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Temperature dependence of magnetic properties of a Co-based alloy in amorphous and nanostructured phase
Journal of Magnetism and Magnetic Materials 195 (1999) 583}587
Temperature dependence of magnetic properties of a Co-based alloy in amorphous and nanostructured phase G. Bordin, G. Buttino, A. Cecchetti*, M. Poppi Ist. Nazionale Fisica Della Materia, Department of Physics, University of Ferrata, Via Paradiso 12, 44100 Ferrara, Italy Received 14 October 1998; received in revised form 19 January 1999
Abstract The magnetic properties of a Co-based amorphous alloy (Metglas 2714A) are compared with those of the corresponding nanostructured alloy in the temperature range 30 K to the Curie temperature. A minimum appears in the permeability versus temperature curve well below the Hopkinson peak for the amorphous alloy. This minimum is ascribed to a form of induced anisotropy due to structural instabilities. In contrast, the alloy containing the nanostructured phase, having excellent soft magnetic properties, shows a maximum below the Hopkinson peak which is interpreted as a combination of the variations of the anisotropy and the saturation magnetization with temperature. The anisotropy "eld distribution is also evaluated in the low-temperature range for both the amorphous and nanostructured phase of the alloy. The most probable anisotropy "eld for the nanostructured sample is ten times lower than that of the amorphous sample. 1999 Elsevier Science B.V. All rights reserved. PACS: 75.50.Kj; 75.60.Nt Keywords: Amorphous alloys; Nanocrystallization
1. Introduction The excellent soft magnetic properties of some Co-based amorphous alloys may be improved by suitable thermal treatments below the conventional crystallization temperature. Generally, these treatments give rise to a stress relief and, for particular compositions of the alloy, to the formation of
* Corresponding author. Tel.: #39-0532-781811; fax: #390532-781810. E-mail address: [email protected] (A. Cecchetti)
a nanostructured phase embedded in a residual amorphous matrix such as occurs for example, in the commercial alloy Metglas 2714A (manufactured by Allied Chem. Corp., USA) or in the alloy Vitrovac 6025 (manufactured by Vacuumschmelze, Germany) [1}6]. The structural instability of several alloys in the amorphous and nanocrystalline phases also leads to anomalies in the dependence of the magnetic properties on temperature [7}10]. In this paper we compare the evolution of the magnetic properties of the nanostructured alloy 2714A with that of the corresponding amorphous alloy in the temperature range from 30 K to the Curie temperature.
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 2 2 6 - 7
584
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 583}587
2. Experimental results and discussion The nominal composition of the 2714A alloy is Co Fe Ni B Si . The saturation magnetization is 0.55 T and saturation magnetostriction less than 10\. The alloy used here was produced in the form of a ribbon 2.5 cm wide and 20 lm thick. Most of the magnetic measurements were performed on toroidal specimens, mean diameter 2.8 cm, made by winding strips about 30 cm long around an axis parallel to the ribbon width. The best improvement of the soft magnetic properties is obtained by an isothermal treatment of 31 min at a temperature of 743 K, that is below the nominal crystallization temperature ¹ "823 K. This treatment is parti cularly suited to the formation of nanocrystallites of about 2 nm in size embedded in a residual ferromagnetic amorphous matrix [5]. The prevailingly nanocrystalline phase is constituted of Co (HCP) and some Co compounds (Co B, Co B) [2]. The random distribution of the magnetization
orientations in these crystallites and their dimensions below the exchange correlation length make the average crystalline anisotropy very low favoring softening of the magnetic properties [5,11]. The magnetic softening is evident when comparing the hysteresis loop of the amorphous sample with that of the nanostructured sample (Fig. 1a and Fig. 1c) or by comparing the corresponding initial permeabilities (Fig. 2). The initial permeability has been measured by an AC "eld of amplitude h 0.05 A/m at a frequency of 1 kHz. Under these conditions only reversible magnetization processes are involved and the eddy currents are negligible, then the imaginary component of the permeability may be neglected. For the measurements at low temperatures the samples are placed in a cryostat, cooled by liquid helium, where a minimum temperature of 30 K is reached. For the measurements from room temperature to the Curie temperature the samples are placed in a furnace. In both
Fig. 1. Quasi-static hysteresis loops for the alloy 2714A measured at room temperature in the: (a) as-received amorphous sample, (b) amorphous sample after cooling from the Curie temperature, (c) sample containing the nanostructured phase. (d) The loop refers to the sample containing the nanostructured phase at ¹"35 K.
