Bonevich, J.

Seehra, M. S.

Singh, V.

English

The Research Repository @ WVU (West Virginia University)

Faculty Scholarship2009AC susceptibility studies of magnetic relaxation innanoparticles of Ni dispersed in silicaV. SinghM. S. SeehraJ. BonevichFollow this and additional works at: https://researchrepository.wvu.edu/faculty_publicationsThis Article is brought to you for free and open access by The Research Repository @ WVU. It has been accepted for inclusion in Faculty Scholarshipby an authorized administrator of The Research Repository @ WVU. For more information, please contact ian.harmon@mail.wvu.edu.Digital Commons CitationSingh, V.; Seehra, M. S.; and Bonevich, J., "AC susceptibility studies of magnetic relaxation in nanoparticles of Ni dispersed in silica"(2009). Faculty Scholarship. 44.https://researchrepository.wvu.edu/faculty_publications/44ac susceptibility studies of magnetic relaxation in nanoparticles of Ni dispersed insilicaV. Singh, M. S. Seehra, and J. BonevichCitation: Journal of Applied Physics 105, 07B518 (2009); doi: 10.1063/1.3073949View online: https://doi.org/10.1063/1.3073949View Table of Contents: http://aip.scitation.org/toc/jap/105/7Published by the American Institute of PhysicsArticles you may be interested in Unusual enhancement of effective magnetic anisotropy with decreasing particle size in maghemite nanoparticlesApplied Physics Letters 110, 222409 (2017); 10.1063/1.4984903Size-dependent shifts of the Néel temperature and optical band-gap in NiO nanoparticlesJournal of Applied Physics 114, 214307 (2013); 10.1063/1.4838915SuperparamagnetismJournal of Applied Physics 30, S120 (1959); 10.1063/1.2185850Co-existence of ferrimagnetism and spin-glass state in the spinel Co2SnO4Journal of Applied Physics 113, 203905 (2013); 10.1063/1.4807294Size dependence of magnetic parameters and surface disorder in magnetite nanoparticlesJournal of Applied Physics 105, 07B501 (2009); 10.1063/1.3055272Static and dynamic magnetic properties of spherical magnetite nanoparticlesJournal of Applied Physics 94, 3520 (2003); 10.1063/1.1599959ac susceptibility studies of magnetic relaxation in nanoparticles of Nidispersed in silicaV. Singh,1 M. S. Seehra,1,a and J. Bonevich21Department of Physics, West Virginia University, Morgantown, West Virginia 26506, USA2National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USAPresented 13 November 2008; received 5 September 2008; accepted 7 December 2008;published online 25 February 2009Temperature dependence of ac susceptibilities  and  are reported using frequencies fm=0.1, 1,99, 499, and 997 Hz for nanoparticles of Ni dispersed in silica Ni /SiO2:15 /85 with the mean sizesD=3.8, 11.7, 15, and 21 nm 0.2 nm, as determined by transmission electron microscopy. Theblocking temperatures TB, as determined by peaks in  versus T data, are fit to the Vogel–Fulcherlaw based on the following equation: TB=To+Ta / lnfo / fm. Using the attempt frequency fo=1.821010 Hz, Ta K=310 21, 95417, 133414, and 140547 are determined for D=3.8, 11.7,15, and 21 nm, respectively, along with To representing the interparticle interaction=0, 0,6.60.7, and 12.52.5 K respectively. The magnitudes of Ta=KaV /k yield the anisotropy constantKa increasing with decreasing D or volume V due to contributions from surface anisotropy. Thevalidity of the theoretical result =C T /T with C / 2 lnfo /2fm is checked and thecalculated values of fo are consistent with experimental value of fo=1.821010 Hz. © 2009American Institute of Physics. DOI: 10.1063/1.3073949I. INTRODUCTIONAmong several factors that affect the measured proper-ties of magnetic nanoparticles NPs include size and sizedistribution, magnetic field H, temperature T, interparticleinteractions IPIs, and the time scale or frequency fm ofmeasurements.1,2 The intrinsic anisotropy Ka, which is oftensize dependent due to different contributions from bulk an-isotropy Kb and surface anisotropy Ks, also has major effecton