Spin glass behavior of gelatin coated NiO nanoparticles
aa r X i v : . [ c ond - m a t . m e s - h a ll ] A p r Spin glass behavior of gelatin coated NiO nanoparticles
Vijay Bisht ∗ and K.P.Rajeev † Department of Physics, Indian Institute of Technology Kanpur 208016, India
Sangam Banerjee
Surface Physics Division, Saha Institute of Nuclear Physics Kolkata, 700 064, India
We report magnetic studies on gelatin coated NiO nanoparticles of average size 7 nm. Tem-perature and time dependence of dc magnetization, wait time dependence of magnetic relaxation(aging), memory effects in the dc magnetization and frequency dependence of ac susceptibility havebeen investigated. We observe that the magnetic behavior of coated NiO nanoparticles differs sub-stantially from that of bare nanoparticles. The magnetic moment of the coated particles is highlyenhanced and the ZFC magnetization data displays a sharp peak ( T p1 ≈ K) at a low temperaturein addition to a usual high temperature peak ( T p2 ≈ K). We observe that this system exhibitsvarious features characteristic of spin glass like behavior and T p2 corresponds to the average freezingtemperature. We argue that this behavior is due to surface spin freezing within a particle. Thenature of the low temperature peak is however ambiguous, as below T p1 some features observed arecharacteristic of superparamagnetic blocking while some other features correspond to spin glass likebehavior. PACS numbers: 75.50.Tt, 75.50.Lk, 75.30.Cr, 75.40.GbKeywords: NiO nanoparticles, spin glass behavior, aging, memory effects.
I. INTRODUCTION
There has been a renewed interest in magneticnanoparticles in the past several decades because of thepromise of various possible technological applicationsthey hold as well as from the perspective of fundamentalunderstanding.
Below a certain size, a ferromagneticparticle consists of a single domain and behaves as a gi-ant magnetic moment. Néel proposed that just as a fer-romagnetic particle, a tiny antiferromagnetic particle canalso develop a net magnetic moment due to uncompen-sated spins at its surface. The behavior of an ensembleof non interacting particle moments is expected to besuperparamagnetic. On the other hand if the particlesinteract with each other they can give rise to superspinglass behavior. Further, surface effects are also impor-tant in nanoparticles because of their large surface-to-volume ratio. For instance it has been shown recentlythat spin glass behavior can arise within an individualnanoparticle due to the freezing of spins at its surface.
Nickel oxide (NiO) is an antiferromagnetic materialwith Néel temperature ( T N ) 523 K. There have been alarge number of studies on NiO nanoparticles and in-deed it is the most well studied among the antiferro-magnetic nanoparticles. These studies include temper-ature dependence of dc and ac susceptibility, their fieldand frequency dependence, hysteresis and exchange bias,time dependence of magnetization and related dynamiceffects. Certain features shown by NiO nanoparti-cles are characteristic of both superparamagnetism andspin glass behavior viz. a bifurcation in FC and ZFCmagnetization, a peak in ZFC magnetization and slowmagnetic relaxation. As a result there have been claimsof superparamagnetism as well as spin glass behavior inthis system.
However, it has been shown that the temperature dependence of magnetization of this systemabove the bifurcation temperature cannot be describedby the Langevin function or a modified version of thesame tailored for antiferromagnetic particles. We notethat this is contrary to what is expected of a superpara-magnetic system. Below the bifurcation temperature, spin glass orspin glass like features have been observed in thissystem.
In a recent paper, we reported agingand memory effects in bare NiO nanoparticles and theresults show that this system indeed shows spin glasslike behavior. Tiwari et al. have argued that suchbehavior arises due to freezing of surface spins on in-dividual particles as the interactions between the par-ticles are too weak to give rise to the observed largefreezing temperatures. The origin of spin glass behav-ior in NiO nanoparticles is still somewhat controversialas there is no universal agreement on whether it is dueto interparticle interactions or due to surface spin frus-tration within individual particles. A possible way tosettle this issue would be through a study of the mag-netic behavior of non-interacting particles. We can re-duce the inter-particle interactions by increasing the dis-tance between them. One way of doing this would beto coat the particles or disperse them in some medium.There have been some works on coated and dispersed NiOnanoparticles and nanorods and widely varying resultshave been reported.
