Magneto-optical techniques to determine Curie temperature of magnetic fluidsRajesh Patel and Alpesh Raval Citation: Applied Physics Letters 90, 254104 (2007); doi: 10.1063/1.2751123 View online: http://dx.doi.org/10.1063/1.2751123 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/90/25?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Nanoscale rheometry of viscoelastic soft matter by oscillating field magneto-optical transmission usingferromagnetic nanorod colloidal probes J. Appl. Phys. 116, 184305 (2014); 10.1063/1.4901575 The magneto-optical behaviors modulated by unaggregated system for γ-Fe2O3–ZnFe2O4 binary ferrofluids AIP Advances 2, 042124 (2012); 10.1063/1.4765645 Magneto-optical properties of ionic magnetic fluids J. Appl. Phys. 101, 09J106 (2007); 10.1063/1.2713205 Magneto-optical imaging of the magnetization process in colossal magnetoresisitive lanthanum manganite J. Appl. Phys. 99, 08A704 (2006); 10.1063/1.2177393 Zero-field birefringence in magnetic fluids: Temperature, particle size, and concentration dependence J. Appl. Phys. 87, 2497 (2000); 10.1063/1.372209

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Magneto-optical techniques to determine Curie temperature of magneticfluids

Rajesh Patela�

Department of Physics, Bhavnagar University, Bhavnagar, Gujarat 364 002, India

Alpesh RavalP. B. Science College, Kapadvamj, Kheda 387 620, India

�Received 24 April 2007; accepted 31 May 2007; published online 21 June 2007�

Magnetic field induced extinction of light and birefringence as a function of temperature is used tostudy the temperature dependence of magnetic moment as well as the domain magnetization of thetemperature sensitive magnetic fluids. Subsequently, the Curie temperature and pyromagneticcoefficient of the same are determined. The results obtained from this technique are comparedwith the results obtained from other techniques. This technique is remarkably simple and lowcost. © 2007 American Institute of Physics. �DOI: 10.1063/1.2751123�

Technological applications of magnetic fluids1–6 such asself-controlled magnetic hyperthermia at tumor site,7 coolingof a transformer,8 magnetocaloric effects,9 etc., require mag-netic particles with low Curie temperature and high pyro-magnetic coefficient.10 One of the possible candidate for thispurpose is Mn–Zn mixed ferrite nanometric size particlesand its dispersion in nonmagnetic liquid carrier called mag-netic fluids. Magnetic fluids are complex and their complex-ity depends on the interaction between magnetic moment �m�and its temperature dependence. Such fluids exhibit field in-duced optical anisotropy when subjected to an external mag-netic field.11–14 The fluid should be diluted for two reasons:�i� to allow light transmission and �ii� to reduce the dipolarenergy less than the thermal energy. The magnetization be-havior in magnetic fluid is described by Langevin’s theory ofparamagnetism for noninteracting single-domain particles.2

In magnetic fluids, the single-domain particle size �d� is�10 nm, and the wavelength ��� of the light used in thisexperiment is 632 nm �i.e., ��d�. Under this condition, thetransmission of light is governed by Rayleigh scatteringtheory. Considering the above described conditions, lighttransmission through the magnetic fluid sample under appli-cation of magnetic field transverse to the direction of propa-gation of light using Langevin function is given by I= I0�L����, where L���= �coth �−1/�� and �=mH /kT. Here I0

is the intensity of incident light, k and T are Boltzmann con-stant and absolute temperature, respectively. The magneticmoment of the particle is defined as m=Md V, whereV=�d3 /6. The nanosized magnetic particles dispersed inmagnetic fluids are not monodispersed; hence one has toinclude polydispersivity in the calculations. It is found thatlog-normal particle-size distribution P�D� provides a reason-ably good fit to experimental measurements in magneticfluids.2 P�D� is obtained by substituting ln�D� for D in aGaussian distribution function, thereby avoiding the unphysi-cal aspect of contribution from negative particle sizes asso-ciated with the Gaussian distribution.

P�D� =1

D���2��exp�−

ln�D/D0�2

2�2 � ,

0

�

P�D�d�D� = 1,

where D is the particle diameter, � is the standard deviationof ln D, and ln D0 is the median of ln D. Taking into accountthe polydispersivity, the transmitted intensity can be obtainedas I=0

