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Effect of thermomagnetic treatment on the magnetic state of a ferrofluid: a polarised neutron study
ARTICLE IN PRESS
Physica B 350 (2004) e211–e215
Effect of thermomagnetic treatment on the magnetic state of a ferrofluid: a polarised neutron study V.N. Zabenkina,*, L.A. Axelroda, G.P. Gordeeva, W.H. Kraanb, I.M. Lazebnika, A.A. Vorobieva,c a
Petersburg Nuclear Physics Institute RAS, 188300 Gatchina, St. Petersburg, Russia b Interfacultair Reactor Instituut, TUDelft, 2629 JB Delft, Netherlands c Max-Plank-Institut fur . Metallforschung, 70569 Stuttgart, Germany
Abstract In magnetic colloids of sufficiently high particle concentration, frustration of dipolar interactions could arise as found in spin-glass systems. To understand this situation, a ferrofluid consisting of magnetite particles was frozen in either a horizontal or a vertical field and then 3D neutron-polarisation analysis was performed around the hysteresis loop in both field configurations. The same was done in the fluid state. A comparison of the data leads to the conclusion that frustration plays a key role in the self-organisation of nanoparticles in a frozen magnetic colloid. r 2004 Elsevier B.V. All rights reserved. PACS: 71.15.Dx; 75.50.Mm Keywords: Frustration; Neutron depolarisation; Hysteresis
1. Introduction The self-organised structures formed by nanoparticles in magnetic colloids (MC) attract a growing interest not only to understand how these structures arise, but also owing to the practical significance of ferrofluids. It is sufficient to mention that MCs are used in medicine for transport to required locations inside the human body or for the healing of surface wounds [1,2]. In such cases the efficacy of MCs depends on the ability of nanoparticles to organise themselves in *Corresponding author. Tel.: + 7-813-714-6715; fax: +7813-713-9023. E-mail address: [email protected] (V.N. Zabenkin).
specific structures under the influence of small magnetic fields. Furthermore, it was reported [3] that the process of self-organisation at an interface results in different structures as compared to the bulk. The concentration of particles in MCs plays a crucial role in this process, as the dipolar interaction between neighbouring particles is essential. It is a very intriguing question whether at sufficiently high concentration of particles, their spatial distribution might give rise to ‘‘frustration’’ of dipolar interactions as found in spin-glass systems. In small magnetic fields the particles usually form chains oriented along the field direction. For high particle concentration however, a parallel alignment of the magnetic moments in adjacent chains
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.053
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V.N. Zabenkin et al. / Physica B 350 (2004) e211–e215
becomes unfavourable. It is most likely that long chains cannot exist, but split up into pieces consisting of particles with antiparallel orientations of magnetic moments. One could imagine that the moments arrange themselves such that the angles between neighbouring moments differ from either 0 or p: This is called frustration of dipolar interactions. Since translational degrees of freedom are practically eliminated in a concentrated colloid, such an arrangement cannot relax. Consequently, a high concentration of particles could be the origin of the frustration of dipolar interactions. In order to observe frustration in our neutron experiment, we prevent the chain-structure formation by freezing the translational degrees of freedom. In this case a decrease in the depolarisation of the transmitted beam would be evidence for a chaotic arrangement of the moments inside the frozen MC.
