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Phase separation and microstructure controlled magnetic properties of rapidly quenched Nd60Fe30Al10
Materials Science and Engineering A 375–377 (2004) 1027–1031
Phase separation and microstructure controlled magnetic properties of rapidly quenched Nd60 Fe30 Al10 A. Bracchi a,∗ , K. Samwer a , P. Schaaf b , J.F. Löffler c , S. Schneider d a
I. Physikalisches Institut, Georg-August-Universität, D-37077 Göttingen, Germany II. Physikalisches Institut, Georg-August-Universität, D-37077 Göttingen, Germany III. Laboratory of Metal Physics and Technology, Department of Materials, ETH Zürich, CH-8092 Zürich, Switzerland d IV. Physikalisches Institut, Georg-August-Universität, D-37077 Göttingen, Germany b
c
Abstract The structure and magnetic properties of glassy Nd60 Fe30 Al10 splat-quenched samples have been investigated by small angle neutron scattering, Mössbauer spectroscopy, and vibrating sample magnetometry. The results of these investigations show the coexistence of two magnetic phases characterized by different ordering temperatures and indicate phase separation in the Nd60 Fe30 Al10 samples. The presence of chemical inhomogeneities in the amorphous sample is confirmed by small angle neutron scattering data, which exhibit power law behaviour with an exponent of −2.3 and indicate the formation of a mass fractal network. Decomposition during the cooling process is discussed as the key to explain the magnetic properties of the glassy Nd60 Fe30 Al10 splat-cooled samples by a domain wall pinning process within the two-phase microstructure. © 2003 Elsevier B.V. All rights reserved. Keywords: Metallic glasses; Phase separation; Mass fractal; Magnetic correlation length; Domain wall pinning; Random anisotropy model
1. Introduction During the past several years the ferromagnetic glassforming system Nd60 Fe30 Al10 has been investigated because of its exceptional hard magnetic properties [1]. It has been shown that the coercivity of the samples depends strongly on the cooling rate. Nd60 Fe30 Al10 as-cast rods exhibit a coercivity of about 280 kA/m at room temperature, while melt–spun ribbons of the same composition exhibit softer magnetic behaviour with Hc of only several kA/m [2]. According to the criterion proposed by Hernando and co-workers [3], this value is relatively high for an amorphous alloy. Therefore, efforts have been spent to study the relationship between structure and “hard” magnetic properties. Most of the technologically relevant magnetic materials are composed of two phases with different magnetic properties. The high value of the coercivity in these samples typically arises from impediments to domain wall motion, such as grain boundaries or other defects playing the role of pinning centres for the magnetization. In contrast, the origin of the high coercivity in amorphous alloys is still under investigation. ∗
Corresponding author. E-mail address: [email protected] (A. Bracchi).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.10.287
This paper presents results indicating that rapidly quenched Nd60 Fe30 Al10 samples show two ferromagnetic-toparamagnetic transitions with different Curie temperatures (Tc1 and Tc2 ). This is in accordance with results found by Sun et al., who show the existence of two amorphous magnetic phases in melt–spun Nd60-x Yx Fe30 Al10 (x = 0, 10 and 30) ribbons [4,5].
2. Experimental Nd60 Fe30 Al10 alloys were prepared by induction melting of the pure elements in a water-cooled silver boat in a Ti-gettered argon atmosphere. Small amounts of about 20 mg were subsequently melted in a high frequency coil and quenched into thin foils with a twin-piston splat quencher under Ar atmosphere. Samples with a thickness of about 30 m were obtained. The samples were characterized by X-ray diffraction in a Siemens D5000 diffractometer. Magnetic measurements were performed with a 5 T Oxford vibrating sample magnetometer (VSM) at temperatures from 4.2 to 650 K. Magnetic small angle neutron scattering (SANS) measurements were carried out at Paul Scherrer Institute, Villigen, Switzerland, using a neutron wavelength of λ = 6 Å and sample-detector
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distances of 1.8 and 8 m. The measurements were performed at room temperature placing the specimens between the pole pieces of an electromagnet. An homogeneous field of up to 1.5 T was applied parallel to the sample plane and perpendicular to the incoming neutron beam. Mössbauer spectroscopy was carried out at room temperature in transmission geometry, with a standard set-up with constant acceleration drive and a 57 Co/Rh source (200 MBq). The spectra were stored in a multiscaler with 1024 channels. Calibration was performed with ␣-Fe absorber and isomer shifts are given relative to ␣-Fe. The spectra were analysed by superimposing Lorentzian lines by a least squares fit routine.
