Dynamic magnetic properties of monodisperse CoFe2O4 nanoparticles synthesized by a facile solvothermal technique

Physica B: Condensed Matter 575 (2019) 311640

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Dynamic magnetic properties of monodisperse CoFe2O4 nanoparticles synthesized by a facile solvothermal technique

T

Arka Chaudhuria,b,∗, Kalyan Mandalb a b

Department of Applied Science, Haldia Institute of Technology, Haldia, 721657, India Department of Condensed Matter Physics and Material Science, S.N. Bose National Centre for Basic Sciences, Block JD, Sector 3, Salt Lake, Kolkata, 700106, India

A B S T R A C T

Monodisperse, unagglomerated nanoparticles of CoFe2O4 were synthesized by a solvothermal technique using various capping agents. Three sets of particles were synthesized having size ∼7 nm, ∼14 nm and ∼23 nm. Detailed morphology study was done by X ray diffraction and High resolution Transmission Electron Microscope. Ac hysteresis loops of these samples were measured at room temperature within a frequency range of 50 Hz–600 Hz. We have reported the frequency dependence of coercivity and Specific absorption rate (SAR) and have found a very interesting result that the coercivity varies with different power of frequency for the particles of different size. Particles of sample A followed the Néel type of relaxation. The relaxation measurements were also done on all the samples to vindicate the occurrence of Néel type of relaxation. The SAR values and the fast relaxation proves that these particles can be utilized for hyperthermia treatment.

1. Introduction Magnetic nanoparticles have become extremely significant during the last few decades because of their manifold applications in the fields of electronics like high density magnetic storage media [1], high frequency devices [2], spintronic devices [3], biomedical fields like targeted drug delivery [4], diagnostics [5], magnetic separation [6], contrast agents in MRI [6], thermoresponsive drug carriers [8], thermal activation therapy of cancer [9]. But one inherent property and problem of magnetic nanoparticle is that they get agglomerated easily due to the strong magnetic dipole interaction which is a drawback in its applications. Particularly for biomedical applications the magnetic nanoparticles must be completely un-agglomerated and preferably superparamagnetic [10]. Generally superparamagnetic particles are those which are less than ∼20 nm. The magnetic moment of a superparamagnetic particle is very high but it behaves as a paramagnet as it has got temporary magnetism. Because of its magnetic property a superparamagnetic particle can be targeted to a particular tumor cell by an external magnetic field. Henceforth by the application of an ac magnetic field heat can be liberated from the superparamagnetic particle because of the hysteresis loss. After sufficient heat is liberated to kill the tumor cell the external ac field can be switched off leading to complete loss of magnetism of the particle. Hence the other cells will be saved from the side effects caused by the magnetic field. Over the years many synthesis techniques have been developed to synthesize the magnetic nanoparticles like co-precipitation method [11], sol-gel process [12], high temperature reactions [13], microwave

∗

irradiation synthesis [14] and polyol methods [15] among others. Hydrothermal or solvothermal technique is an efficient way of producing highly crystalline nanoparticles at a low temperature preferably below 250 °C. Another advantage of it is that it can produce particles of various shapes by controlling the reaction temperature, solvent and pressure. Another advantage of magnetic nanoparticles (MNP) for biological applications is that they can be very easily synthesized and are inexpensive. They can be made colloidally stable and can be conjugated with biological molecules in a straightforward way. They are particularly interesting because apart from the possibility of being conjugated with biological molecules, they can be driven inside the organism with the help of an external magnetic field to the target area where the therapy has to be done. Although known as potentially toxic substance [16–19], have proposed cobalt containing materials as promising heat mediators due to their high anisotropy. The last decade saw a lot of research in materials for magnetic fluid hyperthermia based on materials like Fe3O4 [20,21] and γ Fe2O3 [22,23]. But these particles display very small saturation magnetization. The remedy to this is the substitution of the Fe2+ ions of the magnetite structure by the other metal ions like (M = Co, Ni, Mn) which are called as ferrites [24–28]. Among all these ferrites cobalt ferrite is a hard ferrite and possesses a saturation magnetization which is 90% of the value of Fe3O4 [29]. But the magnetic anisotropy of CoFe2O4 is one order of magnitude larger than Fe3O4. Naturally CoFe2O4 nanoparticles are expected to show larger hysteresis loop area than the other ferrites of same size, even if a larger magnetic field will