the observed magnetic properties.3–6 In this work, we re-port our investigations of the magnetic relaxation of Ni NPschemically dispersed in silica with average particle diam-eters D=3.8, 11.7, 15, and 21 nm by measuring the tempera-ture dependence of the ac susceptibilities  and  at fm=0.1, 1, 99, 499, and 997 Hz. The particles were synthesizedvia the citric acid sol-gel route with the Ni /SiO2 compositionof 15/85 Ref. 7 in order to increase the interparticle sepa-ration and hence reduce the IPI.For noninteracting NPs subjected to a slowly oscillatingmagnetic field h=ho cos mt,  and  are given by2,8 = o/1 + m2 , 1 = om/1 + m2 , 2where the relaxation frequency f =1 / is given by1,2f = fo exp− Ta/T . 3Here Ta=KaV /k for a particle of volume V with k being theBoltzmann constant, o is the static susceptibility for →0,m=2fm and fo is the attempt frequency. For random ori-entation of the easy axis of the particles each with magneticmoment =MsV,  and  of Eqs. 1 and 2 can be writ-ten as8 = Ms2/3Ka1 + Ta/T1/1 + m2 , 4 = Ms2/3KaTa/Tm/1 + m2 . 5The blocking temperature TB of the particles is determinedfrom Eq. 3 for f = fm yieldingTB = Ta/lnfo/fm . 6In the presence of weak IPI, Eq. 6 is replaced by Eq. 7below, derived from the Vogel–Fulcher law,9–11TB = To + Ta/lnfo/fm . 7Here To measures the strength of IPI. According to Eq. 6,TB should increase with increase in fm. Also from the aboveequations, it can be shown that  peaks at m=1 and and  are related by2 = C  T/T , 8where C / 2 lnfo /2fm. In this work, the above equa-tions are used to interpret the frequency dependence of and  and determine TB, fo, and Ta and their variations withthe change in the size of the Ni NPs. We also check thevalidity of Eq. 8II. EXPERIMENTAL RESULTS AND DISCUSSIONThe NPs of Ni /SiO2 15/85 were synthesized followingthe procedure outlines in an earlier paper.7 Annealing thesamples at 400, 500, 600, and 700 °C for 2 h in ultrahighpurity N2 gas produced particles of average size D=3.80.2, 11.70.2, 150.2 and 210.12 nm as determinedby transmission electron microscopy TEM. In Fig. 1, weshow the representative TEM for the 21 nm NPs with log-aAuthor to whom correspondence should be addressed. Electronic mail:mseehra@wvu.edu.JOURNAL OF APPLIED PHYSICS 105, 07B518 20090021-8979/2009/1057/07B518/3/$25.00 © 2009 American Institute of Physics105, 07B518-1normal fit to the histogram of the particle sizes. The x-raydiffraction XRD patterns for all four sizes using Cu Ksource 	=0.154185 nm showed lines only due to fcc Niand a broad line near 222° due to amorphous silica. Thesizes determined from the Scherrer broadening of the XRDlines were consistent with the above sizes determined fromTEM. Measurements of  and  were done using a com-mercial superconducting quantum interference device mag-netometer with the measuring ho=7 Oe and at frequenciesfm=0.1, 1, 99, 499, and 997 Hz. These measured value of and  were normalized to 15% concentration of Ni in theNi /SiO2 15/85 samplesFor one representative samples with size D=21 nm,plots of experimental  and  versus T are shown in Fig. 2.Similar data were obtained for the other three samples. It isevident that TB determined by the peak in  increases withincrease in fm, as predicted by Eqs. 6 and 7. Peaks in are broad and occur at temperatures higher than those for in agreement with the prediction =− /2 ln  / ln .2Using the measured values of TB for each fm, we plot inFig. 