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A mössbauer spectroscopy study of superparamagnetic amorphous alloy particles in a ferrofluid
Journal of Magnetism and Magnetic Materials 67 (1987) 249-254 North-Holland, Amsterdam
249
A MOSSBAUER SPECTROSCOPY STUDY OF SUPERPARAMAGNETIC AMORPHOUS ALLOY P A R T I C L E S I N A F E R R O F L U I D Steen M O R U P , Bjarke R. C H R I S T E N S E N , Jacques van W O N T E R G I - I E M , Morten B. M A D S E N Laboratory of Applied Physics II, Technical University of Denmark, DK.2800 Lyngby, Denmark
Stuart W. C H A R L E S and Stephen WELLS Department of Physics, University College of North Wales, Bangor, Gwynedd LL57 2UW, UK
Received 12 December 1986
A ferrofluid prepared by thermal decomposition of Fe(CO)5 has been studied by use of MSssbauer spectroscopy. From the magnetic field dependence of the spectra obtained above the superparamagneticblocking temperature, we estimate a particle size of about 4.2 nm. At low temperatures the magnetic properties of the sample seem to be influenced by magnetic coupling among the particles. An upper limit for the magnetic anisotropy energy constant of about 0.6 × 105 J m - 3 is estimated. This is considerably smaller than that of crystalfine a-iron particles prepared on a support.
1. Introduction Ferrofluids containing ultrafine particles of amorphous alloys can be prepared by thermal decomposition of Fe(CO)5 in the presence of surfactant molecules [1-3]. In previous publications we have characterized the amorphous alloy particles by use of M~ssbauer spectroscopy and electron microscopy [1,2]. Particle size determination by use of electron microscopy is, however, complicated due to the fact that the particles easily oxidize when exposed to air. In the present study we show that the particle size can be determined from M~ssbauer spectroscopy studies of a frozen ferrofluid in applied magnetic fields. Moreover, the temperature dependence of the MSssbauer spectra gives information about the magnetic anisotropy of the particles.
2. Experimental The preparation of ferrofluids containing amorphous alloy particles in Decalin and with
Sarkosyl-O as a surfactant has been described elsewhere [1,3]. Iti the present work the ferrofluid was prepared in a similar way. The main difference was that we used oleic acid as a surfactant instead of Sarkosyl-O. Mt~ssbauer spectra were obtained by use of a constant acceleration spectrometer. Spectra were obtained at 80 and 161 K in magnetic fields up to 0.7 T applied perpendicular to the 7-ray direction. Spectra at lower temperatures were obtained with magnetic fields up to 4.0 T applied parallel to the 7-ray direction. Velocities are given with respect to the isomer shift of a-Fe at room temperature.
3. Results
Fig. 1 shows some low temperature spectra of the sample. The s p e c t r u m obtained at 5 K could be fitted with two six-line components, both of which have very broad lines. One of them has a magnetic splitting corresponding to a magnetic hyperfine field Bhf = 24.8 T, a negligible quadru-
0304-8853/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
250
S. Morup et al. / Superparamagneticamorphous alloyparticles i
*
i
i
i
!:
•
1.5T
~
, • .
" p
72 K
,.
:
,.'..@"~,
...
, ..
¢
=
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v;.,." ":.:..
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.
:"
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: .':.,'X. O.OT ~ ".
,;•
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nent, whereas the Fe 3+ component is essentially unchanged. At 72 K the'magnetic splitting has partly collapsed, indicating the onset of fast superparamagnetic relaxation at this temperature [7-10]. Fig. 2 shows MSssbaner spectra obtained at 80 K and 161 K with various external magnetic fields applied perpendicular to the y-ray direction. The zero field spectra have relatively sharp lines, and the presence of an Fe 2+ component with AEQ = (2.0 ± 0.1) m m s - 1 and (~Fe (0.95 + 0.02) mm s-1 at 80 K can be seen• The relative area of this component is about 18%. The application of the external magnetic field leads to a substantial broadening and splitting of the spectra. This behavior is expected for superparamagnetic ultrafine particles [7,8,10]•
",
~." 5 K
..
