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Memory effects and magnetic interactions in a γ-Fe[sub 2]O[sub 3] nanoparticle system

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Memory effects and magnetic interactions in a γ-Fe[sub 2]O[sub 3] nanoparticle system
  Memory effects and magnetic interactions in a    -Fe 2 O 3 nanoparticle system G. M. Tsoi, a  U. Senaratne, R. J. Tackett, E. C. Buc, and R. Naik  Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201 P. P. Vaishnava Science and Mathematics Department, Kettering University, Flint, Michigan 48504 V. M. Naik  Department of Natural Sciences, University of Michigan, Dearborn, Michigan 48128  L. E. Wenger  Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294  Presented on 11 November 2004; published online 12 May 2005  The low-temperature dynamics of a magnetic nanoparticle system     -Fe 2 O 3 —alginatenanocomposite with average particle size around 4 nm   have been studied by superconductingquantum interference device measurements. Using different temperature and field protocols,memory phenomena in the dc magnetization and magnetic relaxation have been observed attemperatures below its blocking temperature  T   B =37 K. However, aging experiments show anabsence of any waiting time dependence in the magnetization relaxation. These observationsindicate that the dynamics of this nanoparticle system are governed by a wide distribution of particlerelaxation times which arise from the distribution of particle sizes and weak interparticleinteractions. ©  2005 American Institute of Physics .   DOI: 10.1063/1.1853898  INTRODUCTION The dynamics of magnetic nanoparticles systems hasbeen a subject of considerable interest for the last severaldecades. 1 For a noninteracting assembly of single domainmagnetic nanoparticles the Néel–Brown theory 2,3 predictsthat each particle   superparamagnetic   moment thermallyfluctuates between its easy magnetic anisotropy axes with acharacteristics relaxation time     being dependent upon themagnetic anisotropy, the particle size, the temperature, andapplied magnetic field. The relaxation time increases withdecreasing temperature and eventually becomes equal to themeasuring time  t  m  at the blocking temperature  T   B  where themoment freezes. Even though these “freezing” processes areno longer independent when interparticle interactions arepresent, the dynamical properties are frequently describedwithin this superparamagnetic model, and especially if theinteractions are weak. When the interactions are sufficientlystrong, there is a possibility of collective spin-glass-like be-havior in random interacting systems or even long-rangemagnetic ordering. Observations of critical slowing down, 4 adivergent behavior of the nonlinear susceptibility, 5 aging,and relaxation in the low-frequency ac susceptibility 6 havebeen cited as evidence for distinguishing between archetypalspin-glass behavior and simple superparamagnetic relaxationphenomena.In a recent paper Sun  et al. 7 reported observing memoryeffects in the dc magnetization and the magnetic relaxationof an interacting magnetic nanoparticle system   Ni 81 Fe 19  .Furthermore, the authors indicate that the observed memoryeffects were consistent with the existence of a low-temperature spin-glass phase. In this paper analogous experi-ments were performed on a system of very weakly interact-ing    -Fe 2 O 3  nanoparticles and similar memory effects wereobserved. Only the absence of any aging effect in the dcmagnetization on this nanoparticles system appears to distin-guish its properties from the characteristics of spin glasses. EXPERIMENTAL DETAILS The samples used in the experiments were prepared byusing cross-linked gels of alginic acid. 8 This technique al-lows gels to be prepared containing different amounts of ironoxide. X-ray powder diffraction patterns on the samples in-dicated that the synthesized magnetic nanoparticles aresingle phase with an average particle size of 4 nm. dc mag-netization measurements were performed using a quantumdesign model MPMS-5S SQUID   SQUID—superconductingquantum interference device   magnetometer from 5 to300 K.The saturated magnetic moment at 5 K, obtained by ex-trapolation to 1/   H  =0, was 22 emu/g. Since the saturationmagnetization of bulk     -Fe 2 O 3  is 87.4 emu/g, 9 the volumeconcentration of particles is about 7%, which could lead topotential interparticle interactions. RESULTS AND DISCUSSION The field-cooled   FC   and zero-field-cooled   ZFC   mag-netizations were measured as a function of temperature  5–300 K   and magnetic field   1–5000 Oe  . Figure 1 showsthe temperature dependence of the magnetization  M   T    forthe sample of     -Fe 2 O 3  nanoparticles taken in ZFC and FC a  Present address: Department of Physics, University of Alabama at Bir-mingham, Birmingham, AL 35294. JOURNAL OF APPLIED PHYSICS  97 , 10J507   2005  0021-8979/2005/97  10   /10J507/3/$22.50 © 2005 American Institute of Physics 97 , 10J507-1  conditions at a magnetic field  H  =100 Oe. The curves exhibitthe main features of a superparamagnetic system: the ZFCcurve has a characteristic maximum at the blocking tempera-ture  T   B =37 K and paramagnetic behavior above  T   B , whilethe FC curve below  T   B  continues to increase with decreasingtemperature. The superparamagnetic behavior of the samplewas confirmed by the magnetic hysteresis measurements   theinset to Fig. 1  . Above the blocking temperature the  M    H   curves are described by the Langevin function with a log-normal size distribution of nanoparticles 10 of mean diameter  D v m =3.4 nm   300 K   and standard deviation    =0.42. How-ever, the superparamagnetic scaling law  M    H   /  T   was notstrictly followed, which is consistent with a weakly interact-ing system of nanoparticles. Below  T   B  the system exhibitshysteretic behavior characteristic of a freezing of the nano-particle magnetic moments.The dynamics of the FC magnetization in this nanopar-ticle system were studied following the approach used bySun  et al. 7 The sample was cooled in  H  =100 Oe from 200 Kdown to 5 K at a constant cooling rate of 1 K/min; the mag-netization was then measured during warming and is shownin Fig. 2 as the reference curve. The sample was subse-quently cooled again at the same rate and the magnetizationwas recorded during the cooling, but now with stops at  T  =30, 20, and 10 K for identical waiting times  t  w =1 h   run  A  . The magnetic field was turned off at the beginning of thestop and then set again to 100 Oe at the end of the waitingtime before the cooling process resumed. The cooling curveis shown in Fig. 2 as solid squares. After reaching the lowesttemperature of 5 K, the sample was reheated at the rate of 1 K/min in  H  =100 Oe and the magnetization was recordedagain   open squares  . The system remembered its thermalhistory and demonstrated a memory effect as the warmingcurve exhibits magnetization steps at 10 K, 20 K, and 30 K,identical temperatures where the system was intermittentlystopped during the cooling process. In the second run B, thesample was cooled in  H  =100 Oe with stops at  T  =30, 20,and 10 K for the same waiting times  t  w =1 h, but the mag-netic field was increased from 100 to 200 Oe during thestops   solid circles   and then decreased back to 100 Oe afterthe waiting time. This cooling process produced magnetiza-tion steps in the opposite directions in the magnetizationcurve as compared to run  A . The magnetization recordedduring the reheating process shown as open circles in Fig. 2exhibits the steplike structure as well.The effects of temperature and field change on the timeevolution of the ZFC and thermoremanent magnetization  TRM   were also studied using the protocols from Ref. 7. Inthe ZFC relaxation measurements the sample was cooleddown to  T  =15 K in  H  =0. After applying a magnetic field  H  =100 Oe the relaxation of the magnetization was recordedfor a time period  t  1 =4000 s. The sample was then cooleddown to  T  =10 K in the same magnetic field and the magne-tization was measured for another 4000 s time period  t  2 . Fi-nally the sample was heated back to  T  =15 K and the mag-netization was measured for a time period  t  3   =4000 s  . Thisentire relaxation measurement is displayed in Fig. 3  a  . Theinitial logarithmic increase in the magnetization observed at15 K almost stops during the temporary cooling to 10 K, andthen the magnetization continues to increase after returningto 15 K. The inset in Fig. 3  a   indicates that the relaxationprocess during  t  3  is essentially a continuation of the processduring  t  1 . A similar resumption in the relaxation of the ZFCmagnetization occurred at 15 K after reducing the field from100 Oe to 0 Oe during  t  2  of the temporary cooling to 10 Kand then increasing the field to 100 Oe and heating thesample back to 15 K   not shown  .Memory effects were also observed for the field-cooledprocess by measuring the time evolution of TRM. Figure3  b   shows the TRM as a function of time at 15 K for a time t  1 , cooling to 10 K for  t  2 , and then returning to 15 K. Againthe magnetization essentially resumes its logarithmic relax-ation as seen in the inset. It should be further noted that thesememory effects in the magnetic relaxation have only beenobserved after a temporary cooling and not after a temporaryheating   figure not shown  , similar to the results reported bySun  et al. 7 on an interacting nanoparticle system. FIG. 1. Zero-field cooled   ZFC   and field-cooled   FC   magnetizations uponwarming in a magnetic field of 100 Oe. The inset displays the reducedmagnetization  M   /   M  s  vs  M  s   H   /  T    at high temperatures  T  =150, 200, 250,and 300 K.FIG. 2. The FC magnetization vs temperature with intermittent stops at  T  =30, 20, and 10 K during cooling. Run  A  was measured for  H  =100 Oe withthe field reduced to 0 Oe at each stop. Run  B  was measured for  H  =100 Oe with the field increased to 200 Oe at each stop. The solid symbolswere measured during cooling with the intermittent stops of 1 h while theopen symbols are measured during continuous heating. The solid line is theFC magnetization without any stops during warming. 