The dipole moment of the spin density as a local indicator for phase transitions

Abstract

The intra-atomic magnetic dipole moment - frequently called 〈Tz〉 term - plays an important role in the determination of spin magnetic moments by x-ray absorption spectroscopy for systems with nonspherical spin density distributions. In this work, we present the dipole moment as a sensitive monitor to changes in the electronic structure in the vicinity of a phase transiton. In particular, we studied the dipole moment at the Fe(2+) and Fe(3+) sites of magnetite as an indicator for the Verwey transition by a combination of x-ray magnetic circular dichroism and density functional theory. Our experimental results prove that there exists a local change in the electronic structure at temperatures above the Verwey transition correlated to the known spin reorientation. Furthermore, it is shown that measurement of the dipole moment is a powerful tool to observe this transition in small magnetite nanoparticles for which it is usually screened by blocking effects in classical magnetometry.

Full text

The dipole moment of the spin density as
a local indicator for phase transitions
D. Schmitz
1
, C. Schmitz-Antoniak
2
*, A. Warland
2
, M. Darbandi
2
{, S. Haldar
3
, S. Bhandary
3
, O. Eriksson
3
,
B. Sanyal
3
& H. Wende
2
1
Helmholtz-Zentrum Berlin fu
¨
r Materialien und Energie, Albert-Einstein-Straße 15, D-12489 Berlin, Germany,
2
Fakulta
¨
tfu
¨
r Physik
and Center for Nanointegration Duisburg-Essen (CENIDE), Universita
¨
t Duisburg-Essen, Lotharstr. 1, D-47048 Duisburg, Germany,
3
Division of Materials Theory, Department of Physics and Astronomy, Uppsala University, Box-516, SE 75120 Uppsala, Sweden.
The intra-atomic magnetic dipole moment - frequently called Æ
T
z
æ term - plays an important role in the
determination of spin magnetic moments by x-ray absorption spectroscopy for systems with nonspherical
spin density distributions. In this work, we present the dipole moment as a sensitive monitor to changes in
the electronic structure in the vicinity of a phase transiton. In particular, we studied the dipole moment at
the Fe
21
and Fe
31
sites of magnetite as an indicator for the Verwey transition by a combination of x-ray
magnetic circular dichroism and density functional theory. Our experimental results prove that there exists
a local change in the electronic structure at temperatures above the Verwey transition correlated to the
known spin reorientation. Furthermore, it is shown that measurement of the dipole moment is a powerful
tool to observe this transition in small magnetite nanoparticles for which it is usually screened by blocking
effects in classical magnetometry.
X
-ray absorption near edge spectroscopy (XANES) and its associated magnetic circular dichroism (XMCD)
is an experimental technique that allows for the determinination of magnetic properties element-specif-
ically. Today, it is widely spread as one main advantage of XMCD that the orbital moment and the spin
moment can be determined independently from each other using sum rules
1,2
which have been experimentally
confirmed for the 3d transition metals
3
. The intra-atomic magnetic dipole moment of the 3d spin-density
distribution is one term in the XMCD sum rule for the spin moment. More precisely, with the spin sum rule
the effective spin moment (m
S,eff
), which is the sum of the intrinsic spin moment (22 ÆS
z
æ m
B
) and the dipole
moment (7 ÆT
z
æ m
B
) of the spin density distribution, can be determined from the integrals of the XMCD spectrum
and the isotropic absorption spectrum
2
. Since the sum rule contains two terms, the contributions of the intrinsic
spin moment and the magnetic dipole moment cannot be readily determined. The latter is known to be negligibly
small for cubic symmetry only
2
. Limitations of the spin sum rule and the importance of the magnetic dipole term
in noncubic environments such as surfaces and interfaces were studied with electronic band structure calculations
for iron, cobalt and nickel
4
. The seperate determination of spin and magnetic dipole moments with an angle
averaging spin sum rule was demonstrated theoretically
5
and experimentally
6
for a highly anisotropic 3d trans-
ition metal system where the charge and spin densities were not spherically symmetric. The magnetic dipole
moments of single cobalt atoms and nanoparticles (NPs) were quantified by combining the effective spin moment
determined from measured XMCD spectra using the spin sum rule with the intrinsic spin moment calculated in
the local spin density approximation
7
. According to ab initio studies, the ÆT
z
æ term, in general, cannot be neglected
in the spin sum rule for systems with low dimensionalities like monolayers and monatomic wires
8
and clusters
9
.
Anisotropies of the spin density distributions causing large magnetic dipole moments were also investigated in
molecules on surfaces like Cu-phthalocyanine on Ag(001)
10
and Fe-octaethylporphyrin on Cu(001)
11
.