3. Results and discussion Fig. 1 shows thermomagnetic curves of a zero-field-cooled (ZFC) and field-cooled (FC) Nd60 Fe30 Al10 splat, taken in a vibrating sample magnetometer in the temperature range from 4.2 to 650 K. Two ferromagnetic-to-paramagnetic transitions take place at about Tc1 = 50 K and Tc2 = 525 K, respectively, indicating the presence of two different magnetic phases. Taking into account that the magnetic ordering temperature Tc of a RE1−x Tx system (RE: rare-earth, T: transition metal) usually strongly depends on the concentration, x, of the transition metal [6], we can conclude that the two magnetic transitions indicate the presence of two phases with clearly different chemical compositions. Results of the 57 Fe Mössbauer spectroscopy taken at room temperature on the Nd60 Fe30 Al10 splat are shown in Fig. 2. The considerable broadening of the lines is typical for amorphous alloys. The experimental spectrum can be fitted well with a superposition of (super-)paramagnetic and ferromagnetic contributions. The fit indicates that 65(3)%
of the site population may be attributed to ferromagnetic sites and only 35(3)% to (super-)paramagnetic ones, as the spectrum was fitted by a broad sextet (IS = −0.11(2) mm/s, Bhf = 21.5(15) T) and a doublet (IS = −0.11(2) mm/s, QS = 0.56(2) mm/s). This result is in good agreement with the magnetic measurement indicating two magnetic phases and suggests that the phase with lower magnetic ordering temperature (Tc1 = 50 K) is Nd-rich, while the phase with higher (Tc = 525 K) is supposed to be Fe-rich. No diffraction peaks were revealed by wide angle X-ray diffraction analysis (not reported here). On the basis of these results, we used small angle neutron scattering (SANS) to investigate chemical and magnetic inhomogeneities in the sample. Measurements in zero magnetic field and in a maximum magnetic field of 1.5 T were performed to separate both nuclear and magnetic scattering which might arise from spatial variations of both nuclear and magnetic scattering length densities. For a quantitative analysis of the SANS data we followed a data evaluation procedure described in Ref. [7]. For unpolarized neutrons, the scattering cross section of a sample in an external magnetic field can be described by the sum of the nuclear and magnetic contributions arising from the scattering contrast between one phase and its surroundings:
dσ dΩ
H=1.5 T
= ( bmag )2 sin2 α · imag (Q, R) + ( bnuc )2 inuc (Q, R)
(1)
where imag and inuc are the structure functions of the phase generating the magnetic and compositional contrasts; bmag and bnuc are the magnetic and nuclear scattering lengths and α is the angle between the Q-vector of a single scattered neutron and the external magnetic field.
Fig. 1. Thermomagnetic measurements for zero-field-cooled (ZFC) and field-cooled (FC) Nd60 Fe30 Al10 rapid-quenched splat from 4.2 to 650 K. The Curie temperatures Tc1 and Tc2 are indicated by arrows.
A. Bracchi et al. / Materials Science and Engineering A 375–377 (2004) 1027–1031
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Fig. 2. 57 Fe Mössbauer spectrum of Nd60 Fe30 Al10 rapid-quenched splat taken at room temperature. (The dashed line is the sum of the (super-)paramagnetic and ferromagnetic contributions—solid lines—which result from the fitting procedure.)
