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Ferromagnetic resonance line of ferrite ferrofluids at high microwave power
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 289 (2005) 84–86 www.elsevier.com/locate/jmmm
Ferromagnetic resonance line of ferrite ferrofluids at high microwave power F. Pelegrinia,, A.R. Pereiraa, P.C. Moraisb a
Universidade Federal de Goia´s, Instituto de Fı´sica, Campus Samambaia, Goiaˆna 74001-970, Brazil Universidade de Brası´lia, Instituto de Fı´sica, Nu´cleo de Fı´sica Aplicada, Brası´lia 70919-970, Brazil
b
Available online 26 November 2004
Abstract The effects of high microwave power levels upon the ferromagnetic resonance (FMR) lines of liquid and frozen ferrite ferrofluids are investigated. The distortions of the FMR lines at critical microwave power levels give evidence of the onset of instabilities due to non-linear processes. r 2004 Published by Elsevier B.V. PACS: 75.50.Mm; 76.50.+g Keywords: Ferrofluids; FMR; High-power FMR; FMR line
It is well-known that at sufficiently microwave power levels several instabilities processes can be observed in ferromagnetic resonance (FMR) experiments. They have been investigated since the early years of FMR and were recently revised by Kabos et al. [1], and Cox et al. [2]. These non-linear phenomena, observed even at power levels in the mW range, can be associated with a decrease of the static component of the magnetization vector with increasing microwave power, giving rise to a resonance frequency shift and bi-stable absorption lines, or with the fact that above a well-defined threshold level, at which the amplitude of the uniform resonance mode exceeds a critical value, short-wavelength spin waves become excited in the magnetic material. In a ‘‘firstorder’’ instability process, as subsidiary absorption, these spin waves have half the frequency of the microwave field; in a ‘‘second-order’’ process, as premature saturation, they have the same frequency as the applied RF field. Besides this, auto oscillations of the Corresponding author. Tel./fax: +55 62 521 1029.
E-mail address: pelegrin@fis.ufg.br (F. Pelegrini). 0304-8853/$ - see front matter r 2004 Published by Elsevier B.V. doi:10.1016/j.jmmm.2004.11.024
magnetization and reduced coupling between the microwave field and the original precession breaks down the linear dependence between the pumping field and the precession’s amplitude [3], giving rise to distortions of the resonance line. Indeed, in FMR experiments sweeping the magnetic field at a fixed microwave frequency, second-order instability due to non-linearity was investigated in films of barium ferrite and yttrium iron garnet by observing the shape of the FMR line as a function of microwave power. The power at which the FMR line was visibly distorted was taken as the critical power for the onset of instabilities [4]. So far, the several non-linear FMR processes have been intensively investigated mostly in single-crystal samples of ferrites and garnets with narrow FMR lines. Amorphous magnetic materials, such as ferrite ferrofluids (FF), also have been investigated by FMR and this allowed, for example, the analysis of the interactions between the magnetic nanoparticles [5] and the study of the energy contributions due to the surface anisotropy [6]. FMR measurements at low microwave power, below the critical power for the onset of non-linear processes, also show that the
ARTICLE IN PRESS F. Pelegrini et al. / Journal of Magnetism and Magnetic Materials 289 (2005) 84–86
form of the FMR line depends on contributions from distinct structures, such as monomers, dimers, and chains of particles present in the FF sample [7]. At low microwave power, the lineshape of the usual FMR line of FF is as shown by line (a) in Fig. 1; at a higher power, however, above a critical threshold level, the line is clearly distorted, as it is shown by line (b) also in Fig. 1. These FMR lines of an aqueous solution of oleylsarcosine surface-coated magnetite particles were recorded at room temperature, at the microwave frequency of 9.7939 GHz, employing phase sensitive detection techniques, modulation frequency of 100 kHz and modulation field amplitude of 1.0 Oe. The average diameter of the particles was 6.2 nm and the volume of the sample studied was 1.0 103 cm3, containing 6.6 1016 particles/cm3. The reference resonance field is 3.11 kOe and the g-factor is 2.25. At the microwave power level of 1.0 mW, the resonance line (a) is almost symmetrical and has a line width of 0.93 kOe. At the power level of 100.0 mW, the resonance line (b) is wider and distorted, with a line width of 1.35 kOe and two kinks (shown by the arrows) at which abrupt changes in the level of the reflected microwave power from the cavity are recorded, giving evidence of instabilities as the external field is swept. Indeed, due to the very high Q-factor of the resonators used in this study, as the field is swept from one kink to the other, increasing or decreasing, the very high reflected power do not allow anymore the automatic control of the resonance frequency. As the power is increased, the kinks separate in field and we assume that the first evidence of them in the FMR line gives the critical power for the onset of instabilities. In a previous
(a) 1 mW
(b) 100 mW
1
2
3
4
5
H (kOe) Fig. 1. FMR lines of magnetite FF at the microwave frequency of 9.7939 GHz, and microwave power levels of: (a) 1.0 mW; and (b) 100.0 mW.