Velocity (mm/s)
Fig. 1, Low-temperatureM~Sssbauerspectra of the ferrofluid obtained at the indicated temperatures and applied magnetic fields.
pole shift, and an isomer shift of about 0.4 nun s -x. These parameters are similar to those of a m o r p h o u s F e - C alloy particles studied earlier [1]. The second component exhibits an average magnetic hyperfine field, Bht-----48 T, a negligible quadrupole shift, and an isomer shift of about 0.53 mm s-1. These values indicate that the component is due to Fe 3+ ions in a magnetic compound. The magnitude of Bhf is of the same order of magnitude as those of amorphous Fe203 [4] and FeOOH [5,6], but slightly smaller than those typical for crystalline iron oxides and oxyhydroxides. The broad lines of the component also suggest that it is due to a poorly crystallized material. The relative area of this component is about 30%. The zero field spectrum obtained at 15 K is quite similar to the 5 K spectrum. Application of an external magnetic field of 1.5 T parallel to the y-ray direction results in the disappearance of lines 2 and 5 f n the amorphous alloy compo-
"V
/
0.700T
2
0.500T
V
"~'~'~%'~.
/
o,,sT
"4 •
;"
.
k" d/ f
O.O00T
#
t
O.O00T
./ 80K
..
161K
":
... -12
-8
-4 0 4 Velocity ( r a m / s )
8
12
-8
-4 0 4 Velocity (mm/s)
8
12
Fig. 2. M~ssbauer spectra of the ferrofluid obtained at 80 K and 161 K in various applied magnetic fields•
S. Merup et a L / Superparamagnetic amorphous alloy particles
4. D i s c u s s i o n
The magnetic energy of a small ferromagnetic particle in an applied magnetic field, B, is given by
E=E~-p.B,
(1)
where p is the magnetic moment of the particle, and E a is the magnetic anisotropy energy. For a particle with uniaxial anisotropy Ea is to a first order approximation given by
E~ = KV sin20,
(2)
where K is the magnetic anisotropy energy constant, V is the volume of the particle, and 0 is the angle between the magnetization vector and the easy direction of magnetization. For applied magnetic fields of the order of I T, the anisotropy energy is normally much smaller than the Zeeman energy of ferromagnetic microcrystals, and therefore the first term in eq. (1) may be neglected. At temperatures above the superparamagnetic blocking temperature the magnetic hyperfine splitting in the MiSssbauer spectrum is then proportional to [7,8] Bobs~Bo L ~
+B,
(3)
where Bo is the saturation hyperfine field, L{ } is the Langevin function, k is Boltzmann's constant, and T is the temperature. For #B/kT>> 1 one may use the approximation
251
though the low-temperature spectra clearly show the presence of an Fe 3+ component, it was not possible to distinguish this component in the spectra obtained at 80 and 161 K. This is presumably because this component has very broad lines above 80 K when an external field is applied. Such broad spectra have been obtained in Mbssbauer studies of ferrihydrite in the same temperature range [6]. In the spectra it is, however, possible clearly to identify the line positions of lines 2, 3, 4 and 5 of the amorphous alloy phase, and thus the magnetic hyperfine field can be estimated. Fig. 3 shows a plot o f Bob s + B = JBob s -- B J as a function of B - ] for the amorphous alloy component of the spectra shown in fig. 2. The results obtained both at 80 and 161 K are in accordance with the linear relationship given by eq. (4). From the intercepts of the straight lines we find B 0 = (23.5 + 0.3) T at 80 K, and Bo = (23.0 4- 0.3) T at 161 K. These values are slightly smaller than those of the amorphous Fez0o_xCx alloy particles prepared with Sarkosyl-O as a surfactant [1-3]. This difference can be explained by a larger carbon content in the particles prepared with oleic acid, since the magnetic hyperfine fields of amorphous Fel00_xCx alloys decrease with increasing carbon content [11]. From the slopes of the straight lines in fig. 3 we estimate magnetic moments of #(80 K) = (6.3 4- 0.5) × 10 -20 J T -z and #(161 K) -(6.9 4- 0.5) × 10-2° J T -1. 25
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i
~
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24 23
ISobs- BI -=B0(1-
~).
(4)
According to eq. (4), a plot of I Bobs - - B I as a function of B -z gives a straight line with slope BokT/# and intercept B0, and if the magnetization M(T) is known, the particle volume V = # / M ( T ) can be determined [7,8,10]. In the present work we have made an estimate of the particle size from the magnetic field dependence of the spectra obtained at 80 and 161 K (fig. 2). The spectra were fitted with one six-line component and an Fe 2+ quadrupole doublet. A1-
22
2O
1!
