-
or
oi
Fine particles
Size effectsSurface effects
sedyntzediconhe
Particles with d7 nm have almost single domain behavior and the
monodomain occupies approxi-
very of groerimesed foze effe
noparticles with reduced size as consequence of the
competition
netocrystalline anisotropy.
gnetic coreshelln2O3 [10], Fe3O413] where a spinserved
magneticted spins are in aike phase at lowns have multiple
congurations for any orientation of the core magnetization.
because of the high crystalline anisotropy has also been in-
Contents lists available at ScienceDirect
.el
Journal of Magnetism an
Journal of Magnetism and Magnetic Materials 377 (2015)
4451http://dx.doi.org/10.1016/j.jmmm.2014.10.054tensively studied
because of their possible use in technologicalapplications.
Moreover, the local surface anisotropy due to the ironand cobalt
ions have easy axes with different directions whichfavor the
magnetic disorder canting of the spins at the surface.
0304-8853/& 2014 Elsevier B.V. All rights reserved.
n Corresponding author at: Centro Atmico Bariloche CNEA/
CONICET, S.C.Bariloche 8400, Argentina. Fax: 54 294 4445299.
E-mail address: [email protected] (R.D. Zysler).between the
surface anisotropy and exchange energy plus mag-An interesting
system to study this phenomenon is the cobalt
ferrite (CoFe2O4). The material in bulk has well known nature,
andimportant as the particle size decreases, due to the
increasingsurface-to-volume ratio. The magnetic properties of a
perfectlyaligned single-domain particle where all spins uctuate
coherentlyare not observed for systemwhere the number of misaligned
spinson the surface is a signicant contribution. It is expected
that thedecrease in the coordination number induces a weakening in
theexchange interactions of the surface atoms with the
surroundingones. Such spin disorder propagates from the surface to
the core.There are indications of very complicated spin structures
for na-
netically ordered, and the shell is composedcanted spins.
Several nanocrystals present the mastructure such as: nickel
ferrite [1], NiO [9], M[7,11,12], and also in amorphous
nanoparticles [canting at the surface exist. In these cases, the
obbehavior is explained with a model where the cansurface layer and
they freeze into a spin-glass-ltemperatures. As a consequence, the
surface spinetic properties of nanosized particles and become
increasingly anisotropy compared to the nanoparticle core [1,58].
Such par-ticles have a coreshell structure, where the core spins
are mag-
of disordered or1. Introduction
Surface and nite size effects innanoparticles have been the
subjectyears from both, theoretical and exp3], since they could be
denitively uplication of these systems. Finite-simately the whole
particle. In the sample with d4.5 nm the surface anisotropy is
large enough to alterthe ferrimagnetic order in the particle shell.
Then, a surface/volume ratio of 60% is the crossover be-tween a
single domain nanoparticle and a frustrated order in a magnetic
coreshell structure, due to thecompetition between surface
anisotropy and exchange interactioncrystalline anisotropy in cobalt
fer-rite. In the d2 nm sample the poor crystallinity and the large
surface/volume ratio avoid the ferri-magnetic order in the particle
down to T5 K.
& 2014 Elsevier B.V. All rights reserved.
ne (o7 nm) magneticwing interest in recentntal, points of view
[1r the technological ap-cts dominate the mag-
It is well established that in small size particles, the
surfacespins play a dominant role. These spins cause the reduction
insaturation magnetization and coercivity with decreasing
particlesize at the nanometric range [4]. It has been shown that in
ferritenanoparticles, due to the broken symmetry and exchange bonds
atthe surface, the surface spins do not follow the core
anisotropydirection and become disordered or canted, leading to
even higherSuperparamagnetismMagnetic orderingSize and surface
effects in the magnetic
Betiana N. Pianciola a,b, Enio Lima Jr.b, Horacio E. TrR. Cohen
c, Roberto D. Zysler a,b,n
a Instituto Balseiro, S.C. Bariloche 8400, Argentinab Centro
Atmico Bariloche CNEA/ CONICET, S.C. Bariloche 8400, Argentinac
Instituto de Fsica, Universidade de So Paulo, So Paulo 05508-090,
Brazil
a r t i c l e i n f o
Article history:Received 19 June 2014Received in revised form14
October 2014Available online 22 October 2014
Keywords:
a b s t r a c t
In this work, we have focuof CoFe2O4 nanoparticles sand 7 nm,
with narrow sidiffraction (XRD) proles in2 nm sample has a
poorMssbauer spectroscopy t
journal homepage: wwwder of CoFe2O4 nanoparticles
ani a,b, Luiz C.C.M. Nagamine c,
on the size dependence of the magnetic properties and the
surface effectshesized by high-temperature chemical method with
diameter d2, 4.5,distribution. transmission electron microscopy
(TEM) images and X-rayates that samples with 7 and 4.5 nm present a
high crystallinity while thee. We have investigated by
magnetization measurements and in-eldinuence of the surface in the
internal magnetic order of the particles.
sevier.com/locate/jmmm
d Magnetic Materials
-
diameter 2.0, 4.5, and 7.0 nm respectively, obtained from the
TEManalysis.