2. Experimental The sample is a colloid solution of magnetite ðFe3 O4 Þ particles in heavy water ðD2 OÞ: The volume concentration of magnetite is 7%. The magnetite particles were made by chemical deposition from salts of 2- and 3-valent iron [3,4]. They are surrounded by an organic surfactant to avoid clustering. The shape of particles is spherical and ( A their average diameter is approximately 100 A: quartz container is filled with this solution, without free volume. It is placed either in an electromagnet generating the horizontal field Hx along the x-axis (beam direction) or in a solenoid giving a vertical magnetic field Hz along the z-axis. Measurements are performed after various thermo-magnetic regimes: (1) at room temperature (RT); (2) after freezing the sample in zero field; (3) after freezing in Hz ¼ 110 Oe; and (4) after freezing in Hx ¼ 220 Oe: In each case, a neutron ‘‘depolarisation’’ scan is performed around a full magnetisation/demagnetisation cycle with applied fields Hx and Hz : We chose the values of the applied magnetic field Ha such as to have equal values for the effective field in both directions. The effective field is calculated by H ef ¼ Ha MN;
where N is the geometrical demagnetisation factor, equal to 0.8 and 0.06 for Hx and Hz ; respectively, and M is the mean macroscopic magnetisation. Our experimental technique is the full 3D analysis of the depolarisation of a polarised neutron beam transmitted through the MC sample. The polarisation vector of the incident beam P0 is successively directed along the x; y; or z-axis. The components of the polarisation vector P are measured after the sample. From this experiment the elements Dij of the # are determined by P ¼ D # P0 : We matrix D calculate the depolarisation caused by magnetic fluctuations DB of the induction by means of # DP ¼ ln ðdet DÞ; ð1Þ and the rotation angle F of the polarisation vector around the appropriate axis (see e.g. Ref. [5]) by means of Dyz Dzy FðHxef Þ ¼ arctan ; Dyz þ Dzy Dxy Dyx : ð2Þ FðHzef Þ ¼ arctan Dxy þ Dyx The rotation angle F is proportional to the mean macroscopic magnetisation, FBB Ha ¼ 4pM; where Ha is the applied field.
3. Results and discussion Regime (1): Scans in both field directions at room temperature are distinct in both their mean macroscopic magnetisation (Fig. 1a) and depolarisation (Fig. 1b). One notices that FðHzef Þ is free of hysteresis, whereas FðHxef Þ shows a small hysteresis. The absence of hysteresis confirms the mobility of the MC moments. For scans in the horizontal field, a hysteresis of the same form and area was present in all measurements. Thus, it is most likely that this hysteresis is due to the poles of the electromagnet generating the field rather than to the ferrofluid. Fig. 1b shows that the depolarisation in Hz slowly saturates. This behaviour is similar to that found in our previous investigations [6]. The depolarisation expected on the basis of the nanoparticle size is negligible, so that this
ARTICLE IN PRESS V.N. Zabenkin et al. / Physica B 350 (2004) e211–e215
Fig. 1. Results at room temperature. H jj Z: ðKÞ virgin branch; ð.Þ demagnetisation branch. H jj X: ðJÞ virgin branch; ðXÞ demagnetisation branch; n magnetisation branch.
observation should be explained by the presence of stable chain structures. In the scan with the horizontal field Hx a decrease in magnetisation (Fig. 1a) is accompanied by an increased depolarisation (Fig. 1b). A decrease in magnetisation could arise because particles move out of the probed volume owing to the axial gradient of the field. However, both the high particle concentration and the limited volume hinders the displacement of particles. Both also promote the organisation of particles into structures with reduced magnetic moments, although isolated particles also exist. The hint of a reduction of depolarisation observed at the highest fields (see Fig. 1b) argues for this idea. The fact that such a behaviour is not observed in FðHzef Þ might be due to the demagnetisation field which is considerable for this geometry and increases together with the applied field. Regime (2): The results after freezing the MC in zero field are shown in Fig. 2. The behaviour ef of FðHx;z Þ for both scans is similar up to
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Fig. 2. Results for the MC frozen at Ha ¼ 0: H jj Z: ðKÞ virgin branch; ð.Þ demagnanetisation branch; ðmÞ magnetisation branch. H jj X: ðJÞ virgin branch; ðXÞ demagnetisation branch; ðnÞ magnetisation branch.
