Magnetic induction heating of FeCr nanocrystalline alloys i n f o
Transcription
Magnetic induction heating of FeCr nanocrystalline alloys i n f o
Magnetic induction heating of FeCr nanocrystalline alloys a r t i c l e i n f o abstract Article history: Received 15 September 2011 Received in revised form 16 January 2012 Available online 31 January 2012 In this work the thermal effects of magnetic induction heating in (FeCr)73.5Si13.5Cu1B9Nb3 amorphous and nanocrystalline wires were analyzed. A single piece of wire was immersed in a glass capillary filled with water and subjected to an ac magnetic field (frequency, 320 kHz). The initial temperature rise enabled the determination of the effective Specific Absorption Rate (SAR). Maximum SAR values are achieved for those samples displaying high magnetic susceptibility, where the eddy current losses dominate the induction heating behavior. Moreover, the amorphous sample with Curie temperature around room temperature displays characteristic features of self-regulated hyperthermia. & 2012 Elsevier B.V. All rights reserved. Keywords: Amorphous alloy Nanocrystalline Magnetic susceptibility Induction heating Hyperthermia 1. Introduction High frequency (radio frequency, rf) induction heating represents a topic of growing interest during the last decade. Their main interest ranges within the biomedical applications in the design of new cancer therapies based on the fluid suspensions of ferromagnetic nanoparticles (magnetic hyperthermia) [1]. However, rf induction heating is a widely employed technique in different industrial applications ranging from the steel industry [2], household appliances (cooking) [3] or plastic industry [4]. Among these applications the ferromagnetic based composites (i.e. magnetic nanoparticles dispersed in polymer matrices) stand out, in the biomedical field (magnetic hyperthermia, cancer therapy) [5] and in the polymer industry (sealing, curing and repairing of polymers/epoxies) [6,7]. Magnetic induction heating is based on the heat generated as a consequence of the application of an alternating (ac) field to a magnetic material, both in bulk form (i.e. bars or needles) and nanoparticle systems. In bulk form, eddy-current losses dominate the rf dissipation behavior [8]. However, for magnetic nanoparticles in a viscous medium, the heat dissipation is mainly determined by the Ne´el and Brownian relaxations [9]. The use of ferromagnetic implants for magnetic hyperthermia, and in particular the necrosis of solid tumors, was recognized some decades ago as an adjutant cancer therapy in the treatment of solid tumors [8,10–12]. Due to their multifunctional capacities (MRI resonance imaging, targetable drug carriers), the main recent efforts in this field have been focused on the study and applications of magnetic nanoparticles [13]. However, there are some aspects that prevent their extensive application in clinical use, as toxicity or inhomogeneous distribution in tumors. In fact, the achievement of a homogeneous temperature distribution represents the main challenge regarding solid tumor treatments [14]. In this sense, ferromagnetic needles have been recently shown to display higher efficiency rates than iron oxide ferromagnetic nanoparticles [15]. Therefore, the use of ferromagnetic implants in inductive heating applications, as hyperthermia treatments, represents a renewed research topic in the biomedical field. Besides the spatial distribution, the temperature control and stability is an additional parameter to take into account in the design of optimum rf heating systems. Accordingly, self-regulated systems have been proposed, where the Curie point of the ferromagnetic component controls the maximum heating temperature [16–19]. The main aim of the work is to explore the rf self-heating features in ferromagnetic FeCrSiBCuNb amorphous and nanocrystalline wires. The results indicate that the eddy-current losses basically dominate the induction heating phenomena. Moreover, in these alloys the control of the Curie temperature through the Cr content of the amorphous phase [20] enables the design of selfregulated rf induction systems. 