Ahmed Rassili
Education and Current Position
1986-1990 : Graduated in Physics from the University of Chouaïb
Doukali, El jadida (MOROCCO)
1990-1992 : Masters Graduate in Optoelectronic's From the University
of Liège
Honors thesis : "Thermal conductivity : application to magnetic
rare-earth compounds"
Since November 1992 : PhD student in the Solid State group. Thesis research
supervised by M.Ausloos
Thesis title:"Theory of the Thermal Conductivity
of Metallic Magnetic Systems: The case of REAl2 compounds"
The main research field is theoretical solid state physics, principally
the study of thermal transport properties of magnetic rare-earth compounds
in the presence or absence of a magnetic field and/or crystal field.
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Address
Institut de Physique B5
Université de Liège
B-4000 Liège Belgium
phone: (32) 4/366.37.06
fax: (32) 4/366.29.90
E-mail: rassili@gw.unipc.ulg.ac.be
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Research Interests
- Solid state physics
- Thermal conductivity of cubic structures.
- Thermal conductivity of anisotropic materials.
- Thermal conductivity in a magnetic field.
- Crystal field effect on thermal conductivity.
- Variational method of irreversible processes.
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Publications
A. Rassili and M. Ausloos,
Theory of the thermal conductivity of RE Al2 compounds
J. Magn. Magn. Mat. 147 (1995) 341
A. Rassili and M. Ausloos,
Theory of the thermal conductivity of metallic localized spin
compounds in a magnetic field
J. Magn. Magn. Mater. 163 (1996) 153
A. Rassili and M. Ausloos,
Critical behavior of the thermal conductivity near a
magnetic phase transition
in Magnetic Hysteresis in Novel Magnetic Materials, Series E: Applied Sciences
- vol. 338 ed. G. C. Hadjipanayis, (Kluwer Academic Publishers, Dordrecht,
1997) p. 187.
A.Rassili, K. Durczewski and M. Ausloos,
Crystal field effects on the thermal conductivity of localized
spin metallic compounds
(submitted to Physical Review B)
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Current Activities
- Thermal conductivity of RE Al2 compounds
The thermal conductivity of magnetic metals, alloys and
compounds has not received a great deal of attention even though several
review articles do mention some data . Moreover, the theory of the thermal
conductivity of metallic magnets seems to be in limbo. In view of some
recent success on the theory of the thermal conductivity of high Tc Superconductors,
it seems of interest to reconsider the theory of the thermal conductivity
of metallic magnets. In both cases the systems have a spin (or magnetic
or more generally another "degree of freedom") contribution to
be taken into account in describing basic quantities.
We consider the case of metallic localized spin magnets alone.
We use in order to do so the variational solution of the Boltzmann equation
for calculating the thermal conductivity. Notice that this method has been
used successfully in order to describe the thermoelectric power of such
metallic magnets as well and high Tc Superconductors or semimetals in fact.
Therefore the usual approximations inherent to theoretical work are well
known and under control.
Visual comparison
shows that our results are in very good agreement with the reported data.
We emphasize that the low temperature bump amplitude is clearly due to
the localized impurities and not to the s-f scattering only as usually
thought of. Thus, a better knowledge of the impurity content in a given
materials should be put forward in order to understand the maximum at low
T which is in fact predicted to be sharper than usually observed.
- One could here argue against the use of the free electron approximation
picture, but it is a contraint of any analytical work. Nevertheless it
could be responsible for the lack of smoothness at low temperature.
- Also at higher temperature one could take into account the temperature
dependence of the Fermi energy (chemical potential), as argued by Durczewski
and Ausloos for the resistivity of semimetals. These effects are mainly
due to the electronic structure and not the scattering processes.
- More relevant for this work are the localized spin features. It has
been seen that a break occurs at in the above theory due to a mean field
approximation. It is of interest to investigate therefore the role of a
truly external magnetic field. .
- From a physical model point of view, to take into account crystal field
effects should be also relevant in particular with other RE's than Gd.
- Electronic thermal conductivity in a magnetic field
Boltzman equation contains now an added term due to the
magnetic field as an external force, for which we try to find a solution
by using another set of trial functions taking the anisotropy of the system
into account, for this task we also use the variational method under the
assumption made by Garcia-Molliner in 1958, where he assumed that the magnetic
effect can be taken as an added term to the scattering one. A non trivial
structure is found. The main bump at low temperature as in absence of a
field has its origin in the relative influence of the e--impurity and e--phonon
collision terms. It is enhanced in presence of the field. The intermediate
temperature bump which originates in the magnetic scattering does not change
much in position nor strength and is thus rather field independent. Some
mild modification arises near the critical temperature. At very low temperature
and at moderate field the expected linear temperature dependence is appreciably
seen to be modified. The feature specifically arises from the magnetic
term now since it can be verified that the impurity term is strictly linear
whatever the value of the field. Therefore the increase in the conductivity
at low temperature is attributed to the electron-spin scattering mechanism.
The increase can be understood if one realizes that the spins are obviously
more frozen in a large field, and present then a smaller scattering cross
section. Moreover the spin structure less deforms the unit cell and electrons
can thus better travel like Bloch waves do. The argument holds true also
near the critical temperature where spin fluctuations are also blocked
by the field leading to a smaller cross section. Experimentally, in view
of what is done for the electrical conductivity, it should be possible
to measure the magneto-thermal conductivity. The normalised with respect
to the field free case magneto-thermal conductivity is also calculated
for different values of the temperature normalised to the Debye temperature.