H ef C100 Oe (Fig. 2a). However, the magnetisation increases more slowly than in regime (1). This means that the freezing blocks the degrees of freedom for the particles to move and rotate. The behaviour of DPðHzef Þ (vertical field) after freezing in zero field is similar to that at RT. However, the depolarisation in the horizontal field decreases owing to the formation of the structures mentioned above (Fig. 2b). Probably, these structures in the frozen state are clusters of particles with their moments arranged at odd angles between each other. Since the particle as a whole can no longer rotate, the shape anisotropy has a considerable influence on the formation of the various structures. Regime (3): The MC frozen in a vertical field Ha ¼ 110 Oe (Fig. 3) shows practically the same properties as when frozen in zero field (Fig. 2). However, it has a smaller magnetisation at the
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Fig. 3. Results for the MC frozen at Haz ¼ 110 Oe: H jj Z: ðKÞ 1st demagnetisation branch; ðmÞ magnetisation branch; ð.Þ 2nd demagnetisation branch. H jj X: ðJÞ virgin branch; ðXÞ demagnetisation branch; ðnÞ magnetisation branch.
maximal fields. The structures in this frozen state could be fragments of chains formed in the fluid state at Ha ¼ 110 Oe: Regime (4): When frozen in a horizontal field Ha ¼ 220 Oe; the MC shows a rather unusual behaviour in the scan with horizontal field (Fig. 4). An almost rectangular hysteresis loop is observed at small fields. When the effective field Hxef exceeds 10 Oe, the angle F reaches slowly the same values as in the fluid state at RT or after freezing in Ha ¼ 0: At the same time, the depolarisation changes from 0 to a maximum (Fig. 4b), suggesting that the sample divides into domains with correlated moments, without frustration. The reason for this is a question for future investigations. In the vertical field scan we observed a slow increase in F that did not reach its maximal values until Hzef ¼ 100 Oe: When freezing in a magnetic field (either horizontal or vertical), the particle
Fig. 4. Results for the MC frozen at Hax ¼ 220 Oe: H jj Z: ðKÞ virgin branch; ð.Þ demagnetisation branch; ðmÞ magnetisation branch. H jj X: ðJÞ 1th demagnetisation branch; ðnÞ magnetisation branch; ðXÞ 2nd demagnetisation branch.
structures with shape anisotropy are initially oriented along the field together with their moments; in the frozen state after switching off the field, the moments of the particles are disordered owing to the small crystal-anisotropy energy and the large dipole-interaction energy. Then, the magnetic state of the MC is like a spin glass, or more correctly, a dipole glass. Consequently, the magnetisation and depolarisation in the state of frozen MC vanish in zero field in all these regimes.
4. Conclusion From a comparison of the observed data on MCs after various thermomagnetic treatments, it is likely that a disordering of particle moments
ARTICLE IN PRESS V.N. Zabenkin et al. / Physica B 350 (2004) e211–e215
takes place in a frozen MC owing to frustration and in that state the neutron depolarisation by the moments becomes equal to zero. Therefore, it would be interesting to study less concentrated MCs. This could allow to determine the smallest concentration of MC for which frustration of the dipolar interaction is effective.
Acknowledgements We are thankful to E. Rodzevich, A. Zavediya, A. Lepekhin for technical assistance, the Russian Ministry of Science for financial support (Grant SS-1671-2003.2), and the Russian State Program
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‘‘Neutron Studies of Condensed Media’’ (Contract No. 40.012.1.1.1149).
References [1] A.N. Rusetski, E.K. Ruuge, J. Magn. Magn. Matter 85 (1990) 299. [2] C. Alexiou, W. Arnold, R.J. Klein, et al., Cancer Res. 60 (2000) 6641. [3] A.A Vorobiev, Thesis, PNPI, St. Petersburg, 2002. [4] R.E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, Cambridge, 1985. [5] M.Th. Rekveldt, Textures Microstruct. 11 (1989) 127. [6] V.N. Zabenkin, L.A. Axelrod, G. Gordeev, et al., Appl. Phys. A 74S1 (2002) 710.
