Nuclear resonant scattering of synchrotron radiation: a novel - - PowerPoint PPT Presentation

Johan Meersschaut

Instituut voor Kern- en Stralingsfysica, Katholieke Universiteit Leuven, Belgium Johan.Meersschaut@fys.kuleuven.be

Nuclear resonant scattering

• f synchrotron radiation:

a novel approach to the Mössbauer effect

• C. L’abbé, (…) Instituut voor Kern- en Stralingsfysica, K.U.Leuven, Belgium
• W. Sturhahn, T.S. Toellner, E.E. Alp, Advanced Photon Source, Argonne National Laboratory

J.S. Jiang, S.D. Bader, Materials Science Division, Argonne National Laboratory

Fund for Scientific Research Flanders (F.W.O.-Vlaanderen) and the Inter-University Attraction Pole IUAP P5/1 Work at Argonne and the use of the APS was supported by U.S. DOE, BES Office of Science, under Contract No. W-31-109-ENG-38 European Commission (FP6) STREP NMP4-CT-2003-001516 (DYNASYNC)

Introduction Mössbauer spectroscopy Nuclear Resonant Scattering of SR

part1

Motivation

• XMCD
• element-specific scattering
• study different materials independently
• Mössbauer spectroscopy
• Nuclear resonant scattering of synchrotron radiation
• isotope selective
• study specific sites within

the material separately

Site-selective magnetization measurements :

motivation

Iron Isotopes

57Fe Table of nuclides http: / / atom.kaeri.re.kr/

substrate

57Fe probe layer

Other possible isotopes are 119Sn, 181Ta, 149Sm, 153Eu, …

57Fe isotope

I = 3/2, µ = -0.155 µn Q = 0.16 b

Ground state (stable) Excited level unstable (τ = 141.11 ns) E = 14.413 keV

I = 1/2, µ = 0.090 µn Q = 0 b

∆E = 4.66 neV

Nuclear properties:

27 2

5.05 10

N

Am µ

−

= ×

28 2

1 10 b m

−

=

• 16

6.58212 10 eV s = ⋅ h

Nat 57Fe

Nuclear decay of

57Co to 57Fe

57Co -> 57Fe

Hyperfine Interactions

Electric monopole term:

57Fe 57Fe

I = 3/2

Isomer shift

I = 1/2

Isomer shift Isolated nucleus Electron density at the nucleus depends on the chemical properties

57Fe 57Fe 57Fe

Monopole term

Hyperfine Interactions

Electric quadrupole term:

57Fe 57Fe

I = 3/2

Isomer shift

I = 1/2

Isolated nucleus

57Fe

Electric field gradient due to non-cubic environment: * tetragonal or hexagonal lattice, * surface, * impurity in neigbouring shell

Quadrupo le term

HFI Zeeman

∆E = 107 neV

M

B E m I µ = −

B

H I µ = − ⋅ I B h

Magnetic dipole interaction:

µ = -0.155 µn µn = 5.05 10-27 J/T

+ 3/2 + 1/2

• 1/2
• 3/2
• 1/2

+ 1/2 I = 3/2 I = 1/2

1 J = 6.2415 1018 eV Bhf = + 33 T µn = 31.52 10-9 eV/T

57Fe

Bhf

Hyperfine Interactions

Summary

Electric monopole term: Electric quadrupole interaction: Magnetic dipole interaction:

57Fe

I = 3/2

Isomer shift Quadrupole splitting magnetic splitting

I = 1/2 + 3/2, -3/2 + 1/2, -1/2 + 1/2, -1/2 + 3/2 + 1/2

• 1/2
• 3/2
• 1/2

+ 1/2

∆E = 14.413 keV ∆E = 107 neV Bhf = + 33 T

HFI summary

Introduction Mössbauer spectroscopy Nuclear Resonant Scattering of SR

part2

Mössbauer spectroscopy

Nuclear emission :

57Fe

I = 1/2 I = 3/2

14.4 keV

I = 1/2 I = 3/2

14.4 keV

Nuclear absorption :

57Fe

v 1 E E c ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠

0.2799 mm/s

source drive

detector

Mossbaue r

Mössbauer spectroscopy

Nuclear emission :

57Fe

I = 1/2 I = 3/2

14.4 keV

I = 1/2 I = 3/2

14.4 keV

Nuclear absorption :

