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Applied Surface Science 253 (2006) 2589–2596

Magnetic structure and collective Jahn–Teller distortions in

nanostructured particles of CuFe2O4

I. Nedkov a,*, R.E. Vandenberghe b, Ts. Marinova c, Ph. Thailhades d,T. Merodiiska a, I. Avramova c

a Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko Choussee Blvd., 1784 Sofia, Bulgariab Department of Subatomic and Radiation Physics, University of Gent, B-9000 Gent, Belgium

c Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, Bulgariad Universite, ‘‘Paul Sabatier’’, 118 Route de Narbonne, 31 062 Toulouse Cedex 4, France

Received 24 January 2006; accepted 13 May 2006

Available online 7 July 2006

Abstract

The aim of the present work is to compare the structural, the composition and chemical state of the surface and magnetic properties of different

nanosized CuFe2O4 powders exhibiting collective Jahn–Teller effect. The samples under examination consist of edged nanosized particles (needle

like) with average length 1300 � 20 nm and diameter 300 � 20 nm obtained after high temperature synthesis, and superparamagnetic (at room

temperature) spherical particles (d = 6 � 2 nm), obtained by soft chemistry techniques. The surface composition of the particles was investigated

by X-ray photoelectron spectroscopy (XPS). Mossbauer spectroscopy (MoS), including at high magnetic field up to 5 T and 4.2 K, was used for

characterization of cation distribution in the samples. The data yielded by the XPS and MoS analyses for spherical nanosized particles led us to the

assumption for the existence of a Jahn–Teller effect gradient—from the B-sublattice on the surface to a compensation of the tetragonal distortion in

the two sublattices in the core. The analysis of the contribution of the anisotropy energy in edged and spherical nanoparticles shows that it must be

considered as an effective value reflecting the influence of the individual factors depending on the particle shape and surface.

# 2006 Elsevier B.V. All rights reserved.

PACS: 73.22.-f; 71.70.Ej; 71.45.-d

Keywords: Nanostructured particles; Copper ferrite; Surface effects; Collective Jahn–Teller effect; Magnetism; XPS; Mossbauer spectroscopy

1. Introduction

The contribution of superexchanged magnetic interactions

to the formation of magnetocrystalline anisotropy in nanosized

ferroxides with two and more magnetic sublattices is not well

understood. Previous studies [1] have shown that the crystal

sublattice formation in nanosized spherical ferroxide particle

has some specific peculiarities and, with the same stoichio-

metry, the spinel cell is different from that of the bulk material.

The presence of cations provoking collective distortion effect of

the type of Jahn–Teller effect in the spinel crystal is a good

indicator for the extent of these peculiarities in the nanosized

particle. On the other hand, these peculiarities will inevitably

* Corresponding author. Tel.: +359 2 71 44 482; fax: +359 2 975 3201.

E-mail address: nedkov@ie.bas.bg (I. Nedkov).

0169-4332/$ – see front matter # 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.apsusc.2006.05.049

influence the formation of the particle surface layer which has

disordered and unbalanced magneto-crystalline structure which

will ultimately change the magnetic properties of the system as

a whole. The Kodama–Berkowits model [2] explains the

magnetic properties of these particles by the appearance of

‘‘spin-canting’’, which is the cause of the exchange magnetic

interactions between the disordered spin structure of the surface

layer and the antiferromagnetic arrangement of the moments

inside the particle; this cannot, however, account for the

superexchange and structural peculiarities.

At certain technological conditions, the copper and

manganese ions in substituted spinels can provoke a collective

Jahn–Teller effect [3] which is associated with the alignment of

the Cu2+ ions occupying the tetragonally distorted octahedral

spinel lattice formed by the oxygen ions. The copper ferrospinel

is an inverse ferromagnetic spinel. It is considered that the

CuFe2O4 is a ferrite of Cu2+. The cation distribution in this

I. Nedkov et al. / Applied Surface Science 253 (2006) 2589–25962590

copper ferrite can be presented by the formula: [Cux2+-

Fe1�x3+]A[Cu1�x

2+Fe1+x3+]BO4. The parameter of inversion, x,

is equal to 0 for inversion spinels and to 1, when the spinel is

normal. Cu2+ cations migrate from octahedral (B-sublattice) to

tetrahedral places (A-sublattice). When the spinel is synthe-

sized using classical ceramic technologies (high temperature

treatment of the initial oxides of the metal cations) with strict

stoichiometry (x = 1), it has a tetragonal structure of

hausmannite type with crystal cell parameters a = 8.20 and

c = 8.60; c/a = 1.05 [4]. According to other authors [5]

a = 8.24, c = 8.68, but c/a is again 1.05. The structure of

CuFe2O4 is considered as that of a tetragonally deformed spinel

stretched along the h0 1 1i direction. The c/a ratio can be

changed via decreasing the copper concentration, or alter-

natively, by temperature treatments. Yokoyama et al. [6]

observed changes in the crystal structure of nanosized CuFe2O4

powders obtained by coprecipitation and subsequently

annealed. They proved that the copper spinel is cubic at

temperatures below 300 8C and tetrahedral over 400 8C.

Although the stable low-temperature phase of this type of

ferrite is tetragonal (c/a � 1) a deficit of Cu2+ cations in the B-

sublattice leads to the absence of co-operative-active Jahn–

Teller distortion and the crystal cell transforms into cubic.

According to some authors, the transition from tetragonal to

cubic structure has to do with changes in the oxygen content in

the lattice, i.e. with formation of observable quantities of Cu+.

Kester et al. [7] proved that in the case of the reduction reaction

for quenched samples of CuFe2O4, the mechanism involves the

formation of Cu+. The rate of reduction, i.e. the Cu+ cation

fraction in the B-sublattice strongly depends on the technol-

ogies of synthesis and the subsequent temperature treatment.

Nanosized (10–30 nm) particles of CuFe2O4, obtained by a

classical ceramic technology, have also been studied [8]. The

high temperature treatment of these materials could lead to

structural and magnetic surface disorders. Many reasons, such

as different copper dispersion in the sublattices, appearance of

cations and oxygen vacancies, amorphisation of the structure,

presence of surface layer with crystalline and magnetic

structure different from that of the particles’ core, can cause

these disorders. All these effects [2–4,8,9] strongly impede the

interpretation of the structural influence on the physical

properties of such type of materials.

The aim of the present work is to compare the structural, the

composition and chemical state of the surface and magnetic

properties of different nanosized CuFe2O4 powders exhibiting

collective Jahn–Teller effect. The samples under examination

consist of edged nanosized particles (needle like) with average

length 1300 � 20 nm and diameter 300 � 20 nm obtained after

high temperature synthesis, on the one hand, and super-

paramagnetic (at room temperature) spherical particles (d =

6 � 2 nm), obtained by soft chemistry techniques, on the other.

2. Experimental

Two different methods were used for the synthesis of

CuFe2O4. The first one (sample 1) has been prepared by a ‘‘soft

chemical’’ method—coprecipitation of Fe 2+ and Cu2+cations

in strong alkaline media at room temperature [10,11]. Diluted

water solutions of FeCl2�4H2O and CuCl2�2H2O mixed in the

ratio 2/1 with intensive stirring are used for that purpose. In a

water solution, the chlorides of these elements exist in a

complex form. When concentrated solution of NaOH with pH

13 is added, the water complexes turn into hydroxides and a

black precipitate of CuFe2O4 is produced. After decantation the

precipitate is rinsed in distilled water up to pH 7 and then dried

at 50 8C. The particles thus obtained have a spherical shape

(Sp) with average size of 6 � 2 nm. This sample further on the

text will be indicated as CuFe1-Sp.

The second method was described in [12] and consist of two

main stages: (i) the concentrated solution of cupric and ferrous

is precipitated in oxalic acid at room temperature and (ii) the

oxalic precursors are slowly decomposed in an air flow, treated

at 710 8C for 4 h and slowly cooled (SC) at a rate of 10 8C/h.