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 583}587
585
Fig. 2. Initial permeability as a function of the temperature for the as-received amorphous sample (curve a) and for the sample containing the nanostructured phase (curve b).
Fig. 3. Initial permeability versus temperature in the amorphous sample: (a) for the "rst run of increasing temperature, (b) for the successive run of decreasing temperature after attaining the Curie point, (c) for the second run of increasing temperature.
cases the sample temperature was detected by a thermocouple in direct contact with the sample. Fig. 2 shows the dependence of the initial permeability upon the temperature for the amorphous and the nanostructured sample (the thermal rate is about 5 K/min). A minimum of permeability appears at 426 K in the amorphous sample well below the Hopkinson peak. On the contrary, the nanostructured sample shows a maximum before the Hopkinson peak at a temperature around 370 K. The abrupt decrease of permeability after the Hopkinson peak (Fig. 2) makes possible a good evaluation of the Curie temperature. Thus, for the amorphous and nanostructured sample we have found ¹ "495 and 504 K, respectively. These ! values coincide with those measured by a di!erential scanning calorimeter [12]. The minimum of permeability for the amorphous sample can be attributed to the formation of a form of induced anisotropy due to atom migration activated at that temperature. If the amorphous sample is cooled to room temperature (Fig. 3 curve b) immediately after reaching Curie temperature (Fig. 3 curve a), the permeability versus ¹ curve, for decreasing ¹, shows a more pronounced Hopkinson peak and remains largely above the "rst curve determined for increasing temperature. Furthermore, any trace of the minimum at 426 K
disappears. The increase of permeability, after attaining the Curie temperature, is a consequence of the internal stress relief and the anisotropy reduction. Subsequent successive thermal runs between room temperature and Curie temperature do not modify the behavior of the permeability (Fig. 3 curve c). Also the hysteresis loop in the amorphous sample changes its shape after the "rst thermal treatment up to the Curie temperature (Fig. 1b). The squareness decreases and the approach to saturation becomes slower. These e!ects are ascribed to the change in the anisotropy direction from the longitudinal to the transverse direction, as shown in previous papers [13,14]. The maximum in the permeability below the Hopkinson peak for the nanostructured sample is considered to arise as a combination of two opposite e!ects: the increase of permeability associated with the local anisotropy reduction and the general deterioration of the magnetic properties with increasing temperature. A combined process of domain wall displacements and magnetization rotations [15] may also exist and be added to these e!ects. The dependence of the coercivity on temperature does not show any related anomalies for either the amorphous or the nanostructured sample (Fig. 4). The more rapid decrease of the coercivity for the
586
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 583}587 Table 1 Anisotropy constants and anisotropy "elds for the amorphous and nanostructured alloy
Fig. 4. Coercivity as a function of the temperature for: (a) the amorphous sample, (b) the sample containing the nanostructured phase.
nanostructured sample occurs however in the range of temperature where the permeability shows its maximum according to the previous model [11]. The mean anisotropy constant and the corresponding anisotropy "eld may be estimated roughly, for the various cases analyzed here, by the well-known simple relationships [5,11]: 1k2"I/2k k
(1)
and H "1k2/2I .
