Spin dynamics in Fe2O3-TeO2 glass: Experimental evidence for an amorphous oxide spin glass
Spin dynamics in Fe2O3-TeO2 glass: Experimental evidence
for an amorphous oxide spin glass
Author(s)Akamatsu, H; Tanaka, K; Fujita, K; Murai, S
CitationPHYSICAL REVIEW B (2006), 74(1)
RightCopyright 2006 American Physical Society
KURENAI : Kyoto University Research Information Repository
Spin dynamics in Fe2O3-TeO2glass: Experimental evidence for an amorphous oxide spin glass
Hirofumi Akamatsu, Katsuhisa Tanaka,* Koji Fujita, and Shunsuke Murai
Department of Material Chemistry, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan
?Received 9 May 2006; published 31 July 2006?
We have examined spin dynamics including magnetic aging and memory effects as well as critical slowing
down for 20Fe2O3·80TeO2?mol %? glass. Scaling analysis on critical slowing down reveals that the present
glass exhibits a critical behavior as observed in a prototype of spin glasses. Aging and memory effects peculiar
to spin glasses have been observed in the magnetically ordered phase of the present glass. These experimental
results strongly confirm that the 20Fe2O3·80TeO2glass is converted into a spin glass phase at a very low
temperature. It is thought that a disordered structure of the oxide glass gives rise to randomness and frustration
in the magnetic structure, leading to the spin glass phase transition.
DOI: 10.1103/PhysRevB.74.012411PACS number?s?: 75.50.Lk, 75.50.Kj, 78.55.Qr
Spin glass has attracted considerable attention since its
experimental discovery,1as many vigorous investigations
have been carried out to clarify its curious magnetic structure
and phase transition. The spin glass system is also a matter of
interest from the viewpoint of its analogy to many complex
systems, such as associative memory in the brain.2One of
the most interesting phenomena observed in spin glasses in-
volves spin dynamics. Magnetic moments are frozen in such
a way that the direction of each of the magnetic moments is
randomly oriented in a spin glass below its transition tem-
perature, and it takes an infinite time to reach a thermody-
namic equilibrium state. Experimental, theoretical, and nu-
merical approaches have been performed for clarification of
the spin dynamics peculiar to spin glass phase, such as criti-
cal slowing down and aging phenomena involving rejuvena-
tion and memory effects.3–18
Amorphous solids derived from ionic compounds, such as
oxide and fluoride glasses, bearing a large amount of mag-
netic ions can be categorized into a lattice in which a disor-
dered distribution of magnetic moments is dominant. There
are some reports as to magnetic properties of the oxide and
fluoride glasses. Temperature dependence of field-cooled and
zero-field-cooled susceptibilities indicates that these glasses
exhibit magnetic transitions like those of spin glasses or su-
perparamagnets. For instance, in 1975, just three years after
the discovery of a canonical spin glass of Au-Fe alloys, Ver-
helst et al. found that oxide glasses in a CoO-Al2O3-SiO2
system manifest spin glass-like transitions.19Assuming the
presence of magnetic clusters, they applied a simple super-
paramagnetic model to the magnetic transition observed in
temperature variation of zero-field-cooled susceptibility. For
this glass system, the relaxation process of remanent magne-
tization below the transition temperature was explored by
Rechenberg et al.20They measured the time dependence of
remanent magnetization after the external field was turned
off for a field-cooled sample and analyzed the experimental
results in terms of the superparamagneic model in which a
distribution of anisotropy energy for the superparamagnetic
clusters was assumed. Renard et al. examined temperature
dependence ofac susceptibility
Pb2MnFeF9glasses, and observed a cusp-like maximum of
susceptibility at 11.77 and 5.26 K, respectively.21They also
revealed that the cusp-like maximum was rounded by appli-
cation of an external dc field of 200 Oe for the PbMnFeF7
glass. This fact suggests that nonlinear susceptibility mani-
fests some change at the transition temperature of the
PbMnFeF7glass, although dependence of nonlinear suscep-
tibility on temperature at around the transition temperature
