"Interlayer exchange coupling in metallic and
all-semiconductor multilayered structures"
OUTLINE
• Why are interlayer coupling phenomena interesting and
Important? The explanation will be in the form of a longer
story about magnetoresistance and GMR, a Nobel Prize
effect.
• Why should one study interlayer coupling effects in
all-semiconductor systems?
• Why should we use neutron scattering tools for this
purpose?
• What we have found so far in the course of our studies
of EuS-based all-semiconductor superlattices .
There is much written text on
some slides
Let me explain why. My plan is to post this Power Point
Presentation on the Web. For some people it will perhaps
be a useful tutorial. And, I hope, after doing some more
work on it, it may also serve as sort of “propaganda
movie” for informing people – e.g., prospective students -about research conducted in our Department (we will
then need a whole “package” of such slide shows,
of course).
To begin, we have to go back to 1857...
In 1857 Scottish scientist William Thomson,
who later becomes Lord Kelvin, discovers
that the application of external magnetic
field to a nickel (Ni) wire increases its
electric resistance. The term “magnetoresistance” is introduced for this new
phenomenon.
The picture shows Lord and Lady Kelvin
chairing the ceremony of coronation of King
Edward II in 1902. Scientist at that time were
given all respect they deserved – in sharp
contrast with the present situation!
After the original Kelvin’s discovery...
...physicists rushed to study other metals.
Essentially, it was found that MR effects occur in
any metal. For the non-magnetic ones, those
findings can be summarized as a simlpe „rule of
thumb”: the worse conductor the metal is, the
stronger the MR effects are manifested.
Bismuth (which is not even classified as a metal,
but a “semimetal”) was found to be the “recordholder” – in strong magnetic fields its resistance
could increase by as much as 50%. But in copper
or gold the resistance changed only by a small
fraction of 1%, even in very strong fields. Not
surprisingly, the MR phenomena did not find too
many practical applications…
Soon it was realized…
…that magnetoresistance is not an effect
“standing by itself”, but it belongs to a
larger class of phenomena, called
“galvanomagnetic effects”, or
“magnetotransport effects”, which can be
all described in the framework of the same
theory. Another member of this class is the
well-known Hall Effect.
The theory of “ordinary magnetoresitance” (OMR) and
the Hall Effect for a simple non-magnetic metal
By taking the equation
of motion for electrons:
And intoducing
the cyclotron
frequency:
One obtains a solution in a matrix
form, where the diagonal elements
represent magnetoresistance, and
the off-diagonal – the Hall effect:
Standard Hall Effect
Geometry:
The above theory was found to work pretty well for
non-magnetic metals and semiconductords
In ferromagnets (FMs), B is a
non-linear function of applied
field an T, showing hysteresis.
However, this function can be
readily determined from experiments.
It was therefore expected that if experimental B values
were used, the same theory would work well for FMs.
But it did not work!! Both Hall Effect and magnetoresistance in FMs were found to behave in a highly
unpredictable way. New terms were coined for them:
Anomalous Hall Effect (AHE) and
Anomalous MagnetoResistance (AMR).
It turned out that the AHE and AMR in FM metals can
only be explained on the grounds of quantum theory.
The first successful theory of AHE and AMR was
created by another British scientist-aristocrat ☺,
the famous Sir Nevil Mott (Nobel 1977). He asked
himself: why certain transition metals – Ni, Pd, Pt –
are much poorer conductors than their immediate
neighbors in the Periodic Table, Cu, Ag and Au?
Here is the answer: in transition metals the current is
conducted by electrons from the d-bands and s-bands
(or hybrydized s+p bands)
Electron in the d-bands
are more tightly bound
and less mobile.
But the s-band electrons
may be scattered by defects (always present) or
by phonons, and may
end up in the d-band,
losing mobility and increasing the resistance.
Schematic representation of the bands in
a transition metal with a partially filled
d-band (the bands for spin-up and spindown electrons are shown separately).
In copper, however, the 3d band is completely
filled, so such scattering cannot occur –
therefore, copper is an excellent conductor!
However, in nickel, copper’s next-door
neighbor, the situation is different
The d-band is not completely filled, so that s→d
scattering may occur, making Ni a poorer conductor
There is one more important aspect: in the FM state, the
situation is no longer symmetric – the 3d sub-band for
only one of the spin states is now incompletely filled.
This fact, it turns out, has far-reaching consequences!
