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Small-angle neutron scattering of nanometer-size magnetic particles
Journal of Magnetism and Magnetic Materials 1114-1117(1992) 1585-1586 North-ltoUand
-m'
Small-angle neutron scattering of nanomete;--size magnetic particles J.R. Chiidress
", C . L . C h i e n ", J . J . R h y n c b.~ a n d R . W . E r w i n ~
" l)epartment of Ph.vsics and Astronomy, The Johns ltopkins Unit'cr~'it.v, Baltimore, MD 21218. US,4 t, Research Reactor; Unicersity oJ" Missoto'i, ('ohtmbia, MO 65211, USA ' Reactor Dit'ision, Natiottal Institute oj" Stattdards and TechttohJgy, (;aithcrsbto'g, MD 20St)t). USA Nanoscale Fe particles in an A1,0 3 matrix have been investigated by Small-Angle Neutron Scattering (SANS), in addition to SQUID magnetometry and M6sshauer spectroscopy. SANS data analysis indicates an increase of the ferromagnetic correlation length as the temperature decreases, with saturation at roughly the particle size. The ampliludc of this scattering decreases with temperature, indicating that it is likely dynamic in origin. There is a second component of the SANS at the smallest wavevector transfers, which we believe arises from inter-particle correlations. The amplitude of this component increases with decreasing temperature, as expected for order parameter scattering. Granular magnetic materials, which consist of fine magnetic particles dispersed in an amorphous insulating matrix, display a number of unique properties as a result of their nanomctcr-scalc microstructurc [1]. However, many properties of granular magnetic composites are still poorly understood at the fundamental level, such as the exact nature of the magnetic ordering and magnetic cxcitation~ within and between the grains. A well-known property of single-domain magnetic particlcs is the occurrence of supcrparamagnctic relaxation, resulting from the thermally-activated fluctuation of the particle moment. Supcrparamagnctism can bc observed on different time scales r by using different magnetic probes, such as SQUID naagnctomct~3' (r = 10 s) and 57Fc M6ssbaucr spectroscopy (MS) (r -l0 s s). In contrast. SANS (with a shorter characteristic measurcment time ~- 5 X 10- i: s) mcasures approximately the instantaneous spin-pair correlation function within the particles. Thus small anglc ncutron scattering provides a new window to understanding the basic magnetic interactions in these nanoscale materials. Thc sample cxamined in this study was prepared using RF magnetron sputtering, by co-deposition of Fe and AI20 3 from a single mixed target onto thin AI,O 3 substratcs kept at 2(1(Io C, resulting in a film approximately 7 ~m thick. The granular microstructurc was confirmed by transmission electron microscopy, which rcvcais a narrow distribution of Fc particic sizes around 3 nm in diameter. The film composition of 35 w~lC~ of Fc is well below the granular percolation concentration ( = 60 vol%), and therefore contains well isolated particles [2]. X-ray diffraction analysis shows that the particles retain the b o d y - c n t r c d cubic structure of bulk e~-Fc. Magnetic hystcrcsis loops obtained at T = 5 K show a clear ferromagnetic behavior, with 6(t% remancnt magnetization and a cocrcivity of about 600 Oc.