85
work [8] we have shown that the dependence of the critical microwave power level Pc on the concentration N of magnetic particles in the FF sample is given by Pc ¼ Po =eaðNN o Þ :
(1)
Po is the critical power related to N o particles/cm3 and a is a constant. The measurements for this magnetite FF give Po ¼ 130 mW; corresponding to the lowest concentration N o ¼ 1:0 1016 particles=cm3 ; and a constant a ¼ 7:2 1017 cm3 : Measurements for another magnetite FF containing particles with larger average diameter of 9.4 nm, show the same exponential decay of the critical microwave power on the concentration of particles and give Po ¼ 570 mW; corresponding to N o ¼ 0:75 1016 particles/cm3, and a ¼ 1:4 1016 cm3 : The constant a depends, therefore, on the volume and susceptibility of the magnetic material in the sample. This agrees with the fact that the absorbed power P at the angular frequency o and microwave field h is given by [9] P ¼ ðo=2Þh2 w00 V: 00
(2)
w is the complex susceptibility and V is the volume of the sample. As the measurements are performed with the same sensibility, the critical power for the onset of instabilities depends on the magnetic properties of the FF sample. Evidence that the kink in the resonance line is associated with the magnetic properties of the FF sample, is also given by the angular dependence of the FMR lines of a large volume ionic water-based MnFe2O4 ferrofluid frozen as a film, in a flat quartz cell, in the presence of an applied field of 10.0 kOe, parallel to the cell’s face. The FMR measurements were performed at the microwave frequency of 9.429 GHz and 20.0 mW microwave power, with the film at the temperature of 100 K. The very large 2.48 kOe resonance line, at the resonance field of 2.90 kOe, shows two kinks recorded at the fields of 1.11 and 4.36 kOe, when the applied swiping field is parallel to the film. As the angle between the field and the film varies from 01 to 901, the resonance line is displaced to higher field values but shows the same line width and field separation between the kinks. When the field is perpendicular to the film, the resonance field is at 3.53 kOe and the two kinks are recorded at the fields of 1.71 and 4.96 kOe. As the angle between the field and the film increases from 901 to 1801, the kinks in the resonance lines are recorded at the same lower fields for the equivalent relative orientations. These results show that the onset of instabilities in the reflected power from the cavity is associated with the susceptibility of the sample and give evidence not only of the anisotropy of the magnetic particles and the formation of chains of particles during the cooling process, but also of the lack of any hysteresis in the frozen film. The resonance lines for the applied field
ARTICLE IN PRESS 86
F. Pelegrini et al. / Journal of Magnetism and Magnetic Materials 289 (2005) 84–86
parallel and anti-parallel to the frozen FF film are the same. Besides this, as the temperature increases, the line width of the resonance line reduces and also the field separation between the kinks, giving evidence again that they are associated with the magnetic properties of the FF sample and their behavior with temperature. At the temperature of 250 K, for example, the resonance line has a line width of 1.29 kOe, the parallel resonance field is 3.05 kOe, and the kinks are recorded at the fields of 2.80 and 3.20 kOe. Indeed, at this temperature, for this large volume sample, 20.0 mW is the critical microwave power for the onset of non-linear excitations. In view of these experimental results, we can conclude that the recorded kinks in our FMR lines of liquid or frozen FF samples, give evidence of the onset of secondorder instabilities due to non-linear effects. A theory of FMR instabilities in