NN09, Thessaloniki, Greece, 13-15 July 2009
Two-dimensional carriers
under in-plane magnetic field:
novel phenomena
Constantinos Simserides
Institute of Materials Science, NCSR Demokritos, Athens, Greece
quantum wells, QWs
☺ heterostructure QW
Host crystals:
III-V
(e.g. GaAs),
II-VI
(e.g. CdTe)
conduction
band
or
valence
band
(Ga,Al)As/GaAs/(Ga,Al)As
conduction
band
minimum
(Ga,Al)As
conduction
band
minimum
(Ga,Al)As
Barrier
conduction band offset
Barrier
conduction
band
minimum
GaAs
NO applied fields, NO dopants
quasi two-dimensional carriers under parallel magnetic field
(the elegant concept of Landau levels must be abandoned)
(Ga,Al)As/GaAs/(Ga,Al)As
heterostructure QW
donors
donors
(Ga,Al)As
conduction
band
minimum
(Ga,Al)As
conduction
band
minimum
Β
GaAs
conduction
band
minimum
with selective doping
For this orientation . . .
Comparison with other carrier systems under magnetic / electric field
Quantum mechanical properties & density of states (DOS)
Examples of modified physical properties
(magnetoresistance oscillations, N-type kink in photoluminescence, etc)
Thermodynamic properties
(population, entropy, internal & free energy,
magnetization, magnetic susceptibility)
Spintronic systems (with magnetic impurities):
Spin-subband populations and spin-polarization
Systems without magnetic impurities:
a diamagnetic to paramagnetic transition
of entirely orbital origin is predicted,
while entropy...
Comparison with other carrier systems under magnetic / electric field
B//y
B//y, E//z
B=0, QW(z), [E//z]
B//y, PQW(z)
B//y, QW(z), [E//z]
C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131–5141
C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y.
Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 978-1-60692-557-7
Quasi two-dimensional carriers - Hamiltonian
Free particle along y axis, while in the xz plane:
C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131–5141
C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y.
Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 978-1-60692-557-7
Quasi two-dimensional carriers
Force on the electrons
Magnetic length
C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131–5141
C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y.
Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 978-1-60692-557-7
Quasi two-dimensional carriers: density of states (DOS)
*


m
A
1

(

) 2 
(
E
i)
2

 i,
DOS deviates from
the well-known step-like form
DOS changes qualitatively & quantitatively
*

(
E
k
))
A
2
m
i
,(
x
(
)
2
dk
x


4


E
k
)
i
,
i
,(
x








Equation holds for any type of competition
between spatial and magnetic confinement
Eiσ(kx) must be self-consistently calculated.
The kx-dependence increases the numerical cost by 100-1000.
The main features of this DOS, the Van Hove singularities,
are not –generally- simple saddle points.
The DOS, modification changes the physical properties.
Limit B → 0 or very narrow QWs
Ei(kx) = Ei + ħ2kx2/(2m*)
DOS regains its step-like form
*