57Fe

detector

velocity

absorber absorber detector detector

source drive Mossbaue r

Mössbauer spectrum

The Mössbauer spectrum depends

• n the strength of the magnetic field :

B = 33 T B = 10 T

magnetic splitting

+ 3/2 + 1/2

• 1/2
• 3/2
• 1/2

+ 1/2

M

B E m I µ = −

MS

Mössbauer spectrum

coupling of two nuclear angular momentum states

( )

2 1 1 1 2 2 ,

: 1 , ,

m

Intensity I m m I m

σ θ ϕ ρ

⎡ ⎤ = − ⎣ ⎦ D

radiation probability in a direction with respect to the quantization axis

+ 3/2 + 1/2

• 1/2
• 3/2
• 1/2

+ 1/2 I = 3/2 I = 1/2

∆ m =

• 1

∆ m = ∆ m = + 1 ∆ m =

• 1

∆ m = ∆ m = + 1

Only six possible transitions

m = 1,0,-1 Sel rules

Information from Mössbauer spectra

e.g. hyperfine field along the photon direction

+ 3/2 + 1/2

• 1/2
• 3/2
• 1/2

+ 1/2 I = 3/2 I = 1/2

∆ m =

• 1

∆ m = ∆ m = + 1 ∆ m =

• 1

∆ m = ∆ m = + 1 ∆ m =

• 1

∆ m =

• 1

∆ m = + 1 ∆ m = + 1

( )

2 1 1 1 2 2 ,

: 1 , ,

m

Intensity I m m I m

σ θ ϕ ρ

⎡ ⎤ = − ⎣ ⎦ D

B = + 33 T

• rientation

M

Mössbauer spectra

Random orientation of M, |B| = 33 T External magnetic field along photon Thin film magnetized perpendicular to photon Mössbauer spectra on polycrystalline Fe powder : k B M µ0H = 1 T

MS

Information from Mössbauer spectra

Mössbauer spectroscopy is sensitive to

the direction of the hyperfine field the magnitude of the hyperfine field

Can we determine the sign? k B

absorber

k B

absorber

• r

M || -k M || k M M

Info from M

Determine the sign of Bhf ?

∆m = -1 ∆m = -1 ∆m = +1 ∆m = +1

B = 33 T, i.e. M || -k

+ 3/2 + 1/2

• 1/2
• 3/2
• 1/2

+ 1/2 I = 3/2 I = 1/2

∆ m =

• 1

∆ m = ∆ m = + 1 ∆ m =

• 1

∆ m = ∆ m = + 1

• 3/2
• 1/2

+ 1/2 + 3/2 + 1/2

• 1/2

∆ m = + 1 ∆ m = ∆ m =

• 1

∆ m = + 1 ∆ m = ∆ m =

• 1

B = - 33 T, i.e. M || k

∆m = +1 ∆m = +1 ∆m = -1 ∆m = -1 M

B E m I µ = −

Sign Bhf?

because the incident radiation is unpolarized the scattering process is not sensitive to the sign of B Explanation : Solution : Use circularly polarized radiation Spectra are NOT sensitive to the sign of the magnetization vector

Frauenfelder Frauenfelder

Use left circularly polarized source!

B = 33 T

+ 3/2 + 1/2

• 1/2
• 3/2
• 1/2

+ 1/2 I = 3/2 I = 1/2

∆ m =

• 1

∆ m = ∆ m = + 1 ∆ m = ∆ m = + 1

• 3/2
• 1/2

+ 1/2 + 3/2 + 1/2

• 1/2

∆ m = + 1 ∆ m = ∆ m =

• 1

∆ m = + 1 ∆ m = ∆ m =

• 1

B = - 33 T

∆ m =

• 1

∆m = +1 ∆m = +1 ∆m = +1 ∆m = +1

Use circ

How to create circularly polarized radiation ?