Physica B 350 (2004) e211–e215
Effect of thermomagnetic treatment on the magnetic state of a ferrofluid: a polarised neutron study V.N. Zabenkina,*, L.A. Axelroda, G.P. Gordeeva, W.H. Kraanb, I.M. Lazebnika, A.A. Vorobieva,c a
Petersburg Nuclear Physics Institute RAS, 188300 Gatchina, St. Petersburg, Russia b Interfacultair Reactor Instituut, TUDelft, 2629 JB Delft, Netherlands c Max-Plank-Institut fur . Metallforschung, 70569 Stuttgart, Germany
Abstract In magnetic colloids of sufficiently high particle concentration, frustration of dipolar interactions could arise as found in spin-glass systems. To understand this situation, a ferrofluid consisting of magnetite particles was frozen in either a horizontal or a vertical field and then 3D neutron-polarisation analysis was performed around the hysteresis loop in both field configurations. The same was done in the fluid state. A comparison of the data leads to the conclusion that frustration plays a key role in the self-organisation of nanoparticles in a frozen magnetic colloid. r 2004 Elsevier B.V. All rights reserved. PACS: 71.15.Dx; 75.50.Mm Keywords: Frustration; Neutron depolarisation; Hysteresis
1. Introduction The self-organised structures formed by nanoparticles in magnetic colloids (MC) attract a growing interest not only to understand how these structures arise, but also owing to the practical significance of ferrofluids. It is sufficient to mention that MCs are used in medicine for transport to required locations inside the human body or for the healing of surface wounds [1,2]. In such cases the efficacy of MCs depends on the ability of nanoparticles to organise themselves in *Corresponding author. Tel.: + 7-813-714-6715; fax: +7813-713-9023. E-mail address: [email protected] (V.N. Zabenkin).
specific structures under the influence of small magnetic fields. Furthermore, it was reported [3] that the process of self-organisation at an interface results in different structures as compared to the bulk. The concentration of particles in MCs plays a crucial role in this process, as the dipolar interaction between neighbouring particles is essential. It is a very intriguing question whether at sufficiently high concentration of particles, their spatial distribution might give rise to ‘‘frustration’’ of dipolar interactions as found in spin-glass systems. In small magnetic fields the particles usually form chains oriented along the field direction. For high particle concentration however, a parallel alignment of the magnetic moments in adjacent chains
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.053
ARTICLE IN PRESS e212
V.N. Zabenkin et al. / Physica B 350 (2004) e211–e215
becomes unfavourable. It is most likely that long chains cannot exist, but split up into pieces consisting of particles with antiparallel orientations of magnetic moments. One could imagine that the moments arrange themselves such that the angles between neighbouring moments differ from either 0 or p: This is called frustration of dipolar interactions. Since translational degrees of freedom are practically eliminated in a concentrated colloid, such an arrangement cannot relax. Consequently, a high concentration of particles could be the origin of the frustration of dipolar interactions. In order to observe frustration in our neutron experiment, we prevent the chain-structure formation by freezing the translational degrees of freedom. In this case a decrease in the depolarisation of the transmitted beam would be evidence for a chaotic arrangement of the moments inside the frozen MC.
