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Domain wall propagation in Fe-rich microwires
ARTICLE IN PRESS
Physica B 403 (2008) 382–385 www.elsevier.com/locate/physb
Domain wall propagation in Fe-rich microwires V. Zhukovaa,, J.M. Blancoa, M. Ipatovb, R. Vargab, J. Gonzalezb, A. Zhukovb,c,d a
Dpto. Fı´sica Aplicada, EUPDS, Universidad del Pais Vasco, 20018 San Sebastia´n, Spain b Dpto. Fı´sica de Materiales, Fac. Quı´micas, UPV/EHU, 20009 San Sebastia´n, Spain c TAMAG Ibe´rica S.L., Parque Tecnol. Miramo´n, P. Mikeletegi 56, 11, 20009 San Sebastia´n, Spain d Magnetic and Cryoelectronic Systems, 142190 IZMIRAN, Troitsk, Moscow Region, Russia
Abstract We studied the velocity of domain wall propagation, v, of Fe69Si10B15C6 with different metallic nucleus diameter, d, and different total diameter, D (d ¼ 14 mm, D ¼ 33 mm and d ¼ 18 mm, D ¼ 23.4 mm, respectively) in the temperature range between 78 and 300 K and at different frequencies of applied magnetic field. It is worth mentioning that v(H) dependence is essentially not linear, showing significantly higher domain wall mobility, S ¼ dv/dH, at lower field limit. Domain wall mobility, S, increases significantly with increase in temperature. From v(H) dependence, the critical field, Hcr, associated with the change of the slope on v(H) dependence and critical propagation fields H01 and H02 for the lower and higher field regions, respectively, are determined. All characteristics, v(H) dependence, S(H) dependence and Hcr are sensitive to the sample geometry, i.e., to the internal stresses. The origin of such dependence on internal stresses is discussed in terms of magnetoelastic energy contribution. r 2007 Published by Elsevier B.V. Keywords: Amorphous ferromagnetic wires; Coercivity; Domain walls
1. Introduction Recently, great attention has been paid to studies of thin glass-coated microwires consisting of ferromagnetic thin nucleus (typically of diameter between 1 and 30 mm) coated by the glass exhibit excellent soft magnetic properties useful for the technological applications (magnetic bistability, GMI effect, enhanced magnetic softness, etc.) [1,2], presenting special interest for the magnetic sensors applications mostly because of their thin dimensions. These microwires with positive magnetostriction constant are convenient magnetic materials to study the domain wall (DW) propagation because of their peculiar domain structure consisting of single and large axially magnetized domain surrounded by the outer domain structure Corresponding author. Tel.: +34 943018611; fax: +34 943017130.
E-mail addresses: [email protected] (V. Zhukova), [email protected] (J.M. Blanco), [email protected] (M. Ipatov), [email protected] (R. Varga), [email protected] (J. Gonzalez), [email protected] (A. Zhukov). 0921-4526/$ - see front matter r 2007 Published by Elsevier B.V. doi:10.1016/j.physb.2007.08.055
that consists of domains with radial magnetization (see schematical presentation in Fig. 1). In addition, a small closure domain appears at the end of the wire, in order to decrease the magnetostatic energy [3]. Such peculiar domain structure appears because of the stresses originating from the simultaneous quenching of the metallic nucleus surrounded by the glass coating with the different thermal expansion coefficient of the glass coating and metallic nucleus. Such magnetic microwires with positive magnetostriction constant exhibit a phenomenon of magnetic bistability characterized by the appearance of a rectangular hysteresis loop at low applied magnetic field. This magnetic bistable behavior is related to the presence of a single large Barkhausen jump, which was interpreted as the magnetization reversal in a large single domain [1,3,4]. Regarding the critical length, it can be correlated well with the demagnetizing factor [3], indicating that the closure domains penetrate from the wire ends inside the internal axially magnetized core destroying the single-domain structure. This rectangular hysteresis loop also disappears when the
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383
Fig. 2. Schematic representation of the experimental set-up for measuring domain wall velocity. Fig. 1. Schematic representation of the domain structure of microwires with positive magnetostriction constant.
magnetic field is below some critical value denominated as the switching field [3]. Such rectangular hysteresis loop was interpreted in terms of nucleation or depinning of the reversed domains inside the internal single domain and the consequent domain wall propagation [4]. The perfectly rectangular shape of the hysteresis loop has been related with a very high velocity of such domain wall propagation. It is demonstrated by few methods that the remagnetization process of such magnetic microwire starts from the sample ends as a consequence of the depinning of the domain walls and subsequent domain wall propagation from the closure domains [3–5]. Quite surprising results such as exiting of the domain wall propagation below the switching field [4] and negative critical propagation field [5] have been reported. Magnetic domain wall propagation becomes a hot topic of research because of its use in magnetic devices (such as magnetic random access memory, integrated circuits, hard disks, etc.) to transmit the information along the magnetic wire of submicrometer diameter [6,7]. This motion can be driven both magnetically or electronically. As mentioned above, glass coating induces strong internal stresses. The strength of such internal stresses depends on the ratio between metallic diameter and glass coating thickness [8]. In this paper, we report the experimental results on domain wall propagation in Fe69Si10B15C6 microwires with different metallic nucleus diameter, d, and different total diameter, D, in the temperature range between 78 and 300 K and at different frequencies of applied magnetic field.
Fig. 3. Magnetic field dependence of domain wall velocity in Fe69 Si10B15C6 sample with d ¼ 14 mm.
domain wall (see Fig. 2). The coils system allows us to identify the propagating wall direction, whose velocity is calculated as v ¼ L/t, where t is the time between two maxima in the emf recorded peaks. This system has been placed inside the cryostat in order to perform the measurements in the temperature range between 78 and 300 K. Different frequencies of applied square-shaped magnetic field have been used. Amorphous Fe69Si10B15C6 microwires with different metallic nucleus diameter, d, and different total diameter, D (d ¼ 14 mm, D ¼ 33 mm and d ¼ 18 mm, D ¼ 23.4 mm, respectively) have been prepared using the Taylor–Ulitovsky technique.
2. Experimental The domain wall dynamics was measured by the classical Sixtus–Tonks [9] experiments, as described recently elsewhere [4,5]. The system consists of three coaxial coils (Fig. 2). The primary coil of 10 cm length generating the exciting field by the AC square current creates a homogeneous field along the wire of 10.5 cm that can be taken as static during wall propagation. Two secondary coils, symmetrically placed at the center of the primary coils and separated by L ¼ 6 cm, are connected in series opposition; hence, two sharp opposite peaks are picked up at an oscilloscope upon passing of the propagating
3. Results and discussion The dependence of v on applied magnetic field, H, measured for the sample with the diameter of metallic nucleus 14 mm at 323 K at different frequencies of the AC field is shown in Fig. 3. It is worth mentioning that v(H) dependence is essentially not linear, showing significantly higher domain wall mobility, S ¼ dv/dH, at low field limit. For higher and lower field regions, the domain wall mobilities, S1 and S2, have been calculated. Both S1 and S2 increase with increase in the temperature (see Fig. 4).
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V. Zhukova et al. / Physica B 403 (2008) 382–385
Fig. 6. Hcr(T) dependence measured at different AC frequencies. Fig. 4. Temperature dependence of the domain wall mobilities, S1 and S2, for low- and high-field regions of Fe69Si10B15C6 sample with d ¼ 14 mm.
Fig. 5. Magnetic field dependence of domain wall velocity in Fe69 Si10B15C6 sample with d ¼ 18 mm.
At the same time, the v(H) dependence measured in a thicker sample with d ¼ 18 mm and D ¼ 23.4 mm exhibits different tendency (see Fig. 5). Again, the shape of v(H) dependence is essentially non-linear, but the character is different, exhibiting three different regimes at low, medium, and high magnetic field. Besides, the AC field frequency affects stronger the v(H) dependence. Such change of the regime from the lower field with smaller domain wall velocity but higher domain wall mobility, S1 to the higher field with enhanced velocity at some critical field, Hcr, can be attributed to the change in structure of the domain wall. It was shown previously by micromagnetic simulations, for the case of nanowires, that the vortex-type domain wall is faster than the transversal one [10]. Additionally, the vortex domain wall is more stable for the case of thicker magnetic wires than for the transversal one [11].
From v(H) dependences measured at different temperatures and frequencies, the critical propagation field, H0, obtained from the approximation to v ¼ 0 is obtained for the case of the sample with the diameter of metallic nucleus 14 mm (see Fig. 6). It is worth mentioning that at around room temperature H0 is close to zero, but drastically decreases with decreasing the temperature (see Fig. 6.). Additionally, H0(T) dependence is affected by f, probably owing to the magnetic after-effect. In the case of the sample with the diameter of metallic nucleus 18 mm, we also observed the third regime when the domain wall velocity and domain wall mobility increase even more (Fig. 5). Such increase in S can be attributed to the Walker limit [12]. Theoretically, the domain wall velocities can reach up to 1000 m/s [12], similar to values observed by us in the case of the sample with the diameter of metallic nucleus 18 mm (see Fig. 5). All characteristics, v(H) dependence, S(H) dependence, Hcr and H0 are sensitive to the sample geometry, i.e., to the internal stresses. As mentioned elsewhere [8], the strength of the internal stresses depends on ratio between the metallic and total microwires’ diameters, d/D. Such ratio r ¼ d/D is much smaller for the sample with metallic nucleus 14 mm, where r ¼ 0.42. For the sample with metallic nucleus 18 mm, the ratio r ¼ 0.77. The origin of such internal stresses is related to the composite structure of the glass-coated microwires and determined by the simultaneous quenching of metallic nucleus coated by glass shell. It is worth mentioning that such non-linear shape of v(H) dependences observed for both microwires can introduce some corrections in the estimations of the critical propagation field recently reported elsewhere and giving large negative values [5]. Indeed, the approximation to zero domain wall velocity from region 2 at intermediate field (see Figs. 3 and 5) with lower S can give negative critical propagation field, H0. On the other hand, such approximation taken from the lowest field region gives much smaller values H0. As has been mentioned above, such
ARTICLE IN PRESS V. Zhukova et al. / Physica B 403 (2008) 382–385
Fig. 7. Estimations of the critical propagation field obtained from two different regions of v(H) dependence.
non-linearity observed at low field can be attributed to the change of the domain wall structure with changing of the applied magnetic field. In fact, the estimation of the critical propagation field should be taken for the domain wall existing for the lower field. As has been mentioned above, such estimation gives the values H0 about 0. As an example, Fig. 7 gives large negative values, H02E570 A/m, from the approximation to v ¼ 0 taken for the intermediate values of the v(H) dependence for temperature 323 K. Alternatively, similar approximation from lower field regions gives values of about H01E0 A/m. This example indicates large difference in the estimation of the critical propagation field obtained from different regions of v(H) dependence. 4. Conclusions To summarize, we studied the velocity of domain wall propagation, v, of Fe69Si10B15C6 with different metallic nucleus diameter, d, and different total diameter, D (d ¼ 14 mm, D ¼ 33 mm and d ¼ 18 mm, D ¼ 23.4 mm,
385
respectively), in the temperature range between 78 and 300 K and at different frequencies of applied magnetic field. The v(H) dependence is essentially not linear, showing significantly higher domain wall mobility, S ¼ dv/dH, at low field limit. Temperature dependences of S1 and S2 are obtained. It is found that the domain wall mobility for lower and higher field regions of v(H), S1 and S2, increase significantly with increase in the temperature. From v(H) dependence, the critical field, Hcr, associated with the change of the slope on v(H) dependence and the critical propagation fields, H01 and H02, are determined. All characteristics, v(H) dependence, S(H) dependence, H0 and Hcr are sensitive to the sample geometry, i.e., to the internal stresses. The origin of such dependence on internal stresses is discussed in terms of magnetoelastic energy contribution.
References [1] A. Zhukov, J. Gonzalez, Amorphous and nanocrystalline soft magnetic materials, in: Y. Liu, D.J. Sellmyer, D. Shindo (Eds.), Advanced Magnetic Materials, Book 3, ‘‘Processing of Advanced Magnetic Materials,’’ vol. 3, Kluwer Academic Publishers, Norwell, MA, 2004, pp. 115–181 (Chapter 5). [2] A. Zhukov, J. Gonza´lez, J.M. Blanco, M. Va´zquez, V. Larin, J. Mater. Res. 15 (2000) 2107. [3] A.P. Zhukov, M. Va´zquez, J. Vela´zquez, H. Chiriac, V. Larin, J. Magn. Magn. Mater. 151 (1995) 132. [4] A. Zhukov, Appl. Phys. Lett. 78 (2001) 3106. [5] R. Varga, A. Zhukov, M. Ipatov, J.M. Blanco, J. Gonzalez, V. Zhukova, P. Vojtanı´ k, Phys. Rev. B 73 (2006) 054408. [6] G.S.D. Beach, C. Nistor, C. Knutson, M. Tsoi, J.L. Erskine, Nat. Mater. 4 (2005) 741. [7] D.A. Allwood, G. Xiong, C.C. Faulkner, D. Atkinson, D. Petit, R.P. Cowburn, Science 309 (2005) 1688. [8] A. Zhukov, M. Va´zquez, J. Vela´zqiez, A. Hernando, V. Larin, J. Magn. Magn. Mater. 170 (1997) 323. [9] K.J. Sixtus, L. Tonks, Phys. Rev. 42 (1932) 419. [10] H. Forster, T. Schrefl, W. Scholz, D. Suess, V. Tsiantos, J. Fidler, J. Magn. Magn. Mater. 249 (2002) 181. [11] R.D. McMichael, M.J. Donahue, IEEE Trans. Magn. 33 (1997) 4167. [12] N.L. Schryer, L.R. Walker, J. Appl. Phys. 45 (1974) 5406.
Physica B 403 (2008) 382–385 www.elsevier.com/locate/physb
Domain wall propagation in Fe-rich microwires V. Zhukovaa,, J.M. Blancoa, M. Ipatovb, R. Vargab, J. Gonzalezb, A. Zhukovb,c,d a
Dpto. Fı´sica Aplicada, EUPDS, Universidad del Pais Vasco, 20018 San Sebastia´n, Spain b Dpto. Fı´sica de Materiales, Fac. Quı´micas, UPV/EHU, 20009 San Sebastia´n, Spain c TAMAG Ibe´rica S.L., Parque Tecnol. Miramo´n, P. Mikeletegi 56, 11, 20009 San Sebastia´n, Spain d Magnetic and Cryoelectronic Systems, 142190 IZMIRAN, Troitsk, Moscow Region, Russia
Abstract We studied the velocity of domain wall propagation, v, of Fe69Si10B15C6 with different metallic nucleus diameter, d, and different total diameter, D (d ¼ 14 mm, D ¼ 33 mm and d ¼ 18 mm, D ¼ 23.4 mm, respectively) in the temperature range between 78 and 300 K and at different frequencies of applied magnetic field. It is worth mentioning that v(H) dependence is essentially not linear, showing significantly higher domain wall mobility, S ¼ dv/dH, at lower field limit. Domain wall mobility, S, increases significantly with increase in temperature. From v(H) dependence, the critical field, Hcr, associated with the change of the slope on v(H) dependence and critical propagation fields H01 and H02 for the lower and higher field regions, respectively, are determined. All characteristics, v(H) dependence, S(H) dependence and Hcr are sensitive to the sample geometry, i.e., to the internal stresses. The origin of such dependence on internal stresses is discussed in terms of magnetoelastic energy contribution. r 2007 Published by Elsevier B.V. Keywords: Amorphous ferromagnetic wires; Coercivity; Domain walls
1. Introduction Recently, great attention has been paid to studies of thin glass-coated microwires consisting of ferromagnetic thin nucleus (typically of diameter between 1 and 30 mm) coated by the glass exhibit excellent soft magnetic properties useful for the technological applications (magnetic bistability, GMI effect, enhanced magnetic softness, etc.) [1,2], presenting special interest for the magnetic sensors applications mostly because of their thin dimensions. These microwires with positive magnetostriction constant are convenient magnetic materials to study the domain wall (DW) propagation because of their peculiar domain structure consisting of single and large axially magnetized domain surrounded by the outer domain structure Corresponding author. Tel.: +34 943018611; fax: +34 943017130.
E-mail addresses: [email protected] (V. Zhukova), [email protected] (J.M. Blanco), [email protected] (M. Ipatov), [email protected] (R. Varga), [email protected] (J. Gonzalez), [email protected] (A. Zhukov). 0921-4526/$ - see front matter r 2007 Published by Elsevier B.V. doi:10.1016/j.physb.2007.08.055
that consists of domains with radial magnetization (see schematical presentation in Fig. 1). In addition, a small closure domain appears at the end of the wire, in order to decrease the magnetostatic energy [3]. Such peculiar domain structure appears because of the stresses originating from the simultaneous quenching of the metallic nucleus surrounded by the glass coating with the different thermal expansion coefficient of the glass coating and metallic nucleus. Such magnetic microwires with positive magnetostriction constant exhibit a phenomenon of magnetic bistability characterized by the appearance of a rectangular hysteresis loop at low applied magnetic field. This magnetic bistable behavior is related to the presence of a single large Barkhausen jump, which was interpreted as the magnetization reversal in a large single domain [1,3,4]. Regarding the critical length, it can be correlated well with the demagnetizing factor [3], indicating that the closure domains penetrate from the wire ends inside the internal axially magnetized core destroying the single-domain structure. This rectangular hysteresis loop also disappears when the
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383
Fig. 2. Schematic representation of the experimental set-up for measuring domain wall velocity. Fig. 1. Schematic representation of the domain structure of microwires with positive magnetostriction constant.
magnetic field is below some critical value denominated as the switching field [3]. Such rectangular hysteresis loop was interpreted in terms of nucleation or depinning of the reversed domains inside the internal single domain and the consequent domain wall propagation [4]. The perfectly rectangular shape of the hysteresis loop has been related with a very high velocity of such domain wall propagation. It is demonstrated by few methods that the remagnetization process of such magnetic microwire starts from the sample ends as a consequence of the depinning of the domain walls and subsequent domain wall propagation from the closure domains [3–5]. Quite surprising results such as exiting of the domain wall propagation below the switching field [4] and negative critical propagation field [5] have been reported. Magnetic domain wall propagation becomes a hot topic of research because of its use in magnetic devices (such as magnetic random access memory, integrated circuits, hard disks, etc.) to transmit the information along the magnetic wire of submicrometer diameter [6,7]. This motion can be driven both magnetically or electronically. As mentioned above, glass coating induces strong internal stresses. The strength of such internal stresses depends on the ratio between metallic diameter and glass coating thickness [8]. In this paper, we report the experimental results on domain wall propagation in Fe69Si10B15C6 microwires with different metallic nucleus diameter, d, and different total diameter, D, in the temperature range between 78 and 300 K and at different frequencies of applied magnetic field.
Fig. 3. Magnetic field dependence of domain wall velocity in Fe69 Si10B15C6 sample with d ¼ 14 mm.
domain wall (see Fig. 2). The coils system allows us to identify the propagating wall direction, whose velocity is calculated as v ¼ L/t, where t is the time between two maxima in the emf recorded peaks. This system has been placed inside the cryostat in order to perform the measurements in the temperature range between 78 and 300 K. Different frequencies of applied square-shaped magnetic field have been used. Amorphous Fe69Si10B15C6 microwires with different metallic nucleus diameter, d, and different total diameter, D (d ¼ 14 mm, D ¼ 33 mm and d ¼ 18 mm, D ¼ 23.4 mm, respectively) have been prepared using the Taylor–Ulitovsky technique.
2. Experimental The domain wall dynamics was measured by the classical Sixtus–Tonks [9] experiments, as described recently elsewhere [4,5]. The system consists of three coaxial coils (Fig. 2). The primary coil of 10 cm length generating the exciting field by the AC square current creates a homogeneous field along the wire of 10.5 cm that can be taken as static during wall propagation. Two secondary coils, symmetrically placed at the center of the primary coils and separated by L ¼ 6 cm, are connected in series opposition; hence, two sharp opposite peaks are picked up at an oscilloscope upon passing of the propagating
3. Results and discussion The dependence of v on applied magnetic field, H, measured for the sample with the diameter of metallic nucleus 14 mm at 323 K at different frequencies of the AC field is shown in Fig. 3. It is worth mentioning that v(H) dependence is essentially not linear, showing significantly higher domain wall mobility, S ¼ dv/dH, at low field limit. For higher and lower field regions, the domain wall mobilities, S1 and S2, have been calculated. Both S1 and S2 increase with increase in the temperature (see Fig. 4).
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Fig. 6. Hcr(T) dependence measured at different AC frequencies. Fig. 4. Temperature dependence of the domain wall mobilities, S1 and S2, for low- and high-field regions of Fe69Si10B15C6 sample with d ¼ 14 mm.
Fig. 5. Magnetic field dependence of domain wall velocity in Fe69 Si10B15C6 sample with d ¼ 18 mm.
At the same time, the v(H) dependence measured in a thicker sample with d ¼ 18 mm and D ¼ 23.4 mm exhibits different tendency (see Fig. 5). Again, the shape of v(H) dependence is essentially non-linear, but the character is different, exhibiting three different regimes at low, medium, and high magnetic field. Besides, the AC field frequency affects stronger the v(H) dependence. Such change of the regime from the lower field with smaller domain wall velocity but higher domain wall mobility, S1 to the higher field with enhanced velocity at some critical field, Hcr, can be attributed to the change in structure of the domain wall. It was shown previously by micromagnetic simulations, for the case of nanowires, that the vortex-type domain wall is faster than the transversal one [10]. Additionally, the vortex domain wall is more stable for the case of thicker magnetic wires than for the transversal one [11].
From v(H) dependences measured at different temperatures and frequencies, the critical propagation field, H0, obtained from the approximation to v ¼ 0 is obtained for the case of the sample with the diameter of metallic nucleus 14 mm (see Fig. 6). It is worth mentioning that at around room temperature H0 is close to zero, but drastically decreases with decreasing the temperature (see Fig. 6.). Additionally, H0(T) dependence is affected by f, probably owing to the magnetic after-effect. In the case of the sample with the diameter of metallic nucleus 18 mm, we also observed the third regime when the domain wall velocity and domain wall mobility increase even more (Fig. 5). Such increase in S can be attributed to the Walker limit [12]. Theoretically, the domain wall velocities can reach up to 1000 m/s [12], similar to values observed by us in the case of the sample with the diameter of metallic nucleus 18 mm (see Fig. 5). All characteristics, v(H) dependence, S(H) dependence, Hcr and H0 are sensitive to the sample geometry, i.e., to the internal stresses. As mentioned elsewhere [8], the strength of the internal stresses depends on ratio between the metallic and total microwires’ diameters, d/D. Such ratio r ¼ d/D is much smaller for the sample with metallic nucleus 14 mm, where r ¼ 0.42. For the sample with metallic nucleus 18 mm, the ratio r ¼ 0.77. The origin of such internal stresses is related to the composite structure of the glass-coated microwires and determined by the simultaneous quenching of metallic nucleus coated by glass shell. It is worth mentioning that such non-linear shape of v(H) dependences observed for both microwires can introduce some corrections in the estimations of the critical propagation field recently reported elsewhere and giving large negative values [5]. Indeed, the approximation to zero domain wall velocity from region 2 at intermediate field (see Figs. 3 and 5) with lower S can give negative critical propagation field, H0. On the other hand, such approximation taken from the lowest field region gives much smaller values H0. As has been mentioned above, such
ARTICLE IN PRESS V. Zhukova et al. / Physica B 403 (2008) 382–385
Fig. 7. Estimations of the critical propagation field obtained from two different regions of v(H) dependence.
non-linearity observed at low field can be attributed to the change of the domain wall structure with changing of the applied magnetic field. In fact, the estimation of the critical propagation field should be taken for the domain wall existing for the lower field. As has been mentioned above, such estimation gives the values H0 about 0. As an example, Fig. 7 gives large negative values, H02E570 A/m, from the approximation to v ¼ 0 taken for the intermediate values of the v(H) dependence for temperature 323 K. Alternatively, similar approximation from lower field regions gives values of about H01E0 A/m. This example indicates large difference in the estimation of the critical propagation field obtained from different regions of v(H) dependence. 4. Conclusions To summarize, we studied the velocity of domain wall propagation, v, of Fe69Si10B15C6 with different metallic nucleus diameter, d, and different total diameter, D (d ¼ 14 mm, D ¼ 33 mm and d ¼ 18 mm, D ¼ 23.4 mm,
385
respectively), in the temperature range between 78 and 300 K and at different frequencies of applied magnetic field. The v(H) dependence is essentially not linear, showing significantly higher domain wall mobility, S ¼ dv/dH, at low field limit. Temperature dependences of S1 and S2 are obtained. It is found that the domain wall mobility for lower and higher field regions of v(H), S1 and S2, increase significantly with increase in the temperature. From v(H) dependence, the critical field, Hcr, associated with the change of the slope on v(H) dependence and the critical propagation fields, H01 and H02, are determined. All characteristics, v(H) dependence, S(H) dependence, H0 and Hcr are sensitive to the sample geometry, i.e., to the internal stresses. The origin of such dependence on internal stresses is discussed in terms of magnetoelastic energy contribution.
References [1] A. Zhukov, J. Gonzalez, Amorphous and nanocrystalline soft magnetic materials, in: Y. Liu, D.J. Sellmyer, D. Shindo (Eds.), Advanced Magnetic Materials, Book 3, ‘‘Processing of Advanced Magnetic Materials,’’ vol. 3, Kluwer Academic Publishers, Norwell, MA, 2004, pp. 115–181 (Chapter 5). [2] A. Zhukov, J. Gonza´lez, J.M. Blanco, M. Va´zquez, V. Larin, J. Mater. Res. 15 (2000) 2107. [3] A.P. Zhukov, M. Va´zquez, J. Vela´zquez, H. Chiriac, V. Larin, J. Magn. Magn. Mater. 151 (1995) 132. [4] A. Zhukov, Appl. Phys. Lett. 78 (2001) 3106. [5] R. Varga, A. Zhukov, M. Ipatov, J.M. Blanco, J. Gonzalez, V. Zhukova, P. Vojtanı´ k, Phys. Rev. B 73 (2006) 054408. [6] G.S.D. Beach, C. Nistor, C. Knutson, M. Tsoi, J.L. Erskine, Nat. Mater. 4 (2005) 741. [7] D.A. Allwood, G. Xiong, C.C. Faulkner, D. Atkinson, D. Petit, R.P. Cowburn, Science 309 (2005) 1688. [8] A. Zhukov, M. Va´zquez, J. Vela´zqiez, A. Hernando, V. Larin, J. Magn. Magn. Mater. 170 (1997) 323. [9] K.J. Sixtus, L. Tonks, Phys. Rev. 42 (1932) 419. [10] H. Forster, T. Schrefl, W. Scholz, D. Suess, V. Tsiantos, J. Fidler, J. Magn. Magn. Mater. 249 (2002) 181. [11] R.D. McMichael, M.J. Donahue, IEEE Trans. Magn. 33 (1997) 4167. [12] N.L. Schryer, L.R. Walker, J. Appl. Phys. 45 (1974) 5406.