Corresponding author. Department of Applied Science, Haldia Institute of Technology, Haldia, 721657, India. E-mail address: [email protected] (A. Chaudhuri).

https://doi.org/10.1016/j.physb.2019.08.017 Received 17 June 2019; Received in revised form 29 July 2019; Accepted 11 August 2019 Available online 12 September 2019 0921-4526/ © 2019 Elsevier B.V. All rights reserved.

(440)

(511)

(422)

(311)

(222)

(220)

Intensity (a.u.)

be required to saturate them [30]. Among all the ferrites CoFe2O4 produced the maximum specific absorption rate (SAR) as observed by Ref. [31]. We have prepared completely un-agglomerated and mono-disperse CoFe2O4 nanoparticles by the solvothermal technique using Olyl Amine and Sodium Oleate as a capping agent. Spinel ferrites are particularly useful for medical applications because of their nontoxicity, biocompatibility, and thermal activation figure of merit (SAR, the specific absorption rate) in the presence of a radio frequency (RF) magnetic field. Hyperthermia therapy is advantageous as because it is a minimally invasive technique. Bare magnetic nanoparticles will definitely agglomerate with each other. To reduce their dipole attraction the particles must be coated or in a way functionalized by a capping agent. Hence we have capped these particles with Oleic acid and Sodium Oleate. Oleic acid has a particular affinity towards ferrite nanoparticles. When a nanoparticle is coated by a layer of oleic acid then the outermost layer of the oleic acid bilayer is composed of carboxyl groups, which is very useful as magnetic nanoparticles functionalized by carboxyl group can easily couple with antibodies through covalent forces. The sizes of our particles ranged from 7 nm to 23 nm. To the best of our knowledge the studies on hyperthermia so far have been done on particles greater than 50 nm. J Ding et al. [32] produced Fe3O4 nanoparticles ranging from 43 nm to 98 nm. Mandal et al. [33] produced Fe3O4 nano hollow spheres of average diameter 280 nm. Ahmed et al. [34] reported the killing of cancerous cells by Fe3O4 nanoparticles ∼ 23 nm in diameter. Whereas we have reported the killing of cancerous cells by CoFe2O4 nanoparticles which are of size ∼7 nm and are completely unagglomerated. These particles must be more biologically compatible since the lesser the particle size the less will be the chance of the particle to be detected by the immune system. The ac hysteresis loops measured so far were all for particles ranging from 100 nm to 400 nm [35]. We have investigated the ac hysteresis loops of CoFe2O4 nanoparticles having size ranging from 7 nm to 23 nm which is much smaller than the reported works in literature and in the superparamagnetic range.

(400)

Physica B: Condensed Matter 575 (2019) 311640

A. Chaudhuri and K. Mandal

C B

A

20

30

40 50 2 (degrees)

60

70

Fig. 1. X Ray Diffraction of sample A, B and C.

2. Experimental section 2.1. Materials The salts such as CoCl2, 6H2O; FeCl3, 6H2O; was purchased from Sigma Aldrich whereas the solvent ethanol was purchased from Loba Chemie. Sodium Oleate and Olyl Amine was also purchased from Sigma Aldrich. All the chemicals used were analytically pure and no further purification was required. 2.2. Synthesis procedure

Fig. 2. a(a): HRTEM of the CoFe2O4 particles Sample A.