(2)
In Table 1 values of 1k2 and H are reported corresponding to various experimental temperatures for both the amorphous and the nanostructured samples. The low values of the anisotropy constants and anisotropy "elds in the sample containing the nanostructured phase are due to the reduction of internal stresses present in the amorphous phase and to the small size of the crystallites which, being less than the exchange correlation length, give a greatly reduced contribution to the e!ective anisotropy according to the random anisotropy model [11]. The presence of an appreciable anisotropy direction parallel to the ribbon axis in the as-received
¹ (K)
1k2 (J/m)
H (A/m)
H
Amorphous 30 150 250 300
77 64 52 41
62 55 46 37
63 61 55 37
Nanostructured 30 300
4.2 2.8
3.4 2.5
5.2 4.1
(A/m)
amorphous sample and its dependence on temperature may be established and analyzed by calculating the anisotropy "eld distribution through the relationship proposed by Barandiaran et al. [16]: P(H )"!H dm/dH,
(3)
where m is the reduced magnetization and the second derivative is performed on the hysteresis curve between saturation and remanence, perpendicularly to the easy direction [5,15]. This calculation is here made for square strips of amorphous ribbon cut from the bulk material so that the hysteresis loop can be monitored perpendicularly to the easy direction (in plane) and then corrected by the demagnetizing "eld [5]. Fig. 5 shows the anisotropy "eld distribution P(H ) detected in the range 30}300 K where the intensity of the anisotropy is appreciable. It is interesting to observe that at room temperature the most probable anisotropy "eld H , i.e. the "eld at the peak of P(H ), is around 37 A/m and this value agrees well with that deduced from the experimental value of the permeability employing Eqs. (1) and (2) (Table 1). Also for the other temperatures the most probable anisotropy "elds approach the "elds obtained from the permeability (Table 1). It must be noted that for low temperatures the P(H ) curves show long tails which indicate the strengthening of the anisotropies inside the sample. For the nanostructured sample the anisotropy "elds deduced from the anisotropy "eld distribution
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 583}587
587
anisotropy "eld, deducible from this distribution, agrees well with the mean anisotropy "eld deduced from the measurements of initial permeability.
Acknowledgements This work was supported by the Italian Ministero dell'Universita` e della Ricerca Scienti"ca e Tecnologica.
References Fig. 5. Anisotropy "eld distribution in the amorphous sample for various temperatures.
are about ten times lower than those deduced in the amorphous state (Table 1).
3. Conclusions We have performed a comparison between the behavior of the initial permeability and other magnetic properties for a Co-based amorphous alloy and the corresponding alloy containing a nanostructured phase over the temperature range 30 K to the Curie temperature. The nanostructured sample, obtained by suitable thermal treatments of the amorphous alloy, shows an initial permeability ten times higher than that of the amorphous state and an e!ective anisotropy ten times lower than that of the amorphous state. The evolution of the permeability with the temperature is correlated with the variations of the local anisotropies. The anisotropy "eld distribution has been evaluated for various temperatures and the most probable
[1] P. Quintana, E. Amano, R. Valenzuela, J.T.S. Irvine, J. Appl. Phys. 75 (1994) 6940. [2] I. Betancourt, M. JimeH nez, S. Aburto, V. Marquina, R. GoH mez, M.L. Marquina, R. Ridaura, M. Miki, R. Valenzuela, J. Magn. Magn. Mater. 140}144 (1995) 459. [3] J.L. Porteseil, O. Geo!roy, J. Magn. Magn. Mater. 140}144 (1995) 1855. [4] J. Swierczek, J. Zbroszczyk, S. Szymura, B. Wyslocki, J. Magn. Magn. Mater. 160 (1996) 295. [5] G. Buttino, A. Cecchetti, M. Poppi, J. Magn. Magn. Mater. 172 (1997) 147. [6] G. Bordin, G. Buttino, A. Cecchetti, M. Poppi, J. Phys. D 30 (1997) 2163. [7] K. Hisatake, T. Miyazaki, M. Takahashi, K. Maeda, T. Hattori, I. Matsubara, Phys. Stat. Sol. (a) 93 (1986) 605. [8] D. Drobac, J. Magn. Magn. Mater. 183 (1998) 71. [9] V. Franco, C.F. Conde, A. Conde, J. Magn. Magn. Mater. 185 (1998) 353. [10] L.R. Varga, J. Phys. IV France 8 (1998) Pr2-55. [11] G. Herzer, Phys. Scripta 49 (1993) 307. [12] G. Bordin, G. Buttino, D. Candolfo, A. Cecchetti, M. Poppi, F. Ronconi, J. Phys. IV France 8 (1998) Pr2-91. [13] G. Bordin, G. Buttino, A. Cecchetti, M. Poppi, IEEE Trans. Magn. 30 (1994) 486. [14] G. Bordin, G. Buttino, A. Cecchetti, M. Cecchetti, M. Poppi, J. Magn. Magn. Mater. 153 (1996) 285. [15] J. Castro, H.J. Blythe, J. Phys: Condens. Matter 8 (1996) 851. [16] J.M. Barandiaran, M. VaH zquez, A. Hernando, J. Gonzales, G. Rivero, IEEE Trans. Magn. 25 (1989) 3330.