For our sample, the blocking temperatures TI~ above which the particles become supcrparamagnctic arc 75 K for SQUID measurements (peak in the zero-fieldcooled susceptibility and onset of irrcvcrsibilitics) and 2111 K for MS measurements (onset of magnetic hypcrfine splitting). ,above Ti~, little information on the magnetic ordering can bc obtained by these methods. However, the short interaction time of the neutrons with nanoscalc particles means th~q neutron scattering is insensitive to st, pcrparamagnct.c fluctuations, cvcn at roonl temperature. The neutron scattering experiment was performed at NBSR's S-meter SANS spectrometer. Many film layers wcrc supcrposcd in an alurniniunl sample holder, resulting in a total sample thickness of more than IIII) p.m. The tcmpcr,iturc of the sample was varied between 15 and 35(t K, and the scattering intensity 1 versus wavevcctor Q was obtained over a Q-range from I).17 to 1.5 nm ~, using an incident neutron wavelength of 11.5 nm. A background spectrum was obtained at 425 K and subtracted from the low-temperature data, so that only the temperature-dependent magnetic scattering was analyzed. In the high-Q region, the data is well described by a single Lorcntzian squared scattering function. Preliminary results on data obtained at longer neutron wavelengths suggest that this scattering is essentially wavelength independent. i.e., that no inelasticity corrections arc required in the analysis. Therefore the i.orcmzian-squarcd cross .,,colion is a true representation of the hlstant;mcous spinpair correlation function. Such a functional form is different than the Lorcntzian form sccn in bulk magnetic systems [3], and may bc related to the finite extent of the strongly-corrclatcd magnetic regions in our granular samplc. At the smallest wavcvcctor transfers, wc find additiona! intcnsity, which wc modci by' adding a simple
0312-8853/92/$05.00 (c') 1992 - Elsevier Science Publishers B.V. All rights reserved
J.R. Chihlress et al. / SANS o]"nanometer-size magnetic particles
1586
1,~,,i,,,,,~,,~1,~,,,,i-,,,,,,,,,,,i,,,,,,i,,,|-,,[,,,,,,,
I / Q " term to thc scattering. Thus cxccllcnt fits to thc data arc obtained using: A /((?)
=
B , +
(O-" +
(J)
@'
where ~¢= I/.~ is the inverse correlation length. The I / Q " term corresponds to a Lorentzian cross section with a near-zero inverse correlation length, thus reflecting correlations on a scale larger than what can be measured in our experiment (roughly a few tens of nm's). It is important to note, however, that the form of this cross section is not unique, and that further refining of the data analysis is necessary to pinpoint the functional form and corrclation length associated wire the Iow-Q scattering. Fig, I shows the Lorentzian squared amplitude A as a function of temperature. This amplitude is seen to decrease with decreasing temperature, suggesting that this component of the scattering is dynamic in origin. Thc dccrcasc is sharp below 200 K, flattening out ncar zero below about 121) K. In fig. I we also plot the correlation length ~ = I/K, which shows a related temperature dependence. Starting at room temperature in the I nm range, ~ increases only slightly with dccreasing temperature until about 2(10 K, below which a rapid increase is observcd. However, instead of a divergence of ~, wc obscrvc a saturation at about 4 nm, vcry close to the average particle size. By contrast, the amplitude B of the Lorcntzian component to thc scattcring (fig. 2) is constant and nearly zero at high temperatures. As T is dccrcascd below 200 K, B riscs sharply until leveling off at lower temperatures, a bchavior typical of order parameter scattering. Bccausc of the long correlations lengths associated with this scattering, it is suggestive of inter-particle ordering. 0.5
5
0.4
ql"
4
I.
"~ Okl
3
0.2 < ,'
"'t ¢ " -t ~ ._~5 k~.-
-
10
5
Q
TEMPERATURE (K)
Fig. 2. Amplitude B of the Lorentzian term in the scattering from 3 nm Fe particles (see eq. (1) in text), as a function of temperature. The longer correlations associated with this scattering indicate that the increased amplitude at low temperatures is due to inter-particle ordering. The line is a guide to the eye.