3 nfm versus TB−1 following Eq. 6 rewritten as nfm=nfo− Ta /TB. The data fit the predicted linear behaviorwith the intercept yielding nfo and the slope yielding Ta.Using least-squares fitting of the data shown in Fig. 3, themagnitudes of fo are determined to be 2.83+11.6−2.2 109 Hzfor the D=3.8 nm sample and fo=1.82 +0.94−0.62 1010 Hz, fo=1.72 +0.25−0.23 1011 Hz, and fo=3.96 +4.62−2.13 1011 Hz for theD=11.7 nm, D=15 nm, and D=21 nm samples, respec-tively. For the two larger particles, the magnitude of fo ishigher by an order of magnitude. Since the presence of IPIoften leads to increased magnitudes of fo Ref. 11 when dataare fit to Eq. 6, we next evaluated the parameter =TB / TB log10 fm, which represents fractional change inTB per decade change in fm.12 Experiments have shown that is very small 0.005–0.05 for spin glasses and 0.13for isolated noninteracting NPs.12 For intermediate values of 0.050.13, IPI is present with its effect decreasingwith increase in . Determining TB for maximum andminimum fm in our experiments, =0.16, 0.13, 0.12, and0.12 are found respectively for the D=3.8, 11.7, 15, and 21nm samples. These magnitudes of  suggest the presence ofa weak IPI in the larger D=15 nm and D=21 nm particlespossibly due to larger moment per particle and absence ofIPI in the two smaller particles. Thus it is very likely that thelarger magnitudes of fo in the two larger NPs is due to thepresence of IPI as the magnitudes of To0 determined be-low also suggest. Taking into consideration the relativelylarge uncertainty in fo for the smallest D=3.8 nm NPs, wehave chosen fo=1.821010 Hz for the D=11.7 nm NPs asthe likely magnitude for fo for this system. Using this mag-nitude of fo, the data are plotted as TB against 1 /nfo / fm inFig. 4 to check the validity of Eq. 7. The least-squares fitsare then used to determine To and Ta. It is evident that To isFIG. 1. Color online Inset shows the TEM micrograph for the D=21 nm sample. The solid line is a fit to log-normal distribution of thehistogram of particle sizes.FIG. 2. Experimental  and  vs T for D=21 nm at five frequenciesshown.FIG. 3. Plots of ln fm against TB−1 to determine fo and Ta from the equationfm= fo exp−Ta /TB. The solid lines are least-squares fits to the data.FIG. 4. Plots of TB vs 1 / lnfo / fm following Eq. 7 for the fo value notedon the figure. The lines through the points are least-squares fits with mag-nitudes of Ta shown.07B518-2 Singh, Seehra, and Bonevich J. Appl. Phys. 105, 07B518 2009zero within experimental uncertainties for the two smallerNPs and To=6.60.7 K and 12.52.5 K, respectively, forthe D=15 nm and D=21 nm samples. Also Ta representingthe energy barrier increases with increase in the size D of theNPs see Fig. 4. In an earlier publication, we reported fo=2.6109 Hz for the D=3.8 nm sample using an eye-ballfit of the data7 similar to the value of fo=1.8109 Hz re-ported by Goya et al.13 in a 5% Ni /SiO2 sample. This valueis consistent with fo=1.821010 Hz used here since for fo=2.8+11.6−2.2 109 Hz determined above using least-squaresfitting has large enough uncertainty to accommodate fo=1.821010 Hz. The important result of this analysis is thatusing a size independent fo, the presence of measurable IPI isevident in the two larger sizes and Ta increases with increasein the size of D of the NPs as qualitatively expected. Laterwe show that the magnitude of fo=1.81010 Hz determinedabove is consistent with calculations also using a theoreticalexpression.Next, the magnitudes of Ta=KaV /k are used to deter-mine Ka representing the energy barrier assuming sphericalNPs. For the cubic anisotropy of Ni, Ka=K1 /12, where K1 isthe first-order anisotropy constant with K1= 7.5105 ergs /cm3 for bulk Ni.14 The computed values of K1in units of 105 ergs /cm3 are 178.7, 18.8, 12.5, and 4.8 forthe D=3.8, 11.7, 15, and 21 nm samples, respectively. Theobserved increase in K1 with decreasing D has been reportedand discussed in other systems also, the source being increas-ing surface anisotropy with decreasing D.3–6 For the largestD=21 nm sample, the magnitude of K1 is close to the valuefor bulk Ni.To test the validity of the correlation between  andC T /T predicted by Eq. 8, the plots of the experimen-tal  and computed C T /T versus T are shown in Fig.5 using the  versus T data for our representative samplewith D=21 nm. All primary features of experimental such as the frequency and T dependence, are also evident inthe plots of C T /T, except that the peak