For many examples, the measured contribution of the magnetic dipole moment can be regarded as a dis-
advantage of the XMCD impeding the extraction of the spin moment in a straight-forward way. In this work, we
employ it as a monitor for changes in the electronic structure as it is caused by phase transitions. In order to show
the potential of the XMCD technique, we chose magnetite (Fe
3
O
4
) as an example because in magnetite the average
Fe dipole moment in the low-temperature phase according to our electronic structure calculations is sufficiently
large to be reliably quantified with XMCD. In addition, for magnetite XMCD is also site-selective giving the
possibility to distinguish between Fe ions at different lattice sites.
Magnetite crystallizes in the inverse spinel structure in a cubic (isometric) crystal system, with the oxide anions
arranged in a cubic close-packed lattice while the Fe cations are located on octahedral and tetrahedral lattice sites
OPEN
SUBJECT AREAS:
NANOPARTICLES
MAGNETIC PROPERTIES AND
MATERIALS
Received
21 March 2014
Accepted
2 July 2014
Published
21 July 2014
Correspondence and
requests for materials
should be addressed to
D.S. (schmitz@
helmholtz-berlin.de)
* Current address:
Peter Gru
¨
nberg Institut
(PGI-6),
Forschungszentrum
Ju
¨
lich, 52425 Ju
¨
lich,
Germany.
{ Current address:
Department of Physics
and Astronomy,
Vanderbilt University,
Station B #351807,
2301 Vanderbilt
Place, Nashville, TN
37235-1807, USA.
SCIENTIFIC REPORTS | 4 : 5760 | DOI: 10.1038/srep05760 1

in between. In particular, Fe
31
occupies the tetrahedral sites (also
denoted A sites in the literature) and half of the octahedral sites (B
sites), whereas the Fe
21
ions are located at the remaining octahedral
sites. For a schematic diagram of the monoclinic P2/c unit cell of
magnetite containing 56 atoms we refer to Fig. 1 in Ref. [17]. The
strongest interaction is the superexchange between Fe
31
on octahed-
ral and Fe
31
on tetrahedral sites which is negative resulting in an
antiparallel orientation of spins of different sublattices.
At low temperatures, magnetite undergoes a phase transition that
was discovered in 1939 by Verwey as a rapid change of the electronic
conductivity at a certain temperature and was named after him as the
Verwey transition (VT). In the original article
12
it was described as ‘‘a
sudden increase of the resistance at approximately 117 K by a factor
of the order 100’’. The resistance of a magnetite sample was com-
pared with the one of a sample which was further oxidized and
described as ‘‘samples containing an excess of Fe
2
O
3
show a much
smaller jump in the curve at about 120 K or even merely a change in
the temperature coefficient’’
12
. Many years later it was found by heat
capacity studies
13
that with increasing deviation d in Fe
32d
O
4
from
ideal magnetite stoichiometry the VT changes from first to second
order and that the VT temperature decreases linearly with d.
The refined determination of the structural changes at the VT
based on diffraction measurements
14,15
initiated several theoretical
investigations with modern methods
16–18
. The most significant struc-
tural change connected to the VT was explained in the work of H.-T.
Jeng et al.
17
. They reported that in the low-temperature monoclinic
unit cell, a charge and orbital ordering is related to one of the Fe
31
ions on an octahedral lattice site being pulled inwards the cube diag-
onal of the sub-unit cell yielding a lower energy of the system due to
intersite Coulomb attraction with t
2g
orbitals of three neighboring
Fe
21
ions.
With resonant x-ray scattering the changes in the structural,
charge and orbital order were studied in dependence of the temper-
ature across the VT using certain diffraction peaks to indicate struc-
tural, charge or orbital order
19–21
. The interpretation of the diffraction
peaks was discussed and became a controversy.
In a structural study
21
using high-resolution synchrotron x-ray
powder diffraction data of magnetite the charge disproportion found
by J. P. Wright et al.
15
was confirmed between the B1 and B2 sites but
not between the B3 and B4 sites (see Fig. 1). The picture of a wide
distribution of different local environments around the octahedral Fe
ions, caused by the condensation of several phonon modes, was
favored over any bimodal charge disproportion on the octahedral
sites
22
.
Since diffraction studies of magnetite are hampered by different
crystallite orientations and microtwinning, the full low-temperature
superstructure has been quite recently determined with x-ray diffrac-
tion from an almost single-domain grain of only 40 mm size. There it
has also been found that localized electrons are distributed over
linear units of three Fe ions on octahedral sites which leads to the
observed shortening of the two Fe-Fe distances. These three-Fe-units
were viewed as quasiparticles and named ‘‘trimerons’’
23
. More than
30 years earlier the fluctuations of what nowadays is called trimerons
were observed above the VT temperature with critical diffuse neut-
ron scattering
24,25
and interpreted using the Yamada model based on
electron-phonon coupling
24
and later using a pseudospin-phonon
theory
25
.