dispersed magnetic nanoparticles, as in liquid or frozen FF samples, in terms of static and dynamic effective fields, must consider necessarily the interactions between the distinct structures in the sample, dependent on the concentration of magnetic particles, and also the effects due to surface anisotropy. However, the dependence of the critical microwave power on the concentration of magnetic particles shows for each FF sample the experimental conditions to avoid FMR instabilities and obtain resonance lines without distortions. The knowledge of this dependence for each sample is of paramount importance in studies of the line width as a function of concentration of particles, or temperature, for example. At low microwave power levels, below the critical microwave power, single pattern resonance lines will give true values of line width. Above the critical power, for samples with large concentration of magnetic particles, the onset of nonlinear processes can give rise even to two pattern resonance lines, avoiding indeed the measurement of a true line width. At low microwave power, according to Tronconi et al. [5], the line width DH as a function of the mean distance R between the particles of an ionic waterbased MnFe2O4 ferrofluid, in the absence of any electrical interaction between the particles, is given by DH ¼ ðA=R3 Þ tanhð1=2kTÞðB þ C=R3 Þ:
(3)
In this expression, the constant A is related to the magnetic moment of the particles, the constant B, to the Brownian motion, the magnetic anisotropy and the interaction of the particles with the external field, and the constant C, to the dipole interaction between
magnetic particles; k is the Boltzmann constant, and T is the absolute temperature. However, a correction Hs to the dipolar field, implying DH ¼ ðA=R3 þ H s Þ tanhð1=2kTÞðB þ C=R3 Þ:
(4)
was introduced by Hrianca et al. [10] to explain the concentration dependence of the FMR line width from ferrofluids containing magnetite particles or mix ferrite particles of Mn0.6Fe0.4Fe2O4 type, dispersed in kerosene. The need for this correction was deduced from line widths given by two pattern FMR lines [10], and was attributed by Marin [11] to the presence of chains of magnetic particles in the FF sample and to the fact that the number of particles in the chains depends on the concentration of magnetic particles. We consider that some aspects of our experimental results confirm the presence of chains of magnetic particles in the FF sample, and that this depends on the concentration of particles. However, they also show that two pattern resonance lines can be due to the onset of non-linear effects, dependent on the magnetic susceptibility and volume of magnetic material of the FF sample, and microwave power.
References [1] P. Kabos, C.E. Patton, G. Wiese, A.D. Sullins, E.S. Wright, L. Chen, J. Appl. Phys. 80 (1996) 3962. [2] R.G. Cox, C.E. Patton, M.A. Wittenauer, P. Kabos, L. Chen, J. Appl. Phys. 89 (2001) 4454. [3] Y.V. Gulyaev, P.E. Zil0 berman, A.G. Temiryazev, M.P. Tikhomirova, Phys. Solid State 42 (2000) 1094. [4] P. Dorsey, J.B. Sokoloff, C. Vittoria, J. Appl. Phys. 74 (1993) 1938. [5] A.L. Tronconi, P.C. Morais, F. Pelegrini, F.A. Tourinho, J. Magn. Magn. Mater. 122 (1993) 90. [6] A.F. Bakuzis, P.C. Morais, F. Pelegrini, J. Appl. Phys. 85 (1999) 7480. [7] G.R.R. Gonc- alves, A.R. Pereira, A.F. Bakuzis, K. Skeff Neto, F. Pelegrini, P.C. Morais, J. Magn. Magn. Mater. 226–230 (2001) 1896. [8] F. Pelegrini, A.R. Pereira, M.B. Arau´jo, A.L. Tronconi, P.C. Morais, J. Magn. Magn. Mater. 272–276 (2004) 2381. [9] S.V. Vonsovskii (Ed.), Ferromagnetic Resonance, Pergamon, Oxford, 1966, p. 274. [10] I. Hrianca, I. Malaescu, F. Claici, C.N. Marin, J. Magn. Magn. Mater. 201 (1999) 126. [11] C.N. Marin, J. Magn. Magn. Mater. 250 (2002) 197.