magnitudesare off by a factor of about 2. This discrepancy is likelyrelated to the approximations made in deriving the magni-tude of C in Eq. 8.2 Comparison of  and computedC T /T for the other three samples yielded similar re-sults. It may be relevant to note that in bulk antiferromagnetsnear the Néel temperature, T /T is proportional to thespecific heat.15Next we calculate the theoretically expected magnitudeof the attempt frequency fo. Based on the earlier work byBrown,16 a simplified expression for fo in zero field given byAharoni17 for the case of TaT, reduces to the following forthe case of Ni:fo = Ta/T1/2oK1/6Ms. 9Here o is the gyromagnetic ratio and Ms is the saturationmagnetization. For Ni with g=2.2, o=2gB /h=1.935107. For T in Eq. 9, we use the average TB measured atthe frequencies fm used in our experiments since fo was de-termined at these temperatures and the condition TaT isstill valid using the Ta values noted in Fig. 4. We used thevalues of Ms=245, 216, 229, and 274 emu /cm3 measured at5 K for the D=3.8, 11.7, 15, and 21 nm samples, respec-tively. These magnitudes of Ms are only about 50% of thecorresponding magnitude for bulk Ni, likely due to disorderof spins on the surface of a NP. For the D=3.8 nm samplewith Ta=310 K, Eq. 9 yields fo=6.01011 Hz. Similarcalculations for the other samples yield the following fo val-ues: 7.11010 Hz for 11.7 nm, 4.21010 Hz for 15 nm,and 1.31010 Hz for 21 nm. Except for the smallest NPs,these calculated magnitudes of fo using Eq. 9 comparequite favorably with fo=1.81010 Hz derived from theanalysis of the data.In summary, the variations of the magnetic relaxationparameters TB and Ta with size of Ni NPs dispersed in silicamatrix are shown to follow the predictions of Eqs. 1–8with a size independent fo and the presence of a weak IPI inthe larger NPs. The order of magnitude of the calculated fo isin agreement with the measured fo.The research at West Virginia University was supportedin part by U.S. Department of Energy Contract No. DE-FC-26-05NT42456.1L. Néel, Ann. Geophys. 5, 99 1949.2L. Lundgren, P. Svedlindh, and O. Beckman, J. Magn. Magn. Mater. 25,33 1981.3F. Bødker, S. Morup, and S. Linderoth, Phys. Rev. Lett. 72, 282 1994.4K. Gilmore, Y. U. Idzerda, M. T. Klem, M. Allen, T. Douglas and M.Young, J. Appl. Phys. 97, 10B301 2005.5R. Yanes, O. C. Fesenko, H. Kachkachi, D. A. Garanin, R. Evans, and R.W. Chantrell, Phys. Rev. B 76, 064416 2007.6H. Shim, P. Dutta, M. S. Seehra, and J. Bonevich, Solid State Commun.145, 192 2008.7V. Singh, M. S. Seehra and J. Bonevich, J. Appl. Phys. 103, 07D5242008.8J.-O. Andersson, C. Djurberg, T. Jonsson, P. Svedlindh, and P. Nordblad,Phys. Rev. B 56, 13983 1997.9S. Shtrikman and E. P. Wohlfarth, Phys. Lett. 85A, 467 1981.10J. L. Tholence, Solid State Commun. 88, 917 1993.11H. Shim, A. Mannivannan, M. S. Seehra, K. M. Reddy and A. Punnoose,J. Appl. Phys. 99, 08Q503 2006 and references therein.12J. L. Dormann, L. Bessais, and D. Fiorani, J. Phys. C 21, 2015 1988.13G. F. Goya, F. C. Fonseca, R. F. Jardim, R. Muccillo, N. L. V. Carreno, E.Longo, and E. R. Leite, J. Appl. Phys. 93, 6531 2003.14J. I. Gittleman, B. Abeles, and S. Bozowski, Phys. Rev. B 9, 3891 1974.15E. E. Bragg and M. S. Seehra, Phys. Rev. B 7, 4197 1973; M. E. Fisher,Philos. Mag. 7, 1731 1962.16W. F. Brown, Jr., J. Appl. Phys. 34, 1319 1963.17A. Aharoni, Phys. Rev. B 7, 1103 1973.FIG. 5. Plots of experimental  vs T and computed C T /T of Eq. 7using the data of the D=21 nm sample.07B518-3 Singh, Seehra, and Bonevich J. Appl. Phys. 105, 07B518 2009

AC susceptibility studies of magnetic relaxation in nanoparticles of Ni dispersed in silica

https://researchrepository.wvu.edu/cgi/viewcontent.cgi?article=1043&amp;context=faculty_publications

AC susceptibility studies of magnetic relaxation in nanoparticles of Ni dispersed in silica

Abstract

Similar works

Full text

Available Versions

The Research Repository @ WVU (West Virginia University)