Below the VT temperature t
2g
orbital order on octahedral Fe
21
sites has been directly found with resonant soft x-ray diffraction
(RSXD)
26
. For this method it is important to take into account that
there is a layer at the surface of single crystals which contributes to
the absorption but not to the diffraction of the soft x-rays
27
.By
studying the azimuthal dependence of the diffracted intensity it
has been shown that the distortion of the 3d orbitals towards mono-
clinic symmetry is by far larger than that of the lattice
28
. Ultrafast
melting of the charge-orbital order leading to the formation of a
transient phase, which had not been observed in equilibrium, was
observed with time-resolved RSXD with a free-electron laser
29
. Very
recently it was investigated on the ps time scale how trimerons
become mobile across the VT
30
.
In magnetite NPs the VT has already been experimentally
observed with different methods, e.g., magnetization measurements
of a non-diluted system containing strong dipolar interparticle inter-
actions
31
and magnetoresistance measurements of tunneling junc-
tions of stacked monolayers of magnetite NPs of 5.5 nm average
diameter for which a VT temperature of 96 K has been determined
32
.
In these studies it has been found that the VT temperature signifi-
cantly decreases when decreasing the size of the NPs to a small
fraction
31
but that it is not very sensitive to small changes of the order
of 10% of the particle size
32
.
However, one may note that in magnetometry, the VT can only
hardly be distinguished from a spin reorientation transition
that occurs in magnetite at slightly higher temperatures (T
SR
<
132 K
33
). The spin reorientation is characterized by a vanishing mag-
netocrystalline anisotropy constant K
1
, which is negative at room
temperature. With decreasing temperature it decreases, acquiring a
minimum at a temperature of about 250 K
34
. With further decreasing
temperature, it increases and becomes positive at T
SR
. Referring to
the vanishing value of K
1
, this temperature is also called isotropy
point in literature. For single crystalline samples, the different trans-
ition temperatures were measured by recording the saturation iso-
thermal remanent magnetization along a principal axis of the single
crystal
33
. For the case of an arbitrary orientation of the magnetic field
with respect to the principal crystallographic axes, the effects of T
SR
and the VT on the remanence could not be clearly separated. For
polycrystalline samples it seems to be impossible to distinguish
between the two transitions. As pointed out by R
ˇ
eznı
´
c
ˇ
ek et al.
34
, there
exists a correlation between the spin reorientation and the VT. In this
work, the authors connected the contribution to K
1
which leads to
an anomalous increasing behavior with decreasing temperature
between 250 K and T
SR
to a local charge and orbital ordering that
becomes long-range and stable for temperatures below the VT.
The main purpose of the present paper is to study the magnetic
moments, in particular the magnetic dipole moment of Fe as a func-
tion of temperature across the phase transitions in magnetite NPs
Figure 1
|
Part of the magnetite unit cell in the monoclinic crystal
structure. Oxygen atoms are drawn as small red spheres. Iron ions on
different octahedral sites are drawn as large grey (B1), brown (B2), green
(B3) and blue spheres (B4). The linear three-site structure B3–B1–B3
forms a trimeron with reduced B1–B3 bond lengths. The axes of the global
coordinate system are also shown.
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SCIENTIFIC REPORTS | 4 : 5760 | DOI: 10.1038/srep05760 2

with a diameter of 6 nm and a 200 nm thick polycrystalline magnet-
ite film which serves as a reference. For this purpose a combination of
experimental and theoretical methods, i.e. XANES, XMCD, vibrating
sample magnetometry (VSM) and electronic structure calculations
based on density functional theory, has been used. As it will be
described in detail below, a transition of the dipole moment of the
Fe 3d spin-density distribution was experimentally found well above
the VT and theoretically explained.
Results
Density functional theory. Calculations of the electronic structure
were performed based on density functional theory on cubic
(high temperature) and monoclinic (low temperature) structures
of magnetite. Details of the calculations are described in the
methods section. We have considered a monoclinic P2/c structure
with 56 atoms per unit cell obtained by using high-resolution
neutron and x-ray powder-diffraction data by Wright et al.
14,15
.A
part of the monoclinic unit cell with its four inequivalent octahedral
lattice sites, labelled B1–B4, is shown in Fig. 1. The resulting magnetic
moments are shown in table I. The Fe sites are named as shown in
Fig. 1 and like in Ref. [17]. Our calculated values of ÆT
z
æ for the cubic
structure are negligible (,10
25
m
B
) whereas for the monoclinic
structure, they are quite large, especially for the octahedral B sites.