was not directly clarified. Sanchez et al. studied temperature
dependence of ac susceptibility and
trum for FeO-Al2O3-SiO2glasses and clarified that the varia-
tion of magnetic transition temperature with frequency of ac
field along with precession time of
described well in terms of empirical Vogel-Fulcher relation.22
A similar dependence of spin-freezing temperature on fre-
quency of ac field and
demonstrated for Li2O-B2O3-Fe2O3 glasses.23Recently,
Shaw et al. reported that Fe2O3-P2O5glasses show a spin
glass transition due to an antiferromagnetic superexchange
interaction among iron ions.24
Although there exist some reports on magnetic properties
of oxide and fluoride glasses as mentioned above, decisive
evidence has not been provided to ascertain that those oxide
and fluoride glasses truly exhibit a spin glass phase transi-
tion. Further experiments, in particular, those relevant to spin
dynamics, are necessary to comprehend the mechanism of
magnetic transition as well as magnetic structure of the
glasses derived from ionic compounds. In the present inves-
tigation, we have carried out experiments concerning the
spin dynamics for magnetically ordered phase of a glass in
Fe2O3-TeO2system. We have found that the glass manifests
memory effect below its magnetic transition temperature,
and that the critical slowing down is observed at around the
transition temperature as well. We demonstrate that the mag-
netically ordered phase of the present glass has many fea-
tures very similar to those observed for a prototype of spin
The glass with nominal composition of 20Fe2O3·80TeO2
?mol %? was prepared by using a conventional melt-
quenching method. Reagent grade Fe2O3and TeO2powders
were used as starting materials. After they were melted in a
platinum crucible at 1000°C for 1–2 h, the melt was poured
onto a stainless steel plate and cooled in air. X-ray diffraction
analysis with Cu K? radiation was carried out to confirm that
the sample was amorphous.
revealed that most of the Fe ions were present as Fe3+and
occupied octahedral sites in the glass.25It was ascertained by
57Fe Mössbauer spec-
57Fe nuclear spin was
57Fe nuclear precession time was
57Fe Mössbauer spectroscopy
PHYSICAL REVIEW B 74, 012411 ?2006?
©2006 The American Physical Society 012411-1
energy-dispersive x-ray spectroscopy that the actual compo-
sition of the glass was 22Fe2O3·78TeO2because of vapor-
ization of TeO2during the glass melting. For the sake of
simplification, however, the sample is hereafter referred to as
20Fe2O3·80TeO2glass. The glass sample was subjected to
measurements of magnetic properties such as dc and ac sus-
ceptibilities by using a superconducting quantum interfer-
ence device ?SQUID? magnetometer to clarify magnetic ag-
ing effects and critical slowing down. The experimental
protocols employed for clarification of spin dynamics are
described in detail in the following.
Figure 1 illustrates the temperature dependence of the real
part of ac susceptibility obtained by zero-field cooling for the
20Fe2O3·80TeO2glass. The amplitude of the ac magnetic
field was kept at 3 Oe and the ac frequency was varied from
0.1 to 1000 Hz. The spin-freezing temperature Tf?f?, depen-
dent on frequency f, can be defined as a temperature at
which the real part of ac susceptibility ???T,f? manifests a
maximum. In other words, the maximum relaxation time of
the system ? is equal to 1/f at Tf?f?. Although Tf?f? is often
taken as a temperature at which ???T,f? is 0.98 times the
equilibrium susceptibility,3it is reasonable to define Tf?f? as
a temperature of maximum susceptibility in the ???T,f?
curve for dynamical scaling analysis, as demonstrated
previously.3,4It is found in Fig. 1 that Tf?f? increases with an
increase in f; ? becomes longer as the temperature is low-
ered. According to the dynamic scaling hypothesis, provided
that this system exhibits a conventional critical slowing
down toward the transition temperature Tc, the variation of
maximum relaxation time with transition temperature is de-
? = ?0?Tf?f? − Tc
where z? is the dynamic exponent and ?0is a microscopic
relaxation time. In the present case, the best fitting of Eq. ?1?
to the experimental data yields z?=10, Tc=8.8 K, and ?0
=10−13s, as shown in the inset of Fig. 1. The values of z?
