Temperature dependence of magnetic anisotropy constant in CoFe 2 O 4 nanoparticles examined by Mössbauer spectroscopy

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1 Hyperfine Interact DOI /s Temperature dependence of magnetic anisotropy constant in CoFe 2 O 4 nanoparticles examined by Mössbauer spectroscopy Sunghyun Yoon Springer International Publishing Switzerland 2015 Abstract The temperature dependence of the effective magnetic anisotropy constant of CoFe 2 O 4 nanoparticles is determined based on the measurements of SQUID magnetometry and Mössbauer spectroscopy. Under an intuitive assumption that the superparamagnetic fraction of the cumulative area in the particle size distribution at a temperature is equal to the doublet fraction in the Mössbauer spectra at that temperature, we are able to get a relation between r and T B, from which the temperature dependence of the effective magnetic anisotropy constant is determined. The resultant magnetic anisotropy constant increases markedly with decreasing temperature from J/m 3 at 300 K to J/m 3 at 125 K. Keywords Magnetic anisotropy constant Magnetic nanoparticles Mössbauer spectroscopy Particle size distribution 1 Introduction Magnetic anisotropy is a core factor that controls the functionality of magnetic nanoparticles in many applications. It plays a key role in manipulating the magnetic nanoparticles with an external magnetic field by either providing an energy barrier for moment reversal or fixing the moment in the particle [1, 2]. When the magnetic anisotropy energy is high enough, the magnetization is blocked into the nanoparticle and it relaxes through Brownian relaxation mechanism. Otherwise, however, the magnetization gets unblocked thru thermal agitation Proceedings of the 5th Joint International Conference on Hyperfine Interactions and International Symposium on Nuclear Quadrupole Interactions (HFI/NQI 2014) Canberra, Australia, September 2014 S. Yoon ( ) Department of Physics, Gunsan National University, Gunsan , South Korea shyoon@kunsan.ac.kr

2 S. Yoon and a Néel type superparamagnetic relaxation would dominantly occur [3]. The superparamagnetic relaxation time τ is generally described by simple Néel relation, assuming that the interactions between particles are negligible, τ = τ 0 e E A/k B T (1) where ΔE A =KV is the anisotropy energy barrier, K is the effective magnetic anisotropy constant, V is the volume, k B is the Boltzmann constant, and T is the temperature. τ 0 is the attempt time of the order of s. It has been known that the anisotropy constants are sensitive functions of temperature. As the temperature is raised to the magnetic ordering temperature, K is reported to decrease to zero [4, 5]. However, its temperature dependence is often overlooked in many studies, in which it is dealt with as a constant of temperature. It has been claimed that ignoring the temperature dependence of magnetic anisotropy constant could sometimes lead to an incorrect result [6, 7]. In this study, an intuitive method for determining the temperature dependence of effective magnetic anisotropy constant in poly-dispersed magnetic nanoparticles using Mössbauer spectroscopy is introduced and applied to CoFe 2 O 4 nanoparticles under a simple independent particle scheme with collective fluctuation criteria. 2 Experiment Poly-dispersed suspension of CoFe 2 O 4 nanoparticles was prepared by conventional coprecipitation method from CoCl 2 6H 2 OandFeCl 3 6H 2 O using oleic acid as a surfactant [8, 9]. 100 μl of suspension sealed in polycarbonate capsule was used for magnetic measurement. Rest of the nanoparticles were dried and subsequently be subjected to the Mössbauer spectroscopy measurements. A superconducting quantum interference device (SQUID) magnetometer was used to obtain the M-H curve at room temperature. A 57 Fe Mössbauer spectrometer of conventional transmission geometry was used in the constant acceleration mode over the temperature range from 20 K up to 300 K. 3 Results and discussion Figure 1 shows the transmission electron microscopy (TEM) image and the X-ray diffraction (XRD) profile of the sample. From the TEM image, nominal radius was roughly estimated to be 3 nm. XRD profile shows pure spinel phase without the other impurities. Analysis of the XRD pattern using the Debye-Scherrer equation for the most intense (311) peak revealed that the averaged size of the particles was 6.7 nm. The M-H curve at room temperature showed a superparamagnetic behavior with no hysteresis. In order to obtain the particle size and its distribution, the first quadrant part of the M-H curve (Fig. 2a) is fitted to the classical Langevin function weight averaged with the log-normal size distribution function f(r): M(H) = εm S L(H,r)f(r)dr, (2) where M S is the saturated magnetization (M S = 5700 G [10]) and ε is the volume fraction of the sample. The optimum median radius was found to be 2.3 nm; the resultant distribution f(r)is shown in Fig. 2b.

