- Email: [email protected]
Fe trilayers
Journal of Magnetism and Magnetic Materials 226}230 (2001) 1770}1772
Temperature dependence of the inter"lm magnetic interaction in Fe/Cr/Fe trilayers C. Chesman *, N.S. Almeida , A. Azevedo, F.M. de Aguiar, S.M. Rezende Departamento de Fn& sica Teo& rica e Experimental, CCET Universidade Federal do Rio Grande do Norte, 59072-970, Natal/RN, Brazil Departamento de Fn& sica, CCEN Universidade Federal de Pernambuco, 50670-901, Recife/PE, Brazil
Abstract The behavior of the inter"lm magnetic interaction in Fe(40 As )/Cr(t )/Fe(40 As ) trilayers (t "11, 13 and 15 As ), grown ! ! on MgO(1 0 0), is investigated theoretically and experimentally through ferromagnetic resonance. The experimental data show that for temperatures well below T the temperature variation of the e!ective interlayer coupling arises mainly from the spin #uctuations of ferromagnetic "lms. 2001 Elsevier Science B.V. All rights reserved. Keywords: Multilayers; E!ective spin exchange; Spin #uctuations
Magnetic structures composed of ferromagnetic "lms separated by a nonmagnetic spacer have many of their physical characteristics determined by the magnetic interactions between adjacent magnetic "lms [1,2]. It is well known that ferromagnetic "lms, separated by nonmagnetic metallic spacer layer, may exhibit antiferromagnetic or even oscillatory interlayer exchange coupling [3]. Giant magnetoresistance [3] and inter"lm interactions that favor a perpendicular alignment of the magnetization of adjacent "lms (biquadratic exchange coupling) observed in magnetic trilayers [4], among others, are phenomena that drive the interest in these systems, since they open up the possibility to synthesize samples to "t di!erent technological requirements. Recent experimental data indicate that the physical characteristics of these system are quite sensitive to variations of the temperature of the sample. One of the source of this variation is the modi"cation of the e!ective inter"lm exchange provided by thermal #uctuations in the spin system [5]. In this paper we report an experimental and theoretical study of the temperature dependence of the e!ective exchange coupling between the Fe "lms in Fe/Cr/Fe trilayers.
* Corresponding author. Fax: #55-84-215-2791. E-mail address: [email protected] (C. Chesman).
We write the magnetic energy as the sum of the anisotropy, exchange (bilinear and biquadratic) and Zeeman energies to analyze the dynamical behavior of the system. The comparison of an analytical dispersion relation, obtained from the linearized torque equations, with the FMR experimental data is used to obtain the parameters necessary to describe the system. We carried out FMR experiments in magnetic trilayers composed by two iron "lms, 40 As thick, separated by chromium layer of thickness t "11, 13 and 15 As , grown ! by magnetron-sputtering deposition in an ultrahigh vacuum chamber onto MgO(1 0 0) substrates. The base pressure prior to the deposition was typically 2;10\ Torr and the sputter pressure was usually 3;10\ Torr of Ar. The FMR measurements were performed at 9.4 GHz by monitoring the derivative of the absorption line for a TE rectangular microwave cavity with Q"2500. All results were obtained with the externally DC magnetic "eld applied parallel to the "lm surface with the sample located at the center of the cavity. In Fig. 1, we display the temperature behavior of the optical (solid circles) and acoustical (solid triangles) resonance "elds of the Fe(40 As )/Cr(15 As )/Fe(40 As ) trilayer obtained for several directions of the DC magnetic "eld. In order to obtain the temperature dependence of the inter"lm exchange coupling, we have modeled the system as a stack of N monoatomic layers, in"nity in the planar $ extend, which form a cubic crystal in the bulk realization
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 0 1 1 - 8
C. Chesman et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1770}1772
Fig. 1. Temperature dependence of the optical (solid circles) and acoustical (solid triangles) resonance "elds of the Fe(40 As )/Cr(15 As )/Fe(40 As ) trilayer. Open circles are optical resonance "eld for "403. &
of the structure. We consider the localized spins coupled with their nearest neighbors by the bilinear interaction everywhere. The spins at the interface are also coupled with their nearest neighbors at the interface of the other magnetic "lm by a biquadratic interaction. We assume that the spins feel a crystalline anisotropy and the presence of an in-plane DC magnetic "eld. The description of the interactions is completed by the inclusion of the dipolar coupling. The temperature dependence is introduced by following the scheme used by Almeida et al. [5] to linearize the equations of motion for the spin wave operators. The complete set of linearized coupled equations of motion is written in a matricial form to obtain the frequency of the spin wave modes. The di!erence between the frequencies of the acoustical and optical modes (two lowest frequency modes) is proportional to the e!ective exchange coupling of the ferromagnetic "lms. In Fig. 2, we show the experimental result (symbols) and theoretical values (lines) for the di!erence between the frequencies of the acoustical and optical modes of the system described above. The parameters used to describe microscopically the system are proportional to the correspondening macroscopic parameter obtained from the FMR data. In the inset, we show the critical temperature obtained from the "tting of the experimental data by the theoretical result. It should be observed that the critical temperature is smaller if the inter"lm interaction is
1771
Fig. 2. Temperature dependence of the normalized e!ective exchange parameter of Fe(40 As )/Cr(t )/Fe(40 As ). Symbols are ! experimental data and lines are theoretical results.