According to Eq. (1), the nuclear cross-section can be estimated by taking into account only those neutrons which have scattering Q-vectors in the direction of the external field (i.e. sin2 α = 0) (in reality, for statistical reason, the so called “sector analysis” has been performed: Q-vectors forming an angle |α| < 15◦ with the external field were analysed). In Fig. 3 we report the absolute nuclear scattering cross-section I(Q) of the splat-cooled sample at 1.5 T following the previous criterion for the angular averaging. An angular average over the “sector” perpendicular to the external field (|α − 90◦ | < 15◦ ) would give the sum of the structural and magnetic radial scattering cross-sections
instead: dσ H=1.5 T = ( bmag )2 imag (Q, R) dΩ ⊥ + ( bnuc )2 inuc (Q, R)
(2)
In zero magnetic field, the magnetization of the ferromagnetic regions is no longer aligned (as indicated by the low ratio Mr /Ms ≈ 0.2), and the corresponding radial cross section can be described as sum of the terms in Eq. (1), now averaged over all possible directions, and the contribution of magnetically correlated regions:
Fig. 3. SANS data of a Nd60 Fe30 Al10 splat sample measured in an external magnetic field of 1.5 T. (For the angular averaging on the detector plane only data whose Q-vector forms an angle smaller than ±15◦ with the direction of the external field have been taken into account). The fit according to [7] (solid line). Inset: difference scattering curve deduced from the SANS data of Nd60 Fe30 Al10 splat sample at room temperature. The fit (solid line) according to [7,11].
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dσ H=0 dΩ 2 2 2 = ( bmag ) · imag (Q, R) + ( bnuc ) · inuc (Q, R) 3 2 + ( bmag )2 · icorr (Q, Rcorr ) 3
(3)
Subtracting the radial scattering at 1.5 T (Eq. (2)) from the radial scattering measured in zero external field (Eq. (3)), we can extract the radial cross section of magnetically correlated regions (denoted by “difference scattering curve” below) and evaluate the magnetic correlation distances. Fig. 3 (inset) shows the difference scattering curve for the splat-cooled sample at room temperature. According to Fig. 3, nuclear cross-section data exhibit a power-law scattering: I(Q) ∝ Q−α with α = 2.3. This value is less than the expected 4 and indicates that the nuclear scattering is due to a mass fractal network formed by the aggregation of small atom-clusters embedded in a residual matrix. The difference in the chemical composition of the fractal network and matrix is responsible for the measured nuclear scattering contrast. In order to determine the structural aspects of the fractal network we fitted the curve in Fig. 3 using the formalism developed by Freltoft et al. [8] and Teixiera [9] and extracted the three parameters describing a mass fractal object: the mass fractal dimension: df = 2.3; the cluster size: r = 0.5 nm; and the mean lateral dimension: 2R = 15 nm. The fractal dimension is smaller than the value of 2.5 already measured for the bulk sample [2] and expected by the diffusion limited aggregation model [10]. But the cooling process is an important parameter for the preparation of a metallic glass and may also control the aggregation mechanisms yielding a mass fractal structure. The cooling rate for a splat-cooled sample is by a factor 104 larger than for a bulk sample and may therefore explain the
lower value of the fractal dimension of the rapidly quenched sample. The magnetic correlation distances in the ferromagnetic phase were evaluated by fitting the difference scattering curve (inset Fig. 3) and assuming exponential decaying correlation with crossover length Rcorr , i.e. Icorr (Q, Rcorr ) ∝ (1 + (Rcorr · Q)2 )−2 [11]. The solid line in the graph represents the fit of the data and corresponds to a mean spatial magnetic correlation length Lex = 2Rcorr = 34 nm. According to the random anisotropy model (RAM) [12], the intrinsic coercivity of an amorphous system has its origin in the value of the effective anisotropy energy, which is given by averaging the local anisotropy energy in the exchange coupled volume (∼L3ex ). The local magnetic anisotropy of the amorphous ferromagnetic Fe-rich phase is strongly affected by the large magnetocrystalline anisotropy of Nd atoms. Hence, we assume that the intrinsic Nd anisotropy averaged over the correlation volume may explain the relatively high coercivity (7 kA/m) shown by Nd60 Fe30 Al10 splat at room temperature [2]. Beyond the complex morphology of the microstructure, the effect of the second paramagnetic phase on the magnetic properties of this alloy has to be taken into account; as well as the difference (MFC − MZFC ) (Fig. 1) and the strong increase of the coercivity at low temperatures (Fig. 4). The, so-called, bifurcation of the magnetization between MFC and MZFC (Fig. 1) is a well known feature of RE–T alloys which appears in samples cooled under different magnetic conditions [6]. The origin of this effect is a thermally activated magnetization process: when the coercive field is close to, or larger than, the applied field, magnetization of the sample by means of domain wall movement is hampered and leads to low M values. It is possible, however, for the wall to break the pinning and move itself in a field H < H0 (H0 = Hc at 0 K), if thermal energy is available and exceeds the activation energy necessary for the unpinning. At low
Fig. 4. Variation of the coercivity vs. temperature recorded for a Nd60 Fe30 Al10 splat sample (the solid line is a guide to the eye visualizing the general 1/2 trend). The inset reports the Hc vs. T2/3 and the relative fit (solid line) according to the domain wall pinning model in [13].
