Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute...
-
Upload
cornelius-carr -
Category
Documents
-
view
226 -
download
6
Transcript of Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute...
![Page 1: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/1.jpg)
Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors
Tomas JungwirthInstitute of Physics in Prague & University of Nottingham
![Page 2: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/2.jpg)
Kvantová relativistická fyzika
),(2
),(
2
2
22
2
trrm
trt
i
m
pE
Spintronics ← relativistic quantum physics
![Page 3: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/3.jpg)
Kvantová relativistická fyzika
)/1(/1
,
22
02
cv
mmmcE
Spintronics ← relativistic quantum physics
![Page 4: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/4.jpg)
Kvantová relativistická fyzika
Spintronics ← relativistic quantum physics
![Page 5: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/5.jpg)
}
}
Ultra-relativistic particles with spin (neutrino): spcE
Spin-orbit coupling
Weaker but also present in electrons in solids
![Page 6: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/6.jpg)
Electron has spin & charge → magnetic moment
Collective behavior of spins due to Coulomb interaction → magnetism Provides sensitivity to weak external fields & yields strong electrical signals
Bm ||
![Page 7: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/7.jpg)
Electron has spin & charge → magnetic moment
Collective behavior of spins due to Coulomb interaction → magnetism Provides sensitivity to weak external fields & yields strong electrical signals
Bm ||
![Page 8: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/8.jpg)
... and memory
Electron has spin & charge → magnetic moment
Collective behavior of spins due to Coulomb interaction → magnetism Provides sensitivity to weak external fields & yields strong electrical signals
Bm ||
![Page 9: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/9.jpg)
Lord Kelvin 1857
First spintronic devicesPoor scalability to small dimensions & small MR (subtle spin-orbit origin)
Current spintrnic devicesInterface effect → nanoscale in nature& large MR (robust ferromagnetic origin)
Fert, Grünberg et al. 1988
Bulk AMR TMR (GMR)
Spintronic magnetoresistance effects in metals
HDD read-head sensors
Magnetic RAM
)()()( 2mRmRmR
)()()( mRmRmR
![Page 10: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/10.jpg)
Towards semiconductor spintronics
FM semiconductors
Ohno et al. Science’98, Dietl et al PRB’00, Jungwirth, MacDonald et al PRB’99
Archetypical material (Ga,Mn)As:
favorable FM and spin-orbit coupled bands & semiconductor nano-fabrication
→ revived interest in spin-orbit phenomena like AMR in nanostructures
![Page 11: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/11.jpg)
Huge (~1000%) AMR-type effects in (Ga,Mn)As nanostructures
Wunderlich, Irvine, Jungwirth et al. PRL’06, Schlapps, Weiss et al. PRB’09
Electrical control of spintronics
B (T) → rotating m→
VG1
VG2
Positive & negative MR
Spintronic control of electronics
m1→
m2
→
p-type & n-type transistor
(m)→
![Page 12: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/12.jpg)
(Ga,Mn)As
(Ga,Mn)As
...FM at huge dopings > 1% (> 1020 cm-3 )→ more of a low-density metallic alloy
Tc below room-T ( 190K)
Novák, Jungwirth et al. PRL ’08
Limitations of ferromagnetic semiconductor (Ga,Mn)As
Tc
Well behaved Itinerant ferromagnet but...
![Page 13: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/13.jpg)
Shick, Jungwirth et al. ‘06Wunderlich, Jungwirth, Shick et al. ’06
Bernand-Mantel, Fert et al. ‘09
Theory predictions
Confirmed by experimentsGao, Tsumbal, Parkin et al. ’07Park,Wunderlich, Jungwirth et al. 08
AMR-type effects predicted and observed in high-Tc FM metal nanostructures
cobaltPtAlOx
Pt/Co
![Page 14: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/14.jpg)
spontaneous moment
spin
-orb
it cou
plin
g
FM AFM
Shick , Wunderlich, Jungwirth, et al., PRB‘10
Magnetic and magneto-transport anisotropy effects present in AFMs with spin-orbit equally well as in FMs
Maximizing the anisotropy phenomena in metals → spintronics in the AFMs
AFM metal AFM metal MMnIrnIr
)( 2mR
![Page 15: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/15.jpg)
Much easier to realize strong AFM-SC than FM-SC
Can AFMs resolve the problem of high-T SEMICONDUCTOR spintronics?
Jungwirth, Novak, et al., preprint ‘10
EFermiEgap
Eexchange
Eexchange competing with Egap in FM-SCs
No Eexchange competing with Egap in AFM-SCs
Strong FM exchange spitting turns the system into metal
![Page 16: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/16.jpg)
II Zn, Cd, ..
IIIAl, Ga, ..
IVSi, Ge, ..
V (pnictides)
N, P, As, ..
VI (chalcogenides)
O, S, Se, Te, ..
Mn (d5 s2) Fe
Eu (f7 s2) Gd
II III
Magnetic (FM & AFM) SCs derived from common 8-valence non-magnetic SCs
Si
Si
2 group-IV Si per elementary cell → 8 (sp) valence electrons
![Page 17: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/17.jpg)
II Zn, Cd, ..