�I0L���P�D�d�D�.In commercial magnetic fluids, magnetite particles are

colloidally dispersed, whose Curie temperature is between728 and 585 K. We have synthesized nanomagnetic particlesof Mn–Zn by chemical coprecipitation techniques and usedthem to synthesize temperature sensitive magnetic fluidswith a low Curie temperature and high pyromagneticcoefficient.10 In this letter we report magneto-optical extinc-tion of light and birefringence of a temperature sensitivemagnetic fluid synthesized by dispersing Mn0.5Zn0.5Fe2O4�MZ5� nanomagnetic particles in nonmagnetic passiveliquid carrier �diester�. The particles are coated with oleicacid as the first surfactant and for better stability of the fluidthe second surfactant GAFAC �RE-610� is used. Frommagnetization measurements, the parameters obtainedare mean diameter Dm=7.1 nm, domain magnetizationMd=210 emu/cc, standard deviation �=0.28, and the satu-ration magnetization of the fluid is Ms=150 Oe. Results ob-tained using magneto-optical technique is compared withthose of the other techniques such as temperature dependentmagnetization measurements and magnetic field induced vis-cosity measurement as a function of temperature. Thus thisstudy provides an alternate technique to determine Curietemperature and pyromagnetic coefficient of temperaturesensitive magnetic fluids. The advantage of this techniqueover other techniques is that the fluid is dilute and conse-quently interparticle interactions are negligible which can bebeneficial for the precise measurement of Curie temperature.

A linearly polarized light beam having wavelength of633 nm and 10 mW power was obtained using polarizedHe–Ne uniphase laser. The polarized monochromatic beamwas made incident on the optically flat glass window of ajacketed cell �path length of 2 mm�. The cell was mountedon a thermally insulated base so as to rest in between the twoflat pole pieces of an electromagnet. The electromagnet gen-erates 0.1 T field at 0.5 A constant current with a pole gap of17.5 mm. Magnetic field was found to be homogeneousa�Electronic mail: rjp@bhavuni.edu

APPLIED PHYSICS LETTERS 90, 254104 �2007�

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within the gap. The temperature of the sample was variedaccurately by coupling the sample cell with a Brookfieldconstant temperature bath EX-100, having an accuracy of±0.01 K. A spatial filter was introduced along the light pathbetween the jacketed cell and the photodetector to avoidscattered light. The transmitted light was recorded on a pi-coammeter �model DPM-11� in terms of photocurrent gener-ated by the photodetector. The picoammeter measured lowestcurrent of the order of 1 pA. The extinction coefficient weremeasured in two orthogonal states of polarization in thetransverse mode �k�H�, i.e., the direction of light propaga-tion is perpendicular to the applied magnetic field, k denotethe direction of propagation of light �i.e., wave vector direc-tion�, �a� E perpendicular to the direction of the applied mag-netic field �E�H� and �b� E parallel to the direction of theapplied magnetic field E �H. In the longitudinal configura-tion, i.e., k �H, the direction of propagation of light coincideswith the direction of the applied magnetic field. For the mea-surements in the longitudinal configuration, an electromagnetwith bored pole pieces was used. The bore size was kept0.006 m, just to allow the light beam to pass through it.From the observed change in intensity ��I� under the appliedfield, parameter QF was calculated using the expression15

QF =Cext�L,R,k�

�Cext�0= 1 −

ln�1 + ��I/It���Cext�0

�1�

and

�Cext�0 = ln� It

I0 , �2�

where It is transmitted intensity in absence of the field. Here�Cext�0 is the extinction coefficient under zero field, while Land R refer to the orientation of the electric vector of theincident light parallel and perpendicular to the direction ofthe applied magnetic field, respectively. Birefringence mea-surements were carried out by placing an analyzer in be-tween the spatial filter and the photodetector. The analyzerwas calibrated and its vernier provided a smallest movementin the step of 8 min. He–Ne laser gives linearly polarizedlight. The direction of E vector of this light was determinedby a magneto-optical technique.16 The colloidal dispersionwas placed between the two cross polaroids �i.e., plane ofpolarized laser and analyzer� oriented at 45° with respect tothe direction of magnetic field. Since in most of the colloidsbirefringence is accompanied by dichroism, it becomes nec-essary to apply the correction due to the “dichroicrotation.”17 The expression for transmitted light is then givenby

I = �I0/4�sin2 2��TL + TR − 2�TLTR�1/2 cos � , �3�

where � is the angle between the applied field and the direc-tion of polarization of the incident light �in this case 45°�; TLand TR are transmittivity when E vector of the incident lightis parallel and perpendicular to the applied field direction,respectively, and �=L−R�, the phase difference producedin the sample. The phase difference is indirectly a measureof the birefringence of the medium when wavelength of lightand optical path length are constant. The relation betweenbirefringence ��n� and phase difference �� is given by =2��n1/�. The phase difference can be obtained as

= ��1 −3L���

�� . �4�

Here, � is the saturation value of the phase difference.In the case of extinction of light in dilute magnetic flu-

ids, particle diameter is very small compare to the wave-length of the incident light; these particles can be consideredto be independent Rayleigh scatterers. The theoretical ex-pressions showing how the three different extinction param-eters, viz., QL, QR, and QK depend on applied field strengthare given by17