=10 and ?0=10−13s are in good agreement with those re-
ported for a prototype of spin glasses.4,26In particular, the
value of ?0=10−13s is identical in magnitude with those for
atomic spin glasses, for which ?0denotes a spin flip time of
individual magnetic moments belonging to atoms or ions. In
contrast, it has been observed that ?0?10−6s for interacting
magnetic nanoparticles systems or super spin glasses, for
which ?0corresponds to a time of reversal of superparamag-
netic magnetizations.3The results of this analysis imply that
a transition takes place from paramagnetic phase to atomic
spin glass phase in the present oxide glass of the
In order to discuss magnetic aging effects in the magneti-
cally ordered phase of 20Fe2O3·80TeO2glass, the tempera-
ture dependence of dc susceptibility ??T? was inspected by
utilizing a protocol of zero-field cooling memory experimen-
tation proposed by Mathieu et al.6In this protocol, ??T? is
measured on heating after zero-field cooling with an inter-
mittent stop at a temperature below the transition tempera-
ture. In the present case, the glass was cooled from a tem-
perature well above Tc=8.8 K to a stopping temperature Ts,
which was lower than Tc, at a rate of 0.2 K/min, and was
kept at Tsfor 3 h. Here, Tswas selected to be 7, 6, and 5 K.
After a stop for 3 h, the glass was cooled to 3 K at a rate of
0.2 K/min. Subsequently, a magnetic field of 50 Oe was ap-
plied and ??T? was measured on heating at a rate of
0.2 K/min. As a reference, ?ref?T? was determined by mea-
suring temperature dependence of zero-field-cooled suscep-
tibility without any intermittent stops. The results thus ob-
tained are shown in Fig. 2. The ??T? curves involving a stop
coincide with the ?ref?T? curve in a temperature range well
below Ts. In contrast, the ??T? curves deviate downward
from the ?ref?T? curve as the temperature approaches Ts. As
the temperature increases in a range above Ts, the ??T?
curves gradually merge with the ?ref?T? curve and eventually
FIG. 1. Temperature dependence of the real part of ac suscepti-
bility for the 20Fe2O3·80TeO2glass. The frequency f is 0.1, 0.3, 1,
3, 10, 30, 100, 300, and 1000 Hz ?from top to bottom?. The inset
illustrates the relationship between maximum relaxation time ? and
spin-freezing temperature Tf?f? in critical slowing down analysis.
FIG. 2. Temperature dependence of dc susceptibility measured
on heating after zero-field cooling with and without an intermittent
stop at Ts. The difference between ??T? and ?ref?T? is illustrated as
BRIEF REPORTSPHYSICAL REVIEW B 74, 012411 ?2006?
coincide with the ?ref?T?. The difference between ??T? and
?ref?T? as a function of temperature is also illustrated in Fig.
2. The effect of aging at Tsis reflected by a dip at around Ts.
For comparison, we performed the same experiments by
making Ts10 K, i.e., a temperature above Tc, and found that
aging at 10 K had no influence on the ??T? curve ?not
shown?. The appearance of memory dips indicates that spin
configurations attained during a stop at Tsare preserved after
cooling and subsequent heating.Afinite temperature range of
the memory dips reflects a temperature chaos in equilibrium
spin configurations. Since an equilibrium spin configuration
at a particular temperature T is completely different from
another spin configuration at a different temperature T+?T if
?T is sufficiently large, an aging effect at T does not affect a
spin structure at T+?T at all. This memory effect has been
confirmed for spin glasses and strongly interacting nanopar-
ticles systems.6–10On the other hand, it has been experimen-
tally and theoretically demonstrated that the memory effect
according to this protocol is not observed in simple super-
paramagnets due to the absence of magnetic interactions
among magnetic particles.9The observation of this memory
effect is generally an indication of collective nature in spin
dynamics,9,10so the present result strongly suggests that the
20Fe2O3·80TeO2glass is a spin glass.
An aging effect in a magnetic field11was also explored for
the present 20Fe2O3·80TeO2glass. The experiments were
performed in the following way. The glass was cooled from
a temperature well above Tc=8.8 K to 3 K at a rate of
0.2 K/min. Subsequently, a magnetic field of 50 Oe was ap-
plied and ??T? was measured upon heating to a stopping
temperature Ts, which was 4 or 5 K, at a rate of 0.2 K/min.
Then the temperature was fixed to be Tsfor 5.5 h, and ??Ts?
as a function of time was measured. After the stop at Ts, ??T?
was determined upon heating further at a rate of 0.2 K/min.
As a reference, ?ref?T? was measured in zero-field and field-
cooling processes without any long-term stops ?5.5 h in the
present case? at fixed temperatures. The ??T? and ?ref?T? thus
obtained are depicted in Fig. 3. As found in the inset of Fig.