This sample will be indicated as CuFe2-SC. Following the same

synthesis the sample which was quenched (Q) from 710 8C to

room temperature is the third object of this investigation and

have been indicated as CuFe3-Q.

The XRD data exhibited consistently a single-phase spinel

structure for all types of samples. The average particle size was

determined by applying Sherrer’s formula from the XRD

spectra with Lorentz broadening and SEM images. Chemical

states of copper ferrite spinel of the particle’s surface were

determined by XPS. The magnetic properties were character-

ized by VSM while the cation distribution in the copper ferrite

spinel structure was obtained by means of Mossbauer

spectroscopy (MoS). Spectra were collected on a conventional

time-mode spectrometer using a 57Co/Rh source. External

longitudinal magnetic field spectra were obtained in a field of

5 T obtained by a split-coil superconducting magnet. The

spectra were analyzed taking hyperfine field distributions into

account where necessary. For the analysis of the external-field

spectra both the hyperfine field and the canting angle have been

considered by using a double distribution [13].

3. Results and discussions

The morphology of the powders was investigated by

scanning electron microscopy (SEM—JEOL JSM 6400) (see

Fig. 1). The X-ray diffraction pattern showed a single-phase

tetragonal structure. The structural studies were presented and

discussed in references [11,12] and showed the presence of a

co-operative Jahn–Teller effect for the of CuFe2O4 stoichio-

metry. The SEM images (Fig. 1) show unambiguously the

difference in the particle shape of samples CuFe1-Sp and

CuFe2-SC. The particle size and shape of sample CuFe3-Q, are

similar to those of sample CuFe2-SC.

The small size and the specific shape of the particles

investigated determine the strong influence of the surface on

their physical properties. This motivated us to carry out a more

detailed study concerning chemical state of constituent

elements of the particles surface. One of the most powerful

and sensitive methods for surface analysis was used for this

purpose, namely, X-ray photoelectron spectroscopy (XPS). The

analyses were performed on a VG ESCALAB Mk II

I. Nedkov et al. / Applied Surface Science 253 (2006) 2589–2596 2591

Fig. 1. High-resolution SEM images of tetragonal distortion vs. annealing temperature for CuFe2O4: (a) sample CuFe2-SC acicular particles and (b) sample CuFe1-

Sp, spherical particles.

spectrometer using an Al Ka excitation source (1486.6 eV)

with a total instrumental resolution of �1 eV, under a base

pressure of 1 � 10�8 Pa. The O 1s, Cu 2p and Fe 2p

photoelectron lines were recorded. All lines recorded were

calibrated to the C 1s line at 285 eV. The surface composition of

the particles was determined from the ratio of the correspond-

ing peak intensities, corrected by the photo-ionization cross-

sections. The spectra are displayed in Fig. 2 (they are compared

with the model spinel structure of magnetite) and the main

results are summarized in Table 1.

The O 1s spectra (see Fig. 2a) exhibit a single peak around

530.1 eV. The Fe 2p3/2 and 2p1/2 main peaks (Fig. 2b) are

accompanied by satellite structures on the higher binding energy

side, at about 8 eV. The binding energy attributed to Fe3+ is about

711.1 eV for CuFe1-Sp and CuFe1-Q. For sample CuFe1-SC it is

710.5 eV; the shoulder on the lower binding energy side of the

main peak evidences some small amounts of Fe2+ ions.

The binding energies for the Fe 2p3/2 level range between

710.5 eV and 711.1 eV. The shift towards higher binding

energies observed for the CuFe1-Sp and CuFe3-Q samples

could be attributed to the presence of very small particles. It is

known that the final state effects in the photoemission process

due to poor screening of the positive hole in particles with small

sizes for the quenched sample could be the reason for this shift

[14,15]. Concerning the Cu 2p spectra, in Fig. 2c one can see

the main peak of Cu 2p3/2 and a satellite located on the higher

Fig. 2. XPS data for: (a) O 1s, (b) Fe 2p and (c) Cu 2p CuFe2O4 samples: (1)

binding energy side, indicating that the copper valence is 2+.