10J507-2 Tsoi  et al.  J. Appl. Phys.  97 , 10J507   2005   The observed memory effects on the interacting nano-particles system 7 were thought initially to be solely a char-acteristic of spin glasses and the asymmetric response withrespect to negative/positive temperature change consistentwith the hierarchical model of the spin-glass phase. 11 It hassince been shown 12 that such memory effects are also presentin superparamagnetic systems and can even be reproducedby using only a model of   isolated   nanoparticles with atemperature-dependent distribution of relaxation times.Moreover, the dynamics of archetypal spin-glass systems aregenerally characterized by an “aging” dependent behavior,i.e., the ZFC   and TRM   magnetic relaxation is dependentupon the time elapsed after the system was quenched. 13,14 Insuch experiments the sample is first cooled to a temperaturebelow the spin-glass transition temperature. Then after awaiting time  t  w , a dc field is applied   or cutoff    and the timeevolution of magnetization is recorded. The relaxation for aspin-glass system exhibits a clear dependence on the waitingtime  t  w  as the relaxation for systems with infinite equilibra-tion times must scale with the only relevant time scale in theexperiment, the waiting time  t  w . However, no such waitingtime dependence was measurable in the ZFC and TRM mag-netic relaxations on our    -Fe 2 O 3  nanoparticle system. Nei-ther were any memory effects detectable with a stop duringcooling in zero field, which is another characteristic found inspin-glass systems. 15 Instead, the relaxation effects in the   -Fe 2 O 3  nanoparticle system appear to be controlled simplyby thermally activated dynamics of individual superpara-magnetic particles. This has been subsequently confirmed 16 by using a simple bistable model with a broad distribution of particle sizes   similar to the approach of Ref. 12   to study thedynamics of this system. Indeed, most of experimentally ob-served memory effects are qualitatively reproduced includingthe absence of a waiting time dependence. Thus, the dynam-ics of noninteracting or weakly interacting magnetic nano-particles can be distinguished from genuine spin-glass be-havior by selecting the appropriate protocols by includingaging-dependent studies in the ZFC magnetization process.In summary, using different temperature and field proto-cols, memory effects in the dc magnetization and magneticrelaxation similar to those observed in spin-glass systemshave been observed in weakly interacting system of    -Fe 2 O 3  nanoparticles at temperatures below its blockingtemperature. However, aging experiments show an absenceof any waiting time dependence in the magnetization relax-ation due to a field change after field cooling or zero-fieldcooling processes. This observation discriminates the dy-namics of our nanoparticle system from the behavior of aclassical spin glass, where frustration and disorder lead to anaging dependence of the system’s magnetic response. More-over, the dynamics of this nanoparticle system are consistentwith the dynamical properties expected from a wide distri-bution of particle relaxation times arising from a broad dis-tribution of particle sizes. ACKNOWLEDGMENT This work was supported by the National Science Foun-dation under Grant No. DGE 9870720. 1 J. L. Dormann, D. Fiorani, and E. Tronc, in  Advances in Chemical Physics  Wiley, New York, 1997  , Vol. 98, p. 283. 2 L. Néel, Ann. Geofis.  5 , 99   1949  . 3 W. F. Brown, Jr., Phys. Rev.  130 , 1677   1963  . 4 C. Djurberg, P. Svedlindh, P. Nordblad, M. F. Hansen, F. Bødker, and S.Mørup, Phys. Rev. Lett.  79 , 5154   1997  . 5 T. Jonsson, P. Svedlindh, and M. F. Hansen, Phys. Rev. Lett.  81 , 3976  1998  . 6 H. Mamiya, I. Nakatani, and T. Furubayashi, Phys. Rev. Lett.  82 , 4332  1999  . 7 Y. Sun, M. B. Salamon, K. Garnier, and R. S. Averback, Phys. Rev. Lett. 91 , 167206   2003  . 8 E. Kroll, F. M. Winnik, and R. F. Ziolo, Chem. Mater.  8 , 1594   1996  . 9 J. M. D. Coey, Phys. Rev. Lett.  27 , 1140   1971  . 10 R. W. Chantrell, J. Popplewell, and S. W. Charles, IEEE Trans. Magn.  14 ,975   1978  . 11 F. Lefloch, J. Hammann, M. Ocio, and E. Vincent, Europhys. Lett.  18 , 647  1992  . 12 M. Sasaki, P. E. Jönsson, H. Takayama, and H. Mamiya, cond-mat/ 0406546, 2004. 13 P. Refregier, E. Vincent, J. Hammann, and M. Ocio, J. Phys.   Paris   48 ,1533   1987  . 14 T. Jonsson, J. Mattsson, C. Djurberg, F. A. Khan, P. Nordblad, and P.Svedlindh, Phys. Rev. Lett.  75 , 4138   1995  . 15 R. Mathieu, P. Jönsson, D. N. H. Nam, and P. Nordblad, Phys. Rev. B  63 ,092401   2001  . 16 G. M. Tsoi   unpublished  .FIG. 3.   a   The ZFC magnetic relaxation measurement at 15 K with a de-crease in the temperature to 10 K for 4000 s.   b   The TRM relaxation mea-surement at 15 K with a decrease in the temperature to 10 K for 4000 s. Theinsets show the data as a function of total time spent at  T  =15 K. 10J507-3 Tsoi  et al.  J. Appl. Phys.  97 , 10J507   2005  View publication statsView publication stats
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