It is clearly observed from the calculations that the Fe
21
ion has a
larger contribution than Fe
31
(see Table I, where we compile the
calculated values of 7 ÆT
z
æ). At the B4 site, the contribution is
as large as 21.44 m
B
with an anti-parallel alignment to the spin
moment. It is only partly compensated by the second largest
contribution of 0.72 m
B
at the B1 site with a parallel alignment to
the spin moment. Therefore, these octahedral sites substantially
modify the effective spin moments, as detected in the XMCD
measurements.
We also calculated the Fe orbital magnetic moments for the mono-
clinic phase in the a, b and c directions as defined in Fig. 1. The
sizeable orbital moments can be as large as 0.035 m
B
along the c
direction for Fe ions on B4 sites and 0.031 m
B
along the b direction
for Fe ions on B1 sites. For all other sites, the orbital moments are
almost isotropic with absolute values of 0.015 m
B
to 0.019 m
B
. The
signs of the orbital moments follow the spin moments. To further
analyze the large values of ÆT
z
æ, we show in Fig. 2, the m
l
projected
density of states (DOS) for different octahedral sites of the mono-
clinic phase. The reason for the high ÆT
z
æ value is the full occupancy
of the d
x
2
{y
2
orbital in the spin down channel of the Fe
21
ion on the
B4 site. For the Fe
31
ion, this orbital is unoccupied. Similarly, a high
value (half of that of the B4 site, and with parallel alignment to the
spin-moment) is observed for the Fe
21
ion on the B1 site. The large
value also for this site is coupled to the fact that the d
xz
and d
yz
orbitals are occupied, although only partially. Again, for the Fe
31
ion, both these orbitals are unoccupied, and do not contribute to ÆT
z
æ.
All of our calculated results can be understood from the ÆT
z
æ
matrix elements explicitly provided in the paper by Crocombette
et al.
35
. For Fe
31
, the spin-up channel is completely filled with almost
no occupancy in the spin-down channel and therefore, much smaller
ÆT
z
æ contributions are observed. Note that XANES and XMCD are
sensitive to the unoccupied DOS so that in these experiments the
magnetic moments due to the lack of unoccupied states instead of the
existence of occupied states is probed. Also note that even for Fe
31
in
the monoclinic phase due to the low symmetry structure compared
to the cubic one, we have higher contribution to ÆT
z
æ compared to the
cubic one. Obviously, there is no noticeable distinction between Fe
21
and Fe
31
in the cubic phase as the charge ordering is non-existent in
the metallic phase.
X-ray absorption spectroscopy . The XANES and XMCD spectra are
defined as the sum and difference of two spectra obtained with
opposite helicities of the incident circularly polarized soft x-ray
radiation, respectively. Measured XANES spectra and corresponding
XMCD spectra of the NPs and the film sample are shown in Fig. 3 and
Fig. 4, respectively, at the Fe L
2,3
absorption edges for various
temperatures. The temperature and magnetic field histories of both
samples were identical, i.e. both samples were field-cooled to 4 K in a
magnetic field of 0.5 T and subsequently heated stepwise to and
measured at the temperatures indicated by the data points in Fig. 5
in a magnetic field of 3 T. The NPs offer significant changes of the
XANES intensity and the XMCD intensity between 50 K and 100 K
and the film sample between 150 K and 175 K. For both samples the
spectra are devided into two groups: Spectra for temperatures below
the change are shown as blue lines, and above as red lines.
XMCD has the advantage that spin and orbital moments can be
determined element-specifica lly by use of sum rules
1,2
. For the deter-
Table I
|
Charge, spin and magnetic dipole moments for 3d orbitals
of Fe atoms at different sites in the monoclinic unit cell. Also, effec-
tive moments (m
S,eff
522 ÆS
z
æ m
B
1 7 ÆT
z
æ m
B
) are provided. The Fe
sites are named as in Ref. [17]
Fe site d-charge 22 ÆS
z
æ 7 ÆT
z
æ m
S,eff
(m
B
)
A1 5.91 23.98 20.015 23.995
A2 5.91 23.98 0.025 23.955
B1 6.08 3.67 0.72 4.39
B2 5.82 4.14 0.043 4.183
B3 5.85 4.08 0.027 4.107
B4 6.1 3.64 21.44 2.20
-2
-1
0
1
2
d
xy
d
yz
d
z
2
d
xz
d
x
2
-y
2
-2
-1
0
1
2
-2
-1
0
1
2
DOS (States/eV)
-2
-1
0
1
2
-8 -6
-4
-2 0 2
4
E - E
F
(eV)
-2
-1
0
1
2
(A-tetrahedral)
(B3-Octahedral, Fe
3+
)
(B4-Octahedral, Fe
2+
)
(B1-Octahedral, Fe
2+
)
(B2-Octahedral, Fe
3+
)
d
x
2
-y
2
d
xz
+d
yz
Figure 2
|
Spin-resolved m
l
projected density of states for the monoclinic
structure. DOS at the tetrahedral A site along with four different
octahedral B sites are shown. The Fe sites are named as shown in Fig. 1 and
like in Ref. [17]. The specific orbitals responsible for the large contribution
in the ÆT
z
æ part are indicated by arrows. The energies in the x-axes are
plotted with respect to the Fermi level E
F
.