Journal of Magnetism and Magnetic Materials 289 (2005) 84–86 www.elsevier.com/locate/jmmm
Ferromagnetic resonance line of ferrite ferrofluids at high microwave power F. Pelegrinia,, A.R. Pereiraa, P.C. Moraisb a
Universidade Federal de Goia´s, Instituto de Fı´sica, Campus Samambaia, Goiaˆna 74001-970, Brazil Universidade de Brası´lia, Instituto de Fı´sica, Nu´cleo de Fı´sica Aplicada, Brası´lia 70919-970, Brazil
b
Available online 26 November 2004
Abstract The effects of high microwave power levels upon the ferromagnetic resonance (FMR) lines of liquid and frozen ferrite ferrofluids are investigated. The distortions of the FMR lines at critical microwave power levels give evidence of the onset of instabilities due to non-linear processes. r 2004 Published by Elsevier B.V. PACS: 75.50.Mm; 76.50.+g Keywords: Ferrofluids; FMR; High-power FMR; FMR line
It is well-known that at sufficiently microwave power levels several instabilities processes can be observed in ferromagnetic resonance (FMR) experiments. They have been investigated since the early years of FMR and were recently revised by Kabos et al. [1], and Cox et al. [2]. These non-linear phenomena, observed even at power levels in the mW range, can be associated with a decrease of the static component of the magnetization vector with increasing microwave power, giving rise to a resonance frequency shift and bi-stable absorption lines, or with the fact that above a well-defined threshold level, at which the amplitude of the uniform resonance mode exceeds a critical value, short-wavelength spin waves become excited in the magnetic material. In a ‘‘firstorder’’ instability process, as subsidiary absorption, these spin waves have half the frequency of the microwave field; in a ‘‘second-order’’ process, as premature saturation, they have the same frequency as the applied RF field. Besides this, auto oscillations of the Corresponding author. Tel./fax: +55 62 521 1029.
E-mail address: pelegrin@fis.ufg.br (F. Pelegrini). 0304-8853/$ - see front matter r 2004 Published by Elsevier B.V. doi:10.1016/j.jmmm.2004.11.024
magnetization and reduced coupling between the microwave field and the original precession breaks down the linear dependence between the pumping field and the precession’s amplitude [3], giving rise to distortions of the resonance line. Indeed, in FMR experiments sweeping the magnetic field at a fixed microwave frequency, second-order instability due to non-linearity was investigated in films of barium ferrite and yttrium iron garnet by observing the shape of the FMR line as a function of microwave power. The power at which the FMR line was visibly distorted was taken as the critical power for the onset of instabilities [4]. So far, the several non-linear FMR processes have been intensively investigated mostly in single-crystal samples of ferrites and garnets with narrow FMR lines. Amorphous magnetic materials, such as ferrite ferrofluids (FF), also have been investigated by FMR and this allowed, for example, the analysis of the interactions between the magnetic nanoparticles [5] and the study of the energy contributions due to the surface anisotropy [6]. FMR measurements at low microwave power, below the critical power for the onset of non-linear processes, also show that the
ARTICLE IN PRESS F. Pelegrini et al. / Journal of Magnetism and Magnetic Materials 289 (2005) 84–86
form of the FMR line depends on contributions from distinct structures, such as monomers, dimers, and chains of particles present in the FF sample [7]. At low microwave power, the lineshape of the usual FMR line of FF is as shown by line (a) in Fig. 1; at a higher power, however, above a critical threshold level, the line is clearly distorted, as it is shown by line (b) also in Fig. 1. These FMR lines of an aqueous solution of oleylsarcosine surface-coated magnetite particles were recorded at room temperature, at the microwave frequency of 9.7939 GHz, employing phase sensitive detection techniques, modulation frequency of 100 kHz and modulation field amplitude of 1.0 Oe. The average diameter of the particles was 6.2 nm and the volume of the sample studied was 1.0 103 cm3, containing 6.6 1016 particles/cm3. The reference resonance field is 3.11 kOe and the g-factor is 2.25. At the microwave power level of 1.0 mW, the resonance line (a) is almost symmetrical and has a line width of 0.93 kOe. At the power level of 100.0 mW, the resonance line (b) is wider and distorted, with a line width of 1.35 kOe and two kinks (shown by the arrows) at which abrupt changes in the level of the reflected microwave power from the cavity are recorded, giving evidence of instabilities as the external field is swept. Indeed, due to the very high Q-factor of the resonators used in this study, as the field is swept from one kink to the other, increasing or decreasing, the very high reflected power do not allow anymore the automatic control of the resonance frequency. As the power is increased, the kinks separate in field and we assume that the first evidence of them in the FMR line gives the critical power for the onset of instabilities. In a previous
(a) 1 mW
(b) 100 mW
1
2
3
4
5
H (kOe) Fig. 1. FMR lines of magnetite FF at the microwave frequency of 9.7939 GHz, and microwave power levels of: (a) 1.0 mW; and (b) 100.0 mW.