MFC(T) curves [20,21]:
B.N. Pianciola et al. / Journal of Magnetism and Magnetic
Materials 377 (2015) 4451 45TEM and high-resolution microscopy
(HRTEM) images weremade in a Philips CM200 (200 kV) transmission
electron micro-scope. The samples were prepared by dropping a
colloidal solutionof nanoparticles onto a carbon-coated copper
grid. XRD patternswere collected in 2 geometry with a Philips W1700
dif-fractometer, using Cu-K radiation.
In order to avoid dipolar interactions among the particles in
themagnetic measurements, the nanoparticles were dispersed in
apolymeric matrix (polyethylamine PEI) in a concentration of1% w/w.
M(T) in zero-eld-cooling (ZFC) and eld-cooling (FC)conditions and
M(H) loops at TZ2 K were measured in a com-mercial SQUID
magnetometer.
In-eld MS were taken at 4.2 K in a liquid He ow cryostat witha
spectrometer in transmission geometry using a 57Co/Rh
source.Mssbauer samples were prepared by dispersing 20 mg of
therespective powder samples in boron nitride and pressing it
be-tween acrylic disks. The sample was mounted in the bore of a140
kOe superconducting magnet, in a vertical source-sample-detector
setup such that the direction of gamma-ray is parallel tothe
direction of applied eld. A sine-shaped velocity waveformwas used
to minimize mechanical noise. All MS spectra were ttedby using
Lorentzian line shapes with a non-linear least-squareFurthermore,
it is possible to synthesize ferrite nanoparticles withsize control
and high crystallinity. In particular, with the decom-position of
organometallic precursors (transition metal acet-ylacetonate)
nanoparticles have been fabricated in a one stepprocess,
controlling the size in the 225 nm range with a narrowsize
distribution [11,14]. Many papers referring size effects onCoFe2O4
nanoparticles can be found in the literature [1518], butnon of them
study these effects for particles less than 5 nm, wherethe surface
effects are absolutely dominant.
In this work, we have focused on the size dependence of
themagnetic properties and the surface effects of CoFe2O4
nano-particles synthesized by high-temperature chemical method
withd2.0, 4.5, and 7.0 nm, with narrow size distribution.
As-madenanoparticles are covered by a monolayer of oleic acid
stronglylinked to the surface. According to our magnetization
measure-ments as function of eld and temperature (M(H,T)), as well
in-eld (up to 12 T) Mssbauer spectroscopy (MS) results, our
sys-tems present strong differences between the behavior of the
lar-ger-nanoparticles (with high ferrimagnetic order degree) and
thesmaller-nanoparticles, which present a coreshell
magneticstructure, with a magnetically ordered core and a
magneticallydisordered shell.
2. Experimental details
Nanoparticles narrow diameter distribution were prepared bythe
high-temperature decomposition of Co(acac)2 and Fe(acac)3with the
1:2 M ratio (0.6:1.2 mmol) together with 12 octanediol,diphenyl
ether (boiling point at 550 K) and oleic acid and oley-lamina as
surfactants. The particle size was tailored by the
sur-factant:precursor molar ratio ([Surf.]:[Prec.]) according to
the re-ference [15]. The preparation was magnetically stirred and
heatedup to the boiling temperature T535 K for 120 min. After
synth-esis the nanoparticles were extracted by adding ethanol
followedby centrifugation (14,000 rpm/30 min). After that, they
were wa-shed with acetone and centrifuged once again. The nal
sampleconsists in a black powder constituted by cobalt ferrite
nano-particles covered with an oleic acid layer, which is strongly
linkedto the surface, improving the chemical stability, and
avoiding ag-glomeration. The samples were labeled S2, S5, and S7
with meanprogram (NORMOS), calibrating the velocity scale with a
-Fe foil f TT
ddT
M T M T( )1
[ ( ) ( )] (1)ZFC FC
This f(T) function presents a maximum at certain temperaturethat
corresponds to the blocking temperature (TB) of the particleswith
size of the mean value of the distribution. Fig. 3b shows theenergy
barrier distribution obtained by the differentiation of theat 300
K. When necessary a hyperne eld distribution was em-ployed. Isomer
shift (IS) values are relative to -Fe at 300 K. As aconsequence of
the experimental setup, the temperature of thesource during the low
temperature spectrum acquisition must tobe considered as an
important factor to the IS values observed inorder to compare with
the expected ones.