QL = �QL�� +3�e − ���e + 2��

�L��� − 1� ,

�QL�� =3e

�e + 2��, �5�

QR = �QR�� −3�e − ��

2�e + 2���L��� − 1� ,

�QR�� =3�

�e + 2��,

QK = QR, �6�

and also,

QL − QR = �QL − QR��

�3L��� − 1�2

. �7�

The relation �QL−1�=2�1−QR� also holds good.Here,

L��� = 1 −2�e� + e−����e� − e−��

+2

�2 , �8�

where �QL�� and �QR�� are the saturation values of the pa-rameters for very high field strengths and is the complexpolarizability. e and � are the parallel and perpendicularcomponents to the symmetry axis. Figure 1 shows the plotsof extinction coefficient QF versus the applied field strengthH recorded at different temperatures for MZ5 sample. Thedeviation and spread from the relation �QL−1�=2�1−QR� isdue to polydispersity of the sample and the small aggregatesin the sample. It is also observed that as the temperature

FIG. 1. Temperature dependent extinction of light for temperature sensitivemagnetic fluid sample �MZ5�. The extinction coefficients QL, i.e., E �H; QR,i.e., E�H; and Qk for k �H, respectively.

254104-2 R. Patel and A. Raval Appl. Phys. Lett. 90, 254104 �2007�

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increases, the extinction coefficient decreases. This showsthe effect of temperature on magnetic property of the sample.Magnetic moments of the particles at different temperatureswere calculated using log-log matching technique discussedby Mehta et al.16 Experimental curves of log�QL−QR� vslog�H� are matched with the theoretical curve of log�3L���−1� vs log���. The experimental curve matches the theoret-ical curve with an appropriate shift in its origin. The abscissagives log�m /kT�, from which the average magnetic moments�m� and temperature dependent Md are calculated.

Figure 2 shows the magnetic field induced retardationfor a temperature sensitive magnetic fluid at three differenttemperatures, i.e., 308, 323, and 343 K. It is observed that astemperature increases the change in retardation decreases,but the shape of the curve remains identical. Which showsthat the physical properties such as particle size and sizedistribution remain unaltered and there is no effect of tem-perature �in this temperature range�. Hence, the reason forthe decrease in retardation may be due to the temperaturedependent change in the magnetization of the sample. Con-sidering this change in magnetic properties as a function oftemperature, the experimental observations are fitted withEq. �4�. In this equation the variable parameters are particlesize, size distribution, saturation magnetization, and domainmagnetization of the particle �Md�. From which the value ofMd at different temperatures is calculated.

Figure 3 shows the comparison of variation in domainmagnetization �Md� as a function of temperature for tempera-ture sensitive magnetic fluid, using four different techniques,viz., temperature dependent extinction of light, birefringencemeasurement, field induced viscosity measurements,18 andmagnetization measurements. The magnetization as a func-tion of magnetic field was measured at different temperaturesusing a PAR 155 vibrating sample magnetometer.10,19 In

magnetization measurements it was observed that sample ex-hibits zero remanence and coercivity. It was also observedthat magnetic field of 10 kOe is not enough to saturate thesystem at room temperature. Thus the system behaves assuperparamagnetic medium and we can used Langevin’stheory to account the observed effects. The domain magne-tization obtained at different temperatures is plotted in Fig. 3.Results obtained from all the four techniques are in goodagreement �Table I�. The magneto-optical techniques providea simple and low cost technique to determine Md and TCcompared to the temperature dependent magnetization mea-surement and field induced viscosity measurements as afunction of temperature.

Authors are thankful to R. V. Mehta for going throughthe manuscript and useful discussion and R. V. Upadhyay forproviding facilities and useful guidance. This work was car-ried out under DST-M-15 project.

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FIG. 2. �Color online� Field induced retardation as a function of temperaturefor temperature sensitive magnetic fluid.

FIG. 3. �Color online� Variation of Md with temperature for MZ ferrofluid.The results obtained using all four techniques are comparable and follow astraight line. TC is obtained by extrapolating the experimental results andslope of it gives pyromagnetic coefficient.

TABLE I. Comparison of different techniques to determine Curie tempera-ture of magnetic fluids. The values obtained for Curie temperature and py-romagnetic coefficient are in good agreement.

Techniques

CurieTemperature

�K�

Pyromagneticcoefficient�emu/K�

Viscosity 356.6 4.26Birefringence 355.0 4.5Light Extinction 352.1 4.44Magnetization 362.7 3.95

254104-3 R. Patel and A. Raval Appl. Phys. Lett. 90, 254104 �2007�

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