2. Experimental procedure Amorphous wires with nominal composition Fe73.5 xCrxSi13.5Cu1 B9Nb3 (x¼3, 7 and 10) were prepared by in-rotating-water quenching technique (diameter E130 mm). The devitrification process of the initial amorphous state was followed by Differential Scanning Calorimetry. The crystallization process takes place in two main ´mez-Polo et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 1897–1901 C. Go 1898 0.16 Glass capilar 10 0.14 S. Generator Water 8 0.12 L (μH) Wire C RF Power Amplifier L (μH/mm) LC 0.10 6 Fig. 1. Schematic diagram of the employed induction heating set-up. 0.08 steps at Tx1 and Tx2, correlated to the precipitation of a-FeSi and boride phases, respectively [21]. The increase of the Cr content of the alloy promotes a shift of the first crystallization process towards higher temperatures [22]. The nanocrystalline structure, obtained through isothermal annealings at annealing temperatures Ta ETx1, was confirmed through X-ray diffractometry in the annealed samples. Mean grain sizes around 10 nm were estimated in the nanocrystalline state through the Debye–Sherrer formula. Four samples were selected: two amorphous wires with x¼3 and 10, Cr3amorp and Cr10amorp, respectively; and two nanocrystalline wires with x¼7 and different crystalline fractions, Cr7nano(1) and Cr7nano(2) (Ta ¼818 K, annealing time, ta ¼90 and 210 min, respectively). With respect to the magnetic characterization, the temperature dependence of the self-inductance, L, was determined through a commercial LCR meter at 10 kHz and a ac excitation voltage of 1 V. An induction method was employed to determine at room temperature the ac hysteresis loops and the magnetic susceptibility, w (f¼100 Hz, amplitude magnetic field 95 A/m). The induction method consist of a long solenoid (1.2 (kA/m)/A) and two secondary coils (2000 turns) connected in series-opposition. In the case of the ac hysteresis loops the pick-up voltage was suitably integrated using a fluxmeter, while in the susceptibility measurements it was analyzed through a lock-in amplifier. The electrical resistivity, r, of the wires was determined through a four-probe technique. The heating effects on the wires were analyzed under the application of an ac magnetic field, Hac, with the help of a home-made hyperthermia set-up. A single piece of wire (length, l¼5 10 3 m, mass, mw ¼1.7 10 6 kg) was immersed in a glass capillary filled with water. The capillary was subjected to the ac magnetic field generated by a water refrigerated coil and connected to a RF power amplifier (see Fig. 1). The temperature increase (DT¼T(t) T0, T0 ¼291 K) was registered as a function of time (t), using a fiber optic thermometer under the action of Hac (frequency 320 kHz). The measurements were repeated 5 times in order to estimate the mean heating response of the samples. 3. Results and discussion Fig. 2a displays the temperature dependence of the selfinductance, L, for the wires in amorphous state. At this low frequency excitation (f ¼10 kHz), the skin effect can be disregarded and the electrical impedance can be expressed as Z ¼ R þ i2pfL ¼ Rdc þ ið/EZ S=IÞl, where Rdc is the electrical resistance of the wire, l the sample length, I the electrical current flowing through the sample and /EzSthe average electrical field originated by the circumferential magnetization process (/EzSp mf, circumferential magnetic permeability). Therefore, since L(T)pmf(T), its temperature dependence can be employed to determine magnetic transitions leading to sharp changes in mf(T) (i.e. the Curie temperature TC, [23] or the martensitic transformation in ferromagnetic shape memory alloys [24]). Fig. 2a shows that the Curie temperature can 4 0.06 300 375 450 525 T (K) 300 350 Fig. 