Practical implementation

with a monochromatic source (Mössbauer source) :

• use a magnetized absorber whose 3rd line coincides with the source line

photons with helicity +1 are absorbed transmitted radiation is highly polarized with helicity -1

• 100
• 50

50 100

energy (Γ)

+1

intensity

20 40 60 80 100 20 40 60 80 100

intensity

∆m = ±1 source magnetized absorber (B || k : M || -k) B = 33 T

MS with circularly polarized radiation

MS Szymanski

• Instrum. Meth. B 119 (1996) 438

MS with left circularly polarized radiation

MS Szymanski

∆m = -1 +1 -1 +1 ∆m = +1

• 1

+1

• 1
• K. Szymanski, NATO ARW’02 proceedings

k B Magnetized iron foil k B B = - 33 T

Information in time spectra

The quantum beat pattern is the signature of the hyperfine interaction :

• isomer shift

~ chemical environment of probe nuclei

• electric field gradient

~ lattice symmetry around the probe nuclei

• magnetic hyperfine field

~ magnetization properties

The magnetic hyperfine field is related to the magnetization vector

in Fe, e.g., the magnetization vector is opposite to the hyperfine field

The quantum beat pattern is the signature of the magnetization vector ! M B

Information from Mössbauer spectra

The hyperfine field is a measure for the magnetization vector :

in Fe the magnetization vector is opposite to the hyperfine field sensitive to the magnitude of the hyperfine field

The Mössbauer spectrum is the signature of the hyperfine interaction :

sensitive to the direction of the hyperfine field

Very simple! Widely used to study magnetic properties of bulk materials. Unsufficient sensitivity (30 nm) to study nanostructures

detector detector

source drive Mos info

Conversion Electron Mössbauer Spectroscopy

Nuclear emission

57Fe

14.4 keV 14.4 keV

Nuclear absorption

57Fe

14.4 keV

Internal conversion

57Fe

e-

+

Cems

Conversion Electron Mössbauer Spectroscopy

Conversion electron Mössbauer spectroscopy is sensitive enough to probe

• ne monolayer

Cems

CEMS Example 1

• Magnetic hyperfine interaction Bhf
• Isomer shift S
• Electric Quadrupole interaction ε

a) 2nd monolayer from interface with Ag b) Interface monolayer with Ag c) Clean surface monolayer

Page 2491

20 ML Fe

W(110) Fe/W(110 )

Multilayer system: Fe/ Multilayer system: Fe/57

57FeSi/Fe

FeSi/Fe

epitaxial CsCl-FeSi on Fe

150°C

MBE growth

Co-evaporated at a low rate (0.068 Å/s)

NatFe (40 Å) 57Fe Si (x Å) 50 50 NatFe (80 Å)

Au-capping MgO(001)

FeSi structure

Conversion electron Mössbauer spectroscopy

α-Fe (22%) en strained B2-FeSi (78%)

Quadrupole splitting

+ 3/2, -3/2 + 1/2, -1/2 + 1/2, -1/2 FeSi Cems

Strain relaxation in CsCl Strain relaxation in CsCl-

• FeSi

FeSi

• B. Croonenborghs et al., Appl. Phys. Lett. 85 (2004) 200

X-ray diffraction

strain

Conversion electron Mössbauer spectroscopy

Epitaxially grown FePt L10

∆m = -1 +1 -1 +1

Unpolarized source : k B

• 3/2
• 1/2

+ 1/2 + 3/2 + 1/2

• 1/2

∆ m = + 1 ∆ m = ∆ m =

• 1

∆ m = + 1 ∆ m = ∆ m =

• 1

B = -28 T

L10 FePt

Conversion electron Mössbauer spectroscopy

Epitaxially grown FePt L10

∆m = -1 +1 -1 +1 ∆m = -1 +1

• 1

+1

Unpolarized source : Polarized source : k B

MS

Perspectives

Mössbauer spectroscopy can be used to probe the local properties of materials (structural & magnetic) The radioactive source illuminates the whole sample: no spatial in-plane resolution Mössbauer spectroscopy or CEMS are difficult to perform under extreme conditions: low/high temperatures applied magnetic field high pressure, possibly in cryomagnets Conversion electron Mössbauer spectroscopy (CEMS) allows to study magnetic properties of monolayer thick nanostructures

Perspectives

Summary

Hyperfine interactions: interaction between the nucleus and its environment (isomer shift, el. Quadr., magn dipole) Mössbauer spectroscopy using a circularly polarized source Mössbauer spectroscopy can probe the hyperfine fields, yielding structural & magnetic information Conversion electron Mössbauer spectroscopy (CEMS) allows to study the structural and magnetic properties of monolayer thin nanostructures Ag/Fe/W(110) Fe/FeSi/Fe L10 FePt