3. Results
The XRD patterns of the samples S2, S5, and S7 are shown inFig.
1. The peaks in the patterns of samples S7 and S5 correspondto the
expected inverse spinel structure of CoFe2O4 (PDF 00-022-1086),
while sample S2 exhibits a poor crystallinity and only abroad peak
associated to the plane (311). There is a broad max-imum in the XRD
pattern of the samples, which is strong forsample S2, notable for
sample S5 and almost imperceptible forsample S7. This broad maximum
is resulting from the organicphase remnant from the washing
procedure; because its reduceddiameter, the washing procedure was
more difcult in sample S2.The crystallite mean size was obtained
from the peak (311) for thethree samples by the Scherrer's equation
[19], obtaining 1.6,4.2 and 7.5 nm, respectively.
Fig. 2 shows the typical TEM images of the as-prepared
nano-particles. The particles appear separated from each other
withoutagglomeration. From several images of different zones of
thesample, the diameter histogram of each sample was determined(see
Fig. 2b). For all samples, the histogram is well tted with
alognormal distribution giving mean diameters of od42.0, 4.5,and
7.0 nm for samples S2, S5, and S7, respectively. A narrow
sizedistribution was found for all samples (s0.10.2). These
nano-particle sizes give a surface/volume ratio (considering a 0.6
nmsurface layer, which is close to the rst atomic layer distance
inlattice) of 0.80, 0.60, and 0.45, respectively. Comparing with
thecrystallite size obtained from XRD proles, the diameter of
sampleS7 is slightly smaller, while for sample S2 and S5 it is
slightlylarger. HRTEM images show high crystallinity of S5 and S7
samplesand poor crystallinity in the S2 sample. A detail of the
crystallineplanes for sample S7 is showed in the respective bottom
panelinset.
Fig. 3a shows the results of M(T) (H50 Oe) as a function
oftemperature for the S7, S5, and S2 samples are reported.
Themeasurements were performed according to the usual ZFC and
FCprocedures. S5 and S7 samples present similar curves, typical
forsingle domains of non-interacting systems where the ZFC and
FCmagnetization curves superimpose at high temperatures
(super-paramagnetic regime) and, below the irreversibility
temperature(Tirr), the ZFC magnetization presents a maximum whereas
the FCmagnetization curve increases monotonically with decreasing
thetemperature. Tirr corresponds to the highest blocking
temperature,i.e. to that of particles with highest energy barrier.
For the S5sample, the FC magnetization curve change the slope at
T50 Kand remains quasi constant at lower temperatures. The shift in
theTirr values, Tirr(S7)300 K and Tirr(S5)130 K is due to the
changeof the nanoparticle volume, and consequently on the
anisotropyenergy barrier KV. For weakly interacting nanoparticles
the energybarrier distribution, f(T), can be calculated from the
MZFC(T) andMZFC(T)MFC(T) curves and divided by T of the samples S5
and S7.
-
B.N. Pianciola et al. / Journal of Magnetism and Magnetic
Materials 377 (2015) 445146The f(T) has the same shape (lognormal
distribution) as the vo-lume distribution obtained by TEM
measurements. Sample S7distribution curve does not follow the
lognormal distribution atT4230 K because the system does not allow
the total super-paramagnetic regime even at room temperature, then
contributionof larger nanoparticles is missing distorting the curve
at hightemperatures (up to 300 K). A more expected behavior is
observedfor sample S5, with a lognormal distribution of energy
barrier withmaximum at 55 K, despite an unexpected and marked
increasein the values of f(T) is observed for To5 K. On the other
hand, inthe sample S2 the ZFC and FC magnetization curves almost
su-perimpose at all temperature range. The small irreversibility
ob-served is a consequence of some larger nanoparticles which
be-come blocked at 60 K.
M(H) curves were performed in ZFC condition at
differenttemperatures. Fig. 4 shows representative M(H) curves for
thethree samples. For samples S5 an S7, above Tirr the
magnetizationcurves are reversible, whereas for ToTirr a hysteretic
behavior isobserved. On the other hand, sample S2 shows only
reversiblebehavior for the entire temperature range. For all
samples, M(H)curves do not saturate up to H5 T, and in Fig. 5a we
plot themagnetization values measured at H5 T as a function of
tem-perature. The M(H5 T) decreases slowly with increasing
tem-perature for S5 and S7 samples, whereas this reduction is
strongerfor the smaller particles (S2).