2. Temperature dependence (T) of the self-inductance, L, for: (a) amorphous wires in as-cast state (—) x ¼3, (&) x¼ 7 and (K) x¼ 10; and (b) in nanocrystalline state (x¼ 7, Ta ¼818 K): (J) ta ¼ 90 min and (D) ta ¼ 210 min. be easily characterized in the soft magnetic amorphous wires by a sharp decrease in L around TC. As previously reported, the substitution of Fe by Cr in the initial amorphous state promotes a linear decrease in the Curie temperature, TC, of the alloy: TC (K) ¼630 K 30 x (K/%Cr). Thus, for x ¼10 the amorphous alloy displays a Curie point around room temperature. With respect to the nanocrystalline state, it is extensively reported the occurrence of a magnetic transition associated with the magnetic decoupling process of the ferromagnetic crystallites around the Curie temperature of the residual amorphous phase, TCa [24–26]. This magnetic transition leads to a sharp decrease in mf at temperatures around TCa and can be characterized by a parallel abrupt diminution in L. Fig. 2b shows the temperature dependence of L for the nanocrystalline wire with x ¼7 (annealing temperature, Ta ¼818 K) and two different crystalline fractions (annealing time, ta ¼90 and 210 min, Cr7nano(1) and Cr7nano(2), respectively). As expected, the nanocrystalization process leads to a significant decrease in TCa as a consequence of the enrichment in Cr of the residual amorphous phase. Thus, the Curie point of the residual amorphous phase can be suitable controlled through the annealing conditions. In particular, values of TCa around 300 K are achieved in the nanocrystalline wire (x¼7) for the highest annealing times (Cr7nano(2)). With respect to the induction heating characteristics of the wires, Fig. 3 shows the temperature rise, DT, (from T0 ¼291 K) versus time, t, under the action of the ac magnetic field (amplitude 4 kA/m). Maximum DT values are found for the amorphous wire with x ¼3 (Cr3amorp) and the nanocrystalline sample Cr7nano(1) (TCa Z350 K). For comparison, the heating curve of a Cu wire with similar mass and geometric characteristics is also displayed. The detected slight temperature decrease should be correlated to the effect of the coil refrigeration. Therefore, the observed heating effects in the FeCr wires should be interpreted as a direct consequence of the ferromagnetic nature of the samples. The obtained results indicate that the experimental set-up departures from an ideal adiabatic zero thermal losses calorimeter. Under the ideal adiabatic conditions, the achieved temperature, T, under the application of the ac magnetic field should linearly increase as a function of time, t [27]. However, the experimental data can be suitably fitted to an exponential law: DT ¼ TðtÞT 0 ¼ ABeCt ð1Þ This exponential law can be derived taking into account the modified heat equation considering the heat transfer ´mez-Polo et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 1897–1901 C. Go contribution [28]: dQ dT 1 ¼ mcP þ ðTT 0 Þ dt dt Rt ð2Þ with Q the thermal energy (heat), mcP ¼ mw cw þ mH2 O cH2 O (mi and ci: mass and specific heat for i¼w and H2O, wire and water, respectively). The second term in Eq. (2) represents the heat transfer with the environment, where Rt is the thermal resistance that in the case of radial heat transfer with cylindrical geometry is given by Rt ¼ Lnðr=r 0 Þ=2pLk (L: axial length, r and r0 radial coordinates at T and T0, respectively), being k the thermal conductivity and T0 the external or environment temperature [29]. This thermal resistance would comprise the heat transfer within the wire and the water bath. Thus, the total heat generated by the ferromagnetic wires can be expressed as that absorbed by the water and the transferred losses to the environment. If we considered T’ as the theoretical temperature achieved under ideal adiabatic conditions (zero losses) Eq. (2) can be rewritten as: dT 0 dT þ gðTT 0 Þ ¼ dt dt ð3Þ with g ¼ 1=Rt mcp . Under ideal adiabatic conditions