Temperature dependence of magnetic properties of a Co-based alloy in amorphous and nanostructured phase G. Bordin, G. Buttino, A. Cecchetti*, M. Poppi Ist. Nazionale Fisica Della Materia, Department of Physics, University of Ferrata, Via Paradiso 12, 44100 Ferrara, Italy Received 14 October 1998; received in revised form 19 January 1999
Abstract The magnetic properties of a Co-based amorphous alloy (Metglas 2714A) are compared with those of the corresponding nanostructured alloy in the temperature range 30 K to the Curie temperature. A minimum appears in the permeability versus temperature curve well below the Hopkinson peak for the amorphous alloy. This minimum is ascribed to a form of induced anisotropy due to structural instabilities. In contrast, the alloy containing the nanostructured phase, having excellent soft magnetic properties, shows a maximum below the Hopkinson peak which is interpreted as a combination of the variations of the anisotropy and the saturation magnetization with temperature. The anisotropy "eld distribution is also evaluated in the low-temperature range for both the amorphous and nanostructured phase of the alloy. The most probable anisotropy "eld for the nanostructured sample is ten times lower than that of the amorphous sample. 1999 Elsevier Science B.V. All rights reserved. PACS: 75.50.Kj; 75.60.Nt Keywords: Amorphous alloys; Nanocrystallization
1. Introduction The excellent soft magnetic properties of some Co-based amorphous alloys may be improved by suitable thermal treatments below the conventional crystallization temperature. Generally, these treatments give rise to a stress relief and, for particular compositions of the alloy, to the formation of
* Corresponding author. Tel.: #39-0532-781811; fax: #390532-781810. E-mail address: [email protected] (A. Cecchetti)
a nanostructured phase embedded in a residual amorphous matrix such as occurs for example, in the commercial alloy Metglas 2714A (manufactured by Allied Chem. Corp., USA) or in the alloy Vitrovac 6025 (manufactured by Vacuumschmelze, Germany) [1}6]. The structural instability of several alloys in the amorphous and nanocrystalline phases also leads to anomalies in the dependence of the magnetic properties on temperature [7}10]. In this paper we compare the evolution of the magnetic properties of the nanostructured alloy 2714A with that of the corresponding amorphous alloy in the temperature range from 30 K to the Curie temperature.
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 2 2 6 - 7
584
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 583}587
2. Experimental results and discussion The nominal composition of the 2714A alloy is Co Fe Ni B Si . The saturation magnetization is 0.55 T and saturation magnetostriction less than 10\. The alloy used here was produced in the form of a ribbon 2.5 cm wide and 20 lm thick. Most of the magnetic measurements were performed on toroidal specimens, mean diameter 2.8 cm, made by winding strips about 30 cm long around an axis parallel to the ribbon width. The best improvement of the soft magnetic properties is obtained by an isothermal treatment of 31 min at a temperature of 743 K, that is below the nominal crystallization temperature ¹ "823 K. This treatment is parti cularly suited to the formation of nanocrystallites of about 2 nm in size embedded in a residual ferromagnetic amorphous matrix [5]. The prevailingly nanocrystalline phase is constituted of Co (HCP) and some Co compounds (Co B, Co B) [2]. The random distribution of the magnetization
orientations in these crystallites and their dimensions below the exchange correlation length make the average crystalline anisotropy very low favoring softening of the magnetic properties [5,11]. The magnetic softening is evident when comparing the hysteresis loop of the amorphous sample with that of the nanostructured sample (Fig. 1a and Fig. 1c) or by comparing the corresponding initial permeabilities (Fig. 2). The initial permeability has been measured by an AC "eld of amplitude h 0.05 A/m at a frequency of 1 kHz. Under these conditions only reversible magnetization processes are involved and the eddy currents are negligible, then the imaginary component of the permeability may be neglected. For the measurements at low temperatures the samples are placed in a cryostat, cooled by liquid helium, where a minimum temperature of 30 K is reached. For the measurements from room temperature to the Curie temperature the samples are placed in a furnace. In both
Fig. 1. Quasi-static hysteresis loops for the alloy 2714A measured at room temperature in the: (a) as-received amorphous sample, (b) amorphous sample after cooling from the Curie temperature, (c) sample containing the nanostructured phase. (d) The loop refers to the sample containing the nanostructured phase at ¹"35 K.