A. Bracchi et al. / Materials Science and Engineering A 375–377 (2004) 1027–1031
temperatures, this process determines the temperature dependency of the coercive field and demonstrates why (MFC − MZFC ) becomes smaller as the temperature increases. Fig. 4 shows the coercive field of the Nd60 Fe30 Al10 splat measured at different temperatures between 100 K and room temperature. We assume that the interplay of the two phases in the temperature range where one of them is paramagnetic might arise in a pinning process of the domain walls of the other phase. In order to determine the characteristic aspects of the pinning process, we take into account the formalism developed by Gaunt [13], which predicts a decrease of the coercivity as temperature increases as expressed by the equation: 2/3 Hc (T) 1/2 T (4) =1− H0 T0 where H0 is the coercivity at T = 0 K and T0 indicates the temperature below which the pinning process takes place. Eq. (4), describing the pinning process of “strong” low-dense pinning centres, is in good agreement with the experimental data (see inset Fig. 4) and the fit procedure gives a coercive field H0 of about 10 T and a temperature T0 of 280 K. The value of Hc at zero temperature represents the intrinsic coercivity of the alloy and the high value which we predicted is in good agreement with previous results on amorphous Nd40 Fe60 [14], Hc = 7.9 T.
4. Conclusion In summary, our results of the rapidly quenched Nd60 Fe30 Al10 confirm the coexistence of two magnetic phases in the X-ray amorphous sample. Phase separation in the undercooled liquid may be responsible for the formation of the complex microstructure which is characterized by mass fractal aggregates whose chemical composition differs from that of the embedding remnant matrix. The spontaneous magnetic correlation length has been found to be 34 nm. The RAM model and the large anisotropy of Nd atoms may be the key to explain the relatively hard mag-
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netic behaviour of the Nd60 Fe30 Al10 alloy shown at room temperature. At low temperatures, the thermal energy does not balance the energy which is necessary for unpinning processes. The variation of the coercive field is in agreement with the domain wall pinning model of the ferromagnetic phase at the boundaries of the paramagnetic phase.
Acknowledgements The authors gratefully thank W. Felsch, I. Physikalisches Institut, Göttingen for stimulating discussions and V. Aswal (PSI) for help during the SANS experiments. The authors also acknowledge financial support by the Deutsche Forschungsgemeinschaft (SFB 602-A5). The work was supported by the state of Niedersachsen via the Lichtenberg Program (A.B.).