“MMM” (Mott’s Motel Model)
From the Mott’s picure, it follows that there are two currents:
For “spin-up” current the resistance is low (no scattering).
For “spin-down” current the resistance is high because such
electrons may be scattered into the 3d sub-band
According to Mott’s theory, an FM conductor can be thought
of as two parallel sets of resistors.
By applying an external magnetic field, one can re-orient
the domains, and thus change the specimen resistance –
as had been originally observed by Lord Kelvin.
In bulk specimens the effect is not particularly strong, though,
which makes practical applications difficult ☹
W. Reed & E. Fawcett’s 1964 experiment
on single-crystal iron (Fe) whiskers
The result was a beautiful confimantion of the Mott
model – yet, whiskers are “technologically unfriendly”
Everything grows giant these days:
Pumpkins, pandas, schnauzers….
Magnetoresistance is NOT an
exception!
The credit for introducing
the term Giant Magnetoresistance should be given
to Dr. S. von Molnar, who
used it in a 1967 paper
reporting unusually strong
magnetoresistance effects
seen in EuSe crystals doped
with Gadolinium (Gd).
However, what we call “GMR” now
is not exactly the same effect as
that observed in bulk specimens
by von Molnar et al. .
Today, “GMR” refers to an effect
occurring in nanometer-thick multilayered structures, discovered by
A.Fert (France) and P. Grünberg
(Germany), for which they were
awarded a Nobel Prize in 2007.
http://urlcut.com/Vive_la_France
http://urlcut.com/German_National_Anthem
Joseph Haydn,
composer of
The German
National Anthem
GMR in a Fe/Cr/Fe “sandwich”
Electron states in a non-magnetic metal (left)
and in a ferromafnetic metal (right)
More detailed explanation of the GMR
mechanism
Spin valves: sophisticated GMR-based sensors
The application of such sensors in the reading heads
of hard-drives made it possible to increase their
capacity by nearly two orders of magnitude…
Since 1997, about 5 billions
of such reading heads have
been produced.
More spin valves
But the reign of GMR-based reading
heads did not last long…
Recently, they have been “dethroned” by even more
efficient sensors utilizing another magnetoresistance
effect – namely, Tunnel MagnetoResistance (TMR)
Outwardly, a TMR system is similar to a GMR one – but now the
two FM conducting layers are separated by a thin (~ 1 nm)
insulating layer (e.g., MgO)
Ferromagnetic coupling:
High tunneling probability
Antiferromagnetic coupling:
Low tunneling probability
However, no matter whether the sensors utilize GMR,
or TMR, they always have one thing in common:
Zero magnetic field
↑↑↑↑↑ Applied field ↑↑↑↑
In the initial state, the magnetization vectors in the two FM
layers must be antiparallel…
...because only then the applied
field will change their mutual
orientation.
If the magnetization vectors
were initially parallel…
…then the applied field would
not change their mutual orientation, and such system would
not be sensitive to the field.
In other words…
…in all types of thin film magnetoresistance
sensors there has to be an interaction that
couples the FM films antiferromagnetically
acros the intervening non-magnetic spacer:
This interaction also assures that the system returns
to its initial configuration after the field is removed.
But how can one obtain a coupling of a desired sign between two FM films?
Well, the whole “GMR saga”
started when one day in
1986 Peter Grunberg prepared a “trilayer” consisting
of two iron films, with a
wedge-shaped non-magnetic chromium metal layer
in between. He observed
that a domain pattern with
alternating magnetization
directions formed in the
top layer, meaning that the
sign of the interaction between the Fe layers was an
oscillating function of the
Cr layer thickness. So,
Grunberg’s discovery showed that the desired configuration can be obtained
by choosing an appropriate spacer thickness.
What is the origin of the interlayer
interaction with oscillating sign?
There is still no consensus among researchers ragarding
this issue. Some argue that it is simply the “old” RKKY
interaction (known since 1950s). It couples magnetic atoms embedded in non-magnetic metals, and its sign oscillates with distance r . It is mediated by Fermi electrons
RKKY
r
Other researchers are of the opinion that Quantum
Well States (QWS) play a crucial role
In this model, the non-magnetic spacer is though of as a quantum well, in
which electrons are confined between two “walls”, with the magnetized
layers playing such a role. There are discrete E levels in such a well (recall
“particle in a box”). When the well expands, these energies decrease.