IIIAl, Ga, ..
IVSi, Ge, ..
V (pnictides)
N, P, As, ..
VI (chalcogenides)
O, S, Se, Te, ..
IV: no magnetic SC analogue
Mn (d5 s2) Fe
Eu (f7 s2) Gd
II III
Magnetic (FM & AFM) SCs derived from common 8-valence non-magnetic SCs
![Page 18: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/18.jpg)
II Zn, Cd, ..
IIIAl, Ga, ..
IVSi, Ge, ..
V (pnictides)
N, P, As, ..
VI (chalcogenides)
O, S, Se, Te, ..
Mn (d5 s2) Fe
Eu (f7 s2) Gd
II III
Si
Si
1 proton transfer
IV III-V
IV: no magnetic SC analogue
Magnetic (FM & AFM) SCs derived from common 8-valence non-magnetic SCs
![Page 19: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/19.jpg)
II Zn, Cd, ..
IIIAl, Ga, ..
IVSi, Ge, ..
V (pnictides)
N, P, As, ..
VI (chalcogenides)
O, S, Se, Te, ..
Magnetic SCs derived from common 8-valence non-magnetic SCs
III-V: FeAs – SC, AFM TN=77K GdN – SC, FM Tc=72K (Ga,Mn)As – low-density metal, FM Tc<190K
Mn (d5 s2) Fe
Eu (f7 s2) Gd
II III
IV: no magnetic SC analogue
Lower moment Fe (Gd) less favorable than high moment Mn → II-VI intrinsic magnetic SCs
![Page 20: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/20.jpg)
II Zn, Cd, ..
IIIAl, Ga, ..
IVSi, Ge, ..
V (pnictides)
N, P, As, ..
VI (chalcogenides)
O, S, Se, Te, ..
Magnetic SCs derived from common 8-valence non-magnetic SCs
Mn (d5 s2) Fe
Eu (f7 s2) Gd
II III
IV: no magnetic SC analogue
III-V: FeAs – SC, AFM TN=77K GdN – SC, FM Tc=72K (Ga,Mn)As – low-density metal, FM Tc<190K
![Page 21: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/21.jpg)
II Zn, Cd, ..
IIIAl, Ga, ..
IVSi, Ge, ..
V (pnictides)
N, P, As, ..
VI (chalcogenides)
O, S, Se, Te, ..
II-VI: MnO, MnS, MnSe, MnTe - SC, AFM TN ~ 100 - 300K EuO, EuS – SC, FM Tc<70K EuSe, EuTe - SC, AFM TN<10K
All III-V and II-VI magnetic SCs have low transition-T
Mn (d5 s2) Fe
Eu (f7 s2) Gd
II III
IV: no magnetic SC analogue
Larger more ionic bonds weaken magnetic interactions in II-V‘s
Magnetic (FM & AFM) SCs derived from common 8-valence non-magnetic SCs
Can we make high moment (Mn) and smaller lattice (pnictides) intrinsic SC?
III-V: FeAs – SC, AFM TN=77K GdN – SC, FM Tc=72K (Ga,Mn)As – low-density metal, FM Tc<190K
![Page 22: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/22.jpg)
II Zn, Cd, ..
IIIAl, Ga, ..
IVSi, Ge, ..
V (pnictides)
N, P, As, ..
VI (chalcogenides)
O, S, Se, Te, ..
I(AM) Li, Na,..
(TM) Cu, Ag, ..
Mn (d5 s2) Fe
Eu (f7 s2) Gd
II III
Magnetic (FM & AFM) SCs derived from common 8-valence non-magnetic SCs
![Page 23: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/23.jpg)
II Zn, Cd, ..
IIIAl, Ga, ..
IVSi, Ge, ..
V (pnictides)
N, P, As, ..
VI (chalcogenides)
O, S, Se, Te, ..
I(AM) Li, Na,..
(TM) Cu, Ag, ..I-II-V: LiMnAs, NaMnAs, LiMnP, LiMnSb... - AFM TN >> room T
Mn (d5 s2) Fe
Eu (f7 s2) Gd
II III
Bronger et al., Z. among. allg. Chem. ’86
Magnetic (FM & AFM) SCs derived from common 8-valence non-magnetic SCs
![Page 24: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/24.jpg)
II Zn, Cd, ..
IIIAl, Ga, ..
IVSi, Ge, ..
V (pnictides)
N, P, As, ..
VI (chalcogenides)
O, S, Se, Te, ..
I(AM) Li, Na,..
(TM) Cu, Ag, ..
Mn (d5 s2) Fe
Eu (f7 s2) Gd
II III
III-V I-II-V
Twin SCs
I-Mn-VBronger et al., Z. among. allg. Chem. ’86
Magnetic (FM & AFM) SCs derived from common 8-valence non-magnetic SCs
I-II-V: LiMnAs, NaMnAs, LiMnP, LiMnSb... - AFM TN >> room T
![Page 25: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/25.jpg)
II Zn, Cd, ..