16
1 15
B '1 (T 11
Fig. 3. Induced magnetic hyperfine splitting in the spectra shown in fig. 2 plotted as a funetion of the reciprocal applied magnetic field.
252
S. Morup et al. / Superparamagneticamorphousalloyparticles
The exact value of the magnetization of the amorphous alloy is not known. However, for iron-rich amorphous alloys the saturation magnetization is normally close to the value for crystalline alloys [12]. If we assume that the saturation magnetization of the present alloy particles is equal to that of crystalline a-iron, we find a mean diameter of (4.1 + 0.2) nm at 80 K and (4.2 _ 0.2) nm at 161 K. The oxide component seen in the low-temperature spectra is presumably due to oxidation of a surface layer of the alloy particles. Before the measurements were carried out, the ferrofluid had been kept in air at room temperature for several days, and such a treatment has been found to result in oxidation [2], If we assume that the iron atoms in the oxide were originally part of the alloy, we find that the particle size immediately after preparation was about 4.6 nm. The particle size in a similar ferrofluid prepared with Sarkosyl-O as a surfactant was about 6.5 nm [2]. Thus the particle size depends on the type of surfaetant molecules. This observation is in accordance with results for particles prepared by decomposition of cobalt carbonyl in the presence of different surfactants [13,14]. The value of the magnetic anisotropy energy constant, K, may be estimated from the spectra obtained at lower temperatures. The magnetic hyperfine splitting in the spectra collapses when the superparamagnetic relaxation time, ~', is of the order of 5 x 10-9 s. For the present sample this occurs between 70 and 80 K. For a particle with magnetic energy given by eq. (2) the relaxation time is given by [7,8]
;r = M ( T ) ~ I / 2 ( k T ] KVo
KV
<,>
where ~'0 is the gyromagnetic ratio. Assuming that M ( T ) is equal to the saturation magnetization of a-Fe, we find from eq. (5) that K = (0.6 + 0.3)x 105 J m -3 for 4.1 nm amorphous alloy particles. The magnetic anisotropy energy constant can also be estimated from the reduction in the magnetic hyperfine splitting due to collective magnetic excitations below the blocking temperature. For a particle with magnetic energy given by eq. (2) the
magnetic hyperfine [7,8,10,15,16] Bobs --
Bo(1
-
splitting
is
given
by
(6)
kT/2KV).
From the low-temperature zero magnetic field spectra, shown in fig. 1, we find Bobs(15 K) = 23.8 T and Bobs(5 K ) = 24.8 T. Assuming that B0 is constant below 15 K, we find by use of eq. (6) that K = (0.6 + 0.3) × 105 J m -3. From the spectrum obtained at an applied magnetic field of 1.5 T at 15 K, we find Bob~ = 22.3 T. By use of eq. (4) we obtain //0(15 K ) = (23.9 _+ 0.3) T. Inserting this value and the value of Bobs(15 K) in eq. (6), we find that K = (0.4 + 0.2) × 105 J m -3. Thus these three independent estimates of the magnetic anisotropy energy constant yield values of about 0.6 × 105 J m -3. The above calculations of K are based on the assumption that the magnetic interaction among the particles is negligible. In ferrofluids there is, however, a high tendency of agglomeration of the magnetic particles, often in long chains. This may result in significant contributions to the magnetic energy due to the magnetic dipole interaction among the particles. The magnetic coupling among the particles may strongly affect the superparamagnetic relaxation, and below a certain temperature the system may be superferromagnetic, i.e. the magnetic coupling results in a state of the system in which the magnetic moments of the particles are aligned [10,17]. At low temperatures this will lead to a smaller reduction in Bob~ than is indicated by eq. (6) [10,17]. In order to estimate the possible influence of magnetic coupling on the magnetic properties of the present sample we consider an infinite linear chain of identical particles with magnetic moments, /~(T), and with a distance between the particles (center to center), d. At 0 K the magnetic moments are aligned along the chain direction. The magnetic field acting at one particle is then given by [18] B,(0) = #___o0~
#(0)
~r n-1 (nd) 3 =
#°#(0) ~(3),
(7)
7rd3
where/~0 is the v a c u u m permeability, and ~(x) is the R i e m a n n zeta function for which ~(3) -- 1.202. If the particles are randomly distributed in the
S. Morup et a L / Superparamagnetic amorphous alloy particles
sample with a mean separation, d, one finds an internal field Bi(0 ) which is of the same order of magnitude as the value given by eq. (7) [18]. The temperature, Tp, at which the superferromagnetic order collapses and the system becomes superparamagnetic is given by [18] Tp
~(0)Bi(0 ) M2(Tp) 3k M2(0)
(8)
Assuming that d = 10 nm, we find for the present ferrofluid that Bi(0 ) = 0.03 T and Tp ~ 50 K. This value for Tl, is of the same order of magnitude as the temperature at which the magnetic hyperfine splitting in the ferrofluid collapses ( T = 75 K). Above Tp the reduced initial susceptibility Xi = x,/M(T) [17] of a superferromagnetic system is given by [18]
Xi = 3 k [ T - TpM2(T)/M2(Tp)]
253
sotropies are also expected to be smaller than for supported particles.