the achieved temperature should linearly increase with t (dT0 /dt¼constant). Thus, the solution of Eq. (3) displays an exponential time dependence as that displayed in Eq. 1 with A¼B¼Tmax T0, being Tmax the maximum temperature achieved under the non adiabatic conditions (t-N) and the time constant C¼ g. Table 1 displays the fitting parameters obtained from the experimental curves of Fig. 3. As expected from the above discussion, the fitting parameters fulfill Affi B. Those samples with the highest Curie temperatures of the amorphous phase (Cr3amorp and Cr7nano(1)) display maximum Tmax T0 values. Moreover, since the wires display similar 8 Cr3amorp ΔT (K) 6 4 Cr7nano(1) Cr7nano(2) 1899 geometrical features and equivalent bath water mass is employed, the time constant g would come mainly determined by the thermal conductivity of the wires. In metallic systems there is a direct relationship between the thermal conductivity and the electrical resistivity (Wiedemann–Franz law) [30]. Table 1 shows the electrical resistivity, r, for the set of the analyzed wires. As expected, the lowest time constant g is found in the amorphous sample with the highest electrical resistivity. In order to further analyze the induction heating features of the samples, the equivalent Specific Absorption Rate (SAR) was estimated through the initial slope of the heating curves, ðdT=dtÞt-0 , according to the following expression: mw cw þ mH2 0 cH2 0 dT SAR ¼ ð4Þ dt t-0 mw with mw ¼1.7 10 6 kg, mH2 O ¼2 10 4 kg, cw ¼ 0.53 103 J kg 1 K 1 [31] and cH2 O ¼4.18 103 J kg 1 K 1. The initial heating rate,ðdT=dtÞt-0 , can be easily calculated through the derivation of Eq. (1): ðdT=dtÞt-0 ¼ ðT max T 0 Þg. Table 1 summarizes the obtained SAR values according Eq. 4 and the calculated ðdT=dtÞt-0 considering (Tmax–T0) ¼(AþB)/2. As expected from the analysis of the temperature heating curves (see Fig. 3), maximum SAR (15.2 103 W/kg) is found in the amorphous wire Cr3amorp with the highest Curie point. These SAR values are below the reported values in Fe-based nanoparticles [32–34]. The physical mechanisms associated to the induction heating can be classified in three main contributions: (i) eddy-current losses, (ii) magnetic hysteresis losses and (iii) relaxation losses (Ne´el and/or Brown rotations). In all the cases, the power dissipation (heat) should be interpreted as a consequence of the magnetization lag with respect to the applied magnetic field. In metallic (bulk) implants the eddy-current losses dominate the heating behavior, while the hysteresis and relaxation losses are the main contribution in the case of nanoparticle systems [35,36]. The energy loss associated to eddy-currents in a metallic medium is proportional to the integral of rj2 (r: electrical resistivity, j: current density) over the volume of the material. In particular, at high frequencies when the penetration of the applied ac field is incomplete the power loss, Pec, can be expressed as [37]: Pec aðmrf Þ1=2 Hac 2 2 Cr10amorp ð5Þ with m ¼ m0 (1þ w), the static (low frequency) magnetic permeability. However, in the case of hysteresis loss, the power loss is a function of the area of the hysteresis loops [38]: I Phys pf HdM ð6Þ Cu 0 0 200 400 t (s) 600 800 Finally, the power loss associated to the relaxation losses (Ne´el and/or Brown rotations) are usually expressed as a function of the imaginary component of the magnetic susceptibility w00 : Prel aw00 ðf Þf Hac 2 Fig. 3. Temperature rise, DT¼T(t) T0 (T0 ¼291 K), as a function of time, t, for the amorphous (x¼ 3, Cr3amorp and x ¼10, Cr10amorp) and nanocrystalline wires (Cr7nano(1): ta ¼ 90 min, Cr7nano(2): ta ¼210 min, x ¼7). For comparison the results in a Cu wire are also included. (Hac ¼ 4 kA/m). ð7Þ However, it has been recently shown that Eq. (7) is just a particular case of Eq. (6) under linear response theory (M linear with H) taking into account the Ne´el–Brown relaxation times [38]. Table 1 Fitting parameters