(
) 2

(

E
i)
i


m
A
C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131
C. Simserides, Physica E 21 (2004) 956
Limit of a simple saddle point,
Ei(kx) = Ei – ħ2kx2/(2n*), (n* > 0)
DOS deviates logarithically
ρ(ε)
 -ln|ε-Ei|
C. Simserides, Phys. Rev. B 69 (2004) 113302
Quasi two-dimensional carriers: Thermodynamic properties
population
internal energy
entropy
free energy
magnetization
C. Simserides, Phys. Rev. B 69 (2004) 113302
C. Simserides, J. Phys.: Condens. Matter 21 (2009) 015304
Energy dispersion, DOS, subband concentrations, QW profile
C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y.
Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 978-1-60692-557-7
Energy dispersion, DOS, subband concentrations, QW profile
C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y.
Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 978-1-60692-557-7
Energy dispersion, DOS, subband concentrations, QW profile
C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y.
Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 978-1-60692-557-7
Energy dispersion, DOS, subband concentrations, QW profile
C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y.
Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 978-1-60692-557-7
Energy dispersion, DOS, subband concentrations, QW profile
C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y.
Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 978-1-60692-557-7
Entirely orbital
Thermodynamic properties of quasi two-dimensional carriers
under parallel magnetic field
C. Simserides, J. Phys.: Condens. Matter 21 (2009) 015304
The magnetic susceptibility
χm = ∂M/∂H oscillates between
< 0 (diamagnetic)
and
> 0 (paramagnetic) values
the NEW phenomenon is important
in comparison with
the ideal de Haas–van Alphen effect
(the corresponding phenomenon under perpendicular magnetic field)
Why increasing temperature, the diamagnetic to paramagnetic oscillation dies out...
Entropy depends CLEARLY on the applied magnetic field
Principal
thermodynamic
properties
Principal
thermodynamic
properties
Principal
thermodynamic
properties
(II) MIN “cohesion”: occupied E0(kx)
splits in two parts ~ |kx| ≈ 0
change DOS => oscillation of M
(III) minima
move apart
(I) Depopulation of E1(kx)
MAX “cohesion”
(IV) Increasing the magnitute of the
system, S minimum increases.
New phenomenon (under in-plane Β)
χm = ∂M/∂H between < 0 & > 0 values:
(purely orbital
diamagnetic - paramagnetic oscillation)
corresponds to ideal de Haas–van Alphen effect (perpendicular Β).
e.g. in case (γ΄), ΔM ~ 10 A/m ~ 1/5
of
ideal de Haas–van Alphen effect.
Ideal
de Haas–van Alphen
effect
Θεωρία
Peierls R 1933 Z. Phys. 81 186
Πείραμα
Wilde M A, Schwarz M P, Heyn C, Heitmann D,
Grundler D, Reuter D and Wieck A D
2006 Phys. Rev. B 73 125325
End
Thank you for your attention!
Relevant Literature
C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131
C. Simserides, Journal of Computational Electronics 2 (2003) 459
C. Simserides, Physica E 21 (2004) 956
C. Simserides, Phys. Rev. B 69 (2004) 113302
C. Simserides, AIP Conf. Proc. 772 (2005) 341
C. Simserides, International Journal of Modern Physics B 18 (2004) 3745
C. Simserides, Journal of Physics: Conference Series 10 (2005) 143
C. Simserides, Phys. Rev. B 75 (2007) 195344
C. Simserides and I. Galanakis, Physica E 40 (2008) 1214
Diploma Thesis of Konstantinos Koumpouras:“Spintronics in dilute magnetic semiconductor quantum wells”.
Materials Science Department, University of Patras (2008).