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 583}587
585
Fig. 2. Initial permeability as a function of the temperature for the as-received amorphous sample (curve a) and for the sample containing the nanostructured phase (curve b).
Fig. 3. Initial permeability versus temperature in the amorphous sample: (a) for the "rst run of increasing temperature, (b) for the successive run of decreasing temperature after attaining the Curie point, (c) for the second run of increasing temperature.
cases the sample temperature was detected by a thermocouple in direct contact with the sample. Fig. 2 shows the dependence of the initial permeability upon the temperature for the amorphous and the nanostructured sample (the thermal rate is about 5 K/min). A minimum of permeability appears at 426 K in the amorphous sample well below the Hopkinson peak. On the contrary, the nanostructured sample shows a maximum before the Hopkinson peak at a temperature around 370 K. The abrupt decrease of permeability after the Hopkinson peak (Fig. 2) makes possible a good evaluation of the Curie temperature. Thus, for the amorphous and nanostructured sample we have found ¹ "495 and 504 K, respectively. These ! values coincide with those measured by a di!erential scanning calorimeter [12]. The minimum of permeability for the amorphous sample can be attributed to the formation of a form of induced anisotropy due to atom migration activated at that temperature. If the amorphous sample is cooled to room temperature (Fig. 3 curve b) immediately after reaching Curie temperature (Fig. 3 curve a), the permeability versus ¹ curve, for decreasing ¹, shows a more pronounced Hopkinson peak and remains largely above the "rst curve determined for increasing temperature. Furthermore, any trace of the minimum at 426 K
disappears. The increase of permeability, after attaining the Curie temperature, is a consequence of the internal stress relief and the anisotropy reduction. Subsequent successive thermal runs between room temperature and Curie temperature do not modify the behavior of the permeability (Fig. 3 curve c). Also the hysteresis loop in the amorphous sample changes its shape after the "rst thermal treatment up to the Curie temperature (Fig. 1b). The squareness decreases and the approach to saturation becomes slower. These e!ects are ascribed to the change in the anisotropy direction from the longitudinal to the transverse direction, as shown in previous papers [13,14]. The maximum in the permeability below the Hopkinson peak for the nanostructured sample is considered to arise as a combination of two opposite e!ects: the increase of permeability associated with the local anisotropy reduction and the general deterioration of the magnetic properties with increasing temperature. A combined process of domain wall displacements and magnetization rotations [15] may also exist and be added to these e!ects. The dependence of the coercivity on temperature does not show any related anomalies for either the amorphous or the nanostructured sample (Fig. 4). The more rapid decrease of the coercivity for the
586
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 583}587 Table 1 Anisotropy constants and anisotropy "elds for the amorphous and nanostructured alloy
Fig. 4. Coercivity as a function of the temperature for: (a) the amorphous sample, (b) the sample containing the nanostructured phase.
nanostructured sample occurs however in the range of temperature where the permeability shows its maximum according to the previous model [11]. The mean anisotropy constant and the corresponding anisotropy "eld may be estimated roughly, for the various cases analyzed here, by the well-known simple relationships [5,11]: 1k2"I/2k k
(1)
and H "1k2/2I .