2. Experimental The sample is a colloid solution of magnetite ðFe3 O4 Þ particles in heavy water ðD2 OÞ: The volume concentration of magnetite is 7%. The magnetite particles were made by chemical deposition from salts of 2- and 3-valent iron [3,4]. They are surrounded by an organic surfactant to avoid clustering. The shape of particles is spherical and ( A their average diameter is approximately 100 A: quartz container is filled with this solution, without free volume. It is placed either in an electromagnet generating the horizontal field Hx along the x-axis (beam direction) or in a solenoid giving a vertical magnetic field Hz along the z-axis. Measurements are performed after various thermo-magnetic regimes: (1) at room temperature (RT); (2) after freezing the sample in zero field; (3) after freezing in Hz ¼ 110 Oe; and (4) after freezing in Hx ¼ 220 Oe: In each case, a neutron ‘‘depolarisation’’ scan is performed around a full magnetisation/demagnetisation cycle with applied fields Hx and Hz : We chose the values of the applied magnetic field Ha such as to have equal values for the effective field in both directions. The effective field is calculated by H ef ¼ Ha MN;
where N is the geometrical demagnetisation factor, equal to 0.8 and 0.06 for Hx and Hz ; respectively, and M is the mean macroscopic magnetisation. Our experimental technique is the full 3D analysis of the depolarisation of a polarised neutron beam transmitted through the MC sample. The polarisation vector of the incident beam P0 is successively directed along the x; y; or z-axis. The components of the polarisation vector P are measured after the sample. From this experiment the elements Dij of the # are determined by P ¼ D # P0 : We matrix D calculate the depolarisation caused by magnetic fluctuations DB of the induction by means of # DP ¼ ln ðdet DÞ; ð1Þ and the rotation angle F of the polarisation vector around the appropriate axis (see e.g. Ref. [5]) by means of Dyz Dzy FðHxef Þ ¼ arctan ; Dyz þ Dzy Dxy Dyx : ð2Þ FðHzef Þ ¼ arctan Dxy þ Dyx The rotation angle F is proportional to the mean macroscopic magnetisation, FBB Ha ¼ 4pM; where Ha is the applied field.
3. Results and discussion Regime (1): Scans in both field directions at room temperature are distinct in both their mean macroscopic magnetisation (Fig. 1a) and depolarisation (Fig. 1b). One notices that FðHzef Þ is free of hysteresis, whereas FðHxef Þ shows a small hysteresis. The absence of hysteresis confirms the mobility of the MC moments. For scans in the horizontal field, a hysteresis of the same form and area was present in all measurements. Thus, it is most likely that this hysteresis is due to the poles of the electromagnet generating the field rather than to the ferrofluid. Fig. 1b shows that the depolarisation in Hz slowly saturates. This behaviour is similar to that found in our previous investigations [6]. The depolarisation expected on the basis of the nanoparticle size is negligible, so that this
ARTICLE IN PRESS V.N. Zabenkin et al. / Physica B 350 (2004) e211–e215
Fig. 1. Results at room temperature. H jj Z: ðKÞ virgin branch; ð.Þ demagnetisation branch. H jj X: ðJÞ virgin branch; ðXÞ demagnetisation branch; n magnetisation branch.
observation should be explained by the presence of stable chain structures. In the scan with the horizontal field Hx a decrease in magnetisation (Fig. 1a) is accompanied by an increased depolarisation (Fig. 1b). A decrease in magnetisation could arise because particles move out of the probed volume owing to the axial gradient of the field. However, both the high particle concentration and the limited volume hinders the displacement of particles. Both also promote the organisation of particles into structures with reduced magnetic moments, although isolated particles also exist. The hint of a reduction of depolarisation observed at the highest fields (see Fig. 1b) argues for this idea. The fact that such a behaviour is not observed in FðHzef Þ might be due to the demagnetisation field which is considerable for this geometry and increases together with the applied field. Regime (2): The results after freezing the MC in zero field are shown in Fig. 2. The behaviour ef of FðHx;z Þ for both scans is similar up to
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Fig. 2. Results for the MC frozen at Ha ¼ 0: H jj Z: ðKÞ virgin branch; ð.Þ demagnanetisation branch; ðmÞ magnetisation branch. H jj X: ðJÞ virgin branch; ðXÞ demagnetisation branch; ðnÞ magnetisation branch.
