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Stress-induced magnetic anisotropy in nanocrystalline alloys
Journal of Magnetism and Magnetic Materials 254–255 (2003) 477–479
Stress-induced magnetic anisotropy in nanocrystalline alloys L.K. Vargaa,*, Zs. Gercsib, Gy. Kova! csb, A. Ka! kaya, F. Mazaleyratc a
KFKI Research Institute for Solid State Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary b ! University, P.O. Box 32, H-1518 Budapest, Hungary Department of General Physics, Eotv . os . Lorand c LESiR-Ecole Normale Superieure de Cachan, 61, Av. du Pres. Wilson, 94235 Cachan Cedex, France
Abstract Stress-annealing experiments were extended to both nanocrystalline alloy families, Finemet and Nanoperm (Hitperm), and, for comparison, to amorphous Fe62Nb8B30 alloy. For both Finemet and bulk amorphous, stressannealing results in a strong induced transversal anisotropy (flattening of hysteresis loop) but yields longitudinal induced anisotropy (square hysteresis loop) in Nanoperm and Hitperm. These results are interpreted in terms of backstress theory. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Nanocrystalline materials; Anisotropy—stress induced; Magnetostriction; Anisotropy—hyperfine fields
For power electronic applications special tailoring of the hysteresis loop characteristics is necessary, which can be accomplished by field and stress annealing. In general, the transversally induced anisotropy is preferred, i.e. F-type loop, which having excellent highfrequency characteristics, makes possible the application in fly back converters and smoothing chokes where storing of magnetic energy is necessary. For amorphous alloys, it was found that the easy axis could be either parallel or perpendicular to the tensile stress-annealing axis [1], depending on the sign of the magnetostriction and the heat treatment. For nanocrystalline Finemet alloy, easy axis perpendicular to the tensile stress is found and the transversally induced anisotropy (Ku B þ 8000 J/m3) [2,3] is two orders of magnitude higher than the one induced by transverse field annealing (Ku B10250 J/m3) [4]. For the time being, two concurrent explanations exist for stress-induced anisotropy: the tensile back-stress theory proposed by Herzer [5] and Ne! el’s model of atomic pair ordering adapted by Hofmann and Kronmuller . [2]. In order to check these two different theories, nanomaterials with different intrinsic properties were prepared.
*Corresponding author. Fax: +13922220. E-mail address: [email protected] (L.K. Varga).
The stress annealing was carried out under protecting atmosphere in a vertical-tube furnace by applying a weight at the free, cold bottom end of the ribbon. Quasistatic magnetization curves (0.01 Hz typical) were obtained using an optical galvanometer as a preamplifier before the integrator and digitized as a set of 3500 points using a 14-bit converter. Following Barandiaran [6], the distribution of the perpendicular magnetic anisotropy was obtained from the second derivative of the experimental magnetization curve as PðHÞ ¼ Hðd2 m=dH 2 Þ: Smoothing has been carried out taking one average point for each neighbouring 5 points and the first and second derivatives were further smoothed by means of 10-point averaging. Figs. 1 and 2 show the hysteresis loops and the corresponding anisotropy distributions obtained for the nanocrystalline Finemet and for the bulk amorphous Fe62Nb8B30 alloys, respectively. The distribution is sharp for the reference sample (s ¼ 0) and widens and shifts to higher HK values with the increased applied stress during annealing. The transversally induced anisotropy, Ku > 0; can be calculated in two ways: (i) as the area between the magnetization curves with and without applied stress, (ii) from the mean value of the anisotropy distribution HK ¼ 2Ku =Js : The constant slope DKu =Ds is about 8.6 ppm for nanocrystalline Finemet and 2 ppm for bulk amorphous alloy. Typical
