and/or temperature.15 a) R. L. Hadimani and J. H. B. Silva contributed equally to this work. Author to whom correspondence should be addressed. Electronic mail: jearaujo@fc.up.pt b) 0003-6951/2015/106(3)/032402/5/$30.00 Since the discovery of the GMCE,1 an intense and devoted effort has been focused in the bulk magnetocaloric materials and in macroscale magnetic refrigeration systems. On the other end of the scale spectrum, the nanoscalling processing has just recently been attracting more attention, resulting in an exponential increase of papers published as shown by Miller and co-workers,19 but still lagging behind other caloric materials in the nanoscalling race, as Moya and co-workers pointed recently.20 From the scientific point of view, the importance to understand the behavior of the magnetostructural coupling with the dimension reduction is crucial. From the magnetic refrigeration point of view, besides the miniaturization of refrigerators, nanostructures can have a great impact by allowing higher operational frequencies on real refrigerators due to their high surface-tovolume ratio that enables faster heat exchange21 and higher cooling powers.22 Moreover, the wide range of technologies that make use of magnetostrictive materials could be empowered by the achievement of strain values in nanostructures such as the ones observed in bulk Gd5(Si,Ge)4 systems. We highlight the sensors/actuators involved in large-infra structures analysis23 and on the straintronics area, where strain is used to mediate magnetoelectric effects towards various applications.24,25 Such artificial multiferroic devices, composed of a piezoelectric and a Gd5(Si,Ge)4 magnetostrictive material, have already presented promising properties for energy harvesting purposes at the micrometric scale.26 106, 032402-1 C 2015 AIP Publishing LLC V 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: 129.186.176.91 On: Tue, 02 Jun 2015 21:19:45 032402-2 Hadimani et al. Appl. Phys. Lett. 106, 032402 (2015) FIG. 1. SEM cross section (a) and top views (b) of the 788 6 59 nm thin film. An EDS spectrum of a representative area is represented in Figure 1(a). The particles diameter histogram is presented in (b) inset. Despite their properties, Gd5(SixGe1x)4 materials were left behind in the nanoscalling race, whereas an increasing number of works have been published on Gd multilayers,27,28 manganites,29–31 FeRh,32,33 NiMnGa,34 and MnAs35,36 materials and also on the MEMS development and numerical simulations.22,37–40 Concerning the Gd5(SixGe1x)4 materials, there is only one not-successful report of a Gd5(SixGe1x)4 thin film.41 Our group has been developing and optimizing the Gd5(SixGe1x)4 thin film deposition by femtosecond pulsed laser ablation technique, but, so far, with low amounts of desired phase and no signs of magnetostructural transition.42,43 Nevertheless, the effort devoted to the optimization of the deposition parameters towards the production of a thin film which retains the magnetostructural transition was finally rewarded resulting in the present work. We have used a femtosecond pulsed laser (9.1 mJ/cm2 laser fluence before focusing and a repetition rate of 1000 Hz) ablation of a multi-grain Gd5Si1.3Ge2.7 target prepared from high purity materials by Tri-arc method. A thin film (t 780 nm) of the same composition was deposited onto a 1 lm SiO2 layer on the top of a (001) silicon substrate at 200 C and 1.2 106 Torr. The rate of deposition was about 0.65 nm/s. As expected from the ultrashort laser pulses used for deposition,44,45 the thin film has a granular-like morphology [Figure 1(b)], consisting on a stack of nanoparticles with a Lorentzian distribution of diameters: median 80 nm and a full width at half maximum of 80 nm[inset of Figure 1(b)]. The thin film chemical composition was inspected by Energy Dispersive Spectroscopy (EDS) analysis [inset of Figure 1(a) and more details in supplementary material46] and was found to be similar to the target material with a 5% variation, i.e., Gd560.25Si1.360.07Ge2.760.14. The structural characterization of the Gd5Si1.3Ge2.7 thin film as a function of temperature was performed using Synchrotron X-ray diffraction: data collected every 5 K on heating in the [150, 250] K range. Figures 2(a) and 2(b) present the spectra obtained as contour plots. In Figure 2(a), at T 170 K, it is clear that the four most intense peaks, associated with (2 3 1), (0 4 2), (1 3 2), and (2 1 2) Miller indices of the O(I) structure, begin to change their relative intensities and 2h positions, whereas at 2h 16.5 an additional peak emerges. In the same temperature interval, other changes on the peaks