of the exponential heating curves according to Eq. (1): A ¼ B¼ Tmax T0; C ¼ g. Electrical resistivity, r, Specific absorption rate (SAR) and magnetic susceptibility, w, for the analyzed wires. Sample A (K) B (K) C (s 1) q (O m) SAR (W/kg) v (a.u.) Cr3amorp (x ¼3 amorphous) Cr10amorp (x¼ 10 amorphous) Cr7nano(1) (x¼ 7 nanocrystal ta ¼ 90 min) Cr7nano(2) (x¼ 7 nanocrystal ta ¼ 210 min) 7.1 2.0 7.4 3.6 7.7 2.0 8.1 4.0 4.3 10 3 2.4 10 3 3.5 10 3 4.4 10 3 1.62 10 6 1.81 10 6 1.50 10 6 1.39 10 6 15.2 103 2.4 103 13.5 103 8.2 103 7695 3635 3812 934 ´mez-Polo et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 1897–1901 C. Go 1900 To discern the main contribution to the induction heating process, the ac hysteresis loops were determined as function of the exciting ac frequency, f. Fig. 4 shows the frequency dependence of the coercive field, HC, for the analyzed wires. As expected, the highest HC values are found in the nanocrystalline sample with lowest Curie temperature of the amorphous phase (Cr7nano(2), TCa o300 K). In this sample the nanocrystalline grains are partially decoupled as a consequence of the decrease in the exchange correlation length due to the paramagnetic state of the residual amorphous phase [26]. However, the nanocrystalline wire with TCa 4300 K (Cr7nano(1)) displays similar low coercive fields that the amorphous samples. In fact, nearly anhysteretic hysteresis loops are found in these soft magnetic samples (see inset of Fig. 4) in spite of their self-heating characteristics. Thus, hysteresis losses should be disregarded as the mean mechanism of the detected induction heating phenomena. On the other hand, assuming that the eddy-current losses dominate the power loss dissipation, SAR values should scale as (wr)1/2 (Eq. (5)). Fig. 5 shows such a relationship (SAR versus 2.0 1.0 1.5 M (a.u.) 0.5 0.0 HC (kA/m) -0.5 -1.0 1.0 -2 0 H (kA/m) 2 0.5 0.0 0 1 2 4 3 f (kHz) 5 Fig. 4. Coercive field, HC, versus frequency, f, for: (—) Cr3amorp, (K) Cr10amorp, (J) Cr7nano(1) and (D) Cr7nano(2). Inset: M–H hysteresis loops at 20 Hz: black—Cr3amorp, gray—Cr10amorp, blue—Cr7nano(1) and red—Cr7nano(2) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.). (wr)1/2; w low frequency values). A linear behavior is found for the samples with higher induction heating power (Cr3amorp and Cr7nano(1,2)), confirming the relevant role of the eddy-current losses in the induction heating process. It should be noted that the nanocrystalline wire with the higher crystalline fraction (Cr7nano(2)) displays a value of TCa, according to Fig. 2b, below T0. Then, its self-heating capacity at 291 K should be interpreted as a result of the dependence of the magnetic transition associated to the magnetic decoupling of the ferromagnetic crystallites on the amplitude of the applied magnetic field. Shifts of the effective transition temperature close to 75 K are detected in FeSiCuNbB nanocrystalline wires. Such an increase is interpreted in terms of magnetization process of the decoupled ferromagnetic grains [23,25]. In the present case, due to closeness of TCa to the initial measuring temperature (T0 ¼291 K), the application of Hac E4 kA/m would be able to magnetize the ferromagnetic grains and thus to shift the effective magnetic transition above TCa. However, the amorphous wire with TC E300 K (x ¼10) displays a significant lower heating capacity (see Fig. 3). In fact, as Fig. 5 shows, this sample departures from the general linear trend (SAR versus (wr)1/2). In this case, although the sample displays high w values (see Table 1), it does not show comparable selfheating rates. This contradictory behavior should be interpreted as a consequence of the features of the w–T curves in these amorphous systems. Firstly, the absence of any significant increase in TC with the applied magnetic field [23]. Secondly, the occurrence around TC of a sharp Hopkinson peak in w (T) that disappears after nanocrystallization [39]. Therefore, starting