For all samples, the main Cu 2p3/2 peak is broad and

asymmetric on lower binding energies side.

Several attempts have been reported to analyze the copper

peak in photoelectron spectra of different copper containing

spinels in terms of a superposition of peaks originating from

copper (Cu2+ and Cu+) cations in octahedral and tetrahedral

environment [16,17]. Many experimental and theoretical

studies of a number of copper compounds have shown a

strong dependence of the core-level photoemission spectrum on

the type of Cu–O network forming the structure of the

compound [18,19]. This made us presume that Cu2+ cations

occupying both tetrahedral and octahedral interstitial sites form

two types of Cu–O networks, which are probably responsible

for the features observed in the spinel systems investigated. For

Cu-containing compounds, the satellite peaks are quite

sensitive to changes in the coordination environment of Cu2+

ions. In particular, the coordination geometry of the surface

Cu2+ ions can be investigated by determining the intensity ratio

of the satellite peaks and the main peaks. Generally, the Isat/Im

ratio decreases as the number of oxygen ions coordinated to a

Cu2+ ion increases [20]. The Isat/Im ratio calculated for the

samples investigated showed that it was close to that for the

bulk CuO standard (0.56) for sample CuFe3-Q only. Bearing in

mind that the coordination number of Cu2+ is six in the distorted

octahedron [21], it is reasonable to suppose that the decrease of

CuFe1-Sp, (2) CuFe2-SC and (3) CuFe3-Q compared with XPS of Fe3O4.

I. Nedkov et al. / Applied Surface Science 253 (2006) 2589–25962592

Table 1

XPS data

Sample O 1s (eV) Cu 2p3/2 (eV) Fe 2p3/2 (eV) Cu/Fe Cu (at. %) Fe (at. %) (Isat/Im)Cu

CuI1 (Sp) 530.1 934.2 711.1 0.77 15.8 20.5 0.72

CuFe2 (SC) 530.3 933.6 710.5 0.69 14.7 21.1 0.72

CuFe3 (Q) 530.3 934.2 711.1 0.73 16.1 22.0 0.65

CuO (Merck) 529.9 934.2 0.56

the Isat/Im ratio should be due to an increase in the surface

octahedral Cu species. This leads to the conclusion that there is

a large amount of CuO on the surface of the last spinel (CuFe3-

Q). For the samples with lower surface concentration of Cu

(CuFe1-Sp and CuFe2-SC) the dispersed copper oxide

simultaneously exists in tetrahedral and octahedral coordina-

tion geometry. The XPS data suggest that the linkage Cu–O

probably is different from this one for the bulk material. The

octahedral coordinated surface Cu species is predominant for

the sample (Q) having higher concentration of Cu (see Table 1).

The studies of the particle surface by XPS showed that edged

particles obtained by different temperature treatment, respec-

tively, slow cooling (SC) from 700 8C and quenching (Q)

exhibit different surface structure. For the sample CuFe3-Q

obtained after quenching—the analysis showed the presence of

a second CuO phase on the surface due to the insufficient time

for completing the solid-phase reaction in the synthesis process

[22]. The edged particles (CuFe2-SC) obtained by solid state

reactions at high temperature and slow cooled and the soft

chemistry product—smaller spherical particles (CuFe1-Sp)

show similar surface Isat/Im ratio but different Fe3+ presence.

The data obtained stimulated our interest in further character-

ization of the magnetic properties of edged (sample CuFe2-SC)

and spherical (CuFe1-Sp) particles since the structural analysis

of both types of nanoparticles showed unambiguously a

monophase structure on the surface and the presence of a co-

operative Jahn–Teller effect.