References [1] A. Inoue, K.T. Zhang, W. Zhang, A. Takeuchi, Mater. Trans. JIM 37 (1996) 636. [2] S. Schneider, A. Bracchi, K. Samwer, M. Seibt, P. Thiyagarajan, Appl. Phys. Lett. 80 (2002) 1749. [3] J. Arcas, A. Hernando, J.M. Barandiarán, C. Prados, M. Vázquez, P. Mar´ın, A. Neuweiler, Phys. Rev. B 58 (1998) 5193. [4] Z.G. Sun, W. Löser, J. Eckert, K.-H. Müller, L. Schultz, Appl. Phys. Lett. 80 (2002) 772. [5] Z.G. Sun, W. Löser, J. Eckert, K.-H. Müller, L. Schultz, J. Appl. Phys. 91 (2002) 9267. [6] K.H.J. Buschow, A.M. van der Kraan, J. Magn. Magn. Mater. 22 (1981) 220. [7] J.F. Löffler, H.B. Braun, W. Wagner, G. Kostorz, W. Wiedenmann, Mater. Sci. Eng. A 304–306 (2001) 1050. [8] T. Freltoft, J.K. Kjems, S.K. Sinha, Phys. Rev. B 33 (1986) 269. [9] J. Teixiera, J. Appl. Crystallogr. 21 (1988) 781. [10] P. Meakin, Phys. Rev. A 27 (1983) 604. [11] P. Debye, H.R. Anderson, H. Brumberger, J. Appl. Phys 28 (1957) 679. [12] R. Alben, J.J. Becker, M.C. Chi, J. Appl. Phys. 49 (1978) 1653. [13] P. Gaunt, Phil. Mag. B 48 (1983) 261. [14] K. Moorjani, J.M.D. Coey, Magnetic Glasses, Elsevier, Amsterdam, 1984.
Phase separation and microstructure controlled magnetic properties of rapidly quenched Nd60 Fe30 Al10 A. Bracchi a,∗ , K. Samwer a , P. Schaaf b , J.F. Löffler c , S. Schneider d a
I. Physikalisches Institut, Georg-August-Universität, D-37077 Göttingen, Germany II. Physikalisches Institut, Georg-August-Universität, D-37077 Göttingen, Germany III. Laboratory of Metal Physics and Technology, Department of Materials, ETH Zürich, CH-8092 Zürich, Switzerland d IV. Physikalisches Institut, Georg-August-Universität, D-37077 Göttingen, Germany b
c
Abstract The structure and magnetic properties of glassy Nd60 Fe30 Al10 splat-quenched samples have been investigated by small angle neutron scattering, Mössbauer spectroscopy, and vibrating sample magnetometry. The results of these investigations show the coexistence of two magnetic phases characterized by different ordering temperatures and indicate phase separation in the Nd60 Fe30 Al10 samples. The presence of chemical inhomogeneities in the amorphous sample is confirmed by small angle neutron scattering data, which exhibit power law behaviour with an exponent of −2.3 and indicate the formation of a mass fractal network. Decomposition during the cooling process is discussed as the key to explain the magnetic properties of the glassy Nd60 Fe30 Al10 splat-cooled samples by a domain wall pinning process within the two-phase microstructure. © 2003 Elsevier B.V. All rights reserved. Keywords: Metallic glasses; Phase separation; Mass fractal; Magnetic correlation length; Domain wall pinning; Random anisotropy model
1. Introduction During the past several years the ferromagnetic glassforming system Nd60 Fe30 Al10 has been investigated because of its exceptional hard magnetic properties [1]. It has been shown that the coercivity of the samples depends strongly on the cooling rate. Nd60 Fe30 Al10 as-cast rods exhibit a coercivity of about 280 kA/m at room temperature, while melt–spun ribbons of the same composition exhibit softer magnetic behaviour with Hc of only several kA/m [2]. According to the criterion proposed by Hernando and co-workers [3], this value is relatively high for an amorphous alloy. Therefore, efforts have been spent to study the relationship between structure and “hard” magnetic properties. Most of the technologically relevant magnetic materials are composed of two phases with different magnetic properties. The high value of the coercivity in these samples typically arises from impediments to domain wall motion, such as grain boundaries or other defects playing the role of pinning centres for the magnetization. In contrast, the origin of the high coercivity in amorphous alloys is still under investigation. ∗
Corresponding author. E-mail address: [email protected] (A. Bracchi).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.10.287
This paper presents results indicating that rapidly quenched Nd60 Fe30 Al10 samples show two ferromagnetic-toparamagnetic transitions with different Curie temperatures (Tc1 and Tc2 ). This is in accordance with results found by Sun et al., who show the existence of two amorphous magnetic phases in melt–spun Nd60-x Yx Fe30 Al10 (x = 0, 10 and 30) ribbons [4,5].