weaker. This should be expected since a stronger inter"lm interaction gives rise to a behavior similar to the one observed in a "lm with a thickness near to the sum of the thickness of the "lms of the sample. On the other hand, a very weak inter"lm interaction gives rise to a behavior similar to one observed for a single thin "lm, which should have the critical temperature smaller than the previous case. We can see in Fig. 2 that the theoretical calculation gives a very good "t for the experimental data for the sample with t "11 As . Despite some #uctuation ! in the experimental data, the theoretical "t for the experimental results of the sample with t "13 As also depicts ! the general features of the physical behavior of this sample. However, the theoretical "tting for the experimental values of the e!ective exchange coupling of the sample with t "15 As is poor. The reason for that is the ! fact that this sample has a very weak inter"lm interaction and consequently has the critical temperature much smaller than the others. Since the approach used to obtain the spin wave dispersion relation is reliable at temperatures well below T , the poor theoretical "tting for this sample might be expected. The results presented in this paper indicate that, at least for the samples investigated, the main source of the temperature variation of the e!ective inter"lm exchange is the interaction of the spin wave excited in the measurement process and the thermally excited spin wave. C.C. and N.S.A. are partially supported by the Brazilian National Research Council (CNPq). The work at
1772
C. Chesman et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1770}1772
UFPE is supported by FINEP, CNPq and CAPES. The authors thank Dr. S.S.P. Parkin who provided all samples analyzed in this work.
References [1] N.S. Almeida, D.L. Mills, Phys. Rev. B 52 (1995) 13504.
[2] T.L. Fonseca, N.S. Almeida, Phys. Rev. B 57 (1998) 13450. [3] B. Heinrich, J.A.C. Bland, Ultrathin Magnetic Structures, Vol. 1, 2, Springer, Berlin, 1994 and references therein. [4] A. Azevedo, C. Chesman, S.M. Rezende, F.M. de Aguiar, X. Bian, S.S.P. Parkin, Phys. Rev. Lett. 76 (1996) 4837. [5] N.S. Almeida, D.L. Mills, M. Teitelamn, Phys. Rev. Lett. 75 (1995) 733.
Temperature dependence of the inter"lm magnetic interaction in Fe/Cr/Fe trilayers C. Chesman *, N.S. Almeida , A. Azevedo, F.M. de Aguiar, S.M. Rezende Departamento de Fn& sica Teo& rica e Experimental, CCET Universidade Federal do Rio Grande do Norte, 59072-970, Natal/RN, Brazil Departamento de Fn& sica, CCEN Universidade Federal de Pernambuco, 50670-901, Recife/PE, Brazil
Abstract The behavior of the inter"lm magnetic interaction in Fe(40 As )/Cr(t )/Fe(40 As ) trilayers (t "11, 13 and 15 As ), grown ! ! on MgO(1 0 0), is investigated theoretically and experimentally through ferromagnetic resonance. The experimental data show that for temperatures well below T the temperature variation of the e!ective interlayer coupling arises mainly from the spin #uctuations of ferromagnetic "lms. 2001 Elsevier Science B.V. All rights reserved. Keywords: Multilayers; E!ective spin exchange; Spin #uctuations
Magnetic structures composed of ferromagnetic "lms separated by a nonmagnetic spacer have many of their physical characteristics determined by the magnetic interactions between adjacent magnetic "lms [1,2]. It is well known that ferromagnetic "lms, separated by nonmagnetic metallic spacer layer, may exhibit antiferromagnetic or even oscillatory interlayer exchange coupling [3]. Giant magnetoresistance [3] and inter"lm interactions that favor a perpendicular alignment of the magnetization of adjacent "lms (biquadratic exchange coupling) observed in magnetic trilayers [4], among others, are phenomena that drive the interest in these systems, since they open up the possibility to synthesize samples to "t di!erent technological requirements. Recent experimental data indicate that the physical characteristics of these system are quite sensitive to variations of the temperature of the sample. One of the source of this variation is the modi"cation of the e!ective inter"lm exchange provided by thermal #uctuations in the spin system [5]. In this paper we report an experimental and theoretical study of the temperature dependence of the e!ective exchange coupling between the Fe "lms in Fe/Cr/Fe trilayers.
* Corresponding author. Fax: #55-84-215-2791. E-mail address: [email protected] (C. Chesman).