IIIAl, Ga, ..
IVSi, Ge, ..
V (pnictides)
N, P, As, ..
VI (chalcogenides)
O, S, Se, Te, ..
I(AM) Li, Na,..
(TM) Cu, Ag, ..
Mn (d5 s2) Fe
Eu (f7 s2) Gd
II III
I-Mn-V
No report on electronic structure of AFM I-Mn-V: Are they SCs?
No report on MBE growth of group-I compounds: Can they be grown as single-crystal epilayers?
Bronger et al., Z. among. allg. Chem. ’86
Magnetic (FM & AFM) SCs derived from common 8-valence non-magnetic SCs
I-II-V: LiMnAs, NaMnAs, LiMnP, LiMnSb... - AFM TN >> room T
![Page 26: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/26.jpg)
InAs
LiMnAsMBE growth of I-Mn-V:
LiMnAs on nearly lattice matched InAs
4.27A
4.28A
![Page 27: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/27.jpg)
[110] [-110]LiMnAs
MnAs
grow
th d
rect
ion
log(intensity)
200
0
400 600 800
100
200
x (m)
prof
ile
(nm
)
wavelength (nm)1000 1200 1400
LiMnAs
InAs cap
substrate
LiMnAs
In situ RHEED In situ optical reflectivity
Ex situ profile
Sharp 2D cubic single-crystal growth
... poor growth of control umatched MnAs
Fabry-Perot oscillations → semiconductor
5.3
2~
![Page 28: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/28.jpg)
log(
inte
nsit
y)
X-ray diffraction
All LiMnAs crystal peaks observed
Fully tensile strained on InAs(0.2% increase of LiMnAs volume)
InAs
LiMnAs
4.27A
4.28A
![Page 29: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/29.jpg)
Expected 45o rotation of LiMnAs with respect to the InAs substrateInAs
LiMnAs
[110]LiMnAs
InAs [100]
X-ray diffraction
![Page 30: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/30.jpg)
M
(104 e
mu)
H (T)
MnAs
Mn S=5/2
LiMnAs
energy (meV)
I T/I
0
InAs
Li:InAs
LiMnAs
MnAs
temperature (K)
Mre
m
(104 e
mu)
LiMnAs
MnAs
Ex situ optical transmission Squid magnetization
Transparent at least up to InAs band-gap
Consistent with in situ Febry-Perot oscillations and compare with non-transparent metal MnAs
Magnetization consistent with compensated AFM moments in LiMnAs upto studied 400K
Compare with FM MnAs with same amount of Mn
![Page 31: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/31.jpg)
Ab initio theory
Stoichiometric I-Mn-V are strong AFMs & intrinsic semiconductors
![Page 32: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/32.jpg)
Magnetic and correlated Mn d-states mixed near band gap
→ low √ (refractive index), strong and gatable magnetic anisotropy effects
LDA
![Page 33: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/33.jpg)
AFM semiconductors for spintronics
AFM
1. Electrically gatable magnetic and magneto-transport anisotropy effects
Feasible to rotate magnetic easy-axis electrically in high-doped (Ga,Mn)As → should be much more accessible in intrinsic SCs I-Mn-V
FM
![Page 34: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/34.jpg)
AFM semiconductors for spintronics
2. Exchange-biasing AFM with embeded conventional semiconductor devices
Fixed by exchange-biasing AFM
Transistor directly in the AFM layer
Opto-electronics directly in the AFM layer
Discrete spintronic and transistor elements in current MRAM
![Page 35: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/35.jpg)
FM SCs (GaMnAs) favorable model spintronic systems but low transition T
AFM I-Mn-V compounds:
- Simplest magnetic counterparts to conventional SCs with high transition T
- We showed that they are semiconductors and that the group-I alkali metal compounds can be grown by MBE as high quality single-crystal epilayers - Admixture of magnetic d-states yields unconventional SC properties and theory predicts very strong and gatable spintronic responses
Conclusions
Prospect for high-T semiconductor spintronics but first sytematic materials research needs to be completed
![Page 36: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/36.jpg)
University of NottinghamTom Foxon, Richard Campion,
Bryan Gallagher, et al.
Hitachi & Cavendish Laboratories at CambridgeJorg Wunderlich, Andrew Irvine et al.
Institute of Physics ASCR, PragueVít Novák, Miroslav Cukr , Jan Mašek, Alexander
Shick, František Máca,Petr Kužel, et al.
Charles University, PragueXavi Marti, Petra Horodyská, Václav Holý, Petr Němec, et al.
Texas A&M and University of TexasJairo Sinova, Allan MacDonald, et al.
![Page 37: Beyond ferromagnetic spintronics: antiferromagnetic I-Mn-V semiconductors Tomas Jungwirth Institute of Physics in Prague & University of Nottingham.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649eac5503460f94bb2e1d/html5/thumbnails/37.jpg)