The behavior of the magneto-thermal conductivity differs in the magnetic
phase from that in the disordered phase as expected from the discussed
temperature dependence. The behavior depends whether the low, intermediate
or critical and normal range are examined. From an experimental point of
view, it seems interesting to further examine the role of the localized
spin scattering term since often a superposition approximation is made
in trying to estimate the relevant contributions. However let us warn again
against such an erroneous analysis in view of the complexity of the thermal
conductivity. Nevertheless it is seen that the localized-spin scattering
term ks decreases as a function of temperature at fixed field, has a minimum
at Tc and increases (as it should then do like an impurity contribution
in absence of a field) above Tc. The fact that the field smoothens up the
break at the critical transition will render very hard any extraction of
critical fluctuations then. Nevertheless, the present calculation shows
that a finite effect should be experimentally observable. As mentioned
in our further work, where we treated the free field case, the impurity
content of the sample has for signature the maximum at low T. In the present
case the sharpest observed feature also contains some magnetic information.
At higher T the linear behavior is a test for checking the temperature
dependence of the Fermi energy (chemical potential), so important for the
related thermo-electric (or Seebeck) coefficient (see the other supras
group's publications). It is clear that the above physical approximations
can be improved; they were made for allowing some analytical work. A more
correct band structure could of course be used. However this will much
more directly impose some numerical work which will obscure a little bit
the basic physics as mentined in the filed free case. Notice that the above
work does not include the case of the thermal conductivity of metallic
magnets, like Fe, Ni, Co, Cr in which non localized spins are very relevant
features. This should be examined elsewhere. However the field and spin
dependence of the band structure should then be completely taken into account.
From a model point of view, to take into account crystal field effects
should be very relevant also: in particular if ions other RE than Gd are
in the structure. Notice also that if the magnetic phase is of another
periodicity than the high temperature phase lattice, the problem is much
more complicated.
- Critical behavior of the thermal conductivity near a magnetic
phase transition
The phenomenological Weiss molecular field approximation
(MFA) allows one to use the dominant coupling forces between neighbouring
spins in order to desribe the production of a spontaneous magnetisation
below the so-called Curie temperature. In the case of ferromagnetic metallic
systems such as REAl2 where RE is any rare earth ion, it was shown under
this MFA that the thermal conductivity k shows a marked change in behavior
at the Curie temperature. This investigation of k in the temperature range
around the Curie point is important for the understanding of the magnetism
of such compounds and to obtain quantitative values of the basic physical
parameters. We have next calculated the behavior of the thermal localized-spin
resistivity versus reduced temperature in the critical region using the
formulae given in our previous papers on the basis of a MFA but also taking
into account the presence of an external magnetic field. In order to take
into account strict non equilibrium conditions and domain effects, we have
also added the contribution from the Barkhausen effect near the Curie temperature.
Furthermore we discuss the possible observations of magneto-thermal avalanches
at a critical organized state in order to measure magnetic wall pinning
energies.
- Crystal field effects on the thermal conductivity of localized
spin metallic compounds
The influence of the 4f-levels of the rare earth ions on
transport properties, of localized spin metallic compounds is called either
specific or strong. Theoretical models investigating this influence have
been presented in a limited number of publications only. The case of the
thermal conductivity does not seem to have been worked out.
- We have calculated the thermal conductivity of localized spin metallic
compounds using a variational method taking into account several scattering
processes, i.e., e--phonon, e--impurity and e--localized spin. Their contributions
were clarified. Continuing in the same path, we show in the following the
influence of the crystal electric field splitting on the thermal conductivity
on the basis of a two-level system model. It will be found that the localized
spin scattering contribution, ks, like the total electronic thermal conductivity,
ke, shows an increase at very low temperatures as compared to the case
in which no crystal electric field splitting is taken into account.
- The splitting of f-shell energy levels of rare earth ions in a crystal
by the electric field surrounding ions (crystal electric field, CEF) is
an intrinsic property. It is known that magnetic properties of rare earth
compounds depend on whether the ground state of the shell is a singlet
or a multiplet. For instance if the magnetic exchange interaction, e.g.,
via the conduction electrons exists in the singlet ground state system,
the magnetic order can exist above a certain temperature only in the case
of sufficiently strong exchange interaction. This fact was discovered by
Bleaney in the sixties and discussed, e.g., Wang. Some preliminary work
on crystalline electric field effect on the electrical resistivity and
thermoelectric power had been presented as early as 1980, by Ausloos.
- We study the results on the thermal conductivity due to the conduction
electron scattering by a doublet due to a crystal electric field. For simplicity
one considers only a shell model with J = 1/2, i.e., pseudo Ising spin
model and one will try to examine whether the energy gained or lost by
an electron in such a scattering process can be seen. This approximation
seems more appropriate in order to gain some preliminary insight. we use
the known transverse Ising model picture, which in the molecular field
approximation that we apply, is a paradigm for most systems e.g. as discussed
by Bleaney and Wang.
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last update: December 22, 1997