85
work [8] we have shown that the dependence of the critical microwave power level Pc on the concentration N of magnetic particles in the FF sample is given by Pc ¼ Po =eaðNN o Þ :
(1)
Po is the critical power related to N o particles/cm3 and a is a constant. The measurements for this magnetite FF give Po ¼ 130 mW; corresponding to the lowest concentration N o ¼ 1:0 1016 particles=cm3 ; and a constant a ¼ 7:2 1017 cm3 : Measurements for another magnetite FF containing particles with larger average diameter of 9.4 nm, show the same exponential decay of the critical microwave power on the concentration of particles and give Po ¼ 570 mW; corresponding to N o ¼ 0:75 1016 particles/cm3, and a ¼ 1:4 1016 cm3 : The constant a depends, therefore, on the volume and susceptibility of the magnetic material in the sample. This agrees with the fact that the absorbed power P at the angular frequency o and microwave field h is given by [9] P ¼ ðo=2Þh2 w00 V: 00
(2)
w is the complex susceptibility and V is the volume of the sample. As the measurements are performed with the same sensibility, the critical power for the onset of instabilities depends on the magnetic properties of the FF sample. Evidence that the kink in the resonance line is associated with the magnetic properties of the FF sample, is also given by the angular dependence of the FMR lines of a large volume ionic water-based MnFe2O4 ferrofluid frozen as a film, in a flat quartz cell, in the presence of an applied field of 10.0 kOe, parallel to the cell’s face. The FMR measurements were performed at the microwave frequency of 9.429 GHz and 20.0 mW microwave power, with the film at the temperature of 100 K. The very large 2.48 kOe resonance line, at the resonance field of 2.90 kOe, shows two kinks recorded at the fields of 1.11 and 4.36 kOe, when the applied swiping field is parallel to the film. As the angle between the field and the film varies from 01 to 901, the resonance line is displaced to higher field values but shows the same line width and field separation between the kinks. When the field is perpendicular to the film, the resonance field is at 3.53 kOe and the two kinks are recorded at the fields of 1.71 and 4.96 kOe. As the angle between the field and the film increases from 901 to 1801, the kinks in the resonance lines are recorded at the same lower fields for the equivalent relative orientations. These results show that the onset of instabilities in the reflected power from the cavity is associated with the susceptibility of the sample and give evidence not only of the anisotropy of the magnetic particles and the formation of chains of particles during the cooling process, but also of the lack of any hysteresis in the frozen film. The resonance lines for the applied field
ARTICLE IN PRESS 86
F. Pelegrini et al. / Journal of Magnetism and Magnetic Materials 289 (2005) 84–86
parallel and anti-parallel to the frozen FF film are the same. Besides this, as the temperature increases, the line width of the resonance line reduces and also the field separation between the kinks, giving evidence again that they are associated with the magnetic properties of the FF sample and their behavior with temperature. At the temperature of 250 K, for example, the resonance line has a line width of 1.29 kOe, the parallel resonance field is 3.05 kOe, and the kinks are recorded at the fields of 2.80 and 3.20 kOe. Indeed, at this temperature, for this large volume sample, 20.0 mW is the critical microwave power for the onset of non-linear excitations. In view of these experimental results, we can conclude that the recorded kinks in our FMR lines of liquid or frozen FF samples, give evidence of the onset of secondorder instabilities due to non-linear effects. A theory of FMR instabilities in