We write the magnetic energy as the sum of the anisotropy, exchange (bilinear and biquadratic) and Zeeman energies to analyze the dynamical behavior of the system. The comparison of an analytical dispersion relation, obtained from the linearized torque equations, with the FMR experimental data is used to obtain the parameters necessary to describe the system. We carried out FMR experiments in magnetic trilayers composed by two iron "lms, 40 As thick, separated by chromium layer of thickness t "11, 13 and 15 As , grown ! by magnetron-sputtering deposition in an ultrahigh vacuum chamber onto MgO(1 0 0) substrates. The base pressure prior to the deposition was typically 2;10\ Torr and the sputter pressure was usually 3;10\ Torr of Ar. The FMR measurements were performed at 9.4 GHz by monitoring the derivative of the absorption line for a TE rectangular microwave cavity with Q"2500. All results were obtained with the externally DC magnetic "eld applied parallel to the "lm surface with the sample located at the center of the cavity. In Fig. 1, we display the temperature behavior of the optical (solid circles) and acoustical (solid triangles) resonance "elds of the Fe(40 As )/Cr(15 As )/Fe(40 As ) trilayer obtained for several directions of the DC magnetic "eld. In order to obtain the temperature dependence of the inter"lm exchange coupling, we have modeled the system as a stack of N monoatomic layers, in"nity in the planar $ extend, which form a cubic crystal in the bulk realization
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 0 1 1 - 8
C. Chesman et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1770}1772
Fig. 1. Temperature dependence of the optical (solid circles) and acoustical (solid triangles) resonance "elds of the Fe(40 As )/Cr(15 As )/Fe(40 As ) trilayer. Open circles are optical resonance "eld for "403. &
of the structure. We consider the localized spins coupled with their nearest neighbors by the bilinear interaction everywhere. The spins at the interface are also coupled with their nearest neighbors at the interface of the other magnetic "lm by a biquadratic interaction. We assume that the spins feel a crystalline anisotropy and the presence of an in-plane DC magnetic "eld. The description of the interactions is completed by the inclusion of the dipolar coupling. The temperature dependence is introduced by following the scheme used by Almeida et al. [5] to linearize the equations of motion for the spin wave operators. The complete set of linearized coupled equations of motion is written in a matricial form to obtain the frequency of the spin wave modes. The di!erence between the frequencies of the acoustical and optical modes (two lowest frequency modes) is proportional to the e!ective exchange coupling of the ferromagnetic "lms. In Fig. 2, we show the experimental result (symbols) and theoretical values (lines) for the di!erence between the frequencies of the acoustical and optical modes of the system described above. The parameters used to describe microscopically the system are proportional to the correspondening macroscopic parameter obtained from the FMR data. In the inset, we show the critical temperature obtained from the "tting of the experimental data by the theoretical result. It should be observed that the critical temperature is smaller if the inter"lm interaction is
1771
Fig. 2. Temperature dependence of the normalized e!ective exchange parameter of Fe(40 As )/Cr(t )/Fe(40 As ). Symbols are ! experimental data and lines are theoretical results.
weaker. This should be expected since a stronger inter"lm interaction gives rise to a behavior similar to the one observed in a "lm with a thickness near to the sum of the thickness of the "lms of the sample. On the other hand, a very weak inter"lm interaction gives rise to a behavior similar to one observed for a single thin "lm, which should have the critical temperature smaller than the previous case. We can see in Fig. 2 that the theoretical calculation gives a very good "t for the experimental data for the sample with t "11 As . Despite some #uctuation ! in the experimental data, the theoretical "t for the experimental results of the sample with t "13 As also depicts ! the general features of the physical behavior of this sample. However, the theoretical "tting for the experimental values of the e!ective exchange coupling of the sample with t "15 As is poor. The reason for that is the ! fact that this sample has a very weak inter"lm interaction and consequently has the critical temperature much smaller than the others. Since the approach used to obtain the spin wave dispersion relation is reliable at temperatures well below T , the poor theoretical "tting for this sample might be expected. The results presented in this paper indicate that, at least for the samples investigated, the main source of the temperature variation of the e!ective inter"lm exchange is the interaction of the spin wave excited in the measurement process and the thermally excited spin wave. C.C. and N.S.A. are partially supported by the Brazilian National Research Council (CNPq). The work at
1772
C. Chesman et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1770}1772
UFPE is supported by FINEP, CNPq and CAPES. The authors thank Dr. S.S.P. Parkin who provided all samples analyzed in this work.
References [1] N.S. Almeida, D.L. Mills, Phys. Rev. B 52 (1995) 13504.
[2] T.L. Fonseca, N.S. Almeida, Phys. Rev. B 57 (1998) 13450. [3] B. Heinrich, J.A.C. Bland, Ultrathin Magnetic Structures, Vol. 1, 2, Springer, Berlin, 1994 and references therein. [4] A. Azevedo, C. Chesman, S.M. Rezende, F.M. de Aguiar, X. Bian, S.S.P. Parkin, Phys. Rev. Lett. 76 (1996) 4837. [5] N.S. Almeida, D.L. Mills, M. Teitelamn, Phys. Rev. Lett. 75 (1995) 733.