The Curie temperature of 3 nm Fe particles, even if much lower than the bulk Fe valuc of 1043 K, is expected to be significantly above room temperature [4]. Thcreforc somc ordering will bc present in the particics at 300 K. Short correlation Icngths, howcvcr, may bc cxpcctcd bccausc of thc thermal spin fluctuations associatcd with the high dcgrcc of disorder typical of nanoscalc matcrials. Indeed, the SANS results (fig. 1) suggest that the magnetic scattcring at high tcmpcraturcs ( T > 200 K) is duc to spin fluctuations wi~.hin the particles. Below 200 K, thcse fluctuations ave slowly frozen out, with increasing corrclation of the spins until the correlation length saturates ncar the ~.~rticlc si,,~c. As the intraparticlc order increases, correlations dcvelop between particlcs (fig. 2) and incrcase as the temperature is lowercd. Further SANS experiments, including a study of the dependence of the scattering on an externally applied magnetic field, arc already undcnvay to bcttcr charactcrizc the low-Q component of the scattering, extract an Fc particle sizc distribution and to further understand thc role of spin fluctuations in the scattcring. These results will bc prcscntcd in a forthcoming paper.
1 ®
0
0
,,,,l--,,I,,,,I,,.,,I,,,,I,,,,I,,,.,
,50
References 0
!~t~3 150 ~ ~ ~ T e m p e r a t m - e (K') Fig. I. Amplitude ,4 (filled circles) and correlation length ,f (open squares) associated with the Lorentzian-squared term in the small-angle neutron magnetic scattering from 3 nm Fc particles (scc eq. (1) in text), as a function of temperature. At low temperatures, the decrease of A suggests that this com|lOllClll i.,,;dynamic in origin, and a saturation of ~ ix observed near the particle size. The lines arc drawn to guide the eye.
[I] C.L. Chien, in Physical Phenomena in Granular Materials, cds. G.D. (ody, T.tt. Gehaile and Ping Sheng, Mat. Rcs. S~c. Syrup. l'roc, vol. !~5 (i~)9()) p. 41 !. [2] B. Abeles, Appl. Solid State Sci. h (197f'0 I. [3] See. e.g., li.E. Stanley, Introduction Io Phase Transitions and Critical Phenomena (O\!~wd Univ. Press, Oxfi~rd, 1971) p. 94 and references lt~,:;,.i,,l. [4] See, e.g., I.S. Jacohs and C.P. ~,~,e'm, in Magnetism, eds. G.T. Radoand lt. Suhl, vol. 3~l ~,3) p. 271.
-m'
Small-angle neutron scattering of nanomete;--size magnetic particles J.R. Chiidress
", C . L . C h i e n ", J . J . R h y n c b.~ a n d R . W . E r w i n ~
" l)epartment of Ph.vsics and Astronomy, The Johns ltopkins Unit'cr~'it.v, Baltimore, MD 21218. US,4 t, Research Reactor; Unicersity oJ" Missoto'i, ('ohtmbia, MO 65211, USA ' Reactor Dit'ision, Natiottal Institute oj" Stattdards and TechttohJgy, (;aithcrsbto'g, MD 20St)t). USA Nanoscale Fe particles in an A1,0 3 matrix have been investigated by Small-Angle Neutron Scattering (SANS), in addition to SQUID magnetometry and M6sshauer spectroscopy. SANS data analysis indicates an increase of the ferromagnetic correlation length as the temperature decreases, with saturation at roughly the particle size. The ampliludc of this scattering decreases with temperature, indicating that it is likely dynamic in origin. There is a second component of the SANS at the smallest wavevector transfers, which we believe arises from inter-particle correlations. The amplitude of this component increases with decreasing temperature, as expected for order parameter scattering. Granular magnetic materials, which consist of fine magnetic particles dispersed in an amorphous insulating matrix, display a number of unique properties as a result of their nanomctcr-scalc microstructurc [1]. However, many properties of granular magnetic composites are still poorly understood at the fundamental level, such as the exact nature of the magnetic ordering and magnetic cxcitation~ within and between the grains. A well-known property of single-domain magnetic particlcs is the occurrence of supcrparamagnctic relaxation, resulting from the thermally-activated fluctuation of the particle moment. Supcrparamagnctism can bc observed on different time scales r by using different magnetic probes, such as SQUID naagnctomct~3' (r = 10 s) and 57Fc M6ssbaucr spectroscopy (MS) (r -l0 s s). In contrast. SANS (with a shorter characteristic measurcment time ~- 5 X 10- i: s) mcasures approximately the instantaneous spin-pair correlation function within the particles. Thus small anglc ncutron scattering provides a new window to understanding the basic magnetic interactions in these nanoscale materials. Thc sample cxamined in this study was prepared using RF magnetron sputtering, by co-deposition of Fe and AI20 3 from a single mixed target onto thin AI,O 3 substratcs kept at 2(1(Io C, resulting in a film approximately 7 ~m thick. The granular microstructurc was confirmed by transmission electron microscopy, which rcvcais a narrow distribution of Fc particic sizes around 3 nm in diameter. The film composition of 35 w~lC~ of Fc is well below the granular percolation concentration ( = 60 vol%), and therefore contains well isolated particles [2]. X-ray diffraction analysis shows that the particles retain the b o d y - c n t r c d cubic structure of bulk e~-Fc. Magnetic hystcrcsis loops obtained at T = 5 K show a clear ferromagnetic behavior, with 6(t% remancnt magnetization and a cocrcivity of about 600 Oc.