C. Simserides, chapter in “Quantum Wells: Theory, Fabrication and Applications”, Nova Science Publishers, N.Y.
Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 978-1-60692-557-7
C. Simserides, J. Phys.: Condens. Matter 21 (2009) 015304
sheet electron concentration – internal energy
Depopulation of E1(kx) for Β ~ 13 T
C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y.
Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 978-1-60692-557-7
Β // in magnetoresistance
Experimentally:
- min of resistance (Rxx): step in DOS at EF (= subband depopulation)
- max of resitance (Rxx): van Hove singularity in DOS at EF
O. N. Makarovskii, L. Smrčka, P. Vašek,
T. Jungwirth, M. Cukr, and L. Jansen,
PRB 62 (2000) 10908
Β // in photoluminescence (PL): N-type kink
Huang D and Lyo S K 1999 Phys. Rev. B 59 7600
theory
Orlita M, Grill R, Hlídek P, Zvára M, Döhler G H,
Malzer S and Byszewski M 2005 Phys. Rev. B 72 165314
experiment
Principal
thermodynamic
properties
Principal
thermodynamic
properties
Hence, increasing T,
the diamagnetic to paramagnetic transition dies out.
Περιοδικός πίνακας
Ενεργειακή διασπορά, DOS, πληθυσμοί υποζωνών, μορφή QW
C. Simserides, invited chapter in the book "Quantum Wells: Theory, Fabrication and Applications", Nova
Science Publishers, NY. Editors: Alfred Ruyter and Harper O'Mahoney, in press
Ενεργειακή διασπορά, DOS, πληθυσμοί υποζωνών, μορφή QW
C. Simserides, invited chapter in the book "Quantum Wells: Theory, Fabrication and Applications", Nova
Science Publishers, NY. Editors: Alfred Ruyter and Harper O'Mahoney, in press
Ενεργειακή διασπορά, DOS, πληθυσμοί υποζωνών, μορφή QW
C. Simserides, invited chapter in the book "Quantum Wells: Theory, Fabrication and Applications", Nova
Science Publishers, NY. Editors: Alfred Ruyter and Harper O'Mahoney, in press
Ενεργειακή διασπορά, DOS, πληθυσμοί υποζωνών, μορφή QW
C. Simserides,
J. Phys.: Condens. Matter 11 (1999) 5131
C. Simserides, invited chapter in the book "Quantum Wells: Theory, Fabrication and Applications", Nova
Science Publishers, NY. Editors: Alfred Ruyter and Harper O'Mahoney, in press
Question:
What about Β // in spintronics?
Host crystals, doping, impurities
Doping = introduction of impurities, on purpose
- donors => electrons, e.g. N, P, As in host crystal Si, Ge
- acceptors => holes, e.g. B, Al, Ga in host crystal Si, Ge
Magnetic impurities, e.g. Mn ( [Ar] 3d5 4s2 )
which provide (also) localized magnetic moments
e.g. Mn in GaAs or in CdTe
☺ DMS = dilute magnetic semiconductor,
a semiconductor doped with (dilute) magnetic impurities
Εικόνα από Ohno, Science 281 (1998) 951
Spintronics = spin + electronics:
use
carrier charge as well as spin
Carriers
(holes, electrons)
induce
ferromagnetism!
Εικόνες από MacDonald Schiffer Samarth, Nature Materials 4 (2005) 195
DMS:
αλλάζουμε
τάση πύλης
“M”
Electric field
control
of ferromagnetism.
αλλάζει
συγκέντρωση οπών
αλλάζει
βρόγχος υστέρησης
Figure from Ohno, J. Crystal Growth 251 (2003) 285
Mn σε ημιαγωγούς III-V
GaAs
Αντικατάσταση MnGa
(καλό => οπές κ
εντοπισμένες
μαγνητικές ροπές
Ενδοπλεγματικό MnI
(κακό! διπλός δότης)
Αντικατάσταση AsGa
antisite
(κακό! Διπλός δότης)
Εικόνα από Jungwirth et al., Rev. Mod. Phys. 78 (2006) 809
Mn σε ημιαγωγούς II-VΙ
Το Mn αντικαθιστά κατιόντα
(Cd, Zn, Mg, . . .)
Καλό, δίνει μόνο εντοπισμένες μαγνητικές ροπές!
Εισάγουμε φορείς ΑΝΕΞΑΡΤΗΤΑ,
εμπλουτίζοντας τα φράγματα των δομών!
II
VI
π.χ.. n- ή p- DMS
ZnSe / Zn1-x-yCdxMnySe / ZnSe
QWs
Cd, Zn, Mg
Se, Te
Η παρουσία μαγνητικών προσμίξεων αυξάνει το spin-splitting των φορέων, Uοσ.
Θεωρία
μέσου
πεδίου



