ALBERTO BOLLERO REAL

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3.3 Magnetisation reversal processes in nanocomposite magnets magnetic grains, the application and removal of a certain applied reversed field smaller than the critical field described above will bring the system back to the state where all the magnetic moments are aligned due to the exchange-coupling effect between the soft and the hard grains. This reversible rotation of the exchange coupled soft phase for fields not large enough to reverse the magnetisation of the hard magnetic phase was discovered by Schneider et al [45] and termed “exchange-spring” mechanism by Kneller and Hawig [31]. General criteria for the presence of the “exchange-spring” mechanism are: (a) although there are two different magnetic phases, the major demagnetisation curve shows a magnetically single-phase behaviour; (b) the ratio of remanence to saturation polarisation is higher than 0.5; (c) the recoil curves show a relatively high degree of reversibility in fields below coercivity (“high recoil permeability”). 3.3.2 Intergrain interactions: δJ-plot The interactions between the grains can also be studied by plotting the quantity δJ defined as: δJ = (J d r (H m ) – (J r – 2J r (H m ))) / J r (also known as δJ- or δM-plot which is a graphical presentation of Wohlfarth’s relation (3.1) in dependence on the applied magnetic field). This relationship gives the deviations from the theoretical value for J d (H m ) given by Wohlfarth’s relation [46]. Two kinds of interactions can be responsible for the deviation from this latter relationship: magnetostatic and exchange interactions. However, different interpretations can be found in the literature concerning the sign of δJ [24,45,48-54]. In this study the working hypothesis of Ding et al [52], that positive values of δJ are indicative of predominant magnetostatic interactions whereas negative ones indicate the main role played by the exchange interactions in two-phase nanocomposite magnets, could be supported by analysing numerous experimental data. 3.3.3 Nucleation field In permanent magnets based on rare-earth transition-metal compounds, the value of the coercive field deviates considerably from the predictions of the conventional Stoner/ Wohlfarth theory. This discrepancy is normally ascribed as Brown’s paradox and attributed to microstructural effects. For an ideal microstructure, where nucleation of reverse 23
3.4 Development of exchange-coupled nanocrystalline magnets domains does not take place, coercivity equals the nucleation field, H no . Thus, the nucleation field can be defined, considering as initial state that of initial saturation remanence [31], as the reversal field required to make the domain wall invade the hard phase. In other words, an applied field H ≥ H no will lead to irreversible polarisation reversal. Reversible polarisation values, J rev , can be obtained from the recoil loops. This quantity is defined as the difference in polarisation obtained when traversing the recoil curve, starting from a point on the demagnetisation curve for a given field and terminating on the recoil curve at zero field. The irreversible polarisation is defined as J irr = [J r – J d r (H m )] / 2. According to the model of Kneller and Hawig [31], the maximum of the derivative dm irr / dH (where m irr = J irr / J r ) would correspond to the nucleation field, H no , for irreversible polarisation. This derivative will be termed for abbreviation irreversible susceptibility, χirr(H), (although it has unit of T -1 ) following the notation used by McCormick et al [55]. Non-simultaneous switching of the hard and the soft magnetic phases leads to differences between the coercivity and the nucleation field. 3.4 Development of exchange-coupled nanocrystalline magnets In the last decade a lot of studies have been focused on the development of twophase or multiphase magnetic materials. These materials present two clear advantages compared to common isotropic (i.e. non-textured) hard magnetic materials: a higher saturation polarisation and a lower rare-earth content which decreases the cost of the magnet. The presence of the soft magnetic phase decreases the coercive field but enhances the remanence with respect to the single hard magnetic phase. Thus, it is expected that, by optimising the contents of the two phases as well as the microstructure, improved values of the energy product can be achieved. Coehoorn et al [43] reported a considerably increased remanence of melt-spun permanent magnets of nominal composition containing a substantial fraction of Fe 3 B grains. The use of specific additives to improve the magnetic properties has been the aim of several studies. Keem and co-workers [38] observed substantial remanence enhancement in the stoichiometric Nd 2 Fe 14 B by adding Si, due to a more refined microstructure. 24
Page 1 and 2: Alberto Bollero Real Isotropic Nano
Page 3 and 4: Die vorliegende Dissertationsschrif
Page 5 and 6: when varying (i) the α-Fe content,
Page 7 and 8: liefert wichtige Informationen übe
Page 9 and 10: 6.1.2. Milled and melt-spun alloys
Page 11 and 12: µ 0 H no nucleation field [T] µ 0
Page 13 and 14: 1 Introduction J s = 0.5 can not be
Page 15 and 16: 2 Magnetism of R-T intermetallic co
Page 17 and 18: 2.2 Magnetic properties 2.2 Magneti
Page 19 and 20: 2.2 Magnetic properties classified
Page 21 and 22: 2.2 Magnetic properties sublattice
Page 23 and 24: 2.2 Magnetic properties where the m
Page 25 and 26: 2.2 Magnetic properties highly stru
Page 27 and 28: 3 The exchange-coupling mechanism A
Page 29 and 30: 3.1 Models enhancement to those obt
Page 31 and 32: 3.2 Wohlfarth’s relation and Henk
Page 33: 3.3 Magnetisation reversal processe
Page 37 and 38: 3.4 Development of exchange-coupled
Page 39 and 40: 4 Systems under investigation 4.1 N
Page 41 and 42: 4.2 NdCoB 4.2 NdCoB The tetragonal
Page 43 and 44: 4.3 PrFeB e 1 p 1 Fig. 4.4: Liquidu
Page 45 and 46: 5 Experimental details The differen
Page 47 and 48: 5.1 Nanocrystalline powder processi
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Page 55 and 56: 6.1 Thermal characterisation The te
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Page 69 and 70: 7.1 Characterisation of the base al
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Page 79 and 80: 8.1 Initial magnetisation processes
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8.3 Analysis of exchange-coupling u
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8.4 Summary An analysis of the init
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Fig. 9.1: Dependence of the lattice
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9.1 Reactive milling of a PrFeB all
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9.2 Reactive milling of Nd(Fe,Co)B
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9.3 Summary of J r = 0.91 T after a
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10 Conclusions and future work 10 C
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10 Conclusions and future work the
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10 Conclusions and future work spin
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10 Conclusions and future work (Mö
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REFERENCES [13] O. Gutfleisch, K. K
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REFERENCES [37] J.J. Croat, J.F. He
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REFERENCES [60] J. Bauer, M. Seeger
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REFERENCES [83] S. Hirosawa, Y. Mat
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REFERENCES [106] R.W. Lee, “Hot-p
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List of publications: Some parts of
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Acknowledgments The realisation of
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ALBERTO BOLLERO REAL

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