0304-8853/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 8 7 0 - 3
L.K. Varga et al. / Journal of Magnetism and Magnetic Materials 254–255 (2003) 477–479
478
direction, i.e. the intensity I2=5 belonging to different sextets are of the same value. As shown in Table 1, I2=5 was found to be 3 for as-cast amorphous state indicating a preferred orientation parallel to the ribbon plane. With increasing induced anisotropy, however, this value steadily decreases, indicating the rotation of magnetization out of plane as it is forced by the distributed induced anisotropy field. It is worth mentioning that the true I2;5 intensities can be determined on the demagnetized samples only. For comparison, we have represented in Table 1 also the reduced half height w=HK ; of the anisotropy distributions fitted with a Gaussian function. To facilitate the comparison, the results were normalized as ðw=HK Þ ¼ 3 for the reference sample. Although both methods need heavy digital processing, the reduced width of anisotropy distribution strikingly . correlates the Mossbauer results. This confirms that the widening of the anisotropy distribution indicates the deviation of spontaneous magnetization from the transversal direction. Figs. 3a and b show the effect of stress annealing on two varieties of Nanoperm and FeCo-based Hitperm. For all these alloys Z-loops have been obtained after stress annealing, i.e. the induced anisotropy is longitudinal (Ku o0). The negative Ku of Nanoperm can be explained neither by back-stress nor by pair ordering (the crystallites being composed of Fe only). In order to explain the different behaviours of the Finemet, Nanoperm and Hitperm type nanocrystalline alloys, induced stress hypothesis was adopted. The induced magneto-elastic anisotropy for the two-phase system is
values of Ku in usual transition metal–metalloid type amorphous alloys are smaller by one order of magnitude [1] similar to the precursor amorphous state of Finemet. In order to check if this deviation may be outside the ribbon’s plane, the intensities I2=5 of the second and fifth . Mossbauer lines were investigated. In derivation of this value from the experimental hyperfine field distribution, it was assumed that all the Fe moments, regardless of the number of their Si neighbours, point in the same
1.0
Fe73.5Si13.5Nb3B9Cu1 Annealed 550˚C, 1 h σ = 0, 20, 41, 62, 82, 102 MPa
0.5
50 40 30 20 10 3 2
=
σ
σ
M Pa
M Pa
10 2
82
σ
-1.0
=
M Pa 41
=
σ
=
62
M Pa
M Pa 0 =
20
σ σ
=
-0.5
M Pa
0.0
P(H)
Magnetic polarization, J (T)
1.5
1 -1.5 -2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
0 2500
Magnetic field, H (Am-1)
Fig. 1. Flat hysteresis loops of nanocrystalline Finemet as a function of applied stress during annealing. Bottom right box shows the corresponding distributions of the anisotropy fields.
Fe62Nb8 B30 Annealed 500 C, 1 h
Ku ¼ 32ðxlc sc þ ð1 xÞla sa Þ;
˚
0.5
0.0
4
-0.5
2
-1.0 -1.5
-1.0
-0.5
0.0
0.5
1.0
ð1Þ
where sc and sa denotes the stresses located in the volume fraction of nanograins and amorphous phase, respectively. In the case of Finemet, one can estimate from XRD the crystal fraction (B66%) and composition of nanograins (Fe80Si20) corresponding to lc ¼ 8 106 ; the composition of the remaining amorphous phase can be approximated as Fe63Nb9Si1B27 very close to the present bulk amorphous sample for which la ¼ þ10 106 was measured by means of SAMR. As shown in Ref. [7], the creeping rate is large during heating when the sample is still amorphous and strongly reduces when the crystallization begins because FeSi crystals do not
σ= 0, 125, 172 MPa
P(H)
Magnetic polarization, J (T)
1.0
0 1.5
-1
Magnetic field, H (kAm )
Fig. 2. Flat hysteresis loops of amorphous Fe62Nb8B30 alloy as a function of applied stress during annealing and corresponding distributions of the anisotropy fields (inset).