5. Conclusions By use of MiSssbauer spectroscopy we have estimated the particle size and an upper limit for the magnetic anisotropy energy constant for ultrafine amorphous alloy particles in a ferrofluid. The particle size depends on the type of surfactant used during the preparation of the ferrofluid. Calculations on the basis of a simple model for a one-dimensional superferromagnetic system indicate that the magnetic coupling among the particles has a significant influence on the magnetic properties at low temperature. The magnetic anisotropy is found to be significantly smaller than that of crystalline a-iron particles.
(9)
which is similar to the Curie-Weiss law apart from the factor M2(T)/M2(Tp), which is close to unity well below the Curie temperature. Magnetic susceptibility studies of ferrofluids have in fact shown a Curie-Weiss behavior with an ordering temperature of the order of 50-100 K [19,20]. Thus the present calculation for a one-dimensional superferromagnetic system as well as the susceptibility measurements on similar ferrofluids indicates that the magnetic coupling has a significant influence on the properties of the samples. The value of the magnetic anisotropy energy constant estimated using the assumption that the magnetic coupling is negligible must therefore be considered as an upper limit of the true value. In previous studies of supported a-iron particles it was found that K -= 1.2 x 105 J m - 3 for 6 nm particles [8], and K -= 7.0 × 105 J m - 3 for 2.5 nm particles [21]. Thus the magnetic anisotropy energy constant for the present particles is significantly smaller. This is in accordance with the fact that the magnetocrystalline anisotropy of amorphous materials should be negligible. Moreover, when the particles are formed in a liquid instead of on a support, they may have approximately spherical shape, and the stress is presumably negligible. Therefore the shape and stress ani-
Acknowledgements The work was supported by the Danish Council for Technical Research, The Danish Natural Science Research Council, Haldor Topsee A / S , and by the Commission of the European Communities.
References [1] J. vail Wonterghem, S. Mzrup, S.W. Charles, S. Wells and J: ViUadsen, Phys. Rev. Lett. 55 (1985) 410. [2] J. van Wonterghem, S. Merup, S.W. Charles, S. Wells and J. Villadsen, Hyperfine Interactions 27 (1986) 333. [3] J. van Wonterghem, S. Morup, S.W. Charles and S. Wells, to be published. [4] A.M. van Diepen and Th.J.A. Popma, Solid State Commun. 27 (1978) 121. [5] J.M.D. Coey and P.W. Readman, Nature 246 (1973) 476. [6] M.B. Madsen, S. Mzrup and C.J.W. Koch, Hyperfine Interactions 27 (1986) 329. [7] S. Merup, J.A. Dumesic, and H. Tops~e, in: Applications of Mt~ssbaner Spectroscopy, vol. II, ed. R.L Cohen (Academic Press, New York, 1980) p. 1. [8] S. Merup, H. Topsee and B.S. Clansen, Phys. Scripta 25 (1982) 713. [9] W. Ktindig, H. BSmmel, G. Constabaris and R.H. Lindquist, Phys. Rev. 142 (1966) 327. [10] S. Merup, J. Magn. Magn. Mat. 37 (1983) 39.