In Fig. 5b the coercive eld as a function of temperaturedata
[HC(T)] for S5 and S7 samples is plotted. The HC(T) valuesfor both
samples can be tted by using the expression
= H T H T T( ) (0) [1 ( / ) ]C C B 1/2 (at T45 K for S5 sample).
This function
od45.6 nm was obtained, assuming spherical particles and a
Fig. 1. X-ray diffraction (XRD) proles of as-made samples S2, S5
and S7.saturation magnetization of 80 emu/g (bulk value [22]). This
dia-meter is slightly smaller than the one obtained by TEM. Taking
thevalue of od4 obtained from TEM analysis (7 nm) and using theNel
model [0exp(KeffV/kBT] for the M(T) measurements, as-suming /01012
and TTB to calculate the effective anisotropyconstant (Keff), the
value of 2.0106 erg/cm3 is obtained, close tothe values expected
for Bulk material [22]. These conclusions arereinforced by MS
analysis of this sample, where the in-eldspectra can be easily
related to the expected for monodomainnanoparticles, since they
show the sextets that can be addressed tothe contribution of Fe
ions in the A and B sites of ferrite with anantiferromagnetic
structure. The ratio of the absorption area be-tween them indicates
that the Co ions substitute the Fe onespreferentially in site B
(octahedral). For this, the result obtainedfrom Energy Disperse
Spectroscopy (EDS) analysis (performed in ascanning electron
microscopy-SEM) is compared with the Mss-bauer one. From EDS
analysis: at% Co/at% Fe0.38, while we ob-serve a relation of the
absorption intensity of site A/site B of about0.7 in the MS for S7
sample at Happ0. For a perfect incorporationof Co ions in the site
B, we expect a relation between the twoabsorptions about 0.85
(considering the amount of Co ions mea-sured in the whole sample),
and 0.45 for a random distribution ofCo ions between A and B sites.
Thus, about 85% of Co ions are insite B. In-eld MS exhibit a
partial alignments of the moments insub-lattice A and B with
applied eld with lower values and anis characteristic for
non-interacting single domains. In the S5sample, for To5 K display
a decrease of the coercivity which maypoint out an internal process
in the magnetic order of the nano-particles and will be discussed
latter.
Fig. 6a and b present the in-eld MS at 4.2 K for sample S7
andS5, respectively. For both samples, the spectra were
well-ttedconsidering two sextets referents to the A (tetrahedral)
and B(octahedral) sites of the Fe in spinel structure. We have
studieddetailed the dependence of D23 (relation A2/A3, where A3 and
A2are the intensities of the third and second line, respectively)
and ofeffective eld (Beff) with applied eld (Happ). Beff and the
hyperne
eld (Bhf) are related by
=
+
B H B H( ) (0)eff app hf app, where is theparticle magnetic
moment. Relevant hyperne parameters ob-tained from the tting
procedure are given in Table 1. Because ofthe strong
antiferromagnetic exchange coupling, the Beff of crys-talline site
A increase, while the one of crystalline site B decreasewith Happ
[11].
Fig. 7a shows the in-eld MS spectra at 4.2 K with Happ0, 30,40,
80, 120 kOe for sample S2, while Fig. 7b exhibits the in-eldMS of
this sample taken with Happ12 kOe and temperature of 4.2,20, 40, 60
and 100 K. All these spectra were tted with a hyperneeld
distribution and a doublet corresponding to a paramagneticor
superparamagnetic contribution. Relevant hyperne para-meters
obtained from the tting procedure are given in Table 2.
4. Discussion
M(T) curves of sample S7 (see Fig. 3a)) show typical mono-domain
behavior with an Tirr of Tirr4300 K. For T4Tirr, the M(H)curves
have a distinct measurement time, a shorter one, with re-spect to
the M(T) curves. In this way, they present a super-paramagnetic
behavior for TZ250 K and they are tted with aLangevin function
giving a monodomain magnetic momentom4(3640740) mB at T250 K. For
ToTirr, the magnetizationcurves show irreversibility with
square-like loops. Also the HC(T)shows monodomain behavior
following a T1/2 law. From theaverage magnetic moment, an estimated
value of the diameteralmost complete alignment for higher ones,
despite a small
-
B.N. Pianciola et al. / Journal of Magnetism and Magnetic
Materials 377 (2015) 4451 47canting that are still observed at 120
kOe (a very small fraction,represented by the no null relation
between the intensities of line2 and line 3 (D23) for both sites at
120 kOe).