Each time a consecutive E level cuts through the Fermi level, the sign of the
coupling changes:
But no matter who is right, there is no doubt
about one point: namely, it is the conduction
electrons that play a crucial role in interlayer
coupling effects seen in multilayered metallic GMR systems.
In semiconductors, in contrast, the concenttration of conduction electrons is orders of
magnitude lower than in metals. Some of
them are nearly-insulating. So, the above
may imply that in analogous systems made
of semiconductors there is no chance of
seeing interlayer coupling effects.
RIGHT?!
NOT RIGHT!
We have been conducting neutron scattering studies on all-semiconductor
multilayered systems consisting of
alternating magnetic and nonmagnetic
layers, and in many of them we observed
pronounced interlayer magnetic coupling
effects.
Is it important to investigate
all-semiconductor system?
The existing all-metal GMR sensors are the
first generation of spintronics systems. But in
the opinion of many experts the future belongs
to semiconductor spintronics. Such devices
can be more easily integrated with existing
electronics. Also, semiconductors have many
highly interesting optical properties. Semiconductor spintronics may become an ideal
partner for photonics!
There is one big problem, though.
For building practical spintronics devices
one would need semicondutors that are
ferromagnetic at room temperature. And
God did not make them. Rather, God left
it as a challenge for us to create such
materials synthetically. Material technogists in many labs worldwide continue
to work hard on this problem…
Room-temperature FM semiconductors:
present situation
The “record-holder” now is epitaxially prepared
Ga(Mn)As alloy, with about 10% of Mn. It stays
FM up to 175 K – still more than 100K below
the “target value”.
What can be done in such situation? Well, there
are some fundamental problems that need to be
studied. For instance – what is the mechanism
giving rise to interlayer coupling effects in systems with low concentration of mobile electrons?
We decided to do such studies on multilayers
containing EuS, a well-known “prototypical” FM
semiconductor (with Curie T of only 16 K, though).
Ferromagnetic EuS/PbS and EuS/YbSe SL’s
EuS – Heisenberg ferromagnet TC = 16.6 K (bulk), Eg=1.5 eV
PbS – narrow-gap (Eg=0.3 eV) semiconductor (n ≈ 1017 cm-3)
YbSe – wide-gap (Eg=1.6 eV) semiconductor (semiinsulator)
all NaCl-type structure with lattice constants:
5.968 Ǻ
5.936 Ǻ
5.932 Ǻ
(lattice mismatch ≈ 0.5%)
4-200 Ǻ
30-60 Å
number of repetitions
10-20
(001)
a=6.29 Å
Neutron reflectivity experiments
onthe EuS/PbS system
Situation corresponding to red data points:
(NG-1 reflectometer,
NIST Center for Neutron Research)
Situat. corresponding to green data points:
Situation corresponding to blue data points
Unpolarized neutron reflectivity experiments on
the EuS/PbS system
(NG-1 reflectometer, NIST Center for Neutron Research)
Our collaborators
Electronic band structure in EuS
Alternative explanations...
• PbS is a narrow-gap material. At low T the
concentrations of carriers may be still
pretty high. Perhaps the effect seen in
EuS/PbS is a carrier-mediated coupling?
• Crucial test: make a EuS/XY system, in
which XY is a wide-gap semiconductor or
an insulator
• An ideal material, YbSe was found for that
purpose.
Interlayer exchange coupling mediated by valence band electrons
J.Blinowski & P.Kacman, Phys. Rev. B 64 (2001) 045302.
P.Sankowski & P.Kacman, Acta Phys. Polon. A 103 (2003) 621
Unpolarized neutron reflectivity experiments
on the EuS/YbSe system
(NG-1 reflectometer, NIST Center for Neutron Research)
CLOSING REMARKS
• It is good to inspiration from the work of others. If these people
got a Nobel Prize, it would add prestige to your work! ☺
• Now, more seriously: Metal-based spintronics has a bright
future. One new application that is emerging is generating GHz
signals, which may lead to further progress in cellullar phone
technology.
• Semiconductor spintronics will more likely utilize TMR than
GMR. Note that in a TMR device the FM films are separated by
an insulating spacer. From that standpoint, our work makes
much sense – essentially, what we are doing, is studying
interlayer coupling between FM films across insulating
spacers. Las fall, for example, we made measurements on
system in which EuS layers are separated with barriers of SrS,
which has energy gap width 4.6 eV, making it a perfect
insulator. And we saw pronounced antiferromagnetic interlayer
coupling in those systems.