H ef C100 Oe (Fig. 2a). However, the magnetisation increases more slowly than in regime (1). This means that the freezing blocks the degrees of freedom for the particles to move and rotate. The behaviour of DPðHzef Þ (vertical field) after freezing in zero field is similar to that at RT. However, the depolarisation in the horizontal field decreases owing to the formation of the structures mentioned above (Fig. 2b). Probably, these structures in the frozen state are clusters of particles with their moments arranged at odd angles between each other. Since the particle as a whole can no longer rotate, the shape anisotropy has a considerable influence on the formation of the various structures. Regime (3): The MC frozen in a vertical field Ha ¼ 110 Oe (Fig. 3) shows practically the same properties as when frozen in zero field (Fig. 2). However, it has a smaller magnetisation at the
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Fig. 3. Results for the MC frozen at Haz ¼ 110 Oe: H jj Z: ðKÞ 1st demagnetisation branch; ðmÞ magnetisation branch; ð.Þ 2nd demagnetisation branch. H jj X: ðJÞ virgin branch; ðXÞ demagnetisation branch; ðnÞ magnetisation branch.
maximal fields. The structures in this frozen state could be fragments of chains formed in the fluid state at Ha ¼ 110 Oe: Regime (4): When frozen in a horizontal field Ha ¼ 220 Oe; the MC shows a rather unusual behaviour in the scan with horizontal field (Fig. 4). An almost rectangular hysteresis loop is observed at small fields. When the effective field Hxef exceeds 10 Oe, the angle F reaches slowly the same values as in the fluid state at RT or after freezing in Ha ¼ 0: At the same time, the depolarisation changes from 0 to a maximum (Fig. 4b), suggesting that the sample divides into domains with correlated moments, without frustration. The reason for this is a question for future investigations. In the vertical field scan we observed a slow increase in F that did not reach its maximal values until Hzef ¼ 100 Oe: When freezing in a magnetic field (either horizontal or vertical), the particle
Fig. 4. Results for the MC frozen at Hax ¼ 220 Oe: H jj Z: ðKÞ virgin branch; ð.Þ demagnetisation branch; ðmÞ magnetisation branch. H jj X: ðJÞ 1th demagnetisation branch; ðnÞ magnetisation branch; ðXÞ 2nd demagnetisation branch.
structures with shape anisotropy are initially oriented along the field together with their moments; in the frozen state after switching off the field, the moments of the particles are disordered owing to the small crystal-anisotropy energy and the large dipole-interaction energy. Then, the magnetic state of the MC is like a spin glass, or more correctly, a dipole glass. Consequently, the magnetisation and depolarisation in the state of frozen MC vanish in zero field in all these regimes.
4. Conclusion From a comparison of the observed data on MCs after various thermomagnetic treatments, it is likely that a disordering of particle moments
ARTICLE IN PRESS V.N. Zabenkin et al. / Physica B 350 (2004) e211–e215
takes place in a frozen MC owing to frustration and in that state the neutron depolarisation by the moments becomes equal to zero. Therefore, it would be interesting to study less concentrated MCs. This could allow to determine the smallest concentration of MC for which frustration of the dipolar interaction is effective.
Acknowledgements We are thankful to E. Rodzevich, A. Zavediya, A. Lepekhin for technical assistance, the Russian Ministry of Science for financial support (Grant SS-1671-2003.2), and the Russian State Program
e215
‘‘Neutron Studies of Condensed Media’’ (Contract No. 40.012.1.1.1149).
References [1] A.N. Rusetski, E.K. Ruuge, J. Magn. Magn. Matter 85 (1990) 299. [2] C. Alexiou, W. Arnold, R.J. Klein, et al., Cancer Res. 60 (2000) 6641. [3] A.A Vorobiev, Thesis, PNPI, St. Petersburg, 2002. [4] R.E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, Cambridge, 1985. [5] M.Th. Rekveldt, Textures Microstruct. 11 (1989) 127. [6] V.N. Zabenkin, L.A. Axelrod, G. Gordeev, et al., Appl. Phys. A 74S1 (2002) 710.