Summary

Introduction Mössbauer spectroscopy Nuclear Resonant Scattering of SR

part3

Perspectives

Mössbauer spectroscopy can be used to probe the local properties of materials (structural & magnetic)

NRS

The radioactive source illuminates the whole sample: no spatial in-plane resolution Mössbauer spectroscopy or CEMS are difficult to perform under extreme conditions: low/high temperatures applied magnetic field high pressure, possibly in cryomagnets Conversion electron Mössbauer spectroscopy (CEMS) allows to study magnetic properties of monolayer thick nanostructures

Nuclear resonant scattering

Motivation : study material properties via the hyperfine interactions

k σ

• linear polarization

100 - 200 ns 50 ps

• pulsed time structure
• broad energy bandwidth

sample detector source

as sample dimensions decrease need for more brilliant sources

Mössbauer spectroscopy : Nuclear resonant scattering with synchrotron radiation :

synchrotron orbit

sample detector

• high brilliance + small beamsize (~ 10 µm)

motivation

57Fe isotope

I = 3/2, µ = -0.155 µn Q = 0.16 b

Ground state (stable) Excited level unstable (τ = 141.11 ns) E = 14.413 keV

I = 1/2, µ = 0.090 µn Q = 0 b

∆E = 4.66 neV

Nuclear properties:

27 2

5.05 10

N

Am µ

−

= ×

28 2

1 10 b m

−

=

• 16

6.58212 10 eV s = ⋅ h

Nat 57Fe

Isolated nucleus :

Energy domain :

57Fe

I = 1/2 I = 3/2

14.4 keV

• 100
• 50

50 100 20 40 60 80 100

intensity energy – 14.4 keV (Γ)

5 neV

50 100 150 200 1 10 100 1000 10000

time (ns) intensity

τ = 141 ns Time domain : exponential decay due to lifetime of excited state

Nucleus embedded in lattice:

Energy domain : I = 1/2 I = 3/2

M1

intensity energy – 14.4 keV (Γ)

• 100
• 50

50 100 20 40 60 80 100

0.5 µeV

time (ns) intensity

50 100 150 200 1 10 100 1000 10000

Time domain : quantum beats due to hyperfine splitting of nuclear states

in-plane

k σ

synchrotron orbit

Information in time spectra

The quantum beat pattern is the signature of the hyperfine interaction :

sensitive to the direction of the hyperfine field

Information in time spectra

• ut-of-plane

in-plane

The quantum beat pattern is the signature of the hyperfine interaction :

sensitive to the direction of the hyperfine field

Information in time spectra

50 100 150 200 1 10 100 1000 10000

time (ns) intensity

B || k x σ

intensity energy (Γ)

• 100
• 50

50 100 20 40 60 80 100

sensitive to orientation of B in-plane and out-of-plane

50 100 150 200 1 10 100 1000 10000

time (ns) intensity

B || k

intensity energy (Γ)

• 100
• 50

50 100 20 40 60 80 100 50 100 150 200 1 10 100 1000 10000

time (ns) intensity

B || σ

intensity energy (Γ)

• 100
• 50

50 100 20 40 60 80 100

The quantum beat pattern is the signature of the hyperfine interaction :

sensitive to the direction of the hyperfine field

Information in time spectra

quantum beat ~ cos(∆E t / ħ) beat frequency ~ magnitude of B

50 100 150 200 1 10 100 1000 10000

time (ns) intensity

B = 11 T

intensity energy (Γ)

• 100
• 50

50 100 20 40 60 80 100 50 100 150 200 1 10 100 1000 10000

time (ns) intensity

B = 33 T

intensity energy (Γ)

• 100
• 50

50 100 20 40 60 80 100

∆E ∆E

The quantum beat pattern is the signature of the hyperfine interaction :

sensitive to the direction of the hyperfine field sensitive to the magnitude of the hyperfine field

Applications for magnetism

Thus, nuclear resonant scattering can be used to probe the magnetic properties of materials Examples :

• measurement of spin rotation in exchange-coupled bilayers
• measurement of spin orientation in nanoscale islands

applications

Fe FePt soft magnet hard magnet with uniaxial anisotropy

M M H

Fe FePt soft magnet hard magnet with uniaxial anisotropy scattering plane 11 nm 0.7 nm 57Fe 20 mm

insert an 57Fe probe layer :