FeCl3.6H2O and CoCl2.6H2O taken in stoichimetric ratio were dissolved in a solvent composed of 40 ml of distilled water and 20 ml of ethanol. Now 4 gm of Sodium Oleate and 4 ml of Olyl Amine were added into the above solution with stirring for 2 h. Sodium Oleate and Olyl Amine were used as surfactants. Oleic Acid has a carboxylic group and Olyl Amine has an amine on its surface. This produces different strengths and selective binding energies of Olyl Amine and Oleic Acid on the surfaces of the nanoparticle and is therefore necessary for controlling the shape as well as size of the nanoparticles. Nguyen T. K. Thanh et al. [36] reported the synthesis of monodisperse Fe–Pt, Fe–Pd and Fe–Pt–Pd alloys due to the presence of a mixture Oleic Acid and Olyl Amine. The magnetic nanoparticles prepared must be hydrophilic in order to make them useable for biomedical purposes. According to Repko et al. [37] formation of hydrophilic particles is enhanced when the water phase contains only sodium oleate and no salts. Hence Sodium Oleate was used as a reaction precursor.

3 Na (oleate) + FeCl3 → Fe (oleate)3 + 3NaCl 2 Na (oleate) + CoCl2 → Co (oleate)2 + 2NaCl The precursor solution was then added into a Teflon Lined steel autoclave of capacity 80 ml. The Teflon chamber was kept at 180 °C for 12 h to crystallize the particles. After that the autoclave was cooled to room temperature naturally [38]. Hexane was added to separate the products from the final reaction solution. Ethanol was added to deposit the as prepared cobalt ferrite and finally it was obtained by centrifugation at a high speed without any size-selecting process. We have prepared three sets of samples and named them as follows. Sample A was prepared using 4 gm of Sodium Oleate, 4 ml of Olyl Amine. Sample B was prepared using 2 gm of Sodium Oleate, 2 ml of Olyl Amine. Sample C was prepared using 1 gm of Sodium Oleate and 1 ml of Olyl Amine.

2

Physica B: Condensed Matter 575 (2019) 311640

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C

Unit Counts

20 15 10 5 0

14

20 16 12 8 4 0 20 15 10 5 0

16

18

20

22

24

26

28 B

8

10

12

14

16

18

20

22 A

5

6

7

8

9

10

11

12

13

14

15

Particle size (nm) Fig. 3. Particle size distribution of the sample A, B and C. Fig. 2b. (b): HRTEM of the CoFe2O4 particles Sample B. Table 1 Comparison of the particle size obtained from XRD with the concentration of Olyl Amine and Sodium Oleate. Concentration of Olyl Amine and Sodium Oleate

Size of particle from XRD (in nm)

A B C

4 ml, 4 gm 2 ml, 2 gm 1 ml, 1 gm

8 16 24

Transmittance ( %)

Sample Name

2342.27 1442.56 2854.76 1533.67

800

Analysis of the phase contents and crystal structures was performed by X-ray diffraction (XRD) with Cu Kα radiation on a Philips X'pert diffractometer. High-resolution Transmission Electron Microscope (HRTEM) analysis was carried out on a FEI-2010 transmission electron microscope with an accelerating voltage of 200 kV. The CoFe2O4 nanoparticles were dispersed in hexane and a single droplet of this solution was taken in a micropipette and dropped on a carbon-coated copper grid. It was then dried naturally before recording the micrographs. Lake Shore 7304 vibrating sample magnetometer (VSM) was used to measure the magnetic properties of the products at room temperature. A Quantum Design MPMS-XL superconducting quantum interference device (SQUID) was used to measure the temperature and field dependences of the samples. ZFC/FC measurements were carried out in the temperature range of 4–330 K with an applied field of 100 Oe. The stretching frequency of the Ferrite particles and Olyl Amine was obtained from the Fourier Transform Infra-Red Spectroscopy (JASCO

2920.47

3432.08

3200

4000

587.4

Fig. 2c. (c): HRTEM of the CoFe2O4 particles Sample C.