dispersed magnetic nanoparticles, as in liquid or frozen FF samples, in terms of static and dynamic effective fields, must consider necessarily the interactions between the distinct structures in the sample, dependent on the concentration of magnetic particles, and also the effects due to surface anisotropy. However, the dependence of the critical microwave power on the concentration of magnetic particles shows for each FF sample the experimental conditions to avoid FMR instabilities and obtain resonance lines without distortions. The knowledge of this dependence for each sample is of paramount importance in studies of the line width as a function of concentration of particles, or temperature, for example. At low microwave power levels, below the critical microwave power, single pattern resonance lines will give true values of line width. Above the critical power, for samples with large concentration of magnetic particles, the onset of nonlinear processes can give rise even to two pattern resonance lines, avoiding indeed the measurement of a true line width. At low microwave power, according to Tronconi et al. [5], the line width DH as a function of the mean distance R between the particles of an ionic waterbased MnFe2O4 ferrofluid, in the absence of any electrical interaction between the particles, is given by DH ¼ ðA=R3 Þ tanhð1=2kTÞðB þ C=R3 Þ:
(3)
In this expression, the constant A is related to the magnetic moment of the particles, the constant B, to the Brownian motion, the magnetic anisotropy and the interaction of the particles with the external field, and the constant C, to the dipole interaction between
magnetic particles; k is the Boltzmann constant, and T is the absolute temperature. However, a correction Hs to the dipolar field, implying DH ¼ ðA=R3 þ H s Þ tanhð1=2kTÞðB þ C=R3 Þ:
(4)
was introduced by Hrianca et al. [10] to explain the concentration dependence of the FMR line width from ferrofluids containing magnetite particles or mix ferrite particles of Mn0.6Fe0.4Fe2O4 type, dispersed in kerosene. The need for this correction was deduced from line widths given by two pattern FMR lines [10], and was attributed by Marin [11] to the presence of chains of magnetic particles in the FF sample and to the fact that the number of particles in the chains depends on the concentration of magnetic particles. We consider that some aspects of our experimental results confirm the presence of chains of magnetic particles in the FF sample, and that this depends on the concentration of particles. However, they also show that two pattern resonance lines can be due to the onset of non-linear effects, dependent on the magnetic susceptibility and volume of magnetic material of the FF sample, and microwave power.
References [1] P. Kabos, C.E. Patton, G. Wiese, A.D. Sullins, E.S. Wright, L. Chen, J. Appl. Phys. 80 (1996) 3962. [2] R.G. Cox, C.E. Patton, M.A. Wittenauer, P. Kabos, L. Chen, J. Appl. Phys. 89 (2001) 4454. [3] Y.V. Gulyaev, P.E. Zil0 berman, A.G. Temiryazev, M.P. Tikhomirova, Phys. Solid State 42 (2000) 1094. [4] P. Dorsey, J.B. Sokoloff, C. Vittoria, J. Appl. Phys. 74 (1993) 1938. [5] A.L. Tronconi, P.C. Morais, F. Pelegrini, F.A. Tourinho, J. Magn. Magn. Mater. 122 (1993) 90. [6] A.F. Bakuzis, P.C. Morais, F. Pelegrini, J. Appl. Phys. 85 (1999) 7480. [7] G.R.R. Gonc- alves, A.R. Pereira, A.F. Bakuzis, K. Skeff Neto, F. Pelegrini, P.C. Morais, J. Magn. Magn. Mater. 226–230 (2001) 1896. [8] F. Pelegrini, A.R. Pereira, M.B. Arau´jo, A.L. Tronconi, P.C. Morais, J. Magn. Magn. Mater. 272–276 (2004) 2381. [9] S.V. Vonsovskii (Ed.), Ferromagnetic Resonance, Pergamon, Oxford, 1966, p. 274. [10] I. Hrianca, I. Malaescu, F. Claici, C.N. Marin, J. Magn. Magn. Mater. 201 (1999) 126. [11] C.N. Marin, J. Magn. Magn. Mater. 250 (2002) 197.