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SCIENTIFIC REPORTS | 4 : 5760 | DOI: 10.1038/srep05760 3

mination of the magnetic moments via sum rules, we normalized the
spectra in the usual way, i.e. first subtracted a constant background,
then normalized at a photon energy above the absorption edge and
finally subtracted a step like function. Please note that the spectra
have been measured from 680 eV to 780 eV in order to be able to
perform a reliable normalization. In Fig. 3 and Fig. 4 only the phys-
ically relevant spectral range from 705 eV to 730 eV has been shown
for the sake of clarity. The effective spin moment (m
S,eff
522 ÆS
z
æ m
B
1 7 ÆT
z
æ m
B
) is defined as the intrinsic spin moment (22 ÆS
z
æ m
B
) plus
the magnetic dipole moment (7 ÆT
z
æ m
B
) of the spin-density distri-
bution
2
where z is defined by the magnetization direction. Its nor-
malized values determined from the measured XMCD spectra as a
function of temperature are shown for the NPs in Fig. 5a and for the
film in Fig. 5b. The effective Fe spin moment of the NPs increases
between 50 K and 100 K by about 7% relative to the value at 100 K
and for the film between 150 K and 175 K by 16% relative to the
value at 175 K. The magnetic moments of the NPs and the film
sample were also measured with VSM and are shown for comparison
as gray lines in Fig. 5a and Fig. 5b, respectively. Increases of the
magnetic moments with increasing temperatures were not observed
with VSM. This important result is due to the fact that the magnetic
dipole moment is observable with XMCD but not with VSM as
discussed in the following section.
Discussion
The electronic structure calculations show a strong change of the
magnetic dipole moment in magnetite when the structure of the
lattice changed from cubic to monoclinic. These changes are most
significant for the case of Fe
21
ions on octahedral lattice sites (B1, B4)
which is in agreement to the experimental XMCD data. The trans-
ition observed with XMCD (Fig. 3b and Fig. 4b) is accompanied by a
change of the asymmetry, which is defined as the XMCD spectrum
devided by the XANES spectrum after adequate background sub-
traction and normalization, at the photon energies 708.2 eV and
710 eV which mainly correspond to octahedral sites
38
. The transition
is also observed in the effective Fe spin moment (Fig. 5). However, in
general this transition could be assigned to a change in the spin
moment, the magnetic dipole moment or both at the same time.
To analyse which contribution to the effective spin moment is mainly
responsible for its significant change, the XMCD results are com-
pared to magnetometry data obtained with VSM. The ÆT
z
æ term only
shows up in XMCD measurements because they involve an excita-
tion from a core level to an unoccupied valence level. It does not show
up in magnetometry or other probes that detect the macroscopic
magnetization. For further discussion, see Ref. [39] and Ref. [40].
As shown in Fig. 5, there is no corresponding increase of the total
magnetic moment in the VSM data although this method certainly is
sufficiently sensitive to detect a change of about 7% for the NPs and
16% for the film. Therefore the transition observed with XMCD
cannot be due to a change in the intrinsic Fe spin moment but must
be due to a change in the second term of the sum rule for the effective
spin moment
2
, i.e. the ÆT
z
æ term which describes the dipole moment
of the Fe spin-density distribution. This conclusion is in accordance
with our theoretical treatment of the VT.
In Fig. 6, we compare the experimentally determined values of
the effective spin magnetic moment of the NPs with the theoretically
observed ones. The calculated 0 K effective moments, averaged
over all Fe sites have been multiplied with the Bloch law 1 2 0.96
(T/850K)
3/2
to obtain magnetic moments as a function of tempera-
ture. The theoretical moments are seen to drop at the known VT
Figure 3
|
Measured XANES (a) and corresponding XMCD spectra (b) of
the nanoparticles at the
L
2,3
absorption edges. The XANES spectra are
shown after subtracting a linear background and normalizing at a photon
energy in the post-edge region.