*
*
g
m
U


yN
J
SB
(
)


o

c
0
sp

d
S
2
m
e
Όρος Zeeman
Σπιν πόλωση
Για ηλεκτρόνια ζώνης αγωγιμότητας
Όρος ανταλλαγής σπιν-σπιν μεταξύ
s- (p-) ηλεκτρονίων ζώνης αγωγιμότητας (σθένους)
και
d- ηλεκτρονίων των κατιόντων Μn
N

N
s,down
s,up

N
s
Ns = Ns,up + Ns,down
n
(
r
)

n
(
r
)
down
up
g
SB

J
S
Mn
B
sp

d
2

k
T
B


(επιφανειακές συγκεντρώσεις)
(II) Υψηλότερες θερμοκρασίες.
(I) Χαμηλές θερμοκρασίες
Μέγιστο spin-splitting
~ 1/3 της ασυνέχειας ζώνης αγωγιμότητας
C. Simserides, Phys. Rev. B 69, 113302 (2004)
Το spin-splitting μικραίνει
Αυξάνεται η συνεισφορά των φορέων μειονότητας
Μηχανισμός ανάδρασης λόγω ndown(r) - nup(r).
C. Simserides, Phys. Rev. B 75 (2007) 195344
(I) Χαμηλές θερμοκρασίες.
Απλά κβαντικά φρέατα
με μαγνητικές προσμίξεις
στη ζώνη αγωγιμότητας
υπό παράλληλο μαγνητικό πεδίο
(μη κλιμακοειδής DOS)
Μέγιστο spin-splitting,
~ 1/3 της ασυνέχειας ζώνης αγωγιμότητας
•
Αλλαγές στις φυσικές ιδιότητες π.χ.
•
Πληθυσμοί σπιν-υποζωνών
•
Εσωτερική ενέργεια, U,
•
Εντροπία, S
•
Μαγνήτιση, M
και
σπιν-πόλωση
και Ελεύθερη ενέργεια, F
• ταλάντωση της M
(ΕΑΝ ισχυρός ανταγωνισμός χωρικού και μαγνητικού εντοπισμού)
C. Simserides, Phys. Rev. B 69, 113302 (2004)
C. Simserides, Phys. Rev. B 69, 113302 (2004)
C. Simserides, Phys. Rev. B 69, 113302 (2004)
C. Simserides, Phys. Rev. B 69, 113302 (2004)
Magnetization
considerable fluctuation of M
(if vigorous competition between
spatial and magnetic confinement)
Magnetization fluctuation:
5 A/m
(as adding 1017 cm -3 Mn).
(II) Υψηλότερες θερμοκρασίες.
Σχετική επίδραση
όρου Zeeman – όρου ανταλλαγής
Απλά κβαντικά φρέατα
με μαγνητικές προσμίξεις
στη ζώνη αγωγιμότητας
υπό παράλληλο μαγνητικό πεδίο
(μη κλιμακοειδής DOS)
C. Simserides, Phys. Rev. B 75 (2007) 195344
C. Simserides, Phys. Rev. B 75, 195344 2007
C. Simserides, Phys. Rev. B 75, 195344 2007
Quasi-two-dimensional carriers
in dilute-magnetic-semiconductor
quantum wells under in-plane magnetic field
Conduction band –valence band (bulk)
From Winkler, http://www.niu.edu/~rwinkler/teaching/spin-04/wh1.pdf
Conduction band–
valence band
(bulk-quantum wells)
Spin orientation of holes in quantum wells,
R. Winkler, D. Culcer, S. J. Papadakis, B. Habib and M. Shayegan, Semicond. Sci. Technol. 23 (2008) 114017
Giant MagnetoResistance (GMR)
discovered in 1988 in Fe/Cr/Fe trilayers.
Grünberg and Fert received the 2007 Nobel Prize in Physics.
alternating
Ferromagnetic (FM) nonmagnetic (NM) layers
- If MFM ↑↓,
spin-dependent scattering maximized,
highest resistance.
- If MFM ↑↑
spin-dependent scattering minimized,
lowest resistance
The directions of MFM
manipulated by external magn. fields.
Devices operate
at relatively small magnetic fields
and at room temperature.
Figure from Prinz, Science 282 (1998) 1660
- read heads in modern hard drives
- random access memory (RAM)
spin-valve
Figure from wikipedia
some spintronic applications
using metals (1998)
Figures from Prinz, Science 282 (1998) 1660
some spintronic applications
using metals (1998)
Figures from Prinz, Science 282 (1998) 1660