intensities occur: the peaks (2 1 1), (0 2 2), (1 1 2) of the O(I) phase are transformed into (1 1 2), (0 2 2), (2 1 1) of the O(II) phase—on heating—as can be seen in Figure 2(b). Such drastic changes of the peak intensities and positions clearly point to a O(I) ! O(II) structural change in accordance with similar behavior observed in bulk materials.47 In the 150–170 K temperature range, the Rietveld refinement reveals the presence of a single phase: Gd5Si4-type [O(I)] structure. Above T ¼ 175 K, an additional structural phase is required for the refinement, namely, the Sm5Ge4-type [O(II)]. From Figure 2(d) it can be observed that the O(II) phase fraction increases continuously from 11% at 175 K up to 54% at 190 K, where it becomes the majority phase. The O(II) phase fraction stabilizes reaching 65% of the total volume at 220 K, showing that major changes in the phase fractions occur in the [175, 220] K temperature interval. At room temperature, the major structural phase possesses the following lattice and volume parameters: a ¼ 0.759(4) nm, b 5 1.472(3) FIG. 2. 2D Contour plot of the collected and analyzed synchrotron x-ray diffracted spectra as a function of temperature ([120, 250] K range) in the [15; 17.6] (a) and [11.5; 14.5] (b) h interval. Temperature dependence of the two phase fractions present (d) and the majority phase lattice parameters and volume, assigned to the left and right y-axis, respectively (c).The standard deviations for the parameters are not shown on the plots because they are smaller than symbol sizes. 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: 129.186.176.91 On: Tue, 02 Jun 2015 21:19:45 032402-3 Hadimani et al. Appl. Phys. Lett. 106, 032402 (2015) FIG. 3. Magnetization as a function of temperature (a) and a focused region in the inset. (b) Magnetization isotherms [M(H)] measured in the [182, 210] K temperature range, at 250 K and at 275 K with increasing (lower curves) and decreasing (upper curves) applied magnetic fields. In (b) inset, the M(H) at 5 K is presented and the magnetization saturation, at H ¼ 50 kOe, is indicated. nm, c 5 0.771(6) nm, and V 5 0.862(7) nm3 which are slightly smaller than bulk counterparts, such as Gd5Si1.5Ge2.5 single crystal: 0.7658 nm, 1.4793 nm, 0.77554 nm, and 0.87863 nm3 (2% higher than the thin film).47 In fact, the shrinkage in nanoparticles unit cell has been observed in previous metallic nanoparticles deposited with a femtosecond pulse laser,48,49 where it was attributed to the nanoparticles intrinsic surface stress48,50,51 (see discussion below). The temperature dependence of majority phase lattice parameters (a, b/2, and c) and volume are represented in Figure 2(c), where a giant and anisotropic change of the lattice parameters is displayed at T ¼ TS 190 K: Da/a ¼ 1.20%, Db/b ¼ 0.03%, and Dc/ c ¼ 0.40%, leading to a DV/V 0.81%, similar to bulk counterparts.47,52 Comparing the obtained values with other reported strain effects, one finds that the Da/a (12000 ppm) is 10 times larger than the recently reported 1300 ppm upper limit on Co1xFex thin films,53 than the 2000 ppm presented by commercial Terfenol-D,54 being in the same order of magnitude as the recently reported strain values of the shape memory alloys MnNi1xFexGe,55 the improved NiMnGa foams,8,56 and the BiFeO3 piezoelectric thin films.57 Figure 3(a) presents the magnetization temperature dependence, on cooling and heating, in the 10–300 K temperature range under a constant applied field of 0.1 T. On heating, two paramagnetic to ferromagnetic transitions are observed: one at T ¼ T00 194 K and a second one around T ¼ T0 247 K. From Fig. 3, it can be observed that there is an overlap between the cooling and heating curves except for the region between 170 and 225 K, where thermal hysteresis is observed (blue area in Figure 3(a)). Such a temperature interval is coincident with the one observed in the XRD data (shown in Figures 2(a) and 2(b)), where the O(II) ! O(I) structural transition is presented, unveiling the occurrence of a simultaneous magnetic and structural transition, i.e., a magnetostructural transition, [O(II),PM] ! [O(I), FM]. This T00 transition occurs about 13 K above the one found for the bulk sample (see supplementary material46 and Ref. 11). Furthermore, the T0 transition constitutes a fingerprint of a purely ferromagnetic ordering of the high-temperature O(I) phase, i.e., T0 ¼ TCO(I), thus corroborating with the structural characterization analysis (35% amount). Moreover, the continuous magnetization increase down to 10 K probably arises from a Gd-based paramagnetic amorphous phase, as previously observed in long ball milling studies.58 