Mossbauer spectroscopy is a widely used tool for the

characterization of nanosized magnetite, the latter being one of

the most interesting magnetic ferrospinels for various applica-

tions. The MoS data for sample CuFe2-SC is shown in Fig. 3.

Fig. 3. Mossbauer spectra at room temperature of sample CuFe2-SC—edged

particles with size 1300 � 20/200 � 20 nm.

Table 2 shows the hyperfine parameters of the sample

CuFe2-SC with edged particles.

The MoS data processing showed the following cation

distribution for the sample CuFe2-SC:

Sample CuFe2-SC

: ðFe0:91Cu0:09ÞA½Fe1:09Cu0:91�BO4ðtetragonal c=a> 1Þ

These structural formulae allowed the elementary magnetic

moment of this system to be determined; at 4.2 K it is in the

range of 1.72mB.

For spherical particles the MoS data processing turned out to

be more complicated since these particles exhibit a typical

superparamagnetic spectrum at room temperature. It can indeed

be expected that the strong reduction of the lattice parameter in

very small particles [1] will enhance the distortion (oxygen

parameter) in the spinel structure. Moreover, the energetically

most favorable spherical shape in such small particles may also

introduce strong deviations from the ideal lattice positions.

However, at 80 K the particles’ spectra reveal the co-existence

of both ferromagnetic and superparamagnetic phases. The

temperature dispersion of the spectrum is presented in Fig. 4. It

shows that the particles have superparamagnetic properties at

room temperature. The cation distribution of these particles was

also studied by MoS at 4.2 K and external magnetic field of 5 T

(Fig. 5).

Cu0:432þFe0:57

3þ½Fe1:433þCu0:57

2þ�O4

This distribution yields a considerably higher elementary

magnetic moment (in the range of 4.44mB). This is in a good

agreement with the increase observed of the saturation

magnetization Ms of spherical particles (Table 3).

The results obtained lead to the conclusion that there is a

gradient of the crystallization in the short-range order in the

spherical particles which is connected with the cavity size in the

A and B sublattices. The migration of Cu2+ cations from the

core to the surface is influenced by that gradient. The octahedral

cavities having higher symmetry are built with priority and their

structure is closer to that of a bulk material and, respectively, to

the edged particles.

Table 2

Hyperfine parameters extracted from MoS spectra of sample CuFe2-SQ with

edged particles

Sample Site Hhf

(T)

2e(mm/s)

dFe

(mm/s)

Relative

area (%)

CuFe2-SC A 47.9 0.00 0.24 46

B 50.7 �0.37 0.36 54

I. Nedkov et al. / Applied Surface Science 253 (2006) 2589–2596 2593

Fig. 4. Evolution of Mossbauer spectra of CuFe2O4 nanoparticles with size 6 � 2 nm—sample CuFe1-Sp at (a) room temperature and (b) 80 K.

This effect has been discussed [1] and it was shown that in

the case of spherical magnetite particles the Laplace pressure

leads to changes in the tetrahedral and octahedral cavity

volumes which creates different filling in comparison to that of

the bulk structure. The increase of the A-sublattice radius

caused by Laplace pressure results in a lower crystal symmetry

and decreased crystal energy.

AVSM model 8810 ADE Techn. Inc. was used to study the

magnetic properties of samples 1-Sp and 2-SC at 4.2 K and

magnetic field up to 3 T. The results are presented in Table 3.

The saturation magnetization (Ms) for sample CuFe2-SC

(larger particles) is slightly lower in comparison to that of bulk

copper ferrospinel, which could be explained by the nanosized

state. However, for spherical particles (CuFe1-Sp) Ms is higher

than that of the bulk material and this is not typical for the

nanosized state [2]. The cation distribution in the two

sublattices can be expressed by Boltzmann equation:

x(1 � x)/(1 � x)2 = e�E/kT, where x is the number of Cu2+

cations passing from octahedral to tetrahedral sites. The cation

re-distribution in the sublattices in spherical nanosized

particles is accompanied by changes in the magnetic moment,

as it could be expected from the theory of the non-compensated

antiferromagnetism. To interpret the magnetic properties of

both types of samples, we considered frozen magnetic

moments and ignored the temperature influence. Our

considerations were based mainly on the crystalline field

energy, E.