In these works, the up-per broad peak is generally associated with superparam-agnetic blocking. Further it has been observed that thecoating tends to decrease the interactions which mani-fests as a lowering of the blocking temperature. Anothersharp peak at a much lower temperature is seen in somereports and the origin of this peak has not been accountedfor in most of the works.
However some authors
40 60 80 R e l a t i v e i n t en s i t y in degrees ( ) ( ) ( ) ( ) ( ) Figure 1: XRD pattern of the sample heated at 350 ◦ C for 15hours. All the peaks correspond to those of NiO. associate this peak to surface spin freezing.
To furthercomplicate matters, some authors observe only the lowtemperature peak with the upper broad peak missing incoated particles and in one report this peak has been seeneven in a bulk sample.
We, therefore, felt that itwill be worth our while to carry out a systematic studyon the magnetic behavior of coated NiO nanoparticles toclear the air.
II. EXPERIMENTAL DETAILS
Gelatin coated NiO nanoparticles are prepared by asol gel method as described in detail by Meneses et al. In brief, 2.5 g of gelatin was dissolved in 100 ml dis-tilled water while stirring continuously at 60 ◦ C. 100 mlof aqueous solution of 2.5 g of NiCl .6H2O (99.99%) wasadded at the same temperature to the above solution.An aqueous solution of NaOH was added to this mixturetill the pH became 12. This mixture was then cooled atroom temperature to form a gel, which was heated at80 ◦ C for 36 hours to obtain a precursor. Nickel oxidenanoparticles were prepared by heating this precursor at350 ◦ C for 24 hours . The sample was characterized by X-ray diffraction (XRD) using a Seifert diffractometer withCu K α radiation and Transmission electron microscopy(TEM) using FEI Technai 20 U Twin Transmission Elec-tron Microscope. The percentage of gelatin by mass wasestimated using thermo-gravimetric analysis(TGA) to be42% and the average thickness of gelatin shell estimatedturned out to be 5 nm. All the magnetic measurementswere done with a SQUID magnetometer (Quantum De-sign, MPMS XL5). III. RESULTS AND DISCUSSIONA. Particle size
The XRD pattern of the sample shown in Figure 1 cor-responds to that of pure NiO which has FCC structure.The average particle size was estimated to be 7 nm fromthe width of XRD peaks (111), (200) and (220) using theScherrer formula. TEM image of the sample is shown inFigure 2 and the insets (a) and (b) of this figure show theparticle size distribution and the selected area diffraction(SAD) pattern. It can be seen that the particles are moreor less of spherical shape and the particle size was esti-mated to be 9.3 nm with a standard deviation 2.8 nm.The SAD pattern consists of concentric diffraction ringswith different radii. The diameter of a diffraction ring inthe SAD pattern is proportional to √ h + k + l , where ( hkl ) are the Miller indices of the planes correspondingto the ring. Counting the rings from the center 1st, 2nd,3rd, 4th and 5th rings correspond to (111), (200), (220),(311) and (222) planes respectively, as would be expectedin the case of a material with FCC crystal structure. B. Temperature and field dependence ofmagnetization
The temperature dependence of magnetization is doneunder field cooled (FC) and zero field cooled (ZFC) pro-tocols at 100 Oe. See Figure 3. It can be seen that
Figure 2: TEM image of the sample. Inset: (a) Histogramof the particle size distribution. Total Number of particlesconsidered is 110. (b) Selected area diffraction (SAD) pattern. -2 -1 0 1 2-202
10 K M ( e m u / g ) H (kOe)
100 K T p1 M ( e m u / g ) T(K)
ZFC FCW FCC T p2 Figure 3: (Color online) FCC, FCW and ZFC magnetizationdata at a magnetic field of 100 Oe. Inset shows the hysteresisloops at 10 K and 100 K including the virgin curve. the FC and ZFC magnetization curves bifurcate slightlybelow 300 K and the magnetization data taken duringheating (FCW) and that taken while cooling (FCC) inthe FC protocol are essentially the same. Further it canbe observed that there are two peaks in the ZFC mag-netization; the first ( T p1 ) is a sharp one at about 14 Kand the second ( T p2 ) is a broad one around 170 K. TheFC magnetization shows a steep low temperature risestarting at about 30 K and keeps on rising till the low-est temperature of measurement, a characteristic featureseen in superparamagnets. In bare nanoparticles, usually a single broad peak,corresponding to T p2 , is observed in the magnetizationvs. temperature plot. However, there are some re-ports on bare, dispersed and coated nanoparticles wheretwo peaks have been observed.