Figure 4
|
Measured XANES (a) and corresponding XMCD spectra (b) of
the film sample at the
L
2,3
absorption edges. The XANES spectra are
shown after subtracting a linear background and normalizing at a photon
energy in the post-edge region.
Figure 5
|
Normalized effective Fe spin moments as determined from the
measured XMCD spectra (solid symbols) and the magnetic moment
measured with VSM (thick gray line) as a function of temperature for the
magnetite NPs (a) and the film sample (b). Errors due to the
reproducibility of the evaluation of the XMCD spectra are within the
symbol size.
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SCIENTIFIC REPORTS | 4 : 5760 | DOI: 10.1038/srep05760 4

temperature for the bulk, where the crystal structure changes from
cubic to monoclinic. Again, it is the value of ÆT
z
æ that changes. The
relative change of the moments nicely agrees between theory and
experiment in particular for the NPs although ÆT
z
æ was calculated
along one crystallographic direction (the c direction as indicated in
Fig. 1) whereas in the measurement it was averaged over all direc-
tions due to the random orientation of the NPs. Nevertheless, it is
clear that a detailed measurement of ÆT
z
æ shows up in an unpreced-
ented way. This then becomes a valuable characterization tool, that
signals not only changes in the local geometry but also the local
electronic structure. It is likely that in general, detailed knowledge
of ÆT
z
æ is a valuable tool for understanding local changes in the
crystal- and electronic structure, not only for complex oxides but
also complex actinide and rare-earth compounds.
For 3d transition metals it has been pointed out by Sto¨hr and
Ko¨nig
5
that spin-orbit correction terms in the perturbative calcula-
tion of ÆT
a
æ can be neglected to a good approximation, leading to the
numerical relation ÆT
x
æ 1 ÆT
y
æ 1 ÆT
z
æ < 0 and to the possibility to
average out the magnetic dipole moment by magnetizing and mea-
suring the sample along the three cartesian axes (a 5 x, y, z). In the
case of our magnetite NPs the average magnetic dipole moment
would vanish in each single measurement geometry because the
NPs are randomly oriented like in a powder sample so that the
integration of the z component T
z
5 S
z
(1 2 3cos
2
h)/2
4
over the solid
angle yields zero. However, according to Ederer et al. the effects of
spin-orbit coupling are larger for low-dimensional systems
8
and in
particular the relation ÆT
x
æ 1 ÆT
y
æ 1 ÆT
z
æ < 0 is strongly violated for
monoatomic Fe, Co and Ni wires
41
. In addition, spin-orbit coupling
is larger for 3d oxides like magnetite than for 3d metals due to a
stronger localization of the 3d electrons. The large spin-orbit coup-
ling becomes noticeable by the large magnetic anisotropy constant in
the monoclinic phase of magnetite
34
. Moreover, it causes that the 3d
charge distribution is no longer independent from the spin dir-
ection
5
. Therefore the effect of spin-orbit coupling in the determina-
tion of the components ÆT
a
æ can no longer be neglected, i.e. the terms
containing the spin-flip operators do no longer vanish (see Appendix
B in Ref. [40]). For the experimental determination of the magnetic
dipole moment this means that at least a part of the magnetic dipole
moment is fixed to the magnetization direction but not to the crystal
lattice when the crystal (here each NP) is rotated relative to the
magnetic field. In this case it is not possible to separate the intrinsic
spin moment and the magnetic dipole moment solely by angle
dependent XMCD measurements because the precondition for aver-
aging out the magnetic dipole moment is no longer fulfilled. The
present results for magnetite NPs with 6 nm diameter demonstrate
that the magnetic dipole moment indeed is not averaged out in the
monoclinic low-temperature phase.
The small average Fe orbital moments of magnetite with values
below 0.03 6 0.02 m
B
as determined with XMCD experiments in Ref.
[37] do not exclude sizeable local spin-orbit effects because, accord-
ing to our calculations, the absolute values of the Fe orbital moments
vary strongly with the lattice site and their signs follow the spin
moments so that they partly cancel each other like the spin moments
and magnetic dipole moments do. In addition, the NPs will show
higher values of the Fe orbital moments due to surface effects. For the
200 nm thick polycrystalline magnetite film which served as a bulk
reference the VT was observed with VSM at 120 K as shown in the
Supplementary Information. With field-cooled/zero-field-cooled
measurements peaks in the blocking temperature distributions were
found at 120 K, which indicate the VT because their temperature
positions were independent of the magnitude of small magnetic
fields. Interestingly, at this temperature no transition was observed
with XMCD in accordance with the results in Ref. [37]. Surprisingly,
with XMCD a transition was detected well above the VT temper-
ature, i.e. between 150 K and 175 K. An error in the temperature
measurement can be excluded because with the used experimental
setup, i.e. the high-field endstation at beamline UE46-PGM1 at the
electron storage ring BESSY II, various transitions between 4 K and
300 K have been found at the known transition temperatures.
Therefore we believe that the enhanced absolute values of the mag-
netic dipole moments of the monoclinic structure persist above the
VT temperature until a temperature between 150 K and 175 K. This
is in agreement with the unusual temperature dependence of the
magnetocrystalline anisotropy that can be explained by a local charge
and orbital ordering well above the VT as suggested by R
ˇ
eznı
´
c
ˇ
ek
et al.
