Interlayer exchange coupling in metallic and all semiconductor multilayered structures
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"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.

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Interlayer exchange coupling in metallic and all semiconductor multilayered structures
"Interlayer exchange coupling in metallic and all-semiconductor multilayered structures"


  • 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
There is much written text on all-semiconductor multilayered structures"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
To begin, we have to go back to all-semiconductor multilayered structures" 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 “magneto-

resistance” is introduced for this new


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
After the original Kelvin’s discovery... all-semiconductor multilayered structures"

...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 “record-holder” – 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
Soon it was realized… all-semiconductor multilayered structures"

…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
The theory of all-semiconductor multilayered structures"“ordinary magnetoresitance” (OMR)andthe Hall Effectfor a simple non-magnetic metal

By taking the equation

of motion for electrons:

And intoducing

the cyclotron


Standard Hall Effect


One obtains a solution in a matrix

form, where the diagonal elements

represent magnetoresistance, and

the off-diagonal – the Hall effect:

The above theory was found to work pretty well for non magnetic metals and semiconductords
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, showinghysteresis.

However, this function can be

readily determined from experi-


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 magneto-resistance 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 AH non-magnetic metals and semiconductordsE and AMR in FM metals can only be explained on thegrounds 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 de-

fects (always present) or

by phonons, and may

end up in the d-band,

losing mobility and incre-

asing the resistance.

Schematic representation of the bands in

a transition metal with a partially filled

d-band (the bands for spin-up and spin-

down electrons are shown separately).

In conducted by electrons from the 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
“MMM” (Mott’s Motel Model) situation is different

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
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
W. Reed & E. Fawcett’s 1964 experiment of as two parallel sets of resistors.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: of as two parallel sets of resistors.

Pumpkins, pandas, schnauzers….

Magnetoresistance is NOT an


The credit for introducing

the term Giant Magneto-

resistanceshould 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 of as two parallel sets of resistors.

  • 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 multi-

  • layered structures, discovered by

  • Fert (France) and P. Grünberg

  • (Germany), for which they were

  • awarded a Nobel Prize in 2007. of as two parallel sets of resistors. of as two parallel sets of resistors.

Joseph Haydn,

composer of

The German

National Anthem

Gmr in a fe cr fe sandwich
GMR in a Fe/Cr/Fe of as two parallel sets of resistors.“sandwich”

Electron states in a non magnetic metal left and in a ferromafnetic metal right
Electron states in a non-magnetic metal (left) of as two parallel sets of resistors.and in a ferromafnetic metal (right)

More detailed explanation of the gmr mechanism
More detailed explanation of the GMR mechanism of as two parallel sets of resistors.

Spin valves sophisticated gmr based sensors
Spin valves: sophisticated GMR-based sensors of as two parallel sets of resistors.

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
More spin valves of as two parallel sets of resistors.

But the reign of gmr based reading heads did not last long
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
However, no matter whether the sensors utilize GMR, the two FM conducting layers are separated by a thin (~ 1 nm)or TMR, they always have one thing in common:

Zero magnetic field

↑↑↑↑↑ Applied field ↑↑↑↑

In the initial state, the magne-

tization vectors in the two FM

layers must be antiparallel…

...because only then the applied

field will change their mutual


…then the applied field would

not change their mutual orien-

tation, and such system would

not be sensitive to the field.

If the magnetization vectors

were initially parallel…

In other words
In other words… the two FM conducting layers are separated by a thin (~ 1 nm)

…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 prepa-

red a “trilayer” consisting

of two iron films, with a

wedge-shaped non-magne-

tic 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 be-

tween the Fe layers was an

oscillating function of the

Cr layer thickness. So,

Grunberg’s discovery sho-

wed that the desired con-

figuration can be obtained

by choosing an approp-

riate spacer thickness.

What is the origin of the interlayer interaction with oscillating sign
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 at- oms embedded in non-magnetic metals, and its sign osc- illates with distance r . It is mediated by Fermi electrons



Other researchers are of the opinion that quantum well states qws play a crucial role
Other researchers are of the opinion that Quantum oscillating sign?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 oscillating sign?

about one point: namely, it is the conduction

electrons that play a crucial role in interlayer

coupling effects seen in multilayered metal-

lic GMR systems.

In semiconductors, in contrast, the concent-

tration 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.


Not right
NOT RIGHT! oscillating sign?

We have been conducting neutron scat-

tering studies on all-semiconductor

multilayered systems consisting of

alternating magnetic and nonmagnetic

layers, and in many of them we observed

pronounced interlayer magnetic coupling


Is it important to investigate all semiconductor system
Is it important to investigate oscillating sign?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. Semicon-

ductor spintronics may become an ideal

partner for photonics!

There is one big problem though
There is one big problem, though. oscillating sign?

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 techno-

gists in many labs worldwide continue

to work hard on this problem…

Room temperature fm semiconductors present situation
Room-temperature FM semiconductors: oscillating sign?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 sys-

tems 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 oscillating sign?EuS/PbSandEuS/YbSeSL’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:


5.936 Ǻ


(lattice mismatch ≈ 0.5%)

4-200 Ǻ

30-60 Å

number of repetitions



a=6.29 Å

N oscillating sign?eutron reflectivity experiments

onthe EuS/PbS system

(NG-1 reflectometer,

NIST Center for Neutron Research)

Situation corresponding tored data points:

Situat. corresponding togreen data points:

Situation corresponding toblue data points

Unpolarized neutron reflectivity experiments on oscillating sign?

the EuS/PbS system

(NG-1 reflectometer, NIST Center for Neutron Research)

Our collaborators
Our collaborators oscillating sign?

Alternative explanations
Alternative explanations... oscillating sign?

  • 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 electrons 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.