M(H) curves of S5 sample (see Fig. 4) exhibit two
contributionsto the magnetization for the entire range both in
super-paramagnetic and blocked regimes: a component that saturates
atlow magnetic elds, and a reversible component of the
magneti-zation that does not saturate even for the maximum applied
eldof 50 kOe. In the superparamagnetic regime (T4170 K) thesecurves
are satisfactorily tted by the equation M(H,T)Mn(H,T)H, where Mn
has a superparamagnetic monodomain behaviordescribed by an integral
of Langevin functions [L(x)coth(x)1/x,xH/kBT] weighted by the
lognormal particle size distributionand H associated to the surface
paramagnetic contribution. An-other possibility is that the linear
contribution at high eld arisesfrom small nanoparticles in
superparamagnetic regime; however,TEM analysis did not indicate the
presence of so small nano-particles or a bimodal distribution. From
these tting the magneticmoment value of the single domain for each
temperature wasobtained. This value increases as the temperature
decreases, as isshown in Fig. 8, indicating a progressive magnetic
order inside thenanoparticle or, in other words, the growth of the
single domain atlower temperatures. This magnetic uctuation intra
particle wasalso observed in NiAg heterogeneous alloys [23]. From a
linear tof the thermal dependence of the magnetic moment, we
obtain
Fig. 2. Transmission electron microscopy (TEM) images of samples
S7, S5 and S2. Thdistribution, and the bottom inset is a
high-resolution TEM image.the extrapolated magnetic moment for T0,
and from this valuewe estimated the value of the highly ordered
monodomain dia-meter od44 nm, close to the value obtained from TEM
ana-lysis. With this monodomain size and the average TB a value
ofKeff2.5106 erg/cm3 was determined by the Nel model, withinthe
order of magnitude of the anisotropy constant calculated fromthe
coercive eld.
Below the Tirr, hysteresis curves are observed in the M(H)
plotas is usual for the blocked regime. The loops exhibit two
con-tributions to the magnetization: a component that saturates at
lowelds, which is characteristic of the blocked single domain, and
areversible component of the magnetization that does not
saturateeven for the maximum applied eld of 50 kOe. With
decreasingtemperature, HC increases, following the usual
(1(T/TB)1/2) lawfor single domains, up to a maximum at TH
maxC5 K, as is showing in
Fig. 5. Below this temperature, the coercive eld decreases.
Thetemperature of the maximum of HC(T) is the same temperaturewhere
the energy distribution f(T) curve starts to grow as thetemperature
decreases. In Fig. 5, HC vs T1/2 is plotted evidencingonly the
typical monodomain behavior down to T5 K, where thedata exhibit a
linear trend.
The simple model of a nanoparticle as a perfect ordered
spinarray, like in the bulk, is not valid to explain our results
for sampleS5, and the large disorder of the ferrimagnetic lattice
due to thehigh surface to volume ratio should be considered. In
fact, the
e right panel is the corresponding diameter histogram tted with
a log normal
-
B.N. Pianciola et al. / Journal of Magnetism and Magnetic
Materials 377 (2015) 445148results for sample S5 can be
satisfactorily interpreted by a coreshell model, which takes into
account the competition betweenthe surface anisotropy and the
exchange interaction plus thecrystalline anisotropy. In this case,
the total energy per particle is
Fig. 3. (a) Magnetization curve as function of the temperature
[M(T)] measured in ZFtemperature distribution of samples S7 and S5
[calculated with Eq. (1)].
Fig. 4. Magnetization curve as function of the applied eld
[M(H)] measured in ZFCmode and different temperatures of samples
S7, S5 and S2.C and FC modes (M (T) and M (T)) of samples S7, S5
and S2. (b) The blockinggiven by [9,13,24,25]
^ ^
=
< >+z H z
n H
E K J K
K
( ) S S (S )
(S )(2)
core core corei a
N
i ashell
i i ai
N
ishell
i
i
N
isurf
i ii
N
i
2
,,
2
2
shell shell
surf shell
where core is the core magnetic moment, Kcore and Ki are
thecrystalline anisotropy constant for the core and shell ions
re-spectively, Ji a
shell, is the exchange constant per ion between shell
shell ions and core spinsshell ions interaction (CoCo, FeFe
orCoFe), Ki
surf is the surface anisotropy per atom (Fe or Co), i in-
dicates a unit vector perpendicular to the surface, and z^
indicatethe direction of the easy axis. The surface anisotropy term
tends toalign the spins perpendicular (parallel) to the surface for
Fe (Co)magnetic moment, as reported in the literature [25]. It is
clear thatwhile the exchange interaction tends to magnetically
order thesystem, the surface anisotropy favors its disorder. In the
high-temperature regime, the surface spins are in a paramagnetic
state,and we observe the superparamagnetic response of the
orderedcore plus the paramagnetic disordered shell. This disorder
isoriginated by the competition between the exchange interactionand
the crystalline anisotropy (which tend to magnetically orderthe
particle), and the surface anisotropy, which depends on
surfacetopology and tends to disorder the spins. Decreasing
temperature,the ordered core volume increases and consequently the
magneticmoment of the particle grows. Below T5 K, the formation
ofsurface spin clusters creates an additional effective eld, and
coremoment-surface clusters moment interactions leading to
theanomalous behaviors observed in the HC(T) and M(T)
curves[13,24,25].