Some workerseven report a single peak at low temperature in coatednanoparticles with the upper broad peak missing andto confound matters even further, some authors have ob-served T p1 even in bulk samples. Winkler et al. have ob-served two peaks in ZFC magnetization for NiO nanopar-ticles of size 3 nm; occurring at 17 K and 70 K for bareparticles and at 15 K and 60 K for dispersed particles. They found that the high temperature peak in the ac susceptibility data follows the Arrhenius law like super-paramagnets while the lower peak follows a power lawsimilar to spin glasses. Further the shape of virgin curvein the hysteresis loop below the low temperature peak isS-shaped, a feature seen in canonical spin glasses whilewell above the lower peak temperature, this feature isabsent. Thus they associate the upper peak with super-paramagnetic blocking of core moments and the lowerpeak to surface spin glass freezing. However Tiwari et al.have reported a single broad peak in the ZFC magnetiza-tion as well as in ac susceptibility in 5 nm bare nanopar-
15 300246
100 200 250 400 500 750 1000 2000 5000 10000
50 100 150 R = 0.96915 T p ( K ) H (b) R = 0.99303 T p / H(Oe) (a)
T(K) M / H ( - e m u / g / O e ) Figure 4: (Color online) Field dependence of ZFC magnetiza-tion data for various fields at low temperatures in the vicinityof T p1 . Insets show plots of (a) T p1 vs H and (b) T p1 vs H . ticles at about 150 K and they have shown that the sys-tem shows spin glass features. For instance, the value ofrelative shift of ac susceptibility peak per decade of fre-quency lies in a range expected for spin glasses, field de-pendence of peak temperature follows Almeida-Thouless(AT) line and the high field data obeys dc scaling law forspin glasses. We carried out hysteresis measurements in the fieldrange − . kOe to +2 . kOe at temperatures 10 K and100 K. The results are shown in the inset of Figure 3and it can be seen that the system shows hysteresis atboth 10 K and 100 K with a larger coercivity at 10 K. Incontrast to what Winkler et al. got, the virgin curve inthis case is not S-shaped either at 10 K or at 100 K. AnS-shaped virgin curve is a feature observed in canonicalspin glasses, but we do not see it in our system. To investigate the field dependence of ZFC magnetiza-tion, we carried out experiments at various fields in thefield range 100 Oe to 10 kOe. These data are shown inFigures 4 and 5. It can be observed that both the peaks ( T p1 and T p2 ) shift to lower temperatures with increas-ing field; the dependence being weaker for the lower peak. T p2 disappears above an applied field of 750 Oe while T p1 disappears only above 2 kOe. For superparamagnets thefield dependence of peak temperature, T p , is expected tobe given by T p ∝ V (cid:18) − HH K (cid:19) , ≤ H ≤ H K (1)where V is the volume of a particle and H K is a positiveconstant depending on anisotropy of the system. Comingto the case of spin glasses we note that the stability limitof spin glasses is defined by the AT line in the H − T phasediagram, below which the spin glass state is stable. Indeed in many spin glass systems, the field dependenceof peak temperature is known to follow the AT line givenby the equation: H ∝ (cid:18) − T p T f (cid:19) , ≤ T p ≤ T f (2)where T f is the spin glass transition temperature in zeroapplied field. Thus, in a superparamagnetic system T p should be linearly related to H whereas in spin glasses T p should decrease linearly with H . In the insets ofFigures 4 and 5, we show the plots of T p vs H and T p vs H for both peaks. The goodness of the fits canbe judged by the coefficient of determination ( R ) whichare shown in the corresponding plots. It can be seen thatfor the lower peak the superparamagnetic fit is betterwhile for the upper peak, the AT line fit is better. Thusfrom these experiments, one can hazard the guess thatthe lower peak arises due to superparamagnetic blockingwhile the upper one corresponds to spin glass behavior.We note that the broad peak, T p2 , in coated nanoparti-cles appears at about 170 K at low field (Figure 3) whichis quite close to the corresponding value 150 K seen inbare particles of comparable size as reported by Tiwariet al. Apparently interparticle interactions have little in-fluence on T p2 and thus cannot be contributing to spinglass behavior. Indeed Tiwari et al. estimate that thedipolar interactions between bare particles can give riseto freezing temperatures at most a few Kelvins. Thuswe conclude that in NiO nanoparticles, whether bare orcoated, the interparticle interactions are quite small andcannot give rise to spin glass like behavior.