2.3. Material characterization

3036.98

1600

2400

Wavenumber (cm-1)

Fig. 4. FTIR spectra of the as-synthesized CoFe2O4 (sample A) nanoparticles.

FTIR-6300). 2.4. Ac hysteresis measurement AC hysteresis loop is commonly measured by the mutual inductance between two coils, one a primary coil (in our case a solenoid) for generating the ac magnetic field and the other a pick up coil used as secondary. Usually the secondary is a set of two oppositely wound identical coils so as to give a zero net signal when there is no sample. Samples are placed near the central zone of the primary coil in order to achieve a uniform magnetic field [39]. The moment of the sample in the AC measurement is actually changing in response to an applied ac field, 3

Physica B: Condensed Matter 575 (2019) 311640

A. Chaudhuri and K. Mandal

7.5

80

4K 50 K 150 K 250 K

60

6.0 4.5

M (emu/g)

3.0 1.5

20 0 -20

10 8

-40

0.0

6

Hc (kOe)

M (emu/g)

40

4 2

-60

0

75

150

225

300

0 0 2 4 6 8 10 12 14 16 T1/2

-80

T (K)

-30

-20

-10

20

30

Fig. 7. Hysteresis loop of the sample A at 4 K, 50 K, 150 K and 250 K. Coercivity vs T1/2 plot.

C

0.2

50 Hz

0.15

250 Hz

0.1

45

B

0

-0.1

-45 45

0.00

0.0

AC Induction (T)

M (emu/g)

10

H (k.Oe.)

Fig. 5. Zero Field Cooled (ZFC) and Field Cooled (FC) curves of sample A.

50 0 -50

0

A

0 -45 -30

-20

-10

0 10 H (kOe)

20

-0.15

-0.2 -40000 0.2

0

40000

-0.30 -80000 0.2

450 Hz

0

40000

80000

600 Hz

0.1 0.0

30

-40000

0.0 -0.1

-0.2

Fig. 6. Hysteresis loops of sample A, B and C at 300 K.

-0.2 -80000

Hc (k.Oe.)

Ms (emu/g)

A B C

0.0116 0.1717 1.0026

51.85 58.81 58.77

0

40000

80000

-40000

0

40000

Applied ac magnetic field (A/m)

Table 2 Comparison of the Coercivity (Hc), Saturation Magnetization (Ms) of samples A, B and C. Sample

-40000

Fig. 8a. (a): AC hysteresis loops of Sample A at 50 Hz, 150 Hz, 250 Hz and 350 Hz at room temperature.

∼8 nm. The average particle size obtained is also in agreement with that obtained from the scherrer formulae. Average size of Sample B is ∼15 nm and that of Sample C is ∼23 nm. It is observed that the particle size as well as shape varied with the variation in concentration of Olyl Amine and Sodium Oleate. The variation of particle size with the concentration of Oleic acid and Olyl Amine is shown in Table 1. This further proves that olyl amine and oleic acid acted as capping agents which arrested the growth of the particles resulting in decrease in size with the increase in concentration. Fig. 3 shows the particle size distribution of sample A, B and C. The FTIR spectra of sample A performed in the range of 500 cm−1 to 4000 cm−1 is shown in Fig. 4. The peak at 587.4 cm−1 is due to the ferrite nanoparticles. The peaks at 1443 cm−1 and 1534 cm−1 correspond to COO− asymmetric and COO− symmetric stretch. Oleic acid shows vibration bands at 2920 cm−1 and 2855 cm−1 that are attributed to the CH2 asymmetric and CH2 symmetric stretch. The sharp peaks are due to the long hydrocarbon chain of olyl amine [40]. The peak at 3037 cm−1 is assigned to the stretching of the vinyl group. The peak at 3432 cm−1 is ascribed to the –NH2 group on the surface of CoFe2O4. Thus the above results proved that oleic acid and olyl amine combined