Fig. 5. Evolution of Mossbauer spectra of CuFe2O4 nanoparticles with size

6 � 2 nm—sample CuFe1-Sp at 4.2 K in external magnetic field 5 T.

Although both types of samples are single-phase and have

the same stoichiometry, the XRD pattern of the larger particles

showed the presence of co-operative Jahn–Teller effect which

was obvious for the spherical particles with very small size [11]

where the XPS data proved tetrahedral deviation in the surface

layer. On the other hand, a comparison between the XPS and

MoS data gives us reason to claim that the crystal surface and

the core exhibit different distortion. The experimental data

showed that the two types of particles have different magnetic

properties defined by the difference in the magnetocrystalline

structure of the shell and the core.

The JT effect exists in crystals containing transitional metal

ions, whose ground orbital state is degenerated so that a

spontaneous degeneration of the orbits of neighboring ions can

arise. It leads to lowering of the crystal field symmetry and a

minimum of system energy. In the case of spherical crystal

symmetry, the state of ions with configuration d9(Cu2+) is a

transitional state between d10 and d7 (low spin in case of a

strong crystal field). For octahedral coordination the external

electron belongs to configurations d6ed

1g , and can occupy one of

the orbits d2x�d2

y , d2z . Orbits de and dg are exchanged when the

cations are in tetrahedral coordination. In both cases the result

is tetrahedral degeneration, lower crystal symmetry and

different crystal cell parameters. For bulk copper ferrospinel

with octahedral JT distortion c/a > 1, while for CuCr2O4 with

tetrahedral distortion c/a < 1 and the changed crystalline

anisotropy leads to different magnetic properties [3].

For copper ferrospinel at room temperature, the value of K1

is negative (K1 = �0.6.105 J/m3) and the easy magnetization

axis coincides with the spatial diagonal h0 1 0i of the

elementary cube. The spin–orbital interactions in a Cu–ferrite

with tetragonal crystal lattice distortion due to co-operative

Jahn–Teller effect predominate in the appearance of magneto-

crystalline anisotropy. The best interpretation of the energy

spectrum of such systems is offered by the single-ion theory,

whereby the physical nature of the uniaxial anisotropy can be

represented by the Hamiltonian of the spin–orbital interactions:

H ¼ Vex þ VLS ¼ 2mBHexSþ lLS (1)

In a low-symmetry field caused by the Jahn–Teller effect the

orbital moment, L, and the spin moment, S, are not zero. In such

I. Nedkov et al. / Applied Surface Science 253 (2006) 2589–25962594

Table 3

Saturation magnetization (Ms) per gram of samples and effective anisotropy (Hc) calculated from M(H) curve of the samples measured at 4.2 K

Sample Particle’s dimensions

(L/D nm or D, nm)

Ms (emu/g) Hc (mT) Keff (erg/cm3) (for bulk tetragonal

CuFe2O4, K1 = �0.6 � 105 J/m3)

Edged particles SC 1300 � 20/200 � 20 32 39 0.62 � 105 J/m3

Spherical particles 6 + 2 35.6 41 0.72 � 105 J/m3

a case, the potential energy of the electrons in the crystalline

field, VLS plays an important role in the energy levels splitting

and the relatively small distance between the cations depends

strongly on the orientation of the exchange interaction field,

Hex. In favorable conditions this may cause strong magneto-

crystalline anisotropy. One should expect this effect to be

substantial in the edged (SC) particles, where the JT effect is

clearly expressed. The data yielded by the XPS and MoS

analyses for spherical nanosized particles led us to the assump-

tion for the existence of a Jahn–Teller effect gradient—from the

B-sublattice on the surface to a compensation of the tetragonal

distortion in the two sublattices in the core (Fig. 6). Inasmuch as

the atoms’ energy spectrum in the crystalline field depends on

the Hex orientation, which determines the orientation of the spin

magnetic moments with respect to the crystalline axes x, y and z

in the complicated crystalline structure picture, as revealed by

the structural studies, we may assume the existence in the

nanoparticle of an effective exchange interaction field Heff.