34
. In this sense, our work gives the first experimental evidence
for this interpretation of changes in the electronic structure above the
VT.
For the NPs, the spectral shapes in Fig. 3a and Fig. 3b indicate that
a charge transfer could be present to ligands which have not been
washed out completely after the synthesis
38
, or that the NPs are
further oxidized at the surface
42
. According to our experience both
processes, charge transfer to ligands and oxidation at the surface,
result in similar spectra
38
. However, the transition observed with
XMCD disppeared after storing the NPs 17 months in solution.
The transition was re-observed with XMCD after treating the NPs
in-situ with a Hydrogen plasma which resulted in perfect magnetite
composition according to the XANES and XMCD spectra. Therefore
we confidently associate the transition observed with XMCD with
magnetite.
Compared to the film sample, the transition temperature of
the NPs is reduced. A reduction of the VT temperature of NPs is
known from other experiments with different methods
26,27
and was
explained with spin canting and reduced thermal stability at the
surface
43
. In our NPs, spin canting has also been experimentally
observed as a finite slope at high magnetic fields in magnetization
hysteresis measurements with XMCD
44
and with Mo¨ßbauer spectro-
scopy as described in Ref. [45]. Thus, a reduced VT temperature
seems to be reasonable and can explain the reduced transition tem-
perature measured with XMCD. For the case of NPs, magnetometry
data may not be sufficient to detect changes in the magnetic prop-
erties caused by a phase transition, due to a strong influence of
blocking effects as discussed in the Supplementary Information
where we present VSM data of our NPs. This shows the importance
of measurements of the magnetic dipole moment as a sensitive
detector for local changes of the electronic structure.
One might ask whether it is reasonable to attribute the observed
transition of the magnetic dipole moment to quasiparticles called
trimerons. Trimerons consist of a linear unit of three Fe ions on
octrahedral sites in which a t
2g
minority-spin electron from the cent-
ral Fe
21
donor site is distributed over two adjecent Fe
31
acceptor
Figure 6
|
Normalized experimental effective Fe spin magnetic moments
of magnetite NPs (blue symbols) compared to theoretically obtained
results (dashed line).
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SCIENTIFIC REPORTS | 4 : 5760 | DOI: 10.1038/srep05760 5

sites
23
. This distribution tends to shorten the two corresponding
Fe
21
-Fe
31
distances which was recently observed with x-ray scatter-
ing
23
. Intuitively, one might expect that this donated t
2g
minority-
spin electron creates an anisotropy of the spin density distribution
which is accompanied by a magnetic dipole moment. According to
our electronic structure calculations the B1–B3 bond length is
shorter than other bond lenghts in the unit cell which corresponds
to B3–B1–B3 trimerons as shown in Fig. 1. The first potential donor
site, B1 Fe
21
, is part of a trimeron and its d
xz
and d
yz
orbitals exhibit a
magnetic dipole moment of 0.72 m
B
. Contrary, the second potential
donor site, B4 Fe
21
, which carries the largest magnetic dipole
moment of 21.44 m
B
in its d
x
2
{y
2
orbital, is not part of a trimeron.
Therefore it is not sufficient to assign the observed total magnetic
dipole moment just to trimerons.