254
S. Morup et al. / Superparamagnetic amorphous alloy particles
[11] E. Bauer-Grosse, G. Le Ca~r and L. Fournes, Hyperfine Interactions 27 (1986) 297. [12] F.E. Luborsky, in: Ferromagnetic Materials, vol. 2, E.P. Wohlfarth (North-Holland, Amsterdam, 1980) p. 451. [13] P.H. Hess and P.H. Parker, J. Appl. Polym. Scl. 10 (1966) 1915. [14] E. Papirer, P. Horny, H. Balard, R. Anthore, C. Petipas and A. Martinet, J. Colloid Interface Sci. 94 (1983) 207. [15] S. Morup and H. Topsze, AppL Phys. 11 (1976) 63. [16] S. Mzrup, H. Topsze and J. Lipka, J. de Phys. Colloq. 37 (1976) C6-287.
[17] S. Mzrup, M.B. Madsen, J. Franck, J. Villadsen and C.J.W. Koch, J. Magn. Magn. Mat. 40 (1983) 163. [18] S. Mzrup, B.S. Clausen and P.H. Christensen, to be pubfished. [19] K. O'Grady, A. Bradbury, S.W. Charles, S. Menear, J. Popplewell and R.W. Chantrell, J. Magn. Magn. Mat. 31-34 (1983) 958. [20] A. Bradbury, S. Menear, K. O'Grady and R.W. Chantrell, IEEE Trans. Mag. MAG-20 (1984) 1846. [21] P.H. Christensen, S. Morup and J.W. Niemantsverdriet, J. Phys. Chem. 89 (1985) 4898.
249
A MOSSBAUER SPECTROSCOPY STUDY OF SUPERPARAMAGNETIC AMORPHOUS ALLOY P A R T I C L E S I N A F E R R O F L U I D Steen M O R U P , Bjarke R. C H R I S T E N S E N , Jacques van W O N T E R G I - I E M , Morten B. M A D S E N Laboratory of Applied Physics II, Technical University of Denmark, DK.2800 Lyngby, Denmark
Stuart W. C H A R L E S and Stephen WELLS Department of Physics, University College of North Wales, Bangor, Gwynedd LL57 2UW, UK
Received 12 December 1986
A ferrofluid prepared by thermal decomposition of Fe(CO)5 has been studied by use of MSssbauer spectroscopy. From the magnetic field dependence of the spectra obtained above the superparamagneticblocking temperature, we estimate a particle size of about 4.2 nm. At low temperatures the magnetic properties of the sample seem to be influenced by magnetic coupling among the particles. An upper limit for the magnetic anisotropy energy constant of about 0.6 × 105 J m - 3 is estimated. This is considerably smaller than that of crystalfine a-iron particles prepared on a support.
1. Introduction Ferrofluids containing ultrafine particles of amorphous alloys can be prepared by thermal decomposition of Fe(CO)5 in the presence of surfactant molecules [1-3]. In previous publications we have characterized the amorphous alloy particles by use of M~ssbauer spectroscopy and electron microscopy [1,2]. Particle size determination by use of electron microscopy is, however, complicated due to the fact that the particles easily oxidize when exposed to air. In the present study we show that the particle size can be determined from M~ssbauer spectroscopy studies of a frozen ferrofluid in applied magnetic fields. Moreover, the temperature dependence of the MSssbauer spectra gives information about the magnetic anisotropy of the particles.
2. Experimental The preparation of ferrofluids containing amorphous alloy particles in Decalin and with
Sarkosyl-O as a surfactant has been described elsewhere [1,3]. Iti the present work the ferrofluid was prepared in a similar way. The main difference was that we used oleic acid as a surfactant instead of Sarkosyl-O. Mt~ssbauer spectra were obtained by use of a constant acceleration spectrometer. Spectra were obtained at 80 and 161 K in magnetic fields up to 0.7 T applied perpendicular to the 7-ray direction. Spectra at lower temperatures were obtained with magnetic fields up to 4.0 T applied parallel to the 7-ray direction. Velocities are given with respect to the isomer shift of a-Fe at room temperature.
3. Results
Fig. 1 shows some low temperature spectra of the sample. The s p e c t r u m obtained at 5 K could be fitted with two six-line components, both of which have very broad lines. One of them has a magnetic splitting corresponding to a magnetic hyperfine field Bhf = 24.8 T, a negligible quadru-
0304-8853/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
250
S. Morup et al. / Superparamagneticamorphous alloyparticles i
*
i
i
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!:
•
1.5T
~
, • .
" p
72 K
,.
:
,.'..@"~,
...
, ..
¢
=
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v;.,." ":.:..
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.
:"
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nent, whereas the Fe 3+ component is essentially unchanged. At 72 K the'magnetic splitting has partly collapsed, indicating the onset of fast superparamagnetic relaxation at this temperature [7-10]. Fig. 2 shows MSssbaner spectra obtained at 80 K and 161 K with various external magnetic fields applied perpendicular to the y-ray direction. The zero field spectra have relatively sharp lines, and the presence of an Fe 2+ component with AEQ = (2.0 ± 0.1) m m s - 1 and (~Fe (0.95 + 0.02) mm s-1 at 80 K can be seen• The relative area of this component is about 18%. The application of the external magnetic field leads to a substantial broadening and splitting of the spectra. This behavior is expected for superparamagnetic ultrafine particles [7,8,10]•
",
~." 5 K
..
Velocity (mm/s)
Fig. 1, Low-temperatureM~Sssbauerspectra of the ferrofluid obtained at the indicated temperatures and applied magnetic fields.
pole shift, and an isomer shift of about 0.4 nun s -x. These parameters are similar to those of a m o r p h o u s F e - C alloy particles studied earlier [1]. The second component exhibits an average magnetic hyperfine field, Bht-----48 T, a negligible quadrupole shift, and an isomer shift of about 0.53 mm s-1. These values indicate that the component is due to Fe 3+ ions in a magnetic compound. The magnitude of Bhf is of the same order of magnitude as those of amorphous Fe203 [4] and FeOOH [5,6], but slightly smaller than those typical for crystalline iron oxides and oxyhydroxides. The broad lines of the component also suggest that it is due to a poorly crystallized material. The relative area of this component is about 30%. The zero field spectrum obtained at 15 K is quite similar to the 5 K spectrum. Application of an external magnetic field of 1.5 T parallel to the y-ray direction results in the disappearance of lines 2 and 5 f n the amorphous alloy compo-
"V
/
0.700T
2
0.500T
V
"~'~'~%'~.
/
o,,sT
"4 •
;"
.
k" d/ f
O.O00T
#
t
O.O00T
./ 80K
..
161K
":
... -12
-8
-4 0 4 Velocity ( r a m / s )
8
12
-8
-4 0 4 Velocity (mm/s)
8
12
Fig. 2. M~ssbauer spectra of the ferrofluid obtained at 80 K and 161 K in various applied magnetic fields•
S. Merup et a L / Superparamagnetic amorphous alloy particles
4. D i s c u s s i o n
The magnetic energy of a small ferromagnetic particle in an applied magnetic field, B, is given by
E=E~-p.B,
(1)
where p is the magnetic moment of the particle, and E a is the magnetic anisotropy energy. For a particle with uniaxial anisotropy Ea is to a first order approximation given by
E~ = KV sin20,
(2)
where K is the magnetic anisotropy energy constant, V is the volume of the particle, and 0 is the angle between the magnetization vector and the easy direction of magnetization. For applied magnetic fields of the order of I T, the anisotropy energy is normally much smaller than the Zeeman energy of ferromagnetic microcrystals, and therefore the first term in eq. (1) may be neglected. At temperatures above the superparamagnetic blocking temperature the magnetic hyperfine splitting in the MiSssbauer spectrum is then proportional to [7,8] Bobs~Bo L ~
+B,
(3)
where Bo is the saturation hyperfine field, L{ } is the Langevin function, k is Boltzmann's constant, and T is the temperature. For #B/kT>> 1 one may use the approximation
251
though the low-temperature spectra clearly show the presence of an Fe 3+ component, it was not possible to distinguish this component in the spectra obtained at 80 and 161 K. This is presumably because this component has very broad lines above 80 K when an external field is applied. Such broad spectra have been obtained in Mbssbauer studies of ferrihydrite in the same temperature range [6]. In the spectra it is, however, possible clearly to identify the line positions of lines 2, 3, 4 and 5 of the amorphous alloy phase, and thus the magnetic hyperfine field can be estimated. Fig. 3 shows a plot o f Bob s + B = JBob s -- B J as a function of B - ] for the amorphous alloy component of the spectra shown in fig. 2. The results obtained both at 80 and 161 K are in accordance with the linear relationship given by eq. (4). From the intercepts of the straight lines we find B 0 = (23.5 + 0.3) T at 80 K, and Bo = (23.0 4- 0.3) T at 161 K. These values are slightly smaller than those of the amorphous Fez0o_xCx alloy particles prepared with Sarkosyl-O as a surfactant [1-3]. This difference can be explained by a larger carbon content in the particles prepared with oleic acid, since the magnetic hyperfine fields of amorphous Fel00_xCx alloys decrease with increasing carbon content [11]. From the slopes of the straight lines in fig. 3 we estimate magnetic moments of #(80 K) = (6.3 4- 0.5) × 10 -20 J T -z and #(161 K) -(6.9 4- 0.5) × 10-2° J T -1. 25
i
,
i
,
,
I
i
i
i
~
i
i
i
J
t
24 23
ISobs- BI -=B0(1-
~).