ZFC FC
-
Fig. 5. (a)M(T) curves measured with Happ50 kOe of samples S7
and S5; (b) dependence of the coercive eld with the temperature
[HC(T)] of samples S7 and S5, where thesolid line correspond to the
t with T1/2.
Fig. 6. (a) and (b) In-eld Mssbauer spectra of samples S7 and
S5, respectively, measured at 4.2 K. Each spectrumwas tted with two
sextets referent to the contributions ofsites A and B.
Table 1Relevant hyperne parameters obtained from the tting
procedure of Mssbauer spectra of samples S7 and S5 at 4.2 K. Beff
is the effective eld, IS is the Isomer Shift, QS isthe Quadrupolar
Spliting and D23 is the ratio between the intensities of lines 2
and 3 of the sextet.
Sample Happ (T) Crystalline site Beff (T) IS (mm/s) QS (mm/s)
D23 Absorption area (%)
S7 0 A 50.90 0.26 0.01 2.00 41B 53.30 0.36 0.04 2.00 59
3 A 53.80 0.27 0.01 0.60 41B 50.30 0.37 0.04 0.66 59
5 A 55.85 0.26 0.01 0.51 41B 48.52 0.40 0.06 0.55 59
8 A 58.79 0.25 0.01 0.40 41B 45.04 0.40 0.06 0.20 59
12 A 62.94 0.26 0.01 0.31 41B 41.04 0.40 0.06 0.28 59
S5 0 A 50.80 0.27 0 2.1 47B 53.30 0.34 0.05 2.0 53
1 A 51.10 0.27 0 1.5 47B 53.20 0.34 0.05 1.4 53
12 A 62.90 0.27 0 0.17 41B 41.40 0.34 0.05 0.23 59
B.N. Pianciola et al. / Journal of Magnetism and Magnetic
Materials 377 (2015) 4451 49
-
ssba
B.N. Pianciola et al. / Journal of Magnetism and Magnetic
Materials 377 (2015) 445150Fig. 7. (a) In-eld Mssbauer spectra of
sample S2 measured at 4.2 K; (b) in-eld Mshows the respective
hyperne eld distribution.Interestingly, the in-eld MS of sample S5
are also composed ofthe contribution of the two sextets (sites A
and B). For this sample,we can estimate that about 90% of Co ions
are in site B. If we focusat lower eld (10 kOe), we observe a large
value for D23 for both Aand B sites for sample S2 in comparison to
sample S7. TheseMssbauer results indicates a larger canting for a
larger number ofmoments in sample S5 in comparison with sample S7
for bothsites, despite they are present for a small number of spins
con-sidering the whole sample and it is more signicant for site B.
Themean value of the canting angle (o4mean angle between
Table 2Hyperne parameters obtained from the tting procedure of
the in-eld Mssbauer specIS (isomer shift), QS (quadrupolar
splitting), D23 (relation between the absorption area
Applied eld (kOe) T (K) Subspectra Bhf (T) IS (m
0 4.2 Distribution 43.4 /47.3 0.25/Doublet 0.35
30 4.2 Distribution 44.3 / 38.5 0.25/Doublet 0.35
50 4.2 Distribution 42.9 / 35.9 0.25/Doublet 0.35
80 4.2 Distribution 48.7 / 43.5 / 35.6 0.25/Doublet 0.35
120 4.2 Distribution 49.8 / 39.4 0.25/Doublet 0.35
120 20 Distribution 14.5 0.35Doublet 0.35
120 40 Distribution 12.6 0.35Doublet 0.35
120 60 Distribution 13.6 0.35Doublet 0.35
120 100 Distribution 12.6 0.35Doublet 0.35uer spectra measured
with Happ120 kOe at different temperatures. The right panelHapp and
the magnetic moment) is given by
=+DD
sin2
4 (3)2 23
23
Our magnetization results at high elds for Sample S5
indicatesthat the value of D23 observed in the MS comes from a
fraction ofmagnetic moments in both sites misaligned with respect
to Happ.In this case, these moments also leads to a change in the
values ofthe Bhf in comparison with the corresponding core
sub-spectrum;however, because of the broad peaks and the small
changes ex-pected in the Bhf (because of the values of D23,
indicating a partial
tra of sample S2: Bhf (most probable hyperne elds), w (half
width at half height),of lines 1 and 3).
