Constantinos SimseridesConstantinos Simserides

Institute of Materials Science, NCSR Demokritos, Athens, Greece

Two-dimensional carriers Two-dimensional carriers under under in-planein-plane magnetic field magnetic field: :

novelnovel phenomenaphenomena

NN09, Thessaloniki, Greece, 13-15 July 2009NN09, Thessaloniki, Greece, 13-15 July 2009

quantum wells, QWsquantum wells, QWs

Host crystals:

III-V (e.g. GaAs),

II-VI (e.g. CdTe)

conduction band

orvalence

band

☺ heterostructure QW (Ga,Al)As/GaAs/(Ga,Al)A

s

conduction band

minimum (Ga,Al)As

conduction band

minimumGaAs

BarrierBarrier

conduction band

minimum(Ga,Al)As

NO applied fields, NO dopants

conduction band offset

(Ga,Al)As/GaAs/(Ga,Al)Asheterostructure QW

(Ga,Al)Asconduction

band minimum

(Ga,Al)As conduction

band minimum

GaAs conduction

band minimum

donors donors

with selective doping

Β

quasi two-dimensional carriers under parallel magnetic field

(the elegant concept of Landau levels must be abandoned)

For this orientation . . .

Systems without magnetic impurities: a diamagnetic to paramagnetic transition of entirely orbital origin is predicted, while entropy...

Quantum mechanical properties & density of states (DOS)

Comparison with other carrier systems under magnetic / electric field

Thermodynamic properties (population, entropy, internal & free energy, magnetization, magnetic susceptibility)

Spintronic systems (with magnetic impurities): Spin-subband populations and spin-polarization

Examples of modified physical properties (magnetoresistance oscillations, N-type kink in photoluminescence, etc)

C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131–5141C. 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

Comparison with other carrier systems under magnetic / electric field

B//yB//y, E//zB=0, QW(z), [E//z]B//y, PQW(z)B//y, QW(z), [E//z]

Quasi two-dimensional carriers - Hamiltonian

C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131–5141C. 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

Free particle along y axis, while in the xz plane:

Quasi two-dimensional carriers Force on the electrons - Magnetic length

C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131–5141C. 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)

i iE

Am)()( 2

*

Limit B → 0 or very narrow QWsEi(kx) = Ei + ħ2kx

2/(2m*)DOS regains its step-like form

Limit of a simple saddle point,Ei(kx) = Ei – ħ2kx

2/(2n*), (n* > 0)DOS deviates logarithically-ln|ε-Ei| ρ(ε)

,

2)(

*

2

1)(

iiE

Am

DOS deviates from the well-known step-like form

C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131C. Simserides, Physica E 21 (2004) 956 C. Simserides, Phys. Rev. B 69 (2004) 113302

, ,

,2

*

)(

))((

4

2)(

i xi

xix

kE

kEdk

mA

DOS changes qualitatively & quantitatively

Equation holds for any type of competition

between spatial and magnetic confinement

The main features of this DOS, the Van Hove singularities, are not –generally- simple saddle points.The DOS, modification changes the physical properties.

Eiσ(kx) must be self-consistently calculated.

The kx-dependence increases the numerical cost by 100-1000.

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 carriersunder 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

change DOS => oscillation of M

Principal thermodynamic

properties

(IV) Increasing the magnitute of the system, S minimum increases.

(I) Depopulation of E1(kx) MAX “cohesion”

(II) MIN “cohesion”: occupied E0(kx)splits in two parts ~ |kx| ≈ 0

(III) minima move apart

χm = ∂M/∂H between < 0 & > 0 values:

(purely orbital diamagnetic - paramagnetic oscillation)

New phenomenon (under in-plane Β) 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

ΘεωρίαPeierls R 1933 Z. Phys. 81 186

ΠείραμαWilde 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 LiteratureRelevant 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

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

Depopulation of E1(kx) for Β ~ 13 T

ΒΒ // in // in magnetoresistancemagnetoresistance

O. N. Makarovskii, L. Smrčka, P. Vašek, T. Jungwirth, M. Cukr, and L. Jansen, PRB 62 (2000) 10908

Experimentally: - min of resistance (Rxx): step in DOS at EF (= subband depopulation)

- max of resitance (Rxx): van Hove singularity in DOS at EF

Β // in photoluminescence (PL): N-type kink

Huang D and Lyo S K 1999 Phys. Rev. B 59 7600Orