DSpace at VNU: Magnetic, Mossbauer and magnetostrictive studies of amorphous Tb(Fe0.55Co0.45)(1.5) films

Magnetic, Mössbauer and magnetostrictive studies of amorphous Tb(Fe 0.55 Co 0.45 ) 1.5 films T M Danh, N H Duc, H N Thanh, and J Teillet Citation: Journal of Applied Physics 87, 7208 (2000); doi: 10.1063/1.372970 View online: http://dx.doi.org/10.1063/1.372970 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/87/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A structural, magnetic, and Mössbauer spectral study of the TbCo x Fe x B compounds with x = , 1, and J Appl Phys 105, 113908 (2009); 10.1063/1.3138808 Mössbauer study of the magnetism and structure of amorphous and nanocrystalline Fe 81x Ni x Zr B 12 (x=10–40) alloys J Appl Phys 94, 638 (2003); 10.1063/1.1578701 Synthesis and magnetostriction of melt-spun Pr 1x Tb x (Fe 0.6 Co 0.4 ) alloys J Appl Phys 91, 271 (2002); 10.1063/1.1420772 Magnetic and magnetostrictive properties in amorphous ( Tb 0.27 Dy 0.73 )( Fe 1x Co x ) films J Appl Phys 87, 834 (2000); 10.1063/1.371950 A Mössbauer spectral study of Tb Fe 17 and the Tb Fe 17x Si x solid solutions J Appl Phys 83, 6736 (1998); 10.1063/1.367708 [This article is copyrighted as indicated in the article Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions Downloaded to ] IP: 130.79.0.174 On: Tue, 13 May 2014 08:17:48 JOURNAL OF APPLIED PHYSICS VOLUME 87, NUMBER 10 15 MAY 2000 Magnetic, Moăssbauer and magnetostrictive studies of amorphous TbFe0.55Co0.451.5 films T M Danh, N H Duc,a) and H N Thanh Cryogenic Laboratory, Faculty of Physics, National University of Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam J Teillet Laboratoire de Magne´tisme et Applications, GMP-UMR 6634, Universite´ de Rouen, 76821 Mont-Saint-Aignan, France ͑Received 13 January 2000; accepted for publication 19 February 2000͒ The Tb͑Fe0.55Co0.45͒1.5 films were fabricated by rf magnetron sputtering from a composite target Samples were investigated by means of x-ray diffraction, vibrating sample magnetometer, conversion electron Moăssbauer spectra, and magnetostriction measurements The as-deposited film is an amorphous alloy with a perpendicular magnetic anisotropy and an intrinsic magnetostriction ␭ϭ1080ϫ10Ϫ6 in an applied field of 0.7 T In this state, it was determined that the hyperfine field B hfϭ23.5 T and the cone-angle between the Fe moment direction and the film-normal direction ␤ ϭ12° After annealing in the temperature range of T A ϭ250– 450 °C the amorphous structure still remained, however the anisotropy was changed to a parallel one The soft magnetostrictive behavior has also been improved by these heat treatments: the parallel magnetostriction ␭ ʈ ϭ465ϫ10Ϫ6 was almost developed in low applied fields of less than 0.1 T and, especially, a huge magnetostrictive susceptibility ␹ ␭ ϭd␭ ʈ /d( ␮ H)ϭ1.8ϫ10Ϫ2 TϪ1 was obtained at ␮ Hϭ15 mT © 2000 American Institute of Physics ͓S0021-8979͑00͒06210-1͔ I INTRODUCTION It has been known for a few years that there has been a growing interest in magnetic thin films with large magnetostriction.1–4 This interest is motivated by the potential such films show for use in microsystems actuators For these applications, large low-field magnetostrictive susceptibilities ␹ ␭ ϭd␭/d( ␮ H)Ͼ2ϫ10Ϫ2 TϪ1, and low coercive fields ␮ H C Ӷ100 mT, are required R–Fe (Rϭrare earth͒ based thin films offer the possibility of developing very large magnetostriction at room temperature Numerous investigations on Tb–Fe and ͑Tb, Dy͒–Fe based thin films have been carried out In order to get low macroscopic anisotropy, materials have been used in the amorphous state In Fe-based amorphous alloys, however, both positive and negative Fe–Fe exchange interactions exist,5 leading to magnetic frustration in the Fe sublattice In amorphous R–Fe ͑a-RFe͒ alloys, where R is a magnetic rare-earth, the additional contributions of R–Fe exchange and local crystalline electric field interactions lead to the formation of sperimagnetic structures.5,6 The ordering temperatures are above room temperature ͓T C ϭ410 K for a-Tb0.33Fe0.66, Ref and references therein͔ It is, however, still rather low and is thus detrimental to large magnetostrictions in such materials at room temperature (␭ϭ300ϫ10Ϫ6 in ␮ Hϭ1 T) The optimization of magnetostriction and ordering temperature have been reported for TbDyFe/Nb multilayers by combining the advantages of a crystallized film ͑high T C and giant ␭͒ with a͒ Author to whom correspondence should be addressed; electronic mail: duc@cryolab.edu.vn soft magnetic properties of an amorphous phase.3 In these materials, however, the coercive fields were raised up ( ␮ H C Ϸ100 mT) Regarding the large magnetostrictions in the amorphous state, the equivalent a-RCo based alloys can be considered Although crystalline RCo2 compounds order below 300 K as the Co is merely paramagnetic, the amorphous state stabilizes a moment on the Co sublattice due to band narrowing These Co moments are strongly ferromagnetically coupled A sperimagnetic structure occurs as in a-RFe alloys but the ordering temperature is now raised up to 600 K ͑Ref 6͒ for Tb0.33Co66 In practice, Betz7 has investigated a-Tbx Co1Ϫx films and shown that large magnetostriction of ␭ϭ350 ϫ10Ϫ6 at 300 K was obtained for xϳ0.33 Recently, we have studied the magnetization and magnetostriction in the amorphous (Tb1Ϫx Dyx )(Fe0.45Co0.55) 2.1 ͑Ref 8͒ and (Tb0.27Dy0.73)(Fe1Ϫx Cox ) ͑Ref 9͒ thin films In these alloys, the R–FeCo exchange energies are stronger than those in the ‘‘pure’’ a-RFe and a-RCo alloys It was thought to be the reason for the enhancement of the R moment at room temperature and thus the magnetostriction Indeed, a magnetostriction of 1020ϫ10Ϫ6 was obtained in the applied field of T for amorphous Tb͑Fe0.45Co0.55͒2.1 In this article, we studied zero-field annealing effects on the magnetization, Moăssbauer spectra, and magnetostriction of the amorphous Tb͑Fe0.55Co0.45͒1.5 films with a perpendicular anisotropy The obtained magnetic and magnetostrictive characters of these annealed films proved to be rather promising for application requirements 0021-8979/2000/87(10)/7208/5/$17.00 7208 © 2000 American Institute of Physics [This article is copyrighted as indicated in the article Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions Downloaded to ] IP: 130.79.0.174 On: Tue, 13 May 2014 08:17:48 Danh et al J Appl Phys., Vol 87, No 10, 15 May 2000 7209 FIG X-ray diffraction patterns of the Tb͑Fe0.55Co0.45͒1.5 films II EXPERIMENT The films were prepared by rf magnetron sputtering The typical power during sputtering was 400 W and the Ar pressure was 10Ϫ2 mbar A composite target consisted of 18 segments of about 20°, of different elements ͑here Tb, Fe, Co͒ The substrates were glass microscope cover slips with a nominal thickness of 150 ␮m Both target and sample holder were water cooled The thickness was measured mechanically using an ␣ step and the sample mass was determined from the mass difference of the substrates before and after sputtering The typical film thickness was 1.2 ␮m without any coating The film structure was investigated by x-ray ͑␪ –2␪͒ diffraction ͑XRD͒ with Cu K ␣ rays The results showed the as-deposited samples to be amorphous ͑see Fig 1͒ Samples were annealed at temperatures from 250 to 450 °C for h in a vacuum of 5ϫ10Ϫ4 mbar in order to relieve any stress induced during the sputtering process Subsequent ␪ –2␪ XRD showed no evidence of a global crystallization after annealing, but the peaks of Tb oxides and ␣-͑Fe, Co͒ ͑see also Fig 1͒ appear to be due to the surface oxidation The magnetization measurements were carried out using a vibrating sample magnetometer in a field of up to 1.3 T at 300 K The conversion electron Moăssbauer spectra CEMS at room temperature was recorded using a conventional spectrometer equipped with a homemade helium–methane proportional counter The source was a 57Co in rhodium matrix The films were set perpendicular to the incident ␥ beam The spectra were fitted with a least-squares technique using a histogram method relative to discrete distributions, constraining the linewidths of each elementary spectrum to be the same Isomer shifts are given relatively to ␣-Fe at 300 K The average ‘‘cone angle’’ ␤ between the incident ␥-ray direction ͑being in the film-normal direction͒ and that of the hyperfine field B hf ͑or the Fe magnetic moment direction͒ is estimated from the line-intensity ratios 3:x:1:1:x:3 of the six Moăssbauer lines, where x is related to by sin2 ␤ ϭ2x/(4ϩx) FIG Magnetic hysteresis loops in the internal magnetic fields at 300 K for Tb͑Fe0.55Co0.45͒1.5 films: ͑a͒ the as-deposited films, ͑b͒ after annealing at 250 °C, ͑c͒ 350 °C, and ͑d͒ 450 °C The magnetostriction was measured using an optical deflectometer ͑resolution of 5ϫ10Ϫ6 rad), in which the bending of the substrate due to the magnetostriction in the film was measured.8–11 III EXPERIMENTAL RESULTS AND DISCUSSION A Magnetization Figure presents the magnetic hysteresis loops measured with applied magnetic field in the film-plane and filmnormal directions for the as-deposited and several annealed Tb͑Fe0.55Co0.45͒1.5 films The magnetization curves have been plotted versus the internal field ␮ H int(ϭ ␮ H ext ϪNM ) using a usual demagnetization factor NϭN ʈ ϭ0 in the film-plane direction but an experimentally determined value of NϭNЌ in the film-normal direction The value of NЌ was chosen in a way that the steepest part of the magnetization curve is transformed into a vertical line.12 The resulting effective values of NЌ are equal to 0.5, 0.9, 0.95, and 1.0 for the as-deposited film, film annealed at T A ϭ250 °C, 350 °C, and 450 °C, respectively Comparing to NЌ ϭ1 as expected for an infinite plate, the obtained value for the asdeposited film is too small This is, however, characteristic of the nucleation of tripe domains.13 For all samples, the in-plane magnetization is almost isotropic The as-deposited sample shows a perpendicular magnetic anisotropy ͓Fig 2͑a͔͒ Its coercive field is rather large ͑film-normal coercivity ␮ H CЌ ϭ0.132 T and film-plane coercivity ␮ H C ʈ ϭ0.08 T) and the magnetization does not completely saturate even at 1.3 T While, intrinsically related to the strong local anisotropy of the R atoms and their random distribution of easy axes present in such sperimagnetic systems, the coercivity is strongly affected by internal stress, microstructure, and homogeneity.14 The high-field suscepti- [This article is copyrighted as indicated in the article Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions Downloaded to ] IP: 130.79.0.174 On: Tue, 13 May 2014 08:17:48 7210 Danh et al J Appl Phys., Vol 87, No 10, 15 May 2000 TABLE I Room temperature magnetic and magnetostrictive characteristics of the amorphous Tb͑Fe0.55Co0.45͒1.5 films: T A , M S , ␮ o H C ʈ , ͗ B hf͘ , ␤, and ␭(ϭ␭ ʈ Ϫ␭Ќ ) are the annealing temperature, saturation magnetization, filmplane coercive field, average hyperfine field, Fe-spin oriented angle, and intrinsic magnetostriction, respectively T A ͑K͒ M S ͑kA/m͒ ␮ o H C ʈ ͑mT͒ ͗ B hf͘ ͑T͒ as-deposed 250 350 450 320 268 250 240 80 25 10 22.5Ϯ0.3 — — — ␤ ͑deg͒ 12Ϯ5 — — — ␭(10Ϫ6 ) 1080 800 820 930 bility is also typical of sperimagnetic systems and is associated with the closing of the cone distribution of R moments as the field is increased.6 After annealing, there are a number of clear differences in the magnetization process First, the magnetic anisotropy changes from a perpendicular to a parallel one ͓see Figs 2͑c͒ and 2͑d͔͒ Second, the coercive field is strongly reduced ͑Table I͒ for instance, with the annealing at 450 °C, ␮ H C ʈ is equal to mT Third, the saturation magnetization decreases ͑see also Table I͒ but can be easily reached at low magnetic fields In agreement with the XRD results, the reduction of the magnetization may relate to the process of oxidation during vacuum heat treatment ͑see Sec III B͒ This effect was previously reported by Wada et al.15 Finally, the annealing also causes a reduction in the high-field susceptibility, indicating that the cone distribution of the Tb moments is easy to close From the magnetization curves measured with applied magnetic field in the film-plane and film-normal directions, we estimated the uniaxial anisotropy constant K u to be 117 KJ/m3 for the as-deposited film This value is comparable with that reported in literature ͑e.g., Refs 12 and 14͒ Regarding the magnetoelastic anisotropy, any magnetostrictive material always tries to compensate the external or internal stress by appropriate rotation of spins For a film with positive magnetostriction, tensile stress leads to a spin orientation in the film plane, whereas for compressive stress the spins orient along the film normal At present, since the thermal expansion coefficients of the Tb–FeCo film and the glass substrate would result in an in-plane anisotropy, it is possible that the observed perpendicular anisotropy must be of intrinsic origin, associating with the structural anisotropy induced during the sputtering process This was already confirmed directly in the most careful studies of the local structures.16,17 The elimination of the coercivity and anisotropy with annealing reflects that an isotropic amorphous structure has lower energy than the as-deposited anisotropy state The relaxation of the anisotropy without crystallization, thus, is a simple relaxation of the amorphous structure resulting in a more stable and homogenous film structure B Moăssbauer spectra The CEMS is suitable to investigate hyperfine parameters of the iron nuclei within a depth range of about 200 nm from the film surface Within this space, however, the contribution of the iron nuclei to the CEM spectrum is not the FIG Moăssbauer spectra and hyperfine-field distributions of TbFe0.55Co0.451.5 films: ͑a͒ the as-deposited film, ͑b͒ after annealing at 450 °C same, but is strongly reduced with increasing depth Figure presents the CEM spectra for the as-deposited and the 450 °C-annealed films Although the statistics are not as good, the information about the average hyperfine field ( ͗ B hf͘ ) and the Fe spin reorientation ͑␤ angle͒ can be extracted from these spectra The perpendicular anisotropy of the as-deposited film is characterized by the almost disappearing second and fifth Moăssbauer lines Fig 3a For this sample, the spectrum has been fitted with a wide contribution of hyperfine field P(B hf) to take into account all the environments experienced by Fe57 nuclei This provides an average value of ͗ B hf͘ ϭ23.5 T and ͗ ␤ ͘ ϭ12° It is worth mentioning here that beside the peak at 22.5 T, which corresponds to the magnetostrictive Tb͑Fe, Co͒1.5 alloy, the P(B hf) distribution extends also to higher hyperfine fields ͑Ϸ30 T͒ The spectrum of the 450 °C-annealed film ͓Fig 3͑b͔͒ is fitted with a wide distribution of hyperfine field P(B hf) too For this sample, the peak at 22.5 T still exists in the P(B hf) curve, however, it is weakened and broadened Moreover, the high hyperfine-field contribution becomes dominant A sharp P(B hf) peak is reached at 34.5 T In accordance with the XRD results, this major ferromagnetic component ͑82% of the total spectrum area͒ is associated with the contribution of the crystallized ␣-͑Fe, Co͒ phase formed at the film surface due to the oxidation The fraction of the magnetostrictive alloy ͑18% of the total spectrum area͒ is small As already mentioned in the beginning of this subsection, this reflects that the thickness of the oxidation layer is sufficiently thick in annealed films The ͗ B hf͘ values obtained for the a-Tb͑Fe0.55Co0.45͒1.5 phase are comparable with those reported for the Laves phase RFe2 compounds Such a value implies a strong 3d – 3d exchange coupling The 3d magnetic moment M 3d is determined by scaling with ͗ B hf͘ , taking ͗ B hf͘ ϭ33 T and M 3d ϭ2.2␮ B /atoms for ␣-Fe It results in M 3d ϭ1.5␮ B / atoms This finding is in good agreement with that deduced from magnetization data for a-͑Tb, Dy͒͑Fe, Co͒2 films.9 This large room-temperature 3d magnetic moment indicates that in the composition under consideration there was sufficient Co to ensure good ferromagnetic T – T coupling as well as sufficient Fe giving the large magnetic moment [This article is copyrighted as indicated in the article Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions Downloaded to ] IP: 130.79.0.174 On: Tue, 13 May 2014 08:17:48 Danh et al J Appl Phys., Vol 87, No 10, 15 May 2000 FIG Parallel magnetostrictive hysteresis loops in the external fields for the Tb͑Fe0.55Co0.45͒1.5 films: ͑1͒ as-deposited film and ͑2͒ after annealing at 350 °C and ͑3͒ 450 °C C Magnetostriction We measured two coefficients ␭ ʈ and ␭Ќ , which correspond to the applied field, in the film plane being, respectively, parallel and perpendicular to the sample length For the films under investigation, magnetostriction is almost isotropic in the plane ␭ ʈ /␭Ќ ϷϪ1 The intrinsic magnetostriction data ␭ϭ␭ ʈ Ϫ␭Ќ , measured in the applied magnetic field of ␮ Hϭ0.7 T, are listed in Table I It is clearly seen that the magnetostriction of a magnitude of 10Ϫ3 was achieved The parallel magnetostrictive hysteresis loops are shown in Fig For the as-deposited sample, the magnetostriction increases almost linearly in the investigated magnetic field ranges This implies that it is rather difficult to rotate spins into the film plane The largest magnetostriction obtained at 0.7 T is ␭ ʈ ϭ550ϫ10Ϫ6 The annealing at temperatures between T A ϭ250 and 450 °C reduces the high-field magnetostriction but enhances the low-field magnetostriction The optimum annealing is at T A ϭ450 °C In this case, the magnetostriction of ␭ ʈ ϭ465ϫ10Ϫ6 is saturated at ␮ Hϭ0.1 T and ␭ ʈ ϭ340ϫ10Ϫ6 is already developed in very low applied magnetic fields of 20 mT In addition, its coercive field is less than mT It is worthwhile to mention that in the applied field of 15 mT, the magnetostrictive susceptibility has reached its maximum value ␹ ␭ ϭ ‫ ␭ ץ‬ʈ / ‫ ␮ ( ץ‬0 H)ϭ1.8 ϫ10Ϫ2 TϪ1 These magnetic and magnetostrictive characteristics are very promising for microsystem applications We can further associate the field dependence of the magnetostriction with different types of magnetization processes For a system of randomly oriented spin and random distribution of the domain walls, the magnetization process takes place in two steps.18 First, the motion of 180° domain walls leads to a magnetization of M without any contribution to magnetostriction In the second step, the spins rotate in the direction of the applied magnetic field, leading to the change of both magnetization and magnetostriction For amorphous alloys of randomly oriented spins and of a random distribution of domain walls, the M is expected to be of M max/2 In this case, the relation between magnetostriction and magnetization is given as19 ␭ ͑ H ͒ /␭ maxϭ ͓ 2M ͑ H ͒ /M maxϪ1 ͔ 3/2 ͑1͒ 7211 FIG Experimental and theoretical relations between normalized magnetostriction and magnetization for amorphous Tb͑Fe0.55Co0.45͒1.5 films ͑1͒ and ͑2͒ theoretical curves described for Eqs ͑1͒ and ͑2͒, respectively ͑᭿͒ as deposed, ͑᭹͒ T A ϭ250 °C, ͑᭡͒ 350 °C, and ͑᭺͒ 450 °C For the motion of 90° domain walls, i.e., the rotation of magnetization out of the easy axis, the magnetostriction is related to magnetization as follows:18 ␭ ͑ H ͒ /␭ maxϭ ͓ M ͑ H ͒ /M max͔ ͑2͒ Taking the values measured in ␮ Hϭ0.7 T as ␭ max and M max , the relation between the normalized magnetostriction and magnetization is presented in Fig For the as-deposited film with the perpendicular anisotropy, almost no magnetostriction takes place at M /M maxϽ0.3 and the experimental data are close to the curve described by Eq ͑2͒ It is possible that, in this film, the magnetization process is governed mainly by the rotation of spins As the annealing temperature increases, the ␭/␭ max starts at a higher M /M max value, for instance M /M maxϭ0.6 and 0.75 for T A ϭ250 and 350 °C, respectively This further confirms the randomly oriented spin structure At T A ϭ450 °C, the ␭/␭ max vs M /M max curve also starts at M /M maxϭ0.6, and follows well that of 250 °C IV CONCLUDING REMARKS It is well known that, in a traditional route, the substitution of Dy for Tb has been used to compensate the anisotropy and then to increase the magnetostriction at low magnetic fields However, it is also accompanied by a reduction in the saturation magnetostriction At present, we have shown that Co substitution, coupled with the effects of zerofield annealing, results in an enhancement of both the lowfield and the saturation magnetostriction Actually, we have obtained a giant magnetostriction of ␭ ʈ ϭ340ϫ10Ϫ6 in field ␮ HϽ20 mT and ␹ ␭ ϭ1.8ϫ10Ϫ2 TϪ1 in amorphous Tb͑Fe0.55Co0.45͒1.5 Such films are very promising for applications In this study, the Co substitution led to the enhancement of the 3d(Fe,Co) – 3d(Fe,Co) as well as f (Tb) – 3d(Fe,Co) exchange energies and then the intrinsic magnetostriction The soft magnetic and magnetostrictive behaviors, on one hand, relate to the closing of the Tb-cone angle, but on the other, may also be associated with the soft magnetic ␣-͑Fe, Co͒ layer, which was segregated at the surface during [This article is copyrighted as indicated in the article Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions Downloaded to ] IP: 130.79.0.174 On: Tue, 13 May 2014 08:17:48 7212 the heat treatments The study of the influence of the soft magnetic layer on the soft magnetostrictive character is in progress ACKNOWLEDGMENTS This work was granted by the National University of Hanoi within Project No QG.99.08 The authors express their thanks to Dr Le Van Vu for the x-ray diffraction measurements The stay of N H Duc at the GMP, University of Rouen is supported by the Ministe`re Franc¸aise de l’Education Nationale, de la Recherche et la Technologie E Quandt, J Alloys Compd 258, 126 ͑1997͒ E Tre´molet de Lacheisserise, K Mackey, J Betz, and J C Peuzin, J Alloys Compd 275–277, 685 1998 S F Fischer, M Kelsch, and H Kronmuăller, J Magn Magn Mater 195, 545 ͑1999͒ N H Duc, in Handbook on the Physics and Chemistry of Rare Earths, edited by K A Gschneidner, Jr and L Eyring ͑North-Holland, Amsterdam, to be published͒, Vol 28 J M D Coey, D Givord, A Lie´nard, and J P Rebouillat, J Phys F: Met Phys 11, 2707 ͑1981͒ Danh et al J Appl Phys., Vol 87, No 10, 15 May 2000 P Hansen, G Much, M Rosenkranz, and K Witter, J Phys 66, 756 ͑1989͒; P Hansen, in Ferromagnetic Materials, edited by K H J Buschow ͑North-Holland, Amsterdam, 1991͒, Vol 6, p 289 J Betz, thesis, University Joseph Fourier of Grenoble, 1997 N H Duc, K Mackay, J Betz, and D Givord, J Appl Phys 79, 973 ͑1996͒ N H Duc, K Mackay, J Betz, and D Givord, J Appl Phys 87, 834 ͑2000͒ 10 E Tre´molet de Lacheisserise and J C Peuzin, J Magn Magn Mater 136, 189 ͑1994͒ 11 J Betz, E du Tre´molet de Lacheisserise, and L T Baczewski, Appl Phys Lett 68, 132 ͑1996͒ 12 K Ried, M Schnell, F Schatz, M Hirscher, B Ludescher, W Sigle, and H Kronmuăller, Phys Status Solidi A 167, 195 ͑1998͒ 13 A Forkl, M Hirscher, T Mizoguchi, H Kronmuăller, and H U Habermeier, J Magn Magn Mater 93, 261 ͑1991͒ 14 F Hellman, M Messer, and E N Abarra, J Appl Phys 86, 1047 ͑1999͒ 15 M Wada, H Uchida, and H Kaneko, J Alloys Compd 258, 169 ͑1997͒ 16 A Hernando, C Prados, and C Prieto, J Magn Magn Mater 157Õ158, 501 ͑1996͒ 17 V G Harris, K D Aylesworth, B N Das, W T Elam, and N C Koon, Phys Rev Lett 68, 1939 ͑1992͒ 18 S Chikazumi, Physics of Magnetism ͑Wiley, New York, 1964͒ 19 F Schatz, M Hirscher, M Schnell, G Flik, and H Kronmuăller, J Appl Phys 76, 5380 ͑1994͒ [This article is copyrighted as indicated in the article Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions Downloaded to ] IP: 130.79.0.174 On: Tue, 13 May 2014 08:17:48 ... direction of the applied magnetic field, leading to the change of both magnetization and magnetostriction For amorphous alloys of randomly oriented spins and of a random distribution of domain... temperature magnetic and magnetostrictive characteristics of the amorphous Tb͑Fe0.55Co0.45͒1.5 films: T A , M S , ␮ o H C ʈ , ͗ B hf͘ , ␤, and ␭(ϭ␭ ʈ Ϫ␭Ќ ) are the annealing temperature, saturation... applications We can further associate the field dependence of the magnetostriction with different types of magnetization processes For a system of randomly oriented spin and random distribution of