m/s) QS (mm/s) W (mm/s) D23 Absorption area (%)
0.41 0.01 2 550.7 1.1 45
0.41 0.01 1.5 720.7 1.3 28
0.41 0.01 1.5 900.7 1.3 10
0.30/0.41 0.01 1.3 900.7 1.3 10
0.41 0.01 1.4 900.7 1.3 10
0.01 2 880.7 1.3 12
0.01 2 610.7 1.1 39
0.01 2 520.7 1.1 48
0.01 2 500.7 1.3 50
-
R. Cohen, H.R. Rechenberg, R.D. Zysler, J. Appl. Phys. 108
(2010) 103919.[12] P. Dutta, A. Manivannan, M.S. Seehra, N. Shah,
G.P. Huffman, Phys. Rev. B 70
Magn. Magn. Mater. 324 (2012) 1182.
B.N. Pianciola et al. / Journal of Magnetism and Magnetic
Materials 377 (2015) 4451 51misalignment), the contribution of the
misaligned magnetic mo-ments is not observed as separated
sextets.
The magnetic behavior of the sample S2 is compatible with
aparamagnetic sample (or not fully magnetically ordered one).
Infact, the calculated mean magnetic moment of the nanoparticles
ofthis sample from the M(H) curves is (T5 K)(4.9270.02)B.This
result give us the evidence that the poor crystallinity of
thesenanoparticles and the large surface/volume ratio avoid the
ferri-magnetic order in the particle down to T5 K. Some
irreversibilityin M(T) curves is observed, but it can be easily
addressed to the asmall amount of larger particles (43 nm) observed
for this samplein TEM images. However, M(H) measurements clearly
reinforcesthe lack of magnetic order in this sample.
In-eld MS of sample S2 at low temperature (4.2 K) were ttedwith
a distribution of hyperne elds and a doublet, whichcorresponds to a
superparamagnetic or paramagnetic contribu-tion, and the obtained t
conrms the analysis frommagnetizationmeasurements. Despite the fact
that the hyperne eld distribu-tions present two maxima, which can
be associated to sites A andB, the variation of these values with
Happ, as well as the variation ofD23, it is not the expected for
two sub-lattice with anti-ferromagnetic alignment in parallel
direction with respect to theapplied eld. The values of Bhf
observed for these two maxima aresmaller than the expected for
sites A and B in the ferrite. In ad-dition, we observe an important
contribution in low values of Bhf,which may correspond to
relaxation phenomena, spins with re-laxation time close to the time
window of the experiment (108 s).This contribution at low values of
Bhf decreases with increasingHapp, indicating some ordering process
with the increment of theexternal eld. The doublet indicates a
superparamagnetic or
Fig. 8. Magnetic moment of sample S5 obtained from the tting
ofM(H) curve withthe Langevin equation plus a linear contribution
as function of the temperature.paramagnetic contribution [2628]
even at 4.2 K. Its relative ab-sorption area decreases, while w
slightly increases, with increasingexternal eld, also indicating
the increment in the magnetic orderwith Happ. Therefore, in-eld MS
at 4.2 K indicates a lack of theantiferromagnetic order in sample
S2, in accordance with themagnetization measurements. In-eld MS
spectra withHapp120 kOe and T4.2, 20, 40, 60 and 100 K shows an
incre-ment in the relative absorption area of the doublet with
increasingT, as expected for a paramagnetic or superparamagnetic
con-tribution. At the same time, the distribution strongly
dislocates forlow values of Bhf, which is also expected as
consequence of theincrement of the relaxation phenomena with
increasingtemperature.
[18] Kai Zhang, T. Holloway, A.K. Pradhan, J. Magn. Magn. Mater.
323 (2011) 1616.
[19] B.D. Cullity, S.R. Stock, Elements of X-Ray diffraction,
3rd ed., Prentice-Hall Inc.
(2001) 167176.[20] M. Knobel, L.M. Socolovsky, J.M. Vargas, Rev.
Mex. Fs. 50 (2004) 828.[21] M.G.M. Miranda, G.J. Bracho Rodrguez,
A.B. Antunes, M.N. Baibich, E.F. Ferrari,
F.C.S. da Silva, M. Knobel, J. Magn. Magn. Mater. 185 (1998)
331338.[22] R.C.O. Handley, Modern Magnetic Materials: Principles
and Applications,
Wiley & Sons, 1999 (Chapter 10).[23] L.C.C.M. Nagamine, B.
