Physica B 279 (2000) 177}180
Electromagnetic properties of superparamagnetic nanocomposites C. Desmarest!, P. Gadenne!, M. Nogue`s!, J. Sztern!, C. Naud", N. Bontemps#, S. Djordjevic#, M. Gadenne",* !Laboratoire de Magne& tisme et d 'Optique de Versailles, UMR CNRS 8634, Universite& de Versailles Saint-Quentin, 78 035 Versailles Cedex, France "Laboratoire d 'Optique des Solides, UMR CNRS 7601, Universite& Pierre et Marie Curie, 4, Place Jussieu, Case 80, 75 252 Paris Cedex 05, France #Laboratoire de Physique de la Matie% re Condense& e, Ecole Normale Supe& rieure, 24 rue Lhomond, 75 231 Paris Cedex 05, France
Abstract We report here new experimental results on superparamagnetic nanocomposites. We compare experimental transmission measurements with calculations based on the Onsager local "eld, taking into account the permanent magnetic moment of the particles. Optical measurements are performed on a Fourier transform spectrometer in the far infrared range, and on a microwave setup. Usually, superparamagnetic relaxation is understood by comparing the relaxation time q of the magnetic moment of the particle with the measuring time q . According to NeH el's model q is temperature . dependent. In our case, q is given by the electromagnetic wave period. As this experimental technique has been proved . to be relevant to investigate superparamagnetism relaxation, we check it with two kinds of nanocomposites: Ni (ferromagnetic) embedded in alumina or aluminum nitride matrix and c-Fe O particles (ferrimagnetic) in a polymer. 2 3 The dominant anisotropy is magnetocrystalline for Ni and shape and/or surface for c-Fe O . This di!erence leads to 2 3 di!erent transmission behaviors while changing sample temperature from 5 to 300 K. The magnetocrystalline anisotropy shows up temperature dependence while the shape or surface anisotropies do not. ( 2000 Elsevier Science B.V. All rights reserved. PACS: 75.50.Tt; 74.25.Gz; 75.30.Gw; 78.66.Sq Keywords: Superparamagnetism; Nanocomposites; Far-infrared measurements
1. Superparamagnetism and optics When put in a variable magnetic "eld small monodomain ferromagnetic particles can behave in two di!erent ways: either the period of variations of the magnetic "eld (q ) is shorter than the relaxation time (q) of the . orientation of the magnetic moments and they are frozen, or q is larger than q and the magnetic moments can . relax (superparamagnetism). According to NeH el's model [1,2], we suppose that the variation of the relaxation time
* Corresponding author. Fax: #33-1-44-27-39-82. E-mail address: [email protected]
follows the law q"q exp(KV/kT ), where q is the initial 0 0 relaxation time, K is the constant of magnetic anisotropy, < is the volume of the particle, k is the Boltzmann constant and ¹ is the absolute temperature. In this work the applied magnetic "eld will be only an electromagnetic wave, the period of which (q ) belongs to . far-infrared and microwave ranges without any other external magnetic "eld. On varying the temperature ¹, the period of the electromagnetic wave may be close to the relaxation time of the moments. By performing spectral measurements in the 5}300 K range of temperature and this wavelength range, one can study the in#uence of the transition between ferromagnetism (q (q) and . superparamagnetism (q 'q) on the optical properties. .
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 7 2 8 - 0
C. Desmarest et al. / Physica B 279 (2000) 177}180
2. Theoretical model For the calculations of the optical properties, based on the refraction index n and the wave admittance g, we need the values of the dielectric function e and magnetic permeability k. We then consider the inhomogeneous medium composed of ferromagnetic metallic inclusions embedded in an insulating matrix as an e!ective homogeneous medium. Considering isolated particles, in the infrared range, we can calculate the dielectric function e and the magnetic permeability k by an e!ective %&& %&& medium theory . The dielectric function is calculated with Maxwell}Garnett approximation in the case of spherical inclusions and the calculation of the e!ective magnetic permeability is based on an extension of the Onsager theory taking into account both the alignment of the ferromagnetic moments of the monodomain metal grains and their induced magnetic moment . Focusing on the transmittance, we make two di!erent calculations, taking q "10~13 s as the initial relaxation 0 time, a log-normal distribution for the inclusions radius where r "50 As , according to TEM measurement, using 0 K"5]104 erg cm~3 as anisotropy constant on the one hand, and on the other hand using K variations with temperature, found in the literature for bulk Ni.
very beginning of the e!ect of the superparamagnetic relaxation on transmission is around 25 lm, while reheating Ni/Al O sample from 5 to 300 K. The 2 3 transition between ferromagnetism (q (q) and super. paramagnetism (q 'q) is characterized by a blocking . temperature (¹ ) of 200}250 K. The e!ect of the relaxB ation increases with j, up to 5% at 50 lm.
Fig. 2. Calculated variation of transmittance with temperature of a cermet Ni/Al O "lm versus wavelength in the 25}50 lm 2 3 spectral range, r "50 As , f "0.1, thickness"1 lm, K(¹) as 0 # bulk Ni.
3. Experimental transmission versus calculation The samples are either cosputtered cermet thin "lms of Ni/Al O and Ni/AlN, or c-Fe O particles embedded in 2 3 2 3 a polymer, prepared by a chemical method . In order to obtain more information about the optical properties of our components, we study a very large spectral range, and so, a very large measuring time (q ) range is covered, from . 10~13 to 10~11 s, giving access to a large range of relaxation time while changing temperature from 5 to 300 K. 3.1. Medium IR: 25}50 lm (q +10~13 s) . We observe a good agreement between experiment (Fig. 1) and calculation (Fig. 2), which point out that the
Fig. 1. Experimental variation of transmittance with temperature of a cermet Ni/Al O "lm versus wavelength in the 2 3 25}50 lm spectral range, r "50 As , f "0.1, thickness"1 lm. 0 #
Fig. 3. Experimental variation of transmittance with temperature of a cermet Ni/Al O "lm versus wavelength in the 2 3 200}450 lm spectral range, r "50 As , f "0.1, thickness"1 lm. 0 #
Fig. 4. Calculated variation of transmittance with temperature of a cermet Ni/Al O "lm versus wavelength in the 200}450 lm 2 3 spectral range, r "50 As , f "0.1, thickness"1 lm, K(¹) as 0 # bulk Ni.
C. Desmarest et al. / Physica B 279 (2000) 177}180
Fig. 5. Experimental variation of transmittance with temperature of a cermet Ni/AlN "lm versus wavelength in the 150}350 lm spectral range, r "30 As , f "0.2, thickness"3 lm. 0 #
Fig. 6. Experimental variation of transmittance with temperature of a c-Fe O nanocomposite versus wavelength in the 2 3 200}450 lm spectral range, r "40 As , ellipticity"0.7. 0
3.2. Far IR: 200}450 lm (q +10~12 s) . The agreement between experiment (Fig. 3) and calculation (Fig. 4) is less obvious, as the general shape shows an e!ect that still increases with k in the experimental results. The e!ect is less important (5%) than expected by simulation (15%). We notice another di!erence in this spectral range: some particles which have relaxation time (q) around 10~12 s seem to unfreeze earlier (¹ "150 K) B than in the calculation (¹ "200 K). Particles still unfreB eze progressively until 300 K. Finally, one can see (Figs. 5}7) that Ni/Al O sample behaves di!erently 2 3 from Ni/AlN or c-Fe O samples, for which ¹ values 2 3 B are close to 50 K, and for which no other change occurs with temperature; this suggests that all the particles present in the samples are able to relax. The behavior of these two last samples is in good agreement with calculation
Fig. 7. Calculated variation of transmittance with temperature of a cermet Ni/Al O "lm versus wavelength in the 200}450 lm 2 3 spectral range, r "50 As , f "0.2, thickness"1 lm, 0 # K"5]104 erg cm~3.
based on dominant anisotropy, insensitive to temperature (Fig. 7). In fact, c-Fe O dominant contribution to 2 3 the energy barrier (here: E "K<) is related to surface B anisotropy , and Ni/AlN particles have an intricate shape as shown by AFM measurements, presented in the same issue of Physica B , which involves a dominant surface anisotropy. 3.3. Microwave: 3000 lm (q +10~11 s) . We have made the "rst microwave transmission measurements (Fig. 8) on these kinds of materials in order to be sure that all the particles present in Ni/Al O 2 3 sample can relax and contribute to the e!ect in the temperature range considered. In fact, we observe a beginning of the e!ect on transmission at ¹"35}150 K
C. Desmarest et al. / Physica B 279 (2000) 177}180
Fig. 8. Experimental variation of transmittance with temperature of a cermet Ni/Al O "lm versus temperature at 2 3 j"30}300}3000 lm, r "50 As , f "0.1, thickness"1 lm, 0 # normalized for ¹"5 K.
Taking into account the temperature variation of the dominant anisotropy, while using simple calculations based on NeH el's model and e!ective media theory, we have been able to understand the di!erent behaviors of our samples, although general shapes or ¹ values were B slightly di!erent. Through the large distribution of ¹ , B and large wavelength range studied, we point out a large distribution of relaxation time, certainly due to di!erent kinds of particules (Ni, NiO, Ni/Al O , etc.) present in 2 4 Ni/Al O sample. 2 3 References
where the signal is stabilized. This large ¹ distributB ion shows up a large q distribution referring to di!erent populations of particles in the sample. Making the assumption that ¹ +100 K for most of the particles, B where q +q, we found K+105 erg cm~3, using . NeH el's formula, that is in good agreement with literature values for Ni. Finally, one can see (Fig. 8) that ¹ deB creases as q increases which is coherent with NeH el's . formulation.
 L. NeH el, Cr. Acad. Sci. Paris 228 (1949) 604, 664.  L. NeH el, J. Phys. Soc. Japan 17 (1962) 676.  M. Gadenne, J. Plon, P. Gadenne, P. Sheng, Opt. Commun. 107 (1994).  P. Sheng, M. Gadenne, J. Phys.: Condens. Matter 4 (1992) 9735.  J.L. Dormann et al., Phys. Rev. B 53 (1996) 14291.  M. Gadenne, O. Schneegans, F. HouzeH , C. Desmarest, J. Sztern, paper presented at ETOPIM5.