(2)
In Table 1 values of 1k2 and H are reported corresponding to various experimental temperatures for both the amorphous and the nanostructured samples. The low values of the anisotropy constants and anisotropy "elds in the sample containing the nanostructured phase are due to the reduction of internal stresses present in the amorphous phase and to the small size of the crystallites which, being less than the exchange correlation length, give a greatly reduced contribution to the e!ective anisotropy according to the random anisotropy model [11]. The presence of an appreciable anisotropy direction parallel to the ribbon axis in the as-received
¹ (K)
1k2 (J/m)
H (A/m)
H
Amorphous 30 150 250 300
77 64 52 41
62 55 46 37
63 61 55 37
Nanostructured 30 300
4.2 2.8
3.4 2.5
5.2 4.1
(A/m)
amorphous sample and its dependence on temperature may be established and analyzed by calculating the anisotropy "eld distribution through the relationship proposed by Barandiaran et al. [16]: P(H )"!H dm/dH,
(3)
where m is the reduced magnetization and the second derivative is performed on the hysteresis curve between saturation and remanence, perpendicularly to the easy direction [5,15]. This calculation is here made for square strips of amorphous ribbon cut from the bulk material so that the hysteresis loop can be monitored perpendicularly to the easy direction (in plane) and then corrected by the demagnetizing "eld [5]. Fig. 5 shows the anisotropy "eld distribution P(H ) detected in the range 30}300 K where the intensity of the anisotropy is appreciable. It is interesting to observe that at room temperature the most probable anisotropy "eld H , i.e. the "eld at the peak of P(H ), is around 37 A/m and this value agrees well with that deduced from the experimental value of the permeability employing Eqs. (1) and (2) (Table 1). Also for the other temperatures the most probable anisotropy "elds approach the "elds obtained from the permeability (Table 1). It must be noted that for low temperatures the P(H ) curves show long tails which indicate the strengthening of the anisotropies inside the sample. For the nanostructured sample the anisotropy "elds deduced from the anisotropy "eld distribution
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 583}587
587
anisotropy "eld, deducible from this distribution, agrees well with the mean anisotropy "eld deduced from the measurements of initial permeability.
Acknowledgements This work was supported by the Italian Ministero dell'Universita` e della Ricerca Scienti"ca e Tecnologica.
References Fig. 5. Anisotropy "eld distribution in the amorphous sample for various temperatures.
are about ten times lower than those deduced in the amorphous state (Table 1).
3. Conclusions We have performed a comparison between the behavior of the initial permeability and other magnetic properties for a Co-based amorphous alloy and the corresponding alloy containing a nanostructured phase over the temperature range 30 K to the Curie temperature. The nanostructured sample, obtained by suitable thermal treatments of the amorphous alloy, shows an initial permeability ten times higher than that of the amorphous state and an e!ective anisotropy ten times lower than that of the amorphous state. The evolution of the permeability with the temperature is correlated with the variations of the local anisotropies. The anisotropy "eld distribution has been evaluated for various temperatures and the most probable
[1] P. Quintana, E. Amano, R. Valenzuela, J.T.S. Irvine, J. Appl. Phys. 75 (1994) 6940. [2] I. Betancourt, M. JimeH nez, S. Aburto, V. Marquina, R. GoH mez, M.L. Marquina, R. Ridaura, M. Miki, R. Valenzuela, J. Magn. Magn. Mater. 140}144 (1995) 459. [3] J.L. Porteseil, O. Geo!roy, J. Magn. Magn. Mater. 140}144 (1995) 1855. [4] J. Swierczek, J. Zbroszczyk, S. Szymura, B. Wyslocki, J. Magn. Magn. Mater. 160 (1996) 295. [5] G. Buttino, A. Cecchetti, M. Poppi, J. Magn. Magn. Mater. 172 (1997) 147. [6] G. Bordin, G. Buttino, A. Cecchetti, M. Poppi, J. Phys. D 30 (1997) 2163. [7] K. Hisatake, T. Miyazaki, M. Takahashi, K. Maeda, T. Hattori, I. Matsubara, Phys. Stat. Sol. (a) 93 (1986) 605. [8] D. Drobac, J. Magn. Magn. Mater. 183 (1998) 71. [9] V. Franco, C.F. Conde, A. Conde, J. Magn. Magn. Mater. 185 (1998) 353. [10] L.R. Varga, J. Phys. IV France 8 (1998) Pr2-55. [11] G. Herzer, Phys. Scripta 49 (1993) 307. [12] G. Bordin, G. Buttino, D. Candolfo, A. Cecchetti, M. Poppi, F. Ronconi, J. Phys. IV France 8 (1998) Pr2-91. [13] G. Bordin, G. Buttino, A. Cecchetti, M. Poppi, IEEE Trans. Magn. 30 (1994) 486. [14] G. Bordin, G. Buttino, A. Cecchetti, M. Cecchetti, M. Poppi, J. Magn. Magn. Mater. 153 (1996) 285. [15] J. Castro, H.J. Blythe, J. Phys: Condens. Matter 8 (1996) 851. [16] J.M. Barandiaran, M. VaH zquez, A. Hernando, J. Gonzales, G. Rivero, IEEE Trans. Magn. 25 (1989) 3330.