In Figure 3(b) M vs H isothermal curves are depicted for the [182, 210] K temperature range and T ¼ 250 and 275 K. These curves were measured according to the loop method,59 i.e., after each isotherm the film was warmed up until the PM region (at 300 K) and then cooled down to 100 K and again heated up till the desired temperature. Magnetic hysteresis (highlighted in color in Figure 3(b)) is present in the [182, 210] K temperature region. Typically in the bulk systems, the metamagnetic transition exhibits a pronounced S-type shape between the two magnetization states13 (see supplementary material for the target sample isotherms46). In this thin film, the M(H)s curves are smoother leading to a drastic hysteresis reduction when compared with the bulk counterpart. In the literature, this peculiar M(H) shape has been generally associated with disorder that might be caused by microstrain, structural defects, chemical disorder, etc.21,60 Moreover, the simultaneous observation of a Tc increase together with the shrinkage of the unit cell are hallmarks of stress and strain presence for the Gd5(Si,Ge)4 materials.18,61,62 Typically, Gd5(Six,Ge1x)4 with x 0.3/0.4 compounds present a TC pressure dependence of @TC/@P 1.2–1.5 K/kilobars.63,64 Considering the 13 K TC increase in thin film comparing with bulk, this results in a pressure in the 8–11 kilobars range. This in total accordance with the pressure estimation performed to account with the observed unit cell shrinkage DV ¼ Vbulk Vfilm, i.e., by calculating the pressure using the compressibility (j ¼ [0.00158, 0.00190] kilobars1)55 and P ¼ (DV/V)(1/j) a pressure value in the 9–11 kilobars range is obtained. Hence, independent structural and magnetic characterization analysis indicate pressure/stress as the most probable cause for the observed changes in the thin film behavior in comparison with the bulk. Such internal stress in thin films can arise from the preparation method and from strain induced by the substrate-film interface stress (which is the main stress mechanism in (hetero)epitaxial thin films65,66). Nevertheless, since the produced thin film presents a granular morphology, it should not be neglected the surface stress that naturally occurs in small nanoparticles. Despite the difficulty associated with the complex calculation of the surface pressure of these nanoparticles, it is known that the surface pressure is inversely proportional to its diameter and that it lies in the 1–10 kilobars values for nanoparticles with less than 100 nm diameter.67 Considering that the mean particle size of the nanoparticles in this thin film is 80 nm, it outcomes that their intrinsic surface stresses can explain the observed results (increase of TC and unit cell volume reduction). Furthermore, the observed smoothening of the magnetic responses and the magnetic hysteresis reduction are a plausible consequence of the distribution of surface pressures associated with the different nanoparticles diameters along the film. This suggestion can lead to advanced production methodologies, namely, tuning 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: 129.186.176.91 On: Tue, 02 Jun 2015 21:19:45 032402-4 Hadimani et al. Appl. Phys. Lett. 106, 032402 (2015) FIG. 4. (a) Magnetic entropy change (DSm) as a function of temperature in the [135, 275] K temperature range. In the inset, the DSmMAX is plotted against the applied magnetic field changes to the 2/3 power. (b) The [0, 5] T –DSm (T) curve, corrected for the 65% mass from the O(II) phase that effectively contributes to the magnetic entropy change in the [135, 235] K temperature, plotted with 15% error bars. the nanoparticle size distribution ensemble (by changing laser parameters49) as a strategy towards magnetic hysteresis reduction, which is of pivotal importance for the efficiency improvement of the magnetic refrigeration process.68,69 In contrast with the observations in bulk specimens13 it is clear that up to 5 T, the magnetization curves do not achieve a fully saturated state: the saturation magnetization at 5 K is lSat 6.2 6 0.8 lB, slightly lower than the theoretical 7 lB. The difference can arise from the presence of small pure Gd amorphous phase(s) amount. The temperature dependence of the magnetic entropy change (DSm(T)), plotted in Figure 4(a), was estimated in accordance with Ref. 59. Its peak value is DSmMAX,8.8 6 1.7 J kg1 K1, occurs at T ¼ Tpeak ¼ TMS 192 K, and the full width at half maximum (FWHM) is 24 K for a field variation of DH ¼ 5 T. Hence, the refrigerant capacity is RCPFWHM 212 J K1. Such a large change in the thin film entropy is a consequence of the strong coupling between the