For our sample, the blocking temperatures TI~ above which the particles become supcrparamagnctic arc 75 K for SQUID measurements (peak in the zero-fieldcooled susceptibility and onset of irrcvcrsibilitics) and 2111 K for MS measurements (onset of magnetic hypcrfine splitting). ,above Ti~, little information on the magnetic ordering can bc obtained by these methods. However, the short interaction time of the neutrons with nanoscalc particles means th~q neutron scattering is insensitive to st, pcrparamagnct.c fluctuations, cvcn at roonl temperature. The neutron scattering experiment was performed at NBSR's S-meter SANS spectrometer. Many film layers wcrc supcrposcd in an alurniniunl sample holder, resulting in a total sample thickness of more than IIII) p.m. The tcmpcr,iturc of the sample was varied between 15 and 35(t K, and the scattering intensity 1 versus wavevcctor Q was obtained over a Q-range from I).17 to 1.5 nm ~, using an incident neutron wavelength of 11.5 nm. A background spectrum was obtained at 425 K and subtracted from the low-temperature data, so that only the temperature-dependent magnetic scattering was analyzed. In the high-Q region, the data is well described by a single Lorcntzian squared scattering function. Preliminary results on data obtained at longer neutron wavelengths suggest that this scattering is essentially wavelength independent. i.e., that no inelasticity corrections arc required in the analysis. Therefore the i.orcmzian-squarcd cross .,,colion is a true representation of the hlstant;mcous spinpair correlation function. Such a functional form is different than the Lorcntzian form sccn in bulk magnetic systems [3], and may bc related to the finite extent of the strongly-corrclatcd magnetic regions in our granular samplc. At the smallest wavcvcctor transfers, wc find additiona! intcnsity, which wc modci by' adding a simple
0312-8853/92/$05.00 (c') 1992 - Elsevier Science Publishers B.V. All rights reserved
J.R. Chihlress et al. / SANS o]"nanometer-size magnetic particles
1586
1,~,,i,,,,,~,,~1,~,,,,i-,,,,,,,,,,,i,,,,,,i,,,|-,,[,,,,,,,
I / Q " term to thc scattering. Thus cxccllcnt fits to thc data arc obtained using: A /((?)