Fig. 6. Canting angle and hyperfine field distribution in both sublattices –

tetrahedral (A) and octahedral (B) of CuFe2O4 nanostructured spherical particle

– sample CuFe1-Sp with diameter 6 � 2 nm.

The spin–orbital interaction, Eq. (1) is one of the main

reasons for the appearance of magneto-crystalline anisotropy in

the oxide crystal. In ferroxide materials, the crystal’s total

magnetic moment has a spin origin and its energy depends on

magnetization vector orientation with respect to the crystal-

lographic axes and is determined by the spin–orbital interac-

tion, since the ions’ orbital magnetic moment is directly related

to the crystal lattice. If one assumes that the atomic magnetic

moments are localized in the crystal lattice sites and are

oriented in parallel, the magnetic dipole interaction contribu-

tion will depend on the orientation of the total magnetic

moment M with respect to the crystallographic axes. The

solution of Landau–Lifshitz equation for Larmor-type motion

for a volume with magnetization will yield:

1

g

@M

@t¼ ½MHeff � (2)

From phenomenological considerations, the energy of the

magneto-crystal anisotropy as a function of the cosines (a) of

the magnetization vector with respect to the crystal axes is

Ea ¼P

nKna2n, where Kn is the constant of crystal anisotropy,

to be determined experimentally; for a cubic crystal (anisotropy

constant K1) with a magnetic field applied at an angle u with

respect to the easy magnetization axis h0 1 0i one will have

a1 = 0, a2 = cos u, a3 = sin u. The energy of magneto-crystal-

line anisotropy of such a particle is described by:

Emc ¼ K1 sin2 u cos u ¼ K1

4sin2 2u (3)

On the other hand, the shape of the edged (SC) particles can

be approximated by an ellipsoid (see Fig. 1). For such a particle

one should expect anisotropic behavior under the application of

an external magnetic field parallel to the c axis for K1 > 0, and

perpendicular to it for K1 < 0. Maxwell’s theory stipulates that

uncompensated charges will arise on the poles of such a

particle, which will lead to magnetic energy dissipation; i.e.,

shape anisotropy will exist, with the energy density depending

on DN = N? � Nk; the shape anisotropy energy can then be

written as:

Esh ¼K1

4sin2 2u þ 0:5m0ðN ? � NkÞM2

s sin2 u

¼ K1

4sin2 2u þ KshM2

s sin 2u (4)

Shape anisotropy’s contribution is present in edged particles

and Eq. (4) describes in practice its energy of anisotropy. In

spherical particles the contribution of the shape anisotropy is

low, so that these particles’ magnetocrystalline anisotropy is

described by Eq. (3). The fact that in the core of a spherical

I. Nedkov et al. / Applied Surface Science 253 (2006) 2589–2596 2595

particle one sees a transition from a tetragonal distortion in

octahedral surrounding to a distortion in both sublattices can

hardly be considered as a two-phase magnetic state of the

system; one should rather speak of sub-structures in the

particle’s core with changed crystal symmetry with Eq. (3)

describing the energy of the entire system, but KSC1 6¼KSp

1 .

In nanosized particles there exists another type of anisotropy

that has to do with surface state of the magnetic moments. The

energy of interaction between two magnetic ions in a crystal

(magnetic moment m) is a function of the angle u between the

vector of spontaneous magnetization and the line connecting

the two ions and depends on the distance, r; assuming magnetic

dipole interaction, this energy is (�3m2/r2). For ions on the

surface, Neel [23] introduced a pseudo-dipole term, l, which,

besides the spin–orbital interaction, accounts for the interaction

between two adjacent ions, so that he arrived at Ea = ((�3m2/

r3) + l)(cos2 u � (1/3)). In a cubic crystal, the value of cos2 u

averaged by summation over close neighbors is 1/3, which

means that the term (�3m2/r2) does not exist in the expression

for the average value of the anisotropy energy of the core; this

condition is violated when the ion is located on the surface. In

long-range order, this interaction can be considered as

demagnetizing.