magnetic spin and the lattice (as in bulk materials), also illustrated by the occurrence of a simultaneous magnetic and structural transition—magnetostructural transition. Furthermore, it is important to stress that the DSmMAX mass and volume normalization performed are clearly an underestimation of the real DSmMAX of the film, since this normalization assumes that the whole film volume contributes to the entropy change and this is not true. There is a 35% amount of O(I) phase which does not transform into O(II) and hence does not contribute to the DSm in the [150, 240] K temperature interval. Recalculating, correcting the 35% volume fraction corresponding to the O(I) phase a DSmMAXcorrected 13.6 J Kg1 K1 for DH ¼ 5 T (see Fig. 4(b)) value is achieved. Such value is lower than that of the DSmMAXbulk (43 J Kg1 K1 for DH ¼ 5 T (Ref. 11)), however, it is complemented with a larger FWHM (which constitutes further evidence of strain disorder60) and reduced hysteretic losses. Such reduction can be estimated by averaging the area in between the M(H) curves over the [TCcooling, TCcooling þ 20]K temperature range, resulting in 12 J Kg1, almost three times lower than the value presented by the target sample, 42 J Kg1. Hence, if the hysteretic losses are subtracted to the thin film refrigerant capacity,68 the efficient RCP is estimated to be RCPeff 200 J K1.The obtained DSmMAX and RCP values are higher than the observed in manganites thin films, such as La0.67Sr0.33MnO3,30 La0.56Sr0.44MnO3,31 or La0.7Sr0.3MnO3 on SrRuO3 superlattices;29 Gd multilayered films;28 or NiMnGa thin films,34 being only lower than the epitaxial MnAs and FeRh thin films23,26 (see supplementary material for comparative table46). In comparison with the bulk GMC materials,10 the thin film presents a lower DSmMAX. However, its reduced hysteretic losses and broadened DSm(T) curve ensure a promising RCP (higher than the recent Pt doped NiMnGa70 and virtually equal to the Gd5Si2Ge1.9Fe0.1 magnetic refrigerant68). Finally, its higher surface to volume ratio is an advantage towards the enhancement of the heat exchanges velocity occurring in a magnetic refrigerator69 thus allowing an increase of the cycling frequency and consequently its cooling power.22 In conclusion, we were able to deposit a Gd5(SixGe1x)4 thin film which retains the magnetostructural transition as observed in its bulk counterpart. It shows a broader magnetic response than the bulk target, exhibiting a lower DSmMAX, but a higher FWHM and a large magnetic hysteretic losses reduction. These changes on the magnetic responsive features are associated with the stress distribution on the nanoparticles surface arising from the broader size distribution of nanoparticles. Such properties result in a promising refrigerant capacity at the nanoscale. Simultaneously, a giant thermal expansion was observed across the magnetostructural transition. In the future, we endeavor to explore the influence of particle size distributions and film thicknesses on the magnetic and structural coupling, the DS(T) curve and the hysteretic loses exploring the nanostructuring process as a strategy to tune the MCE towards the development of nano/ micro refrigerators. Their multifunctionality and giant striction features can help the development of high sensitivity strictive sensors/actuators (due to strain), and bring opportunities for artificial multifunctional materials, such as multilayer deposition with piezoelectric materials. We would like to acknowledge V. K. Pecharsky for the useful discussions. J. H. B. Silva thanks FCT for the grant SFRH/BD/88440/2012 and the project PTDC/CTMNAN/ 115125/2009. A.M.P. acknowledges the project EPSRC EP/ G060940/1 for the financial support. The work performed at the Ames Laboratory was supported by the DOE-Basic Energy Sciences under Contract No. DE-AC02-07CH11358 and Barbara and James Palmer Endowment at the Department of Electrical and Computer Engineering of Iowa State University. 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: 129.186.176.91 On: Tue, 02 Jun 2015 21:19:45 032402-5 1 Hadimani et al. V. K. Pecharsky and K. A. Gschneidner, Phys. Rev. Lett. 78, 4494 (1997). S. Fujieda, A. Fujita, and K. Fukamichi, Appl. Phys. Lett. 81, 1276 (2002). 3 J. Liu, J. D. Moore, K. P. Skokov, M. Krautz, K. L€ owe, A. Barcza, M. Katter, and O. Gutfleisch, Scr. Mater. 67, 584 (2012). 4 J. Lyubina, K. Nenkov, L. Schultz, and O. Gutfleisch, Phys. Rev. Lett. 101, 177203 (2008). 5 K. H. J. Buschow, F. R. De Boer, O. Tegus, and E. Bru, Nature 415, 150 (2002). 6 N. T. Trung, Z. Q. Ou, T. J. Gortenmulder, O. Tegus, K. H. 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