2. Experimental Nd60 Fe30 Al10 alloys were prepared by induction melting of the pure elements in a water-cooled silver boat in a Ti-gettered argon atmosphere. Small amounts of about 20 mg were subsequently melted in a high frequency coil and quenched into thin foils with a twin-piston splat quencher under Ar atmosphere. Samples with a thickness of about 30 m were obtained. The samples were characterized by X-ray diffraction in a Siemens D5000 diffractometer. Magnetic measurements were performed with a 5 T Oxford vibrating sample magnetometer (VSM) at temperatures from 4.2 to 650 K. Magnetic small angle neutron scattering (SANS) measurements were carried out at Paul Scherrer Institute, Villigen, Switzerland, using a neutron wavelength of λ = 6 Å and sample-detector
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A. Bracchi et al. / Materials Science and Engineering A 375–377 (2004) 1027–1031
distances of 1.8 and 8 m. The measurements were performed at room temperature placing the specimens between the pole pieces of an electromagnet. An homogeneous field of up to 1.5 T was applied parallel to the sample plane and perpendicular to the incoming neutron beam. Mössbauer spectroscopy was carried out at room temperature in transmission geometry, with a standard set-up with constant acceleration drive and a 57 Co/Rh source (200 MBq). The spectra were stored in a multiscaler with 1024 channels. Calibration was performed with ␣-Fe absorber and isomer shifts are given relative to ␣-Fe. The spectra were analysed by superimposing Lorentzian lines by a least squares fit routine.
3. Results and discussion Fig. 1 shows thermomagnetic curves of a zero-field-cooled (ZFC) and field-cooled (FC) Nd60 Fe30 Al10 splat, taken in a vibrating sample magnetometer in the temperature range from 4.2 to 650 K. Two ferromagnetic-to-paramagnetic transitions take place at about Tc1 = 50 K and Tc2 = 525 K, respectively, indicating the presence of two different magnetic phases. Taking into account that the magnetic ordering temperature Tc of a RE1−x Tx system (RE: rare-earth, T: transition metal) usually strongly depends on the concentration, x, of the transition metal [6], we can conclude that the two magnetic transitions indicate the presence of two phases with clearly different chemical compositions. Results of the 57 Fe Mössbauer spectroscopy taken at room temperature on the Nd60 Fe30 Al10 splat are shown in Fig. 2. The considerable broadening of the lines is typical for amorphous alloys. The experimental spectrum can be fitted well with a superposition of (super-)paramagnetic and ferromagnetic contributions. The fit indicates that 65(3)%
of the site population may be attributed to ferromagnetic sites and only 35(3)% to (super-)paramagnetic ones, as the spectrum was fitted by a broad sextet (IS = −0.11(2) mm/s, Bhf = 21.5(15) T) and a doublet (IS = −0.11(2) mm/s, QS = 0.56(2) mm/s). This result is in good agreement with the magnetic measurement indicating two magnetic phases and suggests that the phase with lower magnetic ordering temperature (Tc1 = 50 K) is Nd-rich, while the phase with higher (Tc = 525 K) is supposed to be Fe-rich. No diffraction peaks were revealed by wide angle X-ray diffraction analysis (not reported here). On the basis of these results, we used small angle neutron scattering (SANS) to investigate chemical and magnetic inhomogeneities in the sample. Measurements in zero magnetic field and in a maximum magnetic field of 1.5 T were performed to separate both nuclear and magnetic scattering which might arise from spatial variations of both nuclear and magnetic scattering length densities. For a quantitative analysis of the SANS data we followed a data evaluation procedure described in Ref. [7]. For unpolarized neutrons, the scattering cross section of a sample in an external magnetic field can be described by the sum of the nuclear and magnetic contributions arising from the scattering contrast between one phase and its surroundings:
dσ dΩ
H=1.5 T
= ( bmag )2 sin2 α · imag (Q, R) + ( bnuc )2 inuc (Q, R)
(1)
where imag and inuc are the structure functions of the phase generating the magnetic and compositional contrasts; bmag and bnuc are the magnetic and nuclear scattering lengths and α is the angle between the Q-vector of a single scattered neutron and the external magnetic field.
Fig. 1. Thermomagnetic measurements for zero-field-cooled (ZFC) and field-cooled (FC) Nd60 Fe30 Al10 rapid-quenched splat from 4.2 to 650 K. The Curie temperatures Tc1 and Tc2 are indicated by arrows.