allowing the dynamic properties of the magnetic system to be studied. 3. Results and discussions The X Ray Diffraction (XRD) of the samples A, B and C is shown in Fig. 1. All the observed peaks showed the formation of pure phase CoFe2O4. As the quantity of Olyl amine and sodium oleate decreases the particle size increases. As the quantity of Olyl amine and sodium oleate decreases the capping decreases. Hence the particles grow to bigger sizes. The average grain size as calculated from the scherrer formulae for sample A, B and C are ∼8 ± 2 nm, ∼16 ± 2 nm and ∼24 ± 2 nm respectively. Fig. 2 shows the HRTEM images of sample A, B and C. Fig. 3 shows the particle size distribution of sample A having a narrow size distribution. The HRTEM images reveal that the particles were nearly spherical and monodisperse. The average particle size of sample A is 4

Physica B: Condensed Matter 575 (2019) 311640

A. Chaudhuri and K. Mandal

50 Hz 0.2

0.25

0.0

0.00

-0.2

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250 Hz

A

0.6

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0

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0.0 1.2

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450 Hz

40000

80000

600 Hz

0.2

0.0

0

Power Loss (W/g)

Ac Induction (T)

0.3

0.0

-0.2 -80000

-40000

0

40000

80000

0.4 0.0 1.8 1.2 0.6 0.0

C

0

-0.2

-0.4

B

0.8

200

300

-40000

0

40000

τ = τ0 exp(

K eff Vp kB T

)

(1)

where τ is the relaxation time, τ0, a constant estimated to be between 10−9 and 10−13s and KeffVp, the total anisotropy energy EA of the particle. In case of kBT > KeffVp, no hysteresis is observed if the characteristic time of the measuring instrument, τm is higher than τ. This is the reason for not observing any measurable coercivity in our sample. The blocking temperature TB of a particle is the temperature at which τ = τ m, the measurement time of the instrument. For τ < τ m the system behaves as a superparamagnet. For τ > τ m the system behaves as a ferromagnet. Temperature dependence of coercivity Hc of uncoated and coated samples is shown in Fig. 7. The coercivity Hc increases with the decrease in temperature. For an assembly of monodispersed, non-interacting, ferro- or ferrimagnetically ordered single-domain particles, the 0.4

0.3

250 Hz

50 Hz 0.2

0.1 0.0

0.0 -0.1

Ac Induction (T)

600

fluctuate between their two energetically degenerate ground states on a time scale given by Ref. [42].

with the surface of CoFe2O4 nanoparticles. Fig. 5 shows the Zero Field Cooled (ZFC) and Field Cooled (FC) plots of the sample A measured at an applied field of 100 Oe and from temperature 3 K–310 K. The temperature corresponding to the peak value of the ZFC curve is considered as the blocking temperature, TB of the sample above which it behaves as a superparamagnetic material. The TB obtained for our sample is 230 K. TB increases with increasing size of the sample [41]. The room temperature hysteresis loop of the samples is shown in Fig. 6. The Coercivity and Saturation Magnetetization values of the samples are provided in Table 2. The sample does not show any measurable coercivity, Hc and remanence, Mr indicating the presence of superparamagnetic behavior at room temperature. At a finite temperature and in absence of any magnetic field, the ferromagnetically aligned magnetic moments within these single-domain particles

-0.2

-0.2 -0.4 -80000 -40000

0

40000 80000

-80000 -40000

0

40000

80000

0.30 0.30

500

Fig. 9. SAR vs frequency of Sample A, B and C.

Fig. 8b. (b): AC hysteresis loops of Sample B at 50 Hz, 150 Hz, 250 Hz and 350 Hz at room temperature.