The pseudo-dipole interaction between surface ions leads to

the appearance of energy of surface anisotropy, which can be

expressed as:

Esurf ¼ Ksurf cos2 u (5)

where Ksurf is the constant of surface anisotropy density and u is

the angle between easy magnetization axis and the normal to

the surface. This type of anisotropy should be present in both

types of particles.

From a magnetic point of view, the surface of a spherical

nanoparticle is formed by ions with uncompensated magnetic

moments; a surface layer thus exists, which, in contrast with the

antiferromagnetic structure in the core, has an unordered spin-

magnetic structure [23]. The MoS and XPS analyses data give

us grounds to maintain that, besides the unordered magnetic

structure caused by the ‘‘boundary effect’’, this surface layer

exhibits also a magnetocrystalline structure different from that

in the particle’s core. In the spherical nanosized particles

studied here, the relative volume of this layer with respect to the

total volume may be substantial, which may bring about

magnetic exchange interactions [24]. The energy of such

exchange anisotropy between the spin-unordered surface and

the ordered core is usually described as:

Eex ¼ �Kex cos u (6)

Bearing in mind the above considerations, it is clear that in

both types of nanosized particles studied the experimentally

obtained anisotropy coefficients (Table 3) represent compre-

hensive quantities that reflect the specificity of a number of

different magnetic interactions where the direction (u) of the

magnetization vector with respect to an external magnetic field

may be different; one should, therefore, refer to an effective

coefficient of anisotropy where the contribution of the different

magnetic interactions is different in the edged and in the

spherical nanosized particles.

In edged particles;Keff ¼ KSC1 þ Ksh þ Ksurf

In spherical particles;Keff ¼ KSp1 þ Kex þ Ksurf

Our earlier studies of magnetite (a model system for

ferrospinels) by means of low-energy MoS demonstrated [24]

that the thickness of the layer where structural changes and an

unordered magnetic structure are possible is in the order of

3 nm. In the case of a spherical particle with maximal diameter

up to 8 nm, the magnetically ordered crystal lattice occupies

about 25% of the total volume, while for the larger edged

particle this value is approximately 97%. Thus, the larger

deviations in Keff for the smaller particles are due to the larger

relative contribution of the surface and exchange anisotropy.

4. Conclusions

The MoS and XPS studies showed that, in nanosized

spherical particles containing Jahn–Teller ions, the tendency

for a lower particle energy leads to the lower symmetry

propagating in both ferrospinel sublattice. This results in a

cation distribution that is not typical for edged particles and for

the bulk single crystal. We suggest that the changes occur

gradually—from the surface, where one observes tetragonal

distortion in octahedral sites only, to the core, where distortion

also exists in tetrahedral sites. This reflects on the spin–orbital

interactions in the crystal cell, respectively, on the magneto-

crystalline anisotropy and on the formation of the system’s total

magnetic moment, which for a spherical particle may prove to

be different from that of edged particles or bulk crystal, the

identical stoichiometry notwithstanding.

The surface XPS analysis did not reveal the presence of

single-valence copper; i.e., no reduction of copper and oxidation

of iron have taken place, as is typical for the surface layer of

magnetite and some other ferrospinels after heat treatment.

With nanosized particles one deals with the interplay of

several factors affecting the magnetocrystalline anisotropy, the

latter thus having a complex nature; the value of the anisotropy

coefficient, as an experimentally obtained parameter, must,

therefore, be considered an effective value reflecting the

influence of the individual factors on the magnetic anisotropy.

Acknowledgments

This work has been supported by Bulgarian National Found

Project HT-1/01/03, F.W.O., Flanders, Belgium and CNRS,

France.

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