A. Bracchi et al. / Materials Science and Engineering A 375–377 (2004) 1027–1031
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Fig. 2. 57 Fe Mössbauer spectrum of Nd60 Fe30 Al10 rapid-quenched splat taken at room temperature. (The dashed line is the sum of the (super-)paramagnetic and ferromagnetic contributions—solid lines—which result from the fitting procedure.)
According to Eq. (1), the nuclear cross-section can be estimated by taking into account only those neutrons which have scattering Q-vectors in the direction of the external field (i.e. sin2 α = 0) (in reality, for statistical reason, the so called “sector analysis” has been performed: Q-vectors forming an angle |α| < 15◦ with the external field were analysed). In Fig. 3 we report the absolute nuclear scattering cross-section I(Q) of the splat-cooled sample at 1.5 T following the previous criterion for the angular averaging. An angular average over the “sector” perpendicular to the external field (|α − 90◦ | < 15◦ ) would give the sum of the structural and magnetic radial scattering cross-sections
instead: dσ H=1.5 T = ( bmag )2 imag (Q, R) dΩ ⊥ + ( bnuc )2 inuc (Q, R)
(2)
In zero magnetic field, the magnetization of the ferromagnetic regions is no longer aligned (as indicated by the low ratio Mr /Ms ≈ 0.2), and the corresponding radial cross section can be described as sum of the terms in Eq. (1), now averaged over all possible directions, and the contribution of magnetically correlated regions:
Fig. 3. SANS data of a Nd60 Fe30 Al10 splat sample measured in an external magnetic field of 1.5 T. (For the angular averaging on the detector plane only data whose Q-vector forms an angle smaller than ±15◦ with the direction of the external field have been taken into account). The fit according to [7] (solid line). Inset: difference scattering curve deduced from the SANS data of Nd60 Fe30 Al10 splat sample at room temperature. The fit (solid line) according to [7,11].
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dσ H=0 dΩ 2 2 2 = ( bmag ) · imag (Q, R) + ( bnuc ) · inuc (Q, R) 3 2 + ( bmag )2 · icorr (Q, Rcorr ) 3
(3)
Subtracting the radial scattering at 1.5 T (Eq. (2)) from the radial scattering measured in zero external field (Eq. (3)), we can extract the radial cross section of magnetically correlated regions (denoted by “difference scattering curve” below) and evaluate the magnetic correlation distances. Fig. 3 (inset) shows the difference scattering curve for the splat-cooled sample at room temperature. According to Fig. 3, nuclear cross-section data exhibit a power-law scattering: I(Q) ∝ Q−α with α = 2.3. This value is less than the expected 4 and indicates that the nuclear scattering is due to a mass fractal network formed by the aggregation of small atom-clusters embedded in a residual matrix. The difference in the chemical composition of the fractal network and matrix is responsible for the measured nuclear scattering contrast. In order to determine the structural aspects of the fractal network we fitted the curve in Fig. 3 using the formalism developed by Freltoft et al. [8] and Teixiera [9] and extracted the three parameters describing a mass fractal object: the mass fractal dimension: df = 2.3; the cluster size: r = 0.5 nm; and the mean lateral dimension: 2R = 15 nm. The fractal dimension is smaller than the value of 2.5 already measured for the bulk sample [2] and expected by the diffusion limited aggregation model [10]. But the cooling process is an important parameter for the preparation of a metallic glass and may also control the aggregation mechanisms yielding a mass fractal structure. The cooling rate for a splat-cooled sample is by a factor 104 larger than for a bulk sample and may therefore explain the