M H

Fe FePt soft magnet hard magnet with uniaxial anisotropy

exchange spring

Application: exchange springs

depth-selective measurement of spinrotation in exchange-coupled bilayers :

• R. Röhlsberger et al., Phys. Rev. Lett. 89 (2002) 237201
• R. Rohlsb

scattering plane 11 nm 0.7 nm 57Fe 20 mm rotation angle (°) depth (nm)

30 60 90 2 4 6 8 10 12 Ag Fe FePt H = 160 mT H = 240 mT H = 500 mT

Applications

• R. Röhlsberger et al., Phys. Rev. Lett. 89 (2002) 237201
• R. Rohlsb

W(110)

57Fe

2 nm 1 atomic step coverage of 0.57 monolayer

perpendicular spin orientation in Fe islands below 100 K

• R. Röhlsberger et al., Phys. Rev. Lett. 86 (2001) 5597

Application: nanoscale islands

measurement of nanoscale islands Fe/W(110):

Fe/W(110 )

two opposite directions of M give exactly the same time spectrum !

Nuclear resonant scattering permits to retrieve detailed magnetic information There is one restriction :

Polarized radiation

Spectra are NOT sensitive to the sign of the magnetization vector because the incident radiation is linearly polarized the scattering process is not sensitive to the sign of B Explanation :

B || k B || -k

• 100
• 50

50 100

energy (Γ) ∆m = +1 -1 +1 -1

• 1 +1 -1 +1

intensity

20 40 60 80 100

With linearly polarized radiation the same nuclear transitions are excited for opposite directions of the hyperfine field B

Use circularly polarized radiation :

depending on the sign of B, different transitions are excited

∆m = +1 +1 B || k

• 100
• 50

50 100

energy (Γ) intensity

20 40 60 80 100

∆m = +1 +1 B || -k

• 100
• 50

50 100

energy (Γ) intensity

20 40 60 80 100

Sign of the hyperfine field

How can one measure the sign of the hyperfine field (or magnetization) ?

Circ polarization

Even with circularly polarized radiation …

if transitions for two opposite field directions are symmetric around E0 the quantum beat is the same for both field directions

∆m = +1 +1 B || k

• 100
• 50

50 100

energy (Γ) intensity

20 40 60 80 100

∆m = +1 +1 B || -k

• 100
• 50

50 100

energy (Γ) intensity

20 40 60 80 100

B || k B || -k

0 50 100 150 200

time (ns) intensity

100 10 0 50 100 150 200

time (ns)

100 10

intensity

B || k B || -k

0 50 100 150 200

time (ns)

1

intensity

1000 100 10 0 50 100 150 200

time (ns)

1000 100 10 1

intensity

Trick

Break the symmetry by adding an extra single-line transition at E ≠ E0

clear difference between two time spectra

∆m = +1 +1 B || k

• 100
• 50

50 100

energy (Γ)

SL

intensity

20 40 60 80 100

∆m = -1 -1 B || -k

• 100
• 50

50 100

energy (Γ)

SL

intensity

20 40 60 80 100

Extra single-line transition

Practical implementation

can be achieved by adding a single-line reference sample to the beam

∆m = +1 +1 B || k

• 100
• 50

50 100

energy (Γ)

SL

intensity

20 40 60 80 100

single-line reference magnetic sample

k B the resonances in reference and sample are excited coherently

Extra single line

How to create circularly polarized radiation ?

Practical implementation

with a monochromatic source (Mössbauer source) :

• use a magnetized absorber whose 3rd line coincides with the source line

with a broadband source (synchrotron radiation) :

• use an X-ray phase retarder

single crystal with the diffraction planes inclined at 45° Bragg reflection involves both a σ and π component

45°

linearly polarized circularly polarized

• ffset the crystal from exact Bragg condition

a phase retardation between the σ and π components is induced tune offset angle for maximal degree of circular polarization

Phase retarder

To measure the sign of the hyperfine field (magnetization vector)

• ne has to use circularly polarized radiation

and an additional single-line reference sample Now the full magnetization information can be retrieved :

the magnitude of the magnetization vector the direction of the magnetization vector the sign of the magnetization vector

One can perform nuclear resonant magnetometry :

measure magnetization curves as a function of the external field

Interlayer coupling in Fe/Cr multilayers

Fe/Cr multilayers :