100 200 300
200 4008101214 T p / R = 0.91678 H(Oe) (a)
20 40 60100150 T p ( K ) R = 0.93216 H (b)
100 200 250 400 500 750 M / H ( - e m u / g / O e ) T(K)
Figure 5: (Color online) Field dependence of ZFC magneti-zation data for various fields at higher temperatures in thevicinity of T p2 . Insets show plots of (a) T p2 vs H and (b) T p2 vs H .
10 15 20468 " ( - e m u / g ) T(K) ’ ( - e m u / g ) T(K)
33 Hz 90 Hz 330 Hz 1kHz (a) (b)
Figure 6: (Color online) Temperature dependence of the realpart of ac susceptibility for various frequencies with an acfield of 3 Oe. Insets: (a) Temperature dependence of theimaginary part of the susceptibility. (b) A magnified view oflow temperature peak of real part shown in the main panel.Lines have been drawn to guide the eyes. C. Particle moment
Néel proposed that small particles of antiferromagneticmaterials can possess a net magnetic moment due to in-complete compensation of spins between atoms on twosublattices. The number of uncompensated spins, p , isroughly proportional to n x where n is the total numberof atoms in the particle and x can be / , / or / depending on the shape of the particle and the arrange-ment of atoms in it. The particle moment depends on p and thus on the particle size. Kodama et al. have es-timated a magnetic moment µ B per particle for bare15 nm NiO particles using Néel’s two sublattice modeland found that this value is too small compared to µ B ,a value estimated from experimental data. They pro-posed the existence of a multi-sublattice ordering in NiOnanoparticles to account for the anomalously high mag-netic moment.A linear extrapolation of the high field magnetizationdata at 10 K (shown in the inset of Figure 3) givesan estimated moment of about µ B for the gelatincoated 9 nm particles. We see that the particle magneticmoment increases roughly by 2.5 times on coating barenanoparticles with gelatin. A similar enhancement inthe particle moment was observed by Winkler et al. ondispersing 3 nm particles in a non magnetic matrix. Thisobservation is puzzling because it is unclear how a non-magnetic coating leads to an enhancement of magneticmoment of a particle. Winkler et al. have argued that theabsence of demagnetizing character of interparticle inter-actions is responsible for the increase in magnetizationin coated nanoparticles. We disagree with this argumentbecause as we had discussed earlier (section III B), the in-terparticle interactions are quite small and hence cannotgive rise to such an enormous decrease in the magneticmoment of bare particles as opposed to coated particles. D. ac susceptibility We measured the temperature dependence of ac sus-ceptibility at several frequencies: 33, 90, 330 and1000 Hz. The sample is cooled from room temperatureto 5 K in a zero magnetic field and a probing ac mag-netic field of amplitude 3 G is applied to measure thesusceptibility as the temperature is increased to 300 K.In Figure 6, the real part, χ ′ , of the ac susceptibilityis shown and the inset (a) displays the imaginary part, χ ′′ . Inset (b) shows a magnified view of the low tem-perature peak. We note that the real part ( χ ′ ) has asharp peak near 16 K and a broad high temperaturepeak between 200 K and 300 K. This broad high tem-perature peak can be observed more clearly in the imag-inary part. As the frequency is raised the value of χ ′ decreases and the peaks shift slightly to higher temper-atures. A quantitative measure of the variation of peaktemperature with frequency is the relative shift in peaktemperature, ∆ T p /T p , per decade of frequency. Thisquantity lies between 0.0045 and 0.06 for many canonicalspin glasses. For ferritin, a known superparamagnet, itsvalue is approximately . and for another superparam-agnet a-(Ho O )(B O ) it is . . In the present case,for the lower peak, using the real part of susceptibility,this value comes out to be . and using the imaginarypart, its value is . . For the upper peak, using theimaginary part, this value turns out to be . . Thusfor both the peaks, the relative shift lies in the range M ( e m u / g ) T(K)
FCC FCM REF M ( e m u / g ) T(K)
FCC FCM REF
Figure 7: (Color online) Memory experiments in FC protocolwith stops of one hour taken at temperatures 8 K, 15 K and150 K. Magnetic field was switched off during the stops andswitched on before resuming further cooling.