-0.3

400

Frequency (Hz)

Applied ac magnetic field (A/m)

0.2

100

600 Hz

450 Hz 0.15

0.15

0.00

0.00 -0.15

-0.15

-0.30 -80000 -40000

0

40000

80000

-0.30

-40000

0

40000

Applied Ac magnetic field (A/m) Fig. 8c. (c): AC hysteresis loops of Sample C at 50 Hz, 150 Hz, 350 Hz and 650 Hz at room temperature. 5

Physica B: Condensed Matter 575 (2019) 311640

A. Chaudhuri and K. Mandal

Fig. 10. ln (Hc) vs ln (frequency) graph.

are high compared to the measuring time of the instrument. Hence most of the particles behave as superparamagnetic particles. Again as the frequency increases the bigger particles cannot change their spin state within such a short time (less than the relaxation time) and then most of the particles behave as ferromagnetic. Hence the coercivity also increases [45]. At high frequencies we get minor loops because the ac magnetic field is not sufficient to saturate the loops. The Specific Absorption Rate (SAR) vs frequency plot for sample A, B and C is shown in Fig. 9. SAR also called Power Loss is proportional to the product of hysteresis loop area and frequency. SAR of sample A increases from 0.0067 Watt/gm at 50 Hz to 0.779 Watt/g at 600 Hz. SAR of sample A increases from 0.0203 Watt/g at 50 Hz to 1.1859 Watt/g at 600 Hz. Similarly SAR of sample C increases from 0.0285 Watt/g to 1.737 Watt/g at the same frequency range. It proves that the SAR of the CoFe2O4 nanoparticles increases with the increase in frequency of the applied ac field. The maximum ac frequency up to which we have measured in our indigenous set up is 600 Hz because the impedance of the circuit becomes so high after 600 Hz that the reduced field is not enough to saturate the hysteresis loops. As we increase the frequency the power loss increases. We have measured the power loss up to 600 Hz and have seen that the power loss increases proportionately. Hence we can conclude that these particles can produce sufficient amount of heat at high frequency which will be useful in killing the tumor cells. However we can conclude from the results that the CoFe2O4 nanoparticles might contribute enough power loss in the high frequency region (MHz to GHz range). Mandal et al. [33] carried out the in vitro cytotoxic effect of Fe3O4 nanohollow spheres on cancer cells and proved that the cancerous cells can be damaged without damaging the normal cells much. Arun Kumar et al. [46] recently studied the hyperthermic behavior of the as synthesized PEG encapsulated Cobalt Ferrite nanoparticle and concluded that these particles can be used for mild cancer treatments. Ding et al. [47] also proved that octahedral CTAB encapsulated Fe3O4 nanoparticles are biocompatible and can be applied for magnetic hyperthermia. We can therefore predict that these particles will be very useful in destroying the cancer cells by hyperthermia technique. The power loss increases with the increase in frequency. It also increases with increase in particle size. This observation is completely opposite to that observed by Sarkar et al. [44].

temperature dependence of coercivity Hc (T) can be expressed as [43]:

T 1 Hc = Hc (0)[1 − ( ) 2 ] TB

(2) 1/2

in the inset of Fig. 7. Linear deHc (T) is plotted against T pendency of Hc on TB is also an evidence of monodispersed noninteracting, ferromagnetically ordered single domain particles. The ac hysteresis loops of the sample shown in Fig. 8 (a), 8 (b) and 8 (c) was measured by an indigenous set up made in our laboratory where we can produce nearly 92 kA/m AC magnetic field at nearly 600 Hz AC field frequency. The area enclosed within this hysteresis loop represents the irreversible work done which is dissipated in the environment as heat energy which in turn can be utilized in magnetic hyperthermia. This type of heat loss is called as “Specific Absorption Rate” (SAR) and is usually expressed in Watts per gm of nanoparticles. SAR is usually calculated with the help of the equation SAR = Af where A is the area of the hysteresis loop and f is the frequency of the ac field. The dynamic hysteresis loops of the sample were measured at room temperature in the frequency range of 50 Hz–600 Hz. The primary criterion for the determination of the utility of the magnetic nanoparticle for the hyperthermia treatment is the power loss measurement. It is observed that the coercivity of the hysteresis loops increases with the increase in frequency of the ac magnetic field as reported by Sarkar et al. [44]. It is also observed that the area of the loops increases with increase of frequency. In case of sample A the coercivity increases from 3066 A/m at 50 Hz to 20286.85 A/m at 600 Hz. In case of sample B the coercivity increases from 7318.2 A/m at 50 Hz to 26254.64 A/m at 600 Hz. In case of sample C it increases from 9675.09 A/m at 50 Hz to 26158.2279 A/m at 600 Hz. Sarkar et al. [44] prepared Fe3O4 hollow spheres of size 185 nm, 350 nm and obtained high coercivity in ac magnetic field. Madhuri et al. [33] produced Fe3O4 hollow spheres of size 280 nm and applied it for hyperthermia. But we obtained high SAR for only 7 nm CoFe2O4 nanoparticles. Hence these should be more effective in hyperthermia treatment. With the increase of frequency the measuring time of the instrument decreases i.e. τ ≫ τm where τm is the measuring time of the instrument [From equation (3)]. Due to this fact ac hysteresis loops become wider and wider i.e. with the increase in the applied frequency the coercivity increases. At lower frequencies, relaxation times of the nanoparticles 6

Physica B: Condensed Matter 575 (2019) 311640

A. Chaudhuri and K. Mandal

10.5 (a)

80K 85K 90K 95K 100K

9.8 9.1 8.4

M (emu/g)

7.7 7.0 12

0

100

200

300

400

Time (s)

(b)

100K 95K 90K 85K 80K

11 10 9 8 7

1

2

3

4

ln t

5

6

7

Fig. 11. (a): Time evolution of M for sample A (b) M vs. lnt curve of sample.

accounted for the variation of coercivity as given below

In their case the power loss increased with the decrease in particle size from 350 nm to 185 nm. According to Hergt et al. [48] as long as the particle volume is above a critical volume (Vc) the power loss increases with the decrease in particles size. Since our particles are lesser than the superparamagnetic limit hence these particles do not follow this law. Heating of magnetic nanoparticles due to ac magnetic field has four different mechanisms (i) Hysteresis loss (ii) Néel and Brown relaxation (iii) frictional losses in viscous suspension (iv) loss due to Eddy current induced heating. Among all these particularly for magnetic nanoparticles Eddy current loss is negligible. As cited earlier by Fortin et al. [49] the nanoparticles having core diameter lesser than 20 nm are governed by the relaxation of the type of Néel and Brownian. Since we have done all the magnetic measurements in powder sample without employing any fluid we are ignoring the Brownian relaxation part. Since the size of sample A is ∼7 nm hence it might follow Néel relaxation. Sample B and C are also ferrites. Hence it should not follow Eddy current loss. So the maximum probability is that it follows hysteresis loss. The total coercivity or loss has been sometimes approximated to one frequency dependent term [50].

Hc = f α

Hc = [

πfβxHa 1 ]2 M

(4)

where f is the frequency of the applied AC field Ha, x is the average domain wall width, β the eddy current damping constant and M the saturation magnetization. Hence according to this simple model the value of the exponent must be 0.5. In order to calculate the value of α we have plotted log Hc vs log f for all the samples in Fig. 10. The slope of the graph (Fig. 10 (a), (b) and (c)) gives the power of the frequency. In case of sample A we observe that the value of α = 0.85 and for sample B α = 0.54, sample C α = 0.48. Hence although according to Gyorgy it should come as 0.5. But we have obtained a value of 0.85 for sample A of size ∼8 nm. Sarkar et al. [51]. synthesized Fe3O4 nano hollow spheres and found out that the value of α varied from 0.79 to 0.3 with the change in the size of the hollow spheres from 100 nm to 725 nm. Hence it proves that the value of α as proposed by Gyorgy must be size dependent. This also proves that the particles of sample A show Néel relaxation. In case of sample B and C coercivity varies almost as the square root of frequency. Hence they follow hysteresis loss. Evolution in the domain structure and the increase in the activity of domain walls with increasing frequency and are the cause for the non-linear dependence of Hc and losses with increasing frequency [52]. α = 0.48 suggests domain wall