from TrTC, a slight increase in temperature would promote a sharp decrease in w that would drastically decrease the power losses in the sample. Finally, in order to check the self-regulated characteristics of the samples, the experimental set-up was modified in order to reduce the heat losses with the environment. Beside this, to enhance the heating capacity of the samples, the effective mass of the wires was increased and the measurements were taken under a higher magnetic field (Hac ¼29 kA/m). Fig. 6 shows the obtained heating curves (DT versus t) for both amorphous samples (mw,Cr3amorp ¼19.5 10 6 kg; mw,Cr10amorp ¼ 34 10 6 kg; mH2 O ¼0.15 10 3 kg). For the wire with higher Curie temperature, Cr3amorp, T sharply increases within the measuring temperature range. A similar behavior, that is, a continuous increase of T, is detected in the nanocrystalline wires. Conversely, the Cr10amorp wire shows an initial sharp temperature increase 60 2x104 50 Cr7nano(1) 1x104 30 20 Cr7nano(2) Cr10amorp 10 0 0.035 ΔT (K) SAR (W/kg) 40 Cr3amorp 0.070 0.105 (χρ)1/2 (a.u.) Fig. 5. SAR values of the analyzed wires as a function of the relative values of (wr)1/2 (w: magnetic susceptibility; r: electrical resistivity). 0 50 100 150 200 t (s) 250 300 350 400 Fig. 6. Temperature rise, DT¼ T(t) T0 (T0 ¼ 298 K), as a function of time, t, for the amorphous (J) Cr3amorp and (K) Cr10amorp (Hac ¼ 29 kA/m). ´mez-Polo et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 1897–1901 C. Go followed by clear stabilization around TC. This result clearly proves the self-regulated characteristics of this amorphous system, where the Cr content can be suitably tailored to control the maximum temperature distribution. Finally, the estimated SAR values are in this case 3 105 and 0.3 105 W/kg for Cr3amorp and Cr10amorp, respectively. These values come closer to the reported values in Fe-based nanoparticles [30–34] and metallic iron nanostructures [40]. 4. Conclusions In conclusion, the magnetic induction heating effects in amorphous and Fe73.5 xCrxSi13.5Cu1B9Nb3 (x¼3, 7 and 10) nanocrystalline wires have been analyzed. The application of a ac magnetic field give rises to power losses that are able to increase the mean temperature of a capillary water bath where the samples are immersed. The Specific Absorption Rate (SAR) was determined through the initial temperature rise of the system (wire plus water bath). Maximum SAR values are achieved for those samples displaying high magnetic susceptibility and Curie temperature above the initial measuring point (300 K). The analysis of the magnetic susceptibility indicates that the eddy current losses mainly dominate the heating phenomena. In order to explore the self-heating induction characteristics, samples (amorphous and nanocrystalline) with Curie temperature (amorphous phase) around 300 K were analyzed. The different heating response of the amorphous and nanocrystalline samples is analyzed in terms of the main features of the susceptibility–temperature curves. Selfregulated features are found in the amorphous alloy at temperatures around the corresponding Curie point. Acknowledgments The wires were kindly provided by Prof. M. Va´zquez (Instituto de Ciencia de Materiales de Madrid, CSIC). The work has been performed within the framework of the project MET-NANO EFA17/08 (POCTEFA). References ¨ [1] S. Laurent, S. Dutz, U.O. Hafeli, M. Ahmoudi, Advances in Colloid and Interface Science 166 (2011) 8–23. [2] K. Fukutani, K. Umetsu, T. Itou, T. Isobe, T. Kitahara, R. Shimada, IEEE Transactions on Industry Applications 130 (2010) 1131–1138. [3] T. Waeckerle´, H. Fraisse´, B. Boulogne, S.L. Spire, Journal of Magnetism and Magnetic Materials 304 (2006) e844–6846. [4] B.J. Knauf, D.P. Webb, C. Liu, P.P. Conway, Microfluidics and Nanofluidics 9 (2010) 243–252. [5] D.-H. Kim, H.-N. Kim, K.-M. Kim, Y.