Table 1 I2=5 values obtained for Finemet after stress-annealing at 5501C/1 h State
As cast
s¼0
s ¼ 20:5 MPa
s ¼ 61 MPa
s ¼ 124 MPa
I2;5 ðw=HK Þ
3
2.88 3
2.82 3.1
2.21 2.24
1.704 1.85
L.K. Varga et al. / Journal of Magnetism and Magnetic Materials 254–255 (2003) 477–479 2
Fe86Zr7B6Cu1
J (T)
1
0 MPa 275 MPa
0 0
Ta = 600 C ta = 1 h
-1 -2 -150
-100
-50
(a)
0
50
100
150
H (A / m) 2
Fe84.5 Zr2Nb4B8.5Cu1
J (T)
1
0 MPa 680 MPa
0 Ta = 6000C ta = 1 h
-1 -2 -150
-100
-50
(b)
0
50
100
150
H (A / m) 2
J (T)
1
0 MPa 220 MPa 0
Ta = 600 C ta = 1 h
-1 -2 -150
(c)
þ65 106 Þ that regardless the value of la ; Ku is negative. By opposition, the hardness of pure iron is small (290 MPa) and probably creeps during annealing. Indeed, the creep in Nanoperm was found to be twice that of Finemet at the same temperature and stress [8]. It comes out that the remaining stress in Fe crystals can be compressive and again Ku is negative (Z-loop). In conclusion, the tensile back-stress model proposed by Herzer in order to explain stress-induced anisotropy is fully applicable for Finemet and Hitperm, whose crystallites do not creep due to the low dislocation mobility as indicated by the large hardness. In the Nanoperm, however, the crystallites creep yielding a residual compressive stress. The unique large transverse anisotropy found in Finemet results from a combination of the sign of the magnetostriction coefficients and stresses, adding the contributions of the two phases. This work was supported by NATO SfP 97-1930 and Hungarian OTKA-T 034 666 Grants. L.K. Varga thanks the ENS de Cachan for a 1-month hospitality as invited professor.
Fe44Co44Zr7B4Cu1
0
479
-100
-50
0
50
100
150
H (A / m)
Fig. 3. Square hysteresis loops of Nanoperm and Hitperm nanocrystalline alloys: (a) Fe86Zr7B6Cu1, (b) Fe84.5Zr2Nb4B8.5Cu1 and (c) (Fe50Co50)88Zr7B4Cu1 obtained after stress annealing.
creep due to their hardness (HV ¼ 1300 MPa for Fe87Si13). As a result, the crystals are still under tension (sc > 0) after removing the load while the amorphous is under compression (sa o0) and following Eq. (1) Ku is positive. The same situation is with Hitperm due to the hardness of Fe50Co50 (HV ¼ 1180 MPa), the remaining amorphous phase being more or less Fe31Co31Zr24B14. Although this composition cannot be melt-spun due to the high Zr content, lc is so strongly positive ðlS ¼
References [1] O.V. Nielsen, L.K. Hansen, A. Hernando, V. Madurga, J. Magn. Magn. Mater. 36 (1983) 73. [2] B. Hofmann, H. Kronmuller, J. Magn. Magn. Mater. 152 (1996) 91. [3] F. Alves, R. Barrue, M. Delage, J.B. Demoulins, N. Lecaude, J.C. Perron, Mater. Sci. Forum 307 (1999) 89. [4] A. Lovas, L.F. Kiss, B. Varga, P. Kamasa, I. Balogh, I. Bakonyi, J. Phys. IV France 8 (1998) 291. [5] G. Herzer, IEEE Trans. Magn. 30 (1994) 4800. [6] J.M. Barrandiaran, M. Vazquez, A. Hernando, J. Gonzalez, G. Rivero, IEEE Trans. Magn. 25 (1989) 3330. [7] F. Mazaleyrat, J.F. Rialland, J. Phys. IV France 8 (1998) 159. [8] F. Alves, A. Benchabi, R. Barru!e, J.C. Faugi"eres, J.F. Rialland, Eur. Phys. J. Appl. Phys. 15 (2001) 167.
Stress-induced magnetic anisotropy in nanocrystalline alloys L.K. Vargaa,*, Zs. Gercsib, Gy. Kova! csb, A. Ka! kaya, F. Mazaleyratc a
KFKI Research Institute for Solid State Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary b ! University, P.O. Box 32, H-1518 Budapest, Hungary Department of General Physics, Eotv . os . Lorand c LESiR-Ecole Normale Superieure de Cachan, 61, Av. du Pres. Wilson, 94235 Cachan Cedex, France
Abstract Stress-annealing experiments were extended to both nanocrystalline alloy families, Finemet and Nanoperm (Hitperm), and, for comparison, to amorphous Fe62Nb8B30 alloy. For both Finemet and bulk amorphous, stressannealing results in a strong induced transversal anisotropy (flattening of hysteresis loop) but yields longitudinal induced anisotropy (square hysteresis loop) in Nanoperm and Hitperm. These results are interpreted in terms of backstress theory. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Nanocrystalline materials; Anisotropy—stress induced; Magnetostriction; Anisotropy—hyperfine fields
For power electronic applications special tailoring of the hysteresis loop characteristics is necessary, which can be accomplished by field and stress annealing. In general, the transversally induced anisotropy is preferred, i.e. F-type loop, which having excellent highfrequency characteristics, makes possible the application in fly back converters and smoothing chokes where storing of magnetic energy is necessary. For amorphous alloys, it was found that the easy axis could be either parallel or perpendicular to the tensile stress-annealing axis [1], depending on the sign of the magnetostriction and the heat treatment. For nanocrystalline Finemet alloy, easy axis perpendicular to the tensile stress is found and the transversally induced anisotropy (Ku B þ 8000 J/m3) [2,3] is two orders of magnitude higher than the one induced by transverse field annealing (Ku B10250 J/m3) [4]. For the time being, two concurrent explanations exist for stress-induced anisotropy: the tensile back-stress theory proposed by Herzer [5] and Ne! el’s model of atomic pair ordering adapted by Hofmann and Kronmuller . [2]. In order to check these two different theories, nanomaterials with different intrinsic properties were prepared.
*Corresponding author. Fax: +13922220. E-mail address: [email protected] (L.K. Varga).
The stress annealing was carried out under protecting atmosphere in a vertical-tube furnace by applying a weight at the free, cold bottom end of the ribbon. Quasistatic magnetization curves (0.01 Hz typical) were obtained using an optical galvanometer as a preamplifier before the integrator and digitized as a set of 3500 points using a 14-bit converter. Following Barandiaran [6], the distribution of the perpendicular magnetic anisotropy was obtained from the second derivative of the experimental magnetization curve as PðHÞ ¼ Hðd2 m=dH 2 Þ: Smoothing has been carried out taking one average point for each neighbouring 5 points and the first and second derivatives were further smoothed by means of 10-point averaging. Figs. 1 and 2 show the hysteresis loops and the corresponding anisotropy distributions obtained for the nanocrystalline Finemet and for the bulk amorphous Fe62Nb8B30 alloys, respectively. The distribution is sharp for the reference sample (s ¼ 0) and widens and shifts to higher HK values with the increased applied stress during annealing. The transversally induced anisotropy, Ku > 0; can be calculated in two ways: (i) as the area between the magnetization curves with and without applied stress, (ii) from the mean value of the anisotropy distribution HK ¼ 2Ku =Js : The constant slope DKu =Ds is about 8.6 ppm for nanocrystalline Finemet and 2 ppm for bulk amorphous alloy. Typical
0304-8853/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 8 7 0 - 3
L.K. Varga et al. / Journal of Magnetism and Magnetic Materials 254–255 (2003) 477–479
478
direction, i.e. the intensity I2=5 belonging to different sextets are of the same value. As shown in Table 1, I2=5 was found to be 3 for as-cast amorphous state indicating a preferred orientation parallel to the ribbon plane. With increasing induced anisotropy, however, this value steadily decreases, indicating the rotation of magnetization out of plane as it is forced by the distributed induced anisotropy field. It is worth mentioning that the true I2;5 intensities can be determined on the demagnetized samples only. For comparison, we have represented in Table 1 also the reduced half height w=HK ; of the anisotropy distributions fitted with a Gaussian function. To facilitate the comparison, the results were normalized as ðw=HK Þ ¼ 3 for the reference sample. Although both methods need heavy digital processing, the reduced width of anisotropy distribution strikingly . correlates the Mossbauer results. This confirms that the widening of the anisotropy distribution indicates the deviation of spontaneous magnetization from the transversal direction. Figs. 3a and b show the effect of stress annealing on two varieties of Nanoperm and FeCo-based Hitperm. For all these alloys Z-loops have been obtained after stress annealing, i.e. the induced anisotropy is longitudinal (Ku o0). The negative Ku of Nanoperm can be explained neither by back-stress nor by pair ordering (the crystallites being composed of Fe only). In order to explain the different behaviours of the Finemet, Nanoperm and Hitperm type nanocrystalline alloys, induced stress hypothesis was adopted. The induced magneto-elastic anisotropy for the two-phase system is
values of Ku in usual transition metal–metalloid type amorphous alloys are smaller by one order of magnitude [1] similar to the precursor amorphous state of Finemet. In order to check if this deviation may be outside the ribbon’s plane, the intensities I2=5 of the second and fifth . Mossbauer lines were investigated. In derivation of this value from the experimental hyperfine field distribution, it was assumed that all the Fe moments, regardless of the number of their Si neighbours, point in the same
1.0
Fe73.5Si13.5Nb3B9Cu1 Annealed 550˚C, 1 h σ = 0, 20, 41, 62, 82, 102 MPa
0.5
50 40 30 20 10 3 2
=
σ
σ
M Pa
M Pa
10 2
82
σ
-1.0
=
M Pa 41
=
σ
=
62
M Pa
M Pa 0 =
20
σ σ
=
-0.5
M Pa
0.0
P(H)
Magnetic polarization, J (T)
1.5
1 -1.5 -2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
0 2500
Magnetic field, H (Am-1)
Fig. 1. Flat hysteresis loops of nanocrystalline Finemet as a function of applied stress during annealing. Bottom right box shows the corresponding distributions of the anisotropy fields.
Fe62Nb8 B30 Annealed 500 C, 1 h
Ku ¼ 32ðxlc sc þ ð1 xÞla sa Þ;
˚
0.5
0.0
4
-0.5
2
-1.0 -1.5
-1.0
-0.5
0.0
0.5
1.0
ð1Þ
where sc and sa denotes the stresses located in the volume fraction of nanograins and amorphous phase, respectively. In the case of Finemet, one can estimate from XRD the crystal fraction (B66%) and composition of nanograins (Fe80Si20) corresponding to lc ¼ 8 106 ; the composition of the remaining amorphous phase can be approximated as Fe63Nb9Si1B27 very close to the present bulk amorphous sample for which la ¼ þ10 106 was measured by means of SAMR. As shown in Ref. [7], the creeping rate is large during heating when the sample is still amorphous and strongly reduces when the crystallization begins because FeSi crystals do not
σ= 0, 125, 172 MPa
P(H)
Magnetic polarization, J (T)
1.0
0 1.5
-1
Magnetic field, H (kAm )
Fig. 2. Flat hysteresis loops of amorphous Fe62Nb8B30 alloy as a function of applied stress during annealing and corresponding distributions of the anisotropy fields (inset).
Table 1 I2=5 values obtained for Finemet after stress-annealing at 5501C/1 h State
As cast
s¼0
s ¼ 20:5 MPa
s ¼ 61 MPa
s ¼ 124 MPa
I2;5 ðw=HK Þ
3
2.88 3
2.82 3.1
2.21 2.24
1.704 1.85
L.K. Varga et al. / Journal of Magnetism and Magnetic Materials 254–255 (2003) 477–479 2
Fe86Zr7B6Cu1
J (T)
1
0 MPa 275 MPa
0 0
Ta = 600 C ta = 1 h
-1 -2 -150
-100
-50
(a)
0
50
100
150
H (A / m) 2
Fe84.5 Zr2Nb4B8.5Cu1
J (T)
1
0 MPa 680 MPa
0 Ta = 6000C ta = 1 h
-1 -2 -150
-100
-50
(b)
0
50
100
150
H (A / m) 2
J (T)
1
0 MPa 220 MPa 0
Ta = 600 C ta = 1 h
-1 -2 -150
(c)
þ65 106 Þ that regardless the value of la ; Ku is negative. By opposition, the hardness of pure iron is small (290 MPa) and probably creeps during annealing. Indeed, the creep in Nanoperm was found to be twice that of Finemet at the same temperature and stress [8]. It comes out that the remaining stress in Fe crystals can be compressive and again Ku is negative (Z-loop). In conclusion, the tensile back-stress model proposed by Herzer in order to explain stress-induced anisotropy is fully applicable for Finemet and Hitperm, whose crystallites do not creep due to the low dislocation mobility as indicated by the large hardness. In the Nanoperm, however, the crystallites creep yielding a residual compressive stress. The unique large transverse anisotropy found in Finemet results from a combination of the sign of the magnetostriction coefficients and stresses, adding the contributions of the two phases. This work was supported by NATO SfP 97-1930 and Hungarian OTKA-T 034 666 Grants. L.K. Varga thanks the ENS de Cachan for a 1-month hospitality as invited professor.
Fe44Co44Zr7B4Cu1
0
479
-100
-50
0
50
100
150
H (A / m)
Fig. 3. Square hysteresis loops of Nanoperm and Hitperm nanocrystalline alloys: (a) Fe86Zr7B6Cu1, (b) Fe84.5Zr2Nb4B8.5Cu1 and (c) (Fe50Co50)88Zr7B4Cu1 obtained after stress annealing.
creep due to their hardness (HV ¼ 1300 MPa for Fe87Si13). As a result, the crystals are still under tension (sc > 0) after removing the load while the amorphous is under compression (sa o0) and following Eq. (1) Ku is positive. The same situation is with Hitperm due to the hardness of Fe50Co50 (HV ¼ 1180 MPa), the remaining amorphous phase being more or less Fe31Co31Zr24B14. Although this composition cannot be melt-spun due to the high Zr content, lc is so strongly positive ðlS ¼
References [1] O.V. Nielsen, L.K. Hansen, A. Hernando, V. Madurga, J. Magn. Magn. Mater. 36 (1983) 73. [2] B. Hofmann, H. Kronmuller, J. Magn. Magn. Mater. 152 (1996) 91. [3] F. Alves, R. Barrue, M. Delage, J.B. Demoulins, N. Lecaude, J.C. Perron, Mater. Sci. Forum 307 (1999) 89. [4] A. Lovas, L.F. Kiss, B. Varga, P. Kamasa, I. Balogh, I. Bakonyi, J. Phys. IV France 8 (1998) 291. [5] G. Herzer, IEEE Trans. Magn. 30 (1994) 4800. [6] J.M. Barrandiaran, M. Vazquez, A. Hernando, J. Gonzalez, G. Rivero, IEEE Trans. Magn. 25 (1989) 3330. [7] F. Mazaleyrat, J.F. Rialland, J. Phys. IV France 8 (1998) 159. [8] F. Alves, A. Benchabi, R. Barru!e, J.C. Faugi"eres, J.F. Rialland, Eur. Phys. J. Appl. Phys. 15 (2001) 167.