(3)

where α∼0.5 denotes the loss due to eddy current heating. This was proven theoretically by Gyorgy [50] who proposed a model where he 7

Physica B: Condensed Matter 575 (2019) 311640

A. Chaudhuri and K. Mandal

16.8

80 K 85 K 90 K 95 K 100 K 105 K

(a)

16.4 16.0 15.6

M (emu/g)

15.2 14.8 0

100

200

t (sec)

300

400

80K 85K 90K 95K 100K

(b)

16.65

500

16.20 15.75 15.30 14.85 1

2

3

4

ln t

5

6

Fig. 12. (a): Time evolution of M for sample B (b) M vs. ln t curve of sample B.

(B), 21 nm ( ± 2) (C) measured at different temperatures are shown in Figs. 11 (b), Fig. 12 (b) and Fig. 13 (b). For each sample the plots apparently show a linear behavior, which would be expected from the following logarithmic approximation [53].

M (t ) = M (0) − S ln(t )

(5)

where S is the classical rate of relaxation or the classical viscosity and according to Eq. (5) it is defined as,

S=−

1 ∂M M0 ∂ (ln t )

(6)

In Figs. 11 (a), 12 (a) and 13 (a) the M versus time (t) data were plotted at temperatures 80 K, 85 K, 90 K, 95 K and 100 K for samples A, B and C. The value of M at the starting point of the measurement is found to be much smaller in case of A compared to B for all the temperatures. The reason behind this is increased disordered surface effect, which decreases the M value in case of A comprised of smaller particles [54]. The particles of Sample A show a behavior very similar to superparamagnetic particles as the particles relaxed almost instantaneously after the removal of the field [55].

Fig. 13. (a): Time evolution of M for sample C (b) M vs. ln t curve of sample C.

damping due to eddy currents. The particles in sample C are present in an agglomerated form. Hence although they are single domain the contribution of domain wall might arise because of the agglomeration. Magnetic relaxation behaviors that are a dynamic property of the samples were studied. The relaxation phenomenon of samples A, B and C was studied at different temperatures after magnetizing the samples by a magnetic field of 2000 Gauss and then switching off the field. After waiting for 5 s the measurements were performed during a time period of 400 s. After the removal of a field of 2000 Gauss, magnetizations of all samples evolve with time towards a demagnetized state which is shown in Fig. 11 (a), Fig. 12 (a) and Fig. 13 (a). Experiments were carried out for different temperatures from 80 K to 100 K. Relaxation time for a non-interacting single domain particle is given by Néel's theory [29,30]. According to Eq. (3) relaxation rate for a single domain particle is a very sensitive function of particle size. The M vs ln t curves for samples of average particle sizes 8 nm ( ± 0.5) (A), 16 nm ( ± 1.2)

4. Conclusions We have synthesized monodisperse, unagglomerated nanoparticles of CoFe2O4 by a solvothermal technique using various capping agents. Particles of various sizes ∼7 nm, ∼14 nm and ∼23 nm were synthesized. Ac hysteresis loops of all the samples were measured at room temperature within a frequency range of 50 Hz–650 Hz. All the samples showed the increase of coercivity with the increase of frequency. The reason behind this was theoretically investigated. It was observed that the coercivity increased with frequency in a certain power which varied with the variation in the size of the particles. The SAR was also calculated with increasing frequency. These particles can be very effective for magnetic hyperthermia.

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Physica B: Condensed Matter 575 (2019) 311640

A. Chaudhuri and K. Mandal

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