100 10000.560.600.640.680.72
10 100 1000 100000.070.080.09 M ( e m u / g ) Time(sec)
T = 150K(b)
10 100 10000.300.33 M ( e m u / g ) Time(sec)
T = 20K(a)
30 sec 300 sec 3000 sec M ( e m u / g ) Time(sec)
T= 5 K
Figure 8: (Color online) Aging experiments in FC protocol attemperatures 5 K, 20 K and 150 K with wait times t W = 30,300 and 3000 seconds. observed in spin glass and spin glass like systems andprovides an empirical evidence in support of spin glasslike behavior. E. Memory and Aging Experiments
In the past several years, aging and memory ef-fects have been investigated in many nanoparticle sys-tems using ac susceptibility and low field dc magnetiza-tion measurements with various temperature and fieldprotocols. It has been seen that superparamagnets
10 100 1000 100000.100.110.12
10 100 10000.280.29 M ( e m u / g ) Time(sec)
T = 20K(a)
10 100 10000.310.320.33
Time(sec) M ( e m u / g ) T = 150K(b) M ( e m u / g ) Time(sec)
T = 5 K
Figure 9: (Color online) Aging experiments in ZFC protocolat temperatures 5 K, 20 K and 150 K with wait times t W =30, 300 and 3000 seconds. as well as spin glasses show these effects in FC proto-col. However only spin glasses show aging and memoryin ZFC protocol. We have reported memory effects inbare NiO nanoparticles in both FC and ZFC protocolsin a previous work. Therefore, it will be interesting toinvestigate these effects in coated nanoparticles where in-teractions between the particles should be negligible.We carried out memory experiments in both FC andZFC protocols with stops of one hour taken at 8 K, 15 Kand 150 K. The procedure of these experiments is as fol-lows. In the FC protocol, the system is cooled in thepresence of a magnetic field (100 Oe) to 5 K with in-termittent stops of one hour at 8 K, 15 K and 150 K,with the field switched off during the stops. The magne-tization is measured while cooling and then during sub-sequent heating. The results of memory experiments inFC protocol are shown in Figure 7. We found that at150 K, there are no indications of memory but at 8 Kand 15 K, memory is present as is evident from a smalljump in the magnetization at these temperatures. How-ever, these effects are much weaker than those observedin bare NiO nanoparticles. In the ZFC protocol, to be-gin with we record the ZFC magnetization data normallyand then with stops of one hour at 8 K, 15 K and 150 Kwhile cooling. We observed that there is no significantdifference between these two data and this shows thatthe system has no ZFC memory.These experiments indicate that the lower peak cancorrespond to superparamagnetic blocking as the mem-ory is present only in FC measurements and not in ZFCmeasurements. On the other hand absence of memory at150 K in both FC and ZFC protocols is quite unusual asit does not correspond to either spin glass like or super-paramagnetic behavior. However this apparent absenceof memory could be because of some transition associatedwith the lower peak T p1 which can wipe out the memoryof stops taken at higher temperatures.In addition to memory effects, aging has been used asa tool to distinguish superparamagnets and spin glasses.We recall that aging is seen in FC protocol in both su-perparamagnets and spin glasses while in ZFC protocolit is seen only in spin glasses. We investigated agingat three different temperatures 5 K, 20 K and 150 K inboth FC and ZFC protocols. To check for FC aging thesample is cooled in a field of 100 Oe to the temperature ofinterest, and after waiting for a specified duration (waittime, t W ) the field is switched off. Subsequently the mag-netization data is recorded as a function of time. Thesedata are presented in Figure 8. Similarly, in the corre-sponding ZFC aging experiment, the sample is cooled ina zero field to the temperature of interest, and after wait-ing for a specified wait time the field (100 Oe) is switchedon; magnetization as a function of time is recorded sub-sequently. The ZFC aging data are presented in Figure9. We note that a good amount of aging is discernible inboth FC and ZFC magnetizations at 5 K and 150 K butnot at 20 K. The presence of aging in ZFC protocol at5 K and 150 K is a strong evidence which supports the T f = 170 = 2.5140 N L \ H / () t / H Figure 10: (Color online) Linear scaling plot of the dc non-linear susceptibility. The scaled curve is obtained using T f = 170 K , γ = 140 and β = 2 . . ( H is in units of Oeand χ NL is in units of emu/gOe.) thesis that the system is spin glass like. F. Static Scaling