=
B , +
(O-" +
(J)
@'
where ~¢= I/.~ is the inverse correlation length. The I / Q " term corresponds to a Lorentzian cross section with a near-zero inverse correlation length, thus reflecting correlations on a scale larger than what can be measured in our experiment (roughly a few tens of nm's). It is important to note, however, that the form of this cross section is not unique, and that further refining of the data analysis is necessary to pinpoint the functional form and corrclation length associated wire the Iow-Q scattering. Fig, I shows the Lorentzian squared amplitude A as a function of temperature. This amplitude is seen to decrease with decreasing temperature, suggesting that this component of the scattering is dynamic in origin. Thc dccrcasc is sharp below 200 K, flattening out ncar zero below about 121) K. In fig. I we also plot the correlation length ~ = I/K, which shows a related temperature dependence. Starting at room temperature in the I nm range, ~ increases only slightly with dccreasing temperature until about 2(10 K, below which a rapid increase is observcd. However, instead of a divergence of ~, wc obscrvc a saturation at about 4 nm, vcry close to the average particle size. By contrast, the amplitude B of the Lorcntzian component to thc scattcring (fig. 2) is constant and nearly zero at high temperatures. As T is dccrcascd below 200 K, B riscs sharply until leveling off at lower temperatures, a bchavior typical of order parameter scattering. Bccausc of the long correlations lengths associated with this scattering, it is suggestive of inter-particle ordering. 0.5
5
0.4
ql"
4
I.
"~ Okl
3
0.2 < ,'
"'t ¢ " -t ~ ._~5 k~.-
-
10
5
Q
TEMPERATURE (K)
Fig. 2. Amplitude B of the Lorentzian term in the scattering from 3 nm Fe particles (see eq. (1) in text), as a function of temperature. The longer correlations associated with this scattering indicate that the increased amplitude at low temperatures is due to inter-particle ordering. The line is a guide to the eye.
The Curie temperature of 3 nm Fe particles, even if much lower than the bulk Fe valuc of 1043 K, is expected to be significantly above room temperature [4]. Thcreforc somc ordering will bc present in the particics at 300 K. Short correlation Icngths, howcvcr, may bc cxpcctcd bccausc of thc thermal spin fluctuations associatcd with the high dcgrcc of disorder typical of nanoscalc matcrials. Indeed, the SANS results (fig. 1) suggest that the magnetic scattcring at high tcmpcraturcs ( T > 200 K) is duc to spin fluctuations wi~.hin the particles. Below 200 K, thcse fluctuations ave slowly frozen out, with increasing corrclation of the spins until the correlation length saturates ncar the ~.~rticlc si,,~c. As the intraparticlc order increases, correlations dcvelop between particlcs (fig. 2) and incrcase as the temperature is lowercd. Further SANS experiments, including a study of the dependence of the scattering on an externally applied magnetic field, arc already undcnvay to bcttcr charactcrizc the low-Q component of the scattering, extract an Fc particle sizc distribution and to further understand thc role of spin fluctuations in the scattcring. These results will bc prcscntcd in a forthcoming paper.
1 ®
0
0
,,,,l--,,I,,,,I,,.,,I,,,,I,,,,I,,,.,
,50
References 0
!~t~3 150 ~ ~ ~ T e m p e r a t m - e (K') Fig. I. Amplitude ,4 (filled circles) and correlation length ,f (open squares) associated with the Lorentzian-squared term in the small-angle neutron magnetic scattering from 3 nm Fc particles (scc eq. (1) in text), as a function of temperature. At low temperatures, the decrease of A suggests that this com|lOllClll i.,,;dynamic in origin, and a saturation of ~ ix observed near the particle size. The lines arc drawn to guide the eye.
[I] C.L. Chien, in Physical Phenomena in Granular Materials, cds. G.D. (ody, T.tt. Gehaile and Ping Sheng, Mat. Rcs. S~c. Syrup. l'roc, vol. !~5 (i~)9()) p. 41 !. [2] B. Abeles, Appl. Solid State Sci. h (197f'0 I. [3] See. e.g., li.E. Stanley, Introduction Io Phase Transitions and Critical Phenomena (O\!~wd Univ. Press, Oxfi~rd, 1971) p. 94 and references lt~,:;,.i,,l. [4] See, e.g., I.S. Jacohs and C.P. ~,~,e'm, in Magnetism, eds. G.T. Radoand lt. Suhl, vol. 3~l ~,3) p. 271.