3 Temperature dependence of magnetic anisotropy constant It has already been reported that the temperature dependence of the effective magnetic anisotropy constantk(t) can easily be determined if the particle size distribution f(r)and the anisotropy energy barrier distributionf A (T ) is known at the same time [11]. The effective magnetic anisotropy constant is a measure of how strong a net magnetic moment is pinned down to an easy axis within a particle. Mainly due to the particle size distribution and the inter-particle interactions in ploy-dispersed nanoparticles, there will be a distribution of anisotropy energy barrier which give rise to a distribution of blocking temperature and the blocked and the unblocked portions of the particles coexist in the sample at a temperature. The blocked portion comes from the particles with superparamagnetic relaxation time longer compared to the time window of measurement method and the unblocked portion from the particles with shorter relaxation time. As the temperature increases, some anisotropy energy barrier in the distribution gets gradually overcome by thermal activation and hence the blocked portion of nanoparticles decreases. Mössbauer spectroscopy is the most adequate measurement tool that can observe the blocked and the unblocked portions within the same sample simultaneously. Mössbauer spectra for CoFe 2 O 4 nanoparticles taken at various temperatures are illustrated in Fig. 3. Mössbauer spectra at low temperatures show no clear discrimination between the A and the B sites as is the case in other results reported previously [12, 13]. Mössbauer spectrum at 20 K was fitted with four subspectra with hyperfine magnetic fields of 529 koe(b), 482 koe(b), 450 koe(b) and 505 koe(a) with corresponding area fraction of 28.5 %, 24.6 %, 6.3 % and 40.6 %, respectively. From this, cation distribution is (Co 0.19 Fe 0.81 ) A [Co 0.81 Fe 1.19 ] B O 4, which means the sample is close to the inverse spinel. The spectra show a gradual change from magnetic hyperfine sextet to a superparamagnetic doublet with increasing temperature. When the temperature is sufficiently low, magnetic moments of the nanoparticles are blocked and do not flip for a relaxation time window (τ moss = s[14]), giving rise to the observed sextet. If the relaxation time of some particles given by (1) becomes shorter than τ moss with the increase of temperature, the nanoparticles are unblocked and a doublet emerges with the expense of the sextet. Note that small magnetic hyperfine sextet is observed even at room temperature, indicating that there exists small fraction of particles that are still blocked longer than the time-scale of τ moss. Figure 4(a) shows the variation of doublet fraction f D (T ) from the total absorption area with temperature. f D (T ) directly reflects the fraction of nanoparticle moment in the sample that are unblocked within the time scale of τ moss at that temperature. With the assumption that the smaller particles always get unblocked at lower temperature, the value of f D (T ) at a temperature T is the fraction of the cumulative area below some critical radius r below which the particle is superparamagnetic at that temperature in the particle size distribution f(r), thereby one can get a relation between a particle radius r and the corresponding blocking temperature T B. The resultant T B r relation is shown in Fig. 4b, in which the slope decreases with increasing the size of particles. A similar behavior was already reported previously [7, 9]. Mathematically, the temperature dependence of the doublet fraction f D (T ) is then given by f D (T B ) = r(t B ) 0 f(r)dr (3) where f(r)is the particle size distribution function determined from the analysis of M-H curve above and r(t B ) is the upper critical radius of the particles that get unblocked at T B. Previously, similar methods of integrating the size distribution function were introduced, but they ended up only with finding a median blocking temperature by locating the temperature

4 S. Yoon Fig. 1 (a) TEM image and (b) XRD pattern for CoFe 2 O 4 nanoparticles where 50 % in volume fraction of Fe magnetic moments are superparamagnetic, and finally obtained a constant K value [15, 16]. In this study, however, a little different approach is taken in order to get the temperature dependence of effective magnetic anisotropy constant. The values of r and T B in Fig. 4b are substituted into (1) with τ = τ moss, and rearranging it gives K(T B ) = k BT B V(r) ln ( τmoss τ 0 ). (4) Here the unknown τ 0 was assumed as a constant and was determined to be s that gives the value of K at 300 K to be J/m 3, which is the K value reported in other literature [17]. As is obvious in Fig. 5, the resultant magnetic anisotropy constant K(T) decreases with increasing temperature, which is consistent with the behaviors reported previously [18].

5 Temperature dependence of magnetic anisotropy constant Fig. 2 (a) Results of the M-H curve analysis for CoFe 2 O 4 nanoparticles and (b) the corresponding particle size distribution f(r) The anisotropy constant at 125 K is somehow larger than, but still in the same order with those already reported [19, 20]. The anisotropy constant at low temperature is far more than one order of magnitude larger than that at 300 K, indicative of the effects of inter-particle interaction, which is more pronounced for smaller particles that get unblocked at lower temperatures. Fig. 3 Typical Mössbauer spectra for CoFe 2 O 4 nanoparticles taken at various temperatures

6 S. Yoon Fig. 4 (a) Temperature variation of doublet fraction deduced from Mössbauer spectra and (b) the relation between r and T B numerically obtained from (3) Figure 6 shows the relaxation time τ in (1) deduced in this study calculated for several r values. If we assume that the constant K is retained down below 125 K, most particles are in the unblocked regime and considerable portions of doublet should have been observed from the Mössbauerspectratakenbelow125K. Butthis is notthe caseasis obviousfromfig. 3. Therefore, the temperature variation of magnetic anisotropy always has to be taken into account when one studies the blocking-unblocking phenomenon of magnetic nanoparticles throughout a wide temperature range. 4 Conclusion The temperature dependence of the effective magnetic anisotropy constant for CoFe 2 O 4 nanoparticles was determined from the particle size distribution f(r) and the unblocked Fig. 5 Temperature dependence of the effective magnetic anisotropy constant for CoFe 2 O 4 nanoparticles calculated from (4)

7 Temperature dependence of magnetic anisotropy constant Fig. 6 Relaxation time calculated for some sizes of particles. Thick horizontal broken line is the border between the blocked and the unblocked regimes in Mössbauer spectroscopy. Hollow symbols are for the bulk anisotropy constant ( J/m 3 ) independent of temperature fraction of particles f D (T ) in the sample deduced from the SQUID magnetometry and the Mössbauer spectroscopy, respectively. The effective magnetic anisotropy constant K(T) was found to increase markedly as the temperature decreases. In view of the fact that the Mössbauer measurement was done using a dried powder with non-negligible inter-particle interaction, one of the reasons for the enhanced increase in K at lower temperature is attributed to the blocking of smaller particles that are more susceptible to the inter-particle interaction. Smaller particles always get blocked at lower temperatures. In this respect, the inter-particle interaction seems to increase K by heightening the anisotropy energy barrier of magnetic moments for small particles [21, 22]. Acknowledgments NRF of Korea. This was supported by the Basic Science Research Program ( ) through References 1. Krishnan, K.M.: IEEE Trans. Magn. 46, 2523 (2010) 2. Pankhurst, Q.A., Connolly, J., Jones, S.K., Dobson, J.: J. Phys. D Appl. Phys. 36, R167 (2003) 3. Chung, S.H., Hoffmann, A., Bader, S.D., Liu, C., Kay, B., Makowsky, L., Chen, L.: Appl. Phys. Lett. 85, 2971 (2004) 4. Yoda, K., Tachiki, M.: Prog. Theor. Phys. 17, 331 (1957) 5. Kanamori, J. In: Rado, G.T., Suhl, H. (eds.): Magnetism. Academic Press, New York (1963). Vol. 1 Chap Wiekhorst, F., Shevchenko, E., Weller, H., Kötzler, J.: Phys. Rev. B 67, (2003) 7. de Julian Fernandez, D.: Phys. Rev. B 72, (2005) 8. Desautels, R.D., Cadogan, J.M., van Lierop, J.: J. Appl. Phys. 105, 07B506 (2009) 9. Maaz, K., Mumtaz, A., Hasanain, S.K., Ceylan, A.: J. Magn. Magn. Mater. 308, 289 (2007) 10. Krupicka, S., Novak, P. In: Wohlfarth, E.P. (ed.): Ferromagnetic Materials, vol. 3, p North-Holland, Amsterdam (1982) 11. Yoon, S., Krishnan, K.M.: J. Appl. Phys. 109, 07B534 (2011) 12. Lopez, J.L., Pfannes, H.-D., Paniago, R., Sinnecker, J.P., Novak, M.A.: J. Magn. Magn. Mater. 320, e327 (2008)

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