lower value of the fractal dimension of the rapidly quenched sample. The magnetic correlation distances in the ferromagnetic phase were evaluated by fitting the difference scattering curve (inset Fig. 3) and assuming exponential decaying correlation with crossover length Rcorr , i.e. Icorr (Q, Rcorr ) ∝ (1 + (Rcorr · Q)2 )−2 [11]. The solid line in the graph represents the fit of the data and corresponds to a mean spatial magnetic correlation length Lex = 2Rcorr = 34 nm. According to the random anisotropy model (RAM) [12], the intrinsic coercivity of an amorphous system has its origin in the value of the effective anisotropy energy, which is given by averaging the local anisotropy energy in the exchange coupled volume (∼L3ex ). The local magnetic anisotropy of the amorphous ferromagnetic Fe-rich phase is strongly affected by the large magnetocrystalline anisotropy of Nd atoms. Hence, we assume that the intrinsic Nd anisotropy averaged over the correlation volume may explain the relatively high coercivity (7 kA/m) shown by Nd60 Fe30 Al10 splat at room temperature [2]. Beyond the complex morphology of the microstructure, the effect of the second paramagnetic phase on the magnetic properties of this alloy has to be taken into account; as well as the difference (MFC − MZFC ) (Fig. 1) and the strong increase of the coercivity at low temperatures (Fig. 4). The, so-called, bifurcation of the magnetization between MFC and MZFC (Fig. 1) is a well known feature of RE–T alloys which appears in samples cooled under different magnetic conditions [6]. The origin of this effect is a thermally activated magnetization process: when the coercive field is close to, or larger than, the applied field, magnetization of the sample by means of domain wall movement is hampered and leads to low M values. It is possible, however, for the wall to break the pinning and move itself in a field H < H0 (H0 = Hc at 0 K), if thermal energy is available and exceeds the activation energy necessary for the unpinning. At low
Fig. 4. Variation of the coercivity vs. temperature recorded for a Nd60 Fe30 Al10 splat sample (the solid line is a guide to the eye visualizing the general 1/2 trend). The inset reports the Hc vs. T2/3 and the relative fit (solid line) according to the domain wall pinning model in [13].
A. Bracchi et al. / Materials Science and Engineering A 375–377 (2004) 1027–1031
temperatures, this process determines the temperature dependency of the coercive field and demonstrates why (MFC − MZFC ) becomes smaller as the temperature increases. Fig. 4 shows the coercive field of the Nd60 Fe30 Al10 splat measured at different temperatures between 100 K and room temperature. We assume that the interplay of the two phases in the temperature range where one of them is paramagnetic might arise in a pinning process of the domain walls of the other phase. In order to determine the characteristic aspects of the pinning process, we take into account the formalism developed by Gaunt [13], which predicts a decrease of the coercivity as temperature increases as expressed by the equation: 2/3 Hc (T) 1/2 T (4) =1− H0 T0 where H0 is the coercivity at T = 0 K and T0 indicates the temperature below which the pinning process takes place. Eq. (4), describing the pinning process of “strong” low-dense pinning centres, is in good agreement with the experimental data (see inset Fig. 4) and the fit procedure gives a coercive field H0 of about 10 T and a temperature T0 of 280 K. The value of Hc at zero temperature represents the intrinsic coercivity of the alloy and the high value which we predicted is in good agreement with previous results on amorphous Nd40 Fe60 [14], Hc = 7.9 T.
4. Conclusion In summary, our results of the rapidly quenched Nd60 Fe30 Al10 confirm the coexistence of two magnetic phases in the X-ray amorphous sample. Phase separation in the undercooled liquid may be responsible for the formation of the complex microstructure which is characterized by mass fractal aggregates whose chemical composition differs from that of the embedding remnant matrix. The spontaneous magnetic correlation length has been found to be 34 nm. The RAM model and the large anisotropy of Nd atoms may be the key to explain the relatively hard mag-
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netic behaviour of the Nd60 Fe30 Al10 alloy shown at room temperature. At low temperatures, the thermal energy does not balance the energy which is necessary for unpinning processes. The variation of the coercive field is in agreement with the domain wall pinning model of the ferromagnetic phase at the boundaries of the paramagnetic phase.
Acknowledgements The authors gratefully thank W. Felsch, I. Physikalisches Institut, Göttingen for stimulating discussions and V. Aswal (PSI) for help during the SANS experiments. The authors also acknowledge financial support by the Deutsche Forschungsgemeinschaft (SFB 602-A5). The work was supported by the state of Niedersachsen via the Lichtenberg Program (A.B.).
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