Depending on the Cr layer thickness, the Fe magnetization vectors will align : under 0° or 180° : bilinear coupling under 90° : biquadratic coupling Cr Fe

Fe/Cr

strong AF coupling expected

4 nm 4 nm 4 nm 1.1 nm 1.1 nm

Cr Fe

• 0.4
• 0.2

0.2 0.4

• 1.0
• 0.5

0.5 1.0

M/Ms µ0H (T)

molecular beam epitaxy magnetron sputtering

standard magnetization measurement :

• 0.4
• 0.2

0.2 0.4

• 1.0
• 0.5

0.5 1.0

M/Ms µ0H (T)

Study influence of growth mechanism on interlayer coupling : quintalayer samples grown on MgO(100)

5-layers

Measurement yields the magnetization vector of the central Fe layer

56Fe 57Fe 56Fe

buried 57Fe layer grown on thick substrate isotopic enrichment does not change the magnetic properties of the sample

In order to study the interlayer coupling in detail : measure the magnetization of 1 Fe layer selectively use the isotope-selectivity of nuclear resonant scattering

Iso enrichment

phase retarder C (111) phase retarder phase retarder reference SS foil

Experiment at APS beamline 3-ID

H

undulator high-resolution monochromator premono multilayer sample 14.413 keV detector Set-up 3ID

Nuclear resonant magnetometry

• 0.4
• 0.2

0.2 0.4

µ 0H (T) M/ Ms

• 1.0
• 0.5

0.5 1.0

Sample grown with molecular beam epitaxy on MgO(100) :

Time spectra

• 0.4
• 0.2

0.2 0.4

• 1.0
• 0.5

0.5 1.0

M/ Ms µ 0H (T)

at zero field, the central magnetization vector is NOT antiparallel !!

Sample grown with magnetron sputtering on MgO(100) :

NRM sputtered

• 0.4
• 0.2

0.2 0.4

• 1.0
• 0.5

0.5 1.0

M/Ms µ0H (T)

• 0.4
• 0.2

0.2 0.4

• 1.0
• 0.5

0.5 1.0

M/Ms µ0H (T)

nuclear resonant magnetometry : standard magnetometry : central Fe layer M/MS = cos θ all Fe layers M/MS = (2cos ϕ + cos θ)/3

Retrieve quantitative values for coupling angle : ϕ ϕ θ ϕ : angle of outer magnetization vectors θ : angle of central magnetization vector

coupl angle

Retrieve quantitative values for coupling angle : ϕ ϕ θ ϕ : angle of outer magnetization vectors θ : angle of central magnetization vector

• 0.4
• 0.2

0.2 0.4

µ0H (T) | θ − ϕ | ( )

• 45

90 135 180

From the combination of nuclear resonant and standard magnetometry :

coupl angle

at zero field : | θ − ϕ | = 162° ± 4° non-collinear coupling !!

Nuclear Resonant scattering of SR

Nuclear resonant scattering with circularly polarized radiation and an additional single-line reference sample permits to retrieve the full magnetic information This allows to perform nuclear resonant magnetometry We measured a layer-selective magnetization curve in [Fe(5.0nm)/Cr(1.1nm)]3 and found

• bilinear coupling for MBE-grown samples
• non-collinear coupling for sputtered samples

we attribute the existence of non-collinear coupling to extrinsic properties

• f the multilayer which are determined by the preparation conditions
• C. L’abbé et al., Phys. Rev. Lett. 93 (2004) 037201

Summary

Origin of quantum beats in time-domain Sensitivity to the direction of B How and why to introduce circularly polarized radiation into nuclear resonant scattering of synchrotron radiation additional single-line reference sample Examples: exchange system FePt/Fe using isotopic marker layer low-temperature spin state in sub-monolayer Fe/W(110) Example: interlayer coupled Fe/Cr/Fe/Cr/Fe quintalayer with isotope selective hysteresis curve comparison MBE vs sputtered samples

Summary

Applications for magnetism

Mössbauer spectroscopy can be used to probe the magnetic properties of materials (including homogeneous ultrathin films) Nuclear resonant scattering of synchrotron radiation allows to measure magnetization curves of specific parts as a function of the external magnetic field or under extreme conditions

Conclusion