-K. Lee, Journal of Biomedical Materials Research Part A 88 (2009) 1–11. [6] C.C. Corten, M.W. Urbam, Advanced Materials 21 (2009) 5011–5015. [7] K.J. Miller, K.N. Collier, H.B. Soll-Morris, R. Swaminathan, M.E. McHenry, Journal of Applied Physics 105 (2009) 07E714. 1901 [8] P.R. Stauffer, T.C. Cetas, R.C. Jones, IEEE Transactions on Bio-medical Engineering 31 (1984) 235–251. ¨ [9] R. Hergt, S. Dutz, R. Muller, M. Zeisberger, Journal of Physics: Condensed Matter 18 (2006) S2919–S2934. [10] P.R. Stauffer, T.C. Cetas, A.M. Flectcher, D.W. DeYoung, M.E. DeWhirst, J.R. Oleson, R.B. Roemer, IEEE Transactions on Bio-medical Engineering 31 (1984) 76–89. [11] H. Matsuki, K. Murakami, IEEE Transactions on Magnetics 21 (1985) 1927–1929. [12] H. Matsuki, T. Satoh, K. Murakami, T. Hoshino, T. Yanada, S. Kikuchi, IEEE Transactions on Magnetics 26 (1990) 1551–1553. [13] A.J. Cole, V.C. Yang, A.E. David, Trends in Biotechnology 29 (2011) 323–332. [14] V. Zablotskii, O. Lunov, C. Go´mez-Polo, Journal of Nanoscience and Nanotechnology 10 (2010) 690–695. [15] R. Zuchini, H.-W. Tsai, C.-Y. Chen, C.-H. Huang, S.-C. Huang, G.-B. Lee, C.-F. Huang, X.-Z. Lin, European Journal of Surgical Oncology 37 (2011) 604–610. [16] T. Yanada, H. Matsuki, M. Takahashi, T. Satoh, S. Minakawa, S. Kikuchi, K. Murakami, IEEE Transactions on Magnetics 27 (1991) 5390–5392. [17] T. Shimizu, M. Matsui., Science and Technology of Advanced Materials 4 (2003) 469–473. [18] K.L. McNemy, Y. Kim, D.E. Laughlin, M.E. McHenry, Journal of Applied Physics 107 (2010) 09A312. [19] K.J. Miller, A. Colletti, P.J. Papi, M.E. McHenry, Journal of Applied Physics 107 (2010) 09A313. [20] C. Go´mez-Polo, J.I. Pe´rez-Landaza´bal, V. Recarte, IEEE Transactions on Magnetics 39 (2003) 3019–3024. [21] C. Go´mez-Polo, Y. Li, J.I. Pe´rez-Landaza´bal, V. Recarte, M. Va´zquez, Sensors & Actuators A 1–3 (2003) 230–233. [22] V. Franco, C.F. Conde, A. Conde, B. Varga, A. Lovas, Journal of Magnetism and Magnetic Materials 215–216 (2000) 404–406. [23] C. Go´mez-Polo, J.I. Pe´rez-Landaza´bal, V. Recarte, M. Va´zquez, A. Hernando, Physical Review B 70 (2004) 094412. [24] J.I. Pe´rez-Landazabal, C. Go´mez-Polo, V. Recarte, C. Seguı´, E. Cesari, P. Ochin, Journal of Magnetism and Magnetic Materials 290–291 (2005) 826–828. [25] C. Go´mez-Polo, Journal of Magnetism and Magnetic Materials 320 (2008) 1984–1988. [26] A. Hernando, P. Marı´n, M. Va´zquez, J.M. Barandiara´n, G. Herzer, Physical Review B 58 (1998) 366–370. [27] E. Natividad, M. Castro, A. Mediano, Applied Physics Letters 92 (2008) 093116. [28] A. Clalkidou, K. Simeonidis, M. Angelakeris, T. Samaras, C. Martinez-Boubeta, L.l. Balcells, K. Papazisis, C. Dendrinou-Samara, O. Kalogirou, Journal of Magnetism and Magnetic Materials 323 (2011) 775–780. [29] A. Faghari, Y. Zhang, J. Howell, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, 2010., p. 212. [30] C. Kittel, Introduction to Solid State Physics, John Wiley & Sons, New York, 1996., p. 166. [31] E. Vogt, International Journal of Rapid Solidification 3 (1987) 131–146. [32] M. Ma, Y. Wu, J. Zhou, Y. Sun, Y. Zhang, N. Gu, Journal of Magnetism and Magnetic Materials 268 (2004) 33–39. [33] M. Suto, Y. Hirota, H. Mamiya, A. Fujita, R. Kasuya, K. Tohji, B. Jeyadevan, Journal of Magnetism and Magnetic Materials 321 (2009) 1493–1496. [34] T. Yuan, D.A. Borca Tasciuc, Journal of Magnetism and Magnetic Materials 323 (2011) 2463–2469. ¨ [35] J. Jordan, P. Wust, H. Fahling, W. John, A. Hinz, R. Felix, International Journal of Hyperthermia 1 (1993) 51–68. ¨ [36] R. Hergt, S. Dutz, M. Roder, Journal of Physics: Condensed Matter 20 (2008) 385214. [37] R.B. Bozorth, Ferromagnetism, IEEE Press, New York, 1993., pp. 779. [38] J. Carrey, B. Mehdaoui, M. Respaud, Journal of Applied Physics 109 (2011) 083921. [39] Q.Z. Zhi, B.S. Dong, W.Z. Chen, K.Y. He, Materials Science and Engineering A 448 (2007) 249. [40] B. Mehdaoui, A. Meffre, L.-M. Lacroix, J. Carrey, S. Lachaize, M. Gougeon, M. Respaud, B. Chaudret, Journal of Magnetism and Magnetic Materials 322 (2010) L49–L52.