Summary. In summary, magnetite NPs with 6 nm diameter and a
200 nm thick polycrystalline magnetite film which served as a bulk
reference were experimentally investigated with XANES, XMCD and
VSM and compared with electronic structure calculations based
on density functional theory. The measured spectra of the NPs
offered significant changes in the white line intensity and the
XMCD asymmetry between 50 K and 100 K. The film sample also
showed the transition in the XMCD asymmetry which appeared
between 150 K and 175 K. A sum rule analysis of the XMCD
spectra revealed that the transition observed with XMCD is due to
an increase of the effective Fe spin moment with increasing
temperature which was attributed to a change of the dipole
moment of the Fe 3d spin-density distribution. This conclusion
was verified and explained with electronic structure calculations
based on density functional theory. The large absolute value of the
negative magnetic dipole moment in the monoclinic structure is
caused by the full occupancy of the d
x
2
{y
2
orbital in the spin down
channel of the Fe
21
ion on the B4 site resulting in a negative magnetic
dipole moment, which is only partly compensated by the positive
magnetic dipole moment of partially occupied d
xz
and d
yz
orbitals of
the Fe
21
ion on the B1 site. Since the B1 site but not the B4 site is
part of a trimeron it is not meaningful to attribute the observed total
magnetic dipole moment just to trimerons. In the case of magnetite,
the experimental results evidence the occurence of local charge
and orbital ordering well above the VT as suggested in a recent
publication
34
. In general, detailed knowledge of the magnetic
dipole moment is a valuable tool for understanding local changes
in the crystal- and electronic structure, not only for complex oxides
but also complex actinide and rare-earth compounds.
Methods
Synthesis of nanoparticles. The NPs were prepared using a one-pot water-in-oil
microemulsion technique as described in detail elsewhere
45
. FeCl
2
and FeCl
3
were
used as precursors, IGEPAL
H
CO-520 (polyoxyethylene (5) nonylphenylether) as
stabilizing organic surfactant and ammonium hydroxide as catalyst. The water
droplets coated by the surfactant act as nanoreactors in which the magnetite NPs are
formed. The diameters of the NPs (6.3 6 0.9 nm) were determined with transmission
electron microscopy averaging over a few hundred NPs. The NPs were prepared at the
University of Duisburg-Essen, transported in liquid solution to Berlin, deposited onto
substrates and transferred into ultra-high vacuum for the measurements.
X-ray absorption. The XANES and XMCD measurements were performed in the
highfield endstation at beamline UE46-PGM1 with polarized synchrotron radiation
from an elliptical undulator in the electron storage ring BESSY II of the Helmholtz-
Zentrum Berlin. The total electron yield (TEY) method used in the present
measurements to monitor the absorption of the soft x-rays has an information depth
which is determined by the mean free path of the secondary photoelectrons of 1 nm
to 2 nm. Since the magnetite NPs have a mean radius of 3 nm, the element-specific
XANES and XMCD spectra represent the average over the whole particle with a
pronounced signal from the surface with respect to the core.
Magnetometry. The VSM measurements were performed with a Physical Properties
Measurement System from the company Quantum Design which has a sensitivity of
below 10
29
J/T and is operated in the laboratory cluster at the Helmholtz-Zentrum
Berlin.
Density functional theory . The generalized gradient approximation (GGA) as given
by Perdew, Burke and Ernzerhof
36
plus on-site Coulomb interaction U to include
strong electron correlation in the d-orbitals of Fe were used. The Coulomb parameter
U 5 4.5 eV
46
and the exchange parameter J 5 0.89 eV
47
were used for all Fe-d orbitals.
The projector augmented wave method
48,49
as implemented in plane-wave based
density functional code
VASP
50
has been used for the calculations. The plane wave
cutoff energy was set at 400 eV energy. 12 3 12 3 12 and 12 3 12 3 4 Monkhorst-
Pack k-point grids in the Brillouin zone were used for cubic and monoclinic structures
respectively. The geometries were optimized until the force on all each atom was
reduced to 0.1 eV/nm.
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Acknowledgments
Fruitful discussions with C. Schu
¨
ßler-Langeheine, F. M. F. de Groot and P. S. Miedema as
well as support by E. Weschke and B. Klemke are gratefully acknowledged. We thank HZB
for the allocation of synchrotron radiation beamtime. Funded by BMBF (05 ES3XBA/5) and
DFG (WE2623/3-1). We are grateful to NSC under Swedish National Infrastructure for
Computing (SNIC) and the PRACE-2IP project (FP7 RI-283 493) resource Abel
supercomputer based in Norway at University of Oslo for providing computing facility. B.S.
acknowledges VR Swedish Research Links programme and Carl Tryggers Stiftelse for
financial support. O.E. acknowledges support from the eSSENCE, VR, KAW foundation
and the ERC.
Author contributions
D.S. and C.S.A. performed the measurements, the data evaluation and wrote the
manuscript, A.W. performed the XMCD measurements, M.D. prepared the nanoparticles,
S.H. and S.B. performed the calculations, O.E. and B.S. wrote the theoretical part of the
manuscript, and H.W. wrote the manuscript.
Additional information
Supplementary information accompanies this paper at http://www.nature.com/
scientificreports
Competing financial interests: The authors declare no competing financial interests.
How to cite this article: Schmitz, D. et al. The dipole moment of the spin density as a local
indicator for phase transitions. Sci. Rep. 4, 5760; DOI:10.1038/srep05760 (2014).
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