(4)
According to eq. (4), a plot of I Bobs - - B I as a function of B -z gives a straight line with slope BokT/# and intercept B0, and if the magnetization M(T) is known, the particle volume V = # / M ( T ) can be determined [7,8,10]. In the present work we have made an estimate of the particle size from the magnetic field dependence of the spectra obtained at 80 and 161 K (fig. 2). The spectra were fitted with one six-line component and an Fe 2+ quadrupole doublet. A1-
22
2O
1!
16
1 15
B '1 (T 11
Fig. 3. Induced magnetic hyperfine splitting in the spectra shown in fig. 2 plotted as a funetion of the reciprocal applied magnetic field.
252
S. Morup et al. / Superparamagneticamorphousalloyparticles
The exact value of the magnetization of the amorphous alloy is not known. However, for iron-rich amorphous alloys the saturation magnetization is normally close to the value for crystalline alloys [12]. If we assume that the saturation magnetization of the present alloy particles is equal to that of crystalline a-iron, we find a mean diameter of (4.1 + 0.2) nm at 80 K and (4.2 _ 0.2) nm at 161 K. The oxide component seen in the low-temperature spectra is presumably due to oxidation of a surface layer of the alloy particles. Before the measurements were carried out, the ferrofluid had been kept in air at room temperature for several days, and such a treatment has been found to result in oxidation [2], If we assume that the iron atoms in the oxide were originally part of the alloy, we find that the particle size immediately after preparation was about 4.6 nm. The particle size in a similar ferrofluid prepared with Sarkosyl-O as a surfactant was about 6.5 nm [2]. Thus the particle size depends on the type of surfaetant molecules. This observation is in accordance with results for particles prepared by decomposition of cobalt carbonyl in the presence of different surfactants [13,14]. The value of the magnetic anisotropy energy constant, K, may be estimated from the spectra obtained at lower temperatures. The magnetic hyperfine splitting in the spectra collapses when the superparamagnetic relaxation time, ~', is of the order of 5 x 10-9 s. For the present sample this occurs between 70 and 80 K. For a particle with magnetic energy given by eq. (2) the relaxation time is given by [7,8]
;r = M ( T ) ~ I / 2 ( k T ] KVo
KV
<,>
where ~'0 is the gyromagnetic ratio. Assuming that M ( T ) is equal to the saturation magnetization of a-Fe, we find from eq. (5) that K = (0.6 + 0.3)x 105 J m -3 for 4.1 nm amorphous alloy particles. The magnetic anisotropy energy constant can also be estimated from the reduction in the magnetic hyperfine splitting due to collective magnetic excitations below the blocking temperature. For a particle with magnetic energy given by eq. (2) the
magnetic hyperfine [7,8,10,15,16] Bobs --
Bo(1
-
splitting
is
given
by
(6)
kT/2KV).