Mevel, B. Dieny, B. Rodmacq, J.R. Regnard, C. Revenant-
Brizard, I. Manzini, J. Magn. Magn. Mater. 195 (1999)
437451.[24] R.D. Zysler, H. Romero, C.A. Ramos, E. De Biasi, D.
Fiorani, J. Magn. Magn.
Mater. 266 (2003) 233.[25] E. De Biasi, C.A. Ramos, R.D. Zysler,
H. Romero, D. Fiorani, Phys. Rev. B 71
(2005) 104408.[26] S. Mrup, J. Magn. Magn. Mater. 37 (1983)
39.[27] M.S. Kamali-, T. Ericsson, R. Wppling., Thin Solid Films
515 (2006) 721.[28] L. Hggstrm, S. Kamali, T. Ericsson, P.
Nordblad, A. Ahniyaz, L. Bergstrm,
Hyperne Interact. 183 (2008) 49.(2004) 174428.[13] E. De Biasi,
C.A. Ramos, R.D. Zysler, H. Romero, Phys. Rev. B 65 (2002)
144416.[14] Jos M. Vargas, Roberto D. Zysler, Nanotechnology 16
(2005) 1474.[15] C. Vzquez-Vzquez, M.A. Lpez-Quintela, M.C.
Bujn-Nez, J. Rivas, J. Na-
nopart. Res. 13 (2011) 1663.[16] I. Shari, H. Shokrollahi, M.M.
Doroodmand, R. Sa, J. Magn. Magn. Mater 324
(2012) 1854.[17] B. Bittova, J. Poltierova Vejpravova, M.P.
Morales, A.G. Roca, A. Mantlikova, J.We have synthesized CoFe2O4
nanoparticles with sizes in the 27 nm range in order to study the
inuence of the surface anisotropyin the internal magnetic order of
the particles. Particles with d7 nmhave almost single-domain
behavior and the monodomain occupiesapproximately the whole
particle. In the sample with d5 nm, thesurface anisotropy is large
enough to alter the ferrimagnetic order inthe particle shell. Then,
a surface/volume ratio of 60% is the cross-over between a single
domain nanoparticle and a frustrated order in amagnetic coreshell
structure, due to the competition between sur-face anisotropy and
exchange interactioncrystalline anisotropy incobalt ferrite. In the
sample with d2 nm, the poor crystallinity andthe large
surface/volume ratio avoid the ferrimagnetic order in theparticle
down to T5 K.
Acknowledgments
This work was supported by Argentinean grants PIP
1333/08(CONICET), PICT 0832/07 and Universidad Nacional de Cuyo
06-C404, as well as by the Brazilian agency FAPESP (Proc:
2011/50556-0).
References
[1] R.H. Kodama, A.E. Berkovitz, E.J. Mc Niff Jr, S. Foner,
Phys. Rev. Lett. 77 (1996)394.
[2] O. Iglesias, A. Labarta, Phys. Rev. B 63 (2001) 1844416.[3]
Fiorani, D. (Ed.), 2005. Surface Effects in Magnetic Nanoparticles,
Springer.
ISBN 0-387-23279-6.[4] J.M.D. Coey, Phys. Rev. Lett 27 (1971)
1140.[5] R.H. Kodama, A. Salah, A. Makhlouf, A.E. Berkovitz, Phys.
Rev. Lett. 79 (1997)
1393.[6] H. Kachkachi, A. Ezzir, M. Nogus, E. Tronc, Eur. Phys.
J. B 14 (2000) 681.[7] N. Prez, P. Guardia, A.G. Roca, M.P.
Morales, C.J. Serna, O. Iglesias, F. Bartolom,
L.M. Garca, X. Batlle, A. Labarta, Nanotechnology 19 (2008)
475704.[8] J.M. Vargas, E. Lima Jr., R.D. Zysler, J.G. Santos
Duque, E. De Biasi, M. Knobel,
Eur. Phys. J. B 64 (2008) 211.[9] E. Winkler, R.D. Zysler, M.
Vasquez Mansilla, D. Fiorani, Phys. Rev. B 72 (2005)
132409.[10] E. Winkler, R.D. Zysler, D. Fiorani, Phys. Rev. B 70
(2004) 174406.[11] E. Lima Jr., E. De Biasi, M. Vasquez Mansilla,
M.E. Saleta, F. Effenberg, L.M. Rossi,5. Conclusions
Size and surface effects in the magnetic order of CoFe2O4
nanoparticlesIntroductionExperimental
detailsResultsDiscussionConclusionsAcknowledgmentsReferences