3, ??T? increases logarithmically with time at Ts. After a stop
for 5.5 h at Ts, ??T? at first decreases with an increase in
temperature and merges with the ?ref?T? curve at a tempera-
ture well above Ts. A similar behavior was reported for the
Cu0.2Co0.8Cl2-FeCl3 graphite bi-intercalation compound.12
The decrease of ??T? just above Tsobserved in Fig. 3 is
thought to be a rejuvenation effect attributed to a chaotic
nature of spin configurations which depend on temperature.
The present behavior is somewhat different than that ob-
Fe0.5Mn0.5TiO311and the reentrant spin glass phase of
Cu0.2Co0.8Cl2-FeCl3 graphite bi-intercalation compound;12
for these two systems, ??T? monotonically increases as the
temperature is raised from Tsafter a stop and then merges
with a reference curve at a temperature well above Ts. It was
concluded for the Fe0.5Mn0.5TiO3that ??T? is explained well
in terms of a scaling description derived from droplet theory
for spin glasses, where the susceptibility depends on two
length scales RT?tw? and LT?t? as follows:11
magnetic phase ofthe
??T,t? = F?RT?tw?,LT?t??.
Here RT?tw? is the mean size of spin glass domains grown
during a waiting time tw?or a stopping time in zero field?,
and LT?t? is the maximum size of domains excited within a
probing time t. Several kinds of theoretical equations have
been suggested to express the growth laws of RT?tw? and
LT?t?.27–29One of the theories proposes a power law as fol-
where the exponent b?0.17.28For Fe0.5Mn0.5TiO3, by as-
suming that LT?t? grows continuously even if the temperature
is changed discontinuously, ??T? can be scaled by a scaling
function F which increases continuously with LT?t?. The va-
lidity of this scaling law warrants an accumulative nature of
aging dynamics involving the continuous growth of LT?t?
within a laboratory time scale. In the present experiments,
??T? does not increase monotonically with time as reflected
in the decrease of ??T? just above Ts. Hence, it is clear that
this scaling law cannot be applied to the 20Fe2O3·80TeO2
glass. This indicates that the 20Fe2O3·80TeO2glass mani-
fests a nonaccumulative aging effect, presumably due to a
chaotic nature within the laboratory time scale.
As mentioned above, it is demonstrated that the
20Fe2O3·80TeO2glass exhibits critical slowing down and
FIG. 3. Temperature dependence of dc susceptibility measured
on heating with and without an intermittent stop at Tsunder an
external magnetic field of 50 Oe after zero-field cooling. Tempera-
ture dependence of field-cooled dc susceptibility is also shown. The
inset depicts time dependence of susceptibility at Ts.
BRIEF REPORTSPHYSICAL REVIEW B 74, 012411 ?2006?
aging effects similar to those observed for spin glasses. How-
ever, the 20Fe2O3·80TeO2glass has a microscopic feature
different from a prototype of spin glasses. In spin glasses,
ferromagnetic and antiferromagnetic interactions are ran-
domly distributed, while the antiferromagnetic superex-
change interaction via oxide ions is dominant among Fe3+
ions in the 20Fe2O3·80TeO2glass, as speculated from the
negative value of paramagnetic Curie temperature ?
?−142 K?25defined by the following Curie-Weiss equation:
?=3kB?T − ??
It is naturally anticipated that magnetic structure of the
present oxide glass depends on the arrangement of Fe3+ions
in the glass structure. Magnetic frustration in the oxide glass
can be caused by a spatially random distribution of Fe3+ions,
which are connected by the antiferromagnetic interaction.
The strength of superexchange interactions among Fe3+ions
has a distribution due to the site-dependent variations in Fe-
O-Fe bond angles and Fe-O bond lengths. Thus, not only
randomness but also frustration is present in the magnetic
structure of the 20Fe2O3·80TeO2glass, leading to a transi-
tion into spin glass phase at very low temperatures, even in
the absence of random distributions of magnetic interactions
with opposite signs.
20Fe2O3·80TeO2glass displays aging and memory effects
and critical slowing down, indicating that the present oxide
glass exhibits spin glass phase transition. A disordered struc-
ture of the oxide glass is thought to be responsible for the
frustration in spin configuration. The mechanism of magnetic
transition presumably depends on the glass system, the con-
centration of magnetic ions, the preparation process of the
glass, and so forth. Therefore, further extensive studies will
be required to understand the magnetic properties of various
oxide glasses. Investigations of magnetic properties for other
oxide glasses are in progress.
The authors would like to thank S. Kitagawa of Graduate
School of Engineering, Kyoto University for magnetization
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