From the low-temperature zero magnetic field spectra, shown in fig. 1, we find Bobs(15 K) = 23.8 T and Bobs(5 K ) = 24.8 T. Assuming that B0 is constant below 15 K, we find by use of eq. (6) that K = (0.6 + 0.3) × 105 J m -3. From the spectrum obtained at an applied magnetic field of 1.5 T at 15 K, we find Bob~ = 22.3 T. By use of eq. (4) we obtain //0(15 K ) = (23.9 _+ 0.3) T. Inserting this value and the value of Bobs(15 K) in eq. (6), we find that K = (0.4 + 0.2) × 105 J m -3. Thus these three independent estimates of the magnetic anisotropy energy constant yield values of about 0.6 × 105 J m -3. The above calculations of K are based on the assumption that the magnetic interaction among the particles is negligible. In ferrofluids there is, however, a high tendency of agglomeration of the magnetic particles, often in long chains. This may result in significant contributions to the magnetic energy due to the magnetic dipole interaction among the particles. The magnetic coupling among the particles may strongly affect the superparamagnetic relaxation, and below a certain temperature the system may be superferromagnetic, i.e. the magnetic coupling results in a state of the system in which the magnetic moments of the particles are aligned [10,17]. At low temperatures this will lead to a smaller reduction in Bob~ than is indicated by eq. (6) [10,17]. In order to estimate the possible influence of magnetic coupling on the magnetic properties of the present sample we consider an infinite linear chain of identical particles with magnetic moments, /~(T), and with a distance between the particles (center to center), d. At 0 K the magnetic moments are aligned along the chain direction. The magnetic field acting at one particle is then given by [18] B,(0) = #___o0~
#(0)
~r n-1 (nd) 3 =
#°#(0) ~(3),
(7)
7rd3
where/~0 is the v a c u u m permeability, and ~(x) is the R i e m a n n zeta function for which ~(3) -- 1.202. If the particles are randomly distributed in the
S. Morup et a L / Superparamagnetic amorphous alloy particles
sample with a mean separation, d, one finds an internal field Bi(0 ) which is of the same order of magnitude as the value given by eq. (7) [18]. The temperature, Tp, at which the superferromagnetic order collapses and the system becomes superparamagnetic is given by [18] Tp
~(0)Bi(0 ) M2(Tp) 3k M2(0)
(8)
Assuming that d = 10 nm, we find for the present ferrofluid that Bi(0 ) = 0.03 T and Tp ~ 50 K. This value for Tl, is of the same order of magnitude as the temperature at which the magnetic hyperfine splitting in the ferrofluid collapses ( T = 75 K). Above Tp the reduced initial susceptibility Xi = x,/M(T) [17] of a superferromagnetic system is given by [18]
Xi = 3 k [ T - TpM2(T)/M2(Tp)]
253
sotropies are also expected to be smaller than for supported particles.
5. Conclusions By use of MiSssbauer spectroscopy we have estimated the particle size and an upper limit for the magnetic anisotropy energy constant for ultrafine amorphous alloy particles in a ferrofluid. The particle size depends on the type of surfactant used during the preparation of the ferrofluid. Calculations on the basis of a simple model for a one-dimensional superferromagnetic system indicate that the magnetic coupling among the particles has a significant influence on the magnetic properties at low temperature. The magnetic anisotropy is found to be significantly smaller than that of crystalline a-iron particles.
(9)
which is similar to the Curie-Weiss law apart from the factor M2(T)/M2(Tp), which is close to unity well below the Curie temperature. Magnetic susceptibility studies of ferrofluids have in fact shown a Curie-Weiss behavior with an ordering temperature of the order of 50-100 K [19,20]. Thus the present calculation for a one-dimensional superferromagnetic system as well as the susceptibility measurements on similar ferrofluids indicates that the magnetic coupling has a significant influence on the properties of the samples. The value of the magnetic anisotropy energy constant estimated using the assumption that the magnetic coupling is negligible must therefore be considered as an upper limit of the true value. In previous studies of supported a-iron particles it was found that K -= 1.2 x 105 J m - 3 for 6 nm particles [8], and K -= 7.0 × 105 J m - 3 for 2.5 nm particles [21]. Thus the magnetic anisotropy energy constant for the present particles is significantly smaller. This is in accordance with the fact that the magnetocrystalline anisotropy of amorphous materials should be negligible. Moreover, when the particles are formed in a liquid instead of on a support, they may have approximately spherical shape, and the stress is presumably negligible. Therefore the shape and stress ani-
Acknowledgements The work was supported by the Danish Council for Technical Research, The Danish Natural Science Research Council, Haldor Topsee A / S , and by the Commission of the European Communities.
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S. Morup et al. / Superparamagnetic amorphous alloy particles
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