It was shown that magnetic reluctivity measured versus time after demagnetization for pre-annealed samples
of the Fe72Co10Nb6B12 amorphous alloy exhibits highly non-exponential behavior which can be described by
the coupling model. The relaxation intensity and the coupling parameter describing correlation effects in free
volume diffusion decrease with increasing 1 h annealing temperature indicating annealing out of free volume and
formation of iron clusters in amorphous matrix

Chełkowska, Grażyna

Chrobak, Artur

Haneczok, Grzegorz

Kubik, P.

Madej, Ł.

Acta Physica Polonica A

English

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Application of the coupling model to magnetic after effects in the Fe72Co10Nb6B12 amorphous alloy  Author: Artur Chrobak, Grażyna Chełkowska, Grzegorz Haneczok, P. Kubik, Ł. Madej  Citation style: Chrobak Artur, Chełkowska Grażyna, Haneczok Grzegorz, Kubik P., Madej Ł. (2009). Application of the coupling model to magnetic after effects in the Fe72Co10Nb6B12 amorphous alloy. "Acta Physica Polonica A" (Vol. 115, nr 1 (2009), s. 396-398).  Vol. 115 (2009) ACTA PHYSICA POLONICA A No. 1Proceedings of the European Conference “Physics of Magnetism” (PM’08), Poznan´ 2008Application of the Coupling Model to Magnetic AfterEffects in the Fe72Co10Nb6B12 Amorphous AlloyA. Chrobak, G. CheÃlkowskaInstitute of Physics, University of SilesiaUniwersytecka 4, 40-007 Katowice, PolandG. Haneczok, P. Kubik and ÃL. MadejInstitute of Materials Science, University of SilesiaBankowa 12, 40-007 Katowice, PolandIt was shown that magnetic reluctivity measured versus time after demagnetization for pre-annealed samplesof the Fe72Co10Nb6B12 amorphous alloy exhibits highly non-exponential behavior which can be described bythe coupling model. The relaxation intensity and the coupling parameter describing correlation effects in freevolume diffusion decrease with increasing 1 h annealing temperature indicating annealing out of free volume andformation of iron clusters in amorphous matrix.PACS numbers: 75.50.−y, 75.75.+a1. IntroductionIt is known that soft magnetic properties of amorphousalloys based on iron can be improved by applying a suit-able annealing at temperatures close to the crystalliza-tion temperature. After such annealing initial magneticpermeability can be of the order of 104 and coercive fieldeven below 1 A/m [1–6]. This effect is usually explainedby formation of α-Fe nanograins embedded into amor-phous matrix. The microstructure with differently ori-ented nanograins averages out magnetic anisotropy andgives the enhancement of magnetic permeability [1, 4]. Insome cases (e.g. [1, 5, 6]) the permeability enhancementeffect may be observed without formation of a nanocrys-talline phase. This was recognized in [5, 6] for differentamorphous alloys and the observed effect was attributedto annealing out of free volume and internal stresses lead-ing to formation of iron clusters with different magneticorder i.e. to the so-called relaxed amorphous phase [7–9].The aim of the paper is to study free volume diffusionin Fe72Co10Nb6B12 amorphous alloy in the context of thepermeability enhancement effect. Magnetic properties ofthis alloy were studied in [5] and it was found that per-meability determined at room temperature for samplesannealed for 1 h at temperatures Ta (ranging from 300 Kto 900 K) shows a maximum at Ta = 675 K (see Fig. 1in [5]). Moreover, it was also shown that the optimizedmicrostructure is free of α-Fe nanograins, so the exam-ined alloy is a suitable alloy for studying the influenceof structural relaxation on magnetic properties. On theone hand, the paper concentrates on diffusion in corre-lated system and, on the other hand, we intend to clarifythe mechanism of the permeability enhancement effectproposed in [5, 6].2. ExperimentalThe Fe72Co10Nb6B12 amorphous alloy examined inthis paper was fabricated by melt spinning in the formof strips with thickness and width of 25 µm and 1 cm,respectively. As quenched ribbons were annealed for1 h at temperatures selected basing on the results of [5]i.e. 300 K (as quench state), 500 K, 625 K, 675 K and700 K. These annealing as it was shown in [5] changessample microstructure from the as quenched state (amor-phous) to the fully relaxed amorphous state. For thepre-annealed samples (10 cm in length) magnetic suscep-tibility χ at field 0.5 A/m was measured versus time afterdemagnetization by making use of HP RLC 4284A meterworking at frequency about 1 kHz. Figure 1 shows nor-malized magnetic reluctivity r(t) (r = 1/χ) versus timeobtained for all examined samples. The normalizationwas carried out by subtracting r(0) and dividing by themaximum value of reluctivity for the as quenched state.It can be seen that with increasing annealing tempera-ture the curvature of the observed r(t) curves is quite dif-ferent indicating the influence of sample microstructure(progress in structural relaxation) on magnetic proper-ties.3. Coupling model, data analysis and discussionIn ferromagnetic materials any diffusing atom pos-sessing a magnetic moment interacts with magnetization(396)Application of the Coupling Model to Magnetic After Effects . . . 397Fig. 1. Normalized magnetic reluctivity versus time af-ter demagnetization determined at room temperaturefor the Fe72Co10Nb6B12 amorphous alloy preliminaryannealed at different temperatures.which modifies its diffusion walk. Application of an ex-ternal weak magnetic field changes energetic levels of dif-ferent sites and according to the Ne´el approach leads tomagnetic after effects [2, 10–13]. Macroscopically it isobserved as a time increase in magnetic reluctivity mea-sured after demagnetization. The most spectacular caseis the well known Snoek relaxation observed in alpha ironcontaining carbon atoms in solid solution form [2].In ferromagnetic amorphous materials diffusing objectconsists of atomic pairs of alloying additions in the vicin-ity of free volume as it was considered by Kronmu¨ller (seeFigs. 2–5 in [11]). An individual atomic jump requires acorrelated atomic displacement of the nearest neighborsso some correlation effects would play an important role[14, 15]. Let us notice that for a random walk the meandisplacement 〈x(t)〉 of a diffusing atom is zero but the〈x(t)2〉 is proportional to the diffusivity D and time t,so we have 〈x(t)2〉 ∝ Dt. In correlated systems one candefine the so-called diffusion exponent d by the relation√〈x2(t)〉d ∝ Dt , (1)which allows introducing the time dependent transitionrate Wαα′ (the frequency of jump from one site — let ussay α — to another one α′) by taking into account that√〈x2(t)〉dt∝ D and D ∝Wαα′ . (2)According to Eqs. (1) and (2) Wαα′ can be expressed asWαα′ =W0t−n, (3)where W0 is the unperturbed frequency of jump and n isthe coupling parameter defined by the relation n = 1− 2dand restricted to 0 ≤ n ≤ 1 since d ≥ 2. Let us noticethat for the random walk d = 2 and n = 0 which meansthat the transition rate is constant and the correspondingresponse function is proportional to exp(−t/τ), where τis the relaxation time depending on temperature via theArrhenius relation. In correlated systems the transitionrate is time dependent which leads to the response func-tion known as the universal one (i.e. ∝ exp(−(t/τ)1−n))[2, 14, 15], as it can be applied to many correlated sys-tems like polymers, dielectrics, metals etc. Finally, formagnetic reluctivity measured in this paper with the ini-tial condition r(0) = r0 the model function can be writtenasr(t) = I[1− exp(−(t/τ)1−n)] + at+ r0 , (4)where I is the intensity of the observed process and pa-rameters a and r0 correspond to the irreversible compo-nent of the measured magnetic after effects and can beestimated from a long time tail of the measured curves.Numerical analysis was carried out by applying Eq. (4)as the model function in the fitting procedure (for detailsee [13]). Parameters to be fitted are: I, τ , n plus aand r0. In all cases we have got a very good agreementbetween theory and experiment with n ranging from 0.75to 0.50. This means that the observed phenomenon ishighly non-exponential. An example of the fit quality ispresented in Fig. 2. It should be underlined that the rel-ative difference between theory and experiment does notexceed 0.05%. The results of the numerical analysis arepresented in Fig. 3 where the fitted parameters are plot-ted versus the 1 h annealing temperature Ta, so versus adegree of the structural relaxation progress.Fig. 2. Experimental data from Fig. 1 for the asquenched sample and the theoretical curve calculatedaccording to Eq. (4) (only every 10th point is plotted).Fig. 3. Results of numerical analysis of the data pre-sented in Fig. 1 carried out by making use of Eq. (4):(a) intensity I and coupling parameter n versus 1 h an-nealing temperature Ta, (b) relaxation time τ versus Ta.398 A. Chrobak et al.According to Fig. 3a the intensity I of the ob-served phenomenon decreases with increasing Ta indicat-ing annealing out of free volume (and internal stresses)and proving that after the optimization annealing ther-mal/time instabilities characteristic of the as quenchedstate practically disappear.Figure 3a shows also that the coupling parameter n de-creases with Ta but the curvature of this dependence isquite different. Initially in the range 300 K ≤ Ta ≤ 625 Kn decreases relatively slow (i.e. about 0.1 per 300 K) andits main drop is observed for Ta > 625 K (0.15 per 75 K)so just before the optimization annealing. This fact sug-gests that the decrease in the coupling parameter is corre-lated with the increase in magnetic permeability observedin [5] and is caused by a certain kind of short range or-dering cutting out the correlations. Such an order causesthat internal stresses and what follows magnetoelastic en-ergy are significantly reduced. Finally, one can concludethat the obtained results are consistent with the idea offormation of iron clusters in amorphous surroundings be-ing the final stage of structural relaxation just as it wasproposed in [5, 6].Figure 3b shows the relaxation time τ versus Ta. Itcan be seen that τ decreases with increasing Ta whichmeans that the progressing annealing out of free volumecauses a cut-out of the long time components of the fullspectrum of relaxation times.4. ConclusionsThe paper shows that magnetic after effect techniqueand the coupling model describing diffusion processes incorrelated systems are applicable to the examination ofstructural relaxation in amorphous ferromagnetic alloys.The main conclusions of the paper can be summarized asfollows: (i) magnetic reluctivity measured as a functionof time for samples of the Fe72Co10Nb6B12 amorphousalloy pre-annealed at temperatures 300 K ≤ Ta ≤ 700 K(with different progress in structural relaxation) showshighly non-exponential behavior which can be describedby the coupling model, (ii) the relaxation intensity andthe coupling parameter describing correlation effects infree volume diffusion decrease with increasing Ta indicat-ing annealing out of free volume and a short range order-ing which is consistent with the idea of formation of ironclusters in amorphous matrix, and (iii) the progress instructural relaxation causes a cut-out of the long timecomponents of the spectrum of relaxation times.References[1] G. 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Application of the coupling model to magnetic after effects in the Fe72Co10Nb6B12 amorphous alloy

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Application of the coupling model to magnetic after effects in the Fe72Co10Nb6B12 amorphous alloy

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