Static critical scaling has been widely used as an evi-dence for phase transition in spin glasses and an appro-priate quantity to examine the critical behavior is thenonlinear susceptibility, χ NL , given as χ NL = χ − MH = − ( χ H + χ H + ... ) . (3)It should be noted that χ NL should diverge in the criticalregion as χ , χ , ... are divergent in that region. Todescribe χ NL in the critical region, the following scalingequation has been proposed χ NL ∝ H β/ ( β + γ ) ¯ G ( t/H / ( β + γ ) ) , (4)where t is the reduced temperature ( T − T f T f ) , β and γ are critical exponents of the spin glass order parameterand ¯ G is the scaling function.To demonstrate scaling, the parameters β , γ and T f areselected so that all the data points taken at various fieldsare judged to fall on a single master curve on a plot of χ NL /H β/ ( β + γ ) vs. t/H β + γ . Figure 10 shows the scal-ing plot of our data using Equation (4). It is clear thatfour data sets taken at different magnetic fields are fallingwell on a master curve. It has been seen that several setsof β , γ and T f can give reasonably good plots. In Figure10, we used T f = 170 K , γ = 140 and β = 2 . . The valuesof critical exponents β and γ should be unity accordingto mean field theory. However it has been seen that thevalues determined from experiments can be much largerthan unity. Thus the magnetization data follows scalinglaws confirming spin glass behavior in this system. It canbe however noted that the non linear susceptibility doesnot diverge in contrast to canonical spin glasses and thereasons for this could be the finite size of the system andthe distribution of freezing temperatures due to particlesize distribution as has been discussed by Tiwari et al. IV. CONCLUSION
We find that the behavior of gelatin coated NiOnanoparticles is more intriguing than that of bare parti-cles. The particle magnetic moment is enhanced severaltimes on coating and the reasons for this phenomenonare not clear. An additional peak ( T p1 ) is observedin the ZFC magnetization data at 14 K which is usu-ally not present in bare nanoparticles. The field depen-dence of T p2 in ZFC magnetization follows the AT lineas one would expect in the case of a spin glass. Further, ∆ T p /T p , per decade of frequency in ac susceptibility liesin the range seen in spin glasses. Strong aging effects havebeen observed at 150 K in both FC and ZFC protocols,again a feature characteristic of spin glass like systems.The dc scaling analysis presents conclusive evidence insupport of spin glass behavior with T f = 170 K . Thusit is clear that the system goes into a spin glass statewith an average freezing temperature, 170 K. Since theparticles are coated with gelatin it is clear that the spinglass behavior can not be due to interparticle interac- tions. Rather it has to have its origins within a particle.Below T p1 , the behavior of this system shows some fea-tures characteristic of superparamagnetic blocking viz.increase in the FC magnetization on decreasing the tem-perature, H dependence of T p1 and presence of memoryin FC magnetization without a corresponding effect inZFC magnetization. However certain features observedcorrespond to spin glass like behavior viz. frequency de-pendence of susceptibility with a value of ∆ T p /T p , perdecade of frequency in the range of spin glasses and ag-ing effects in ZFC protocol in addition to those in FCprotocol. Thus the nature of the low temperature peakis ambiguous.We have shown that this system shows spin glass be-havior in contrast to most of the earlier reports whichclaimed superparamagnetism. Further we have arguedconvincingly that the reason for this behavior is surfacespin freezing and not interparticle interactions. At lowtemperature, below T p1 , the behavior shows features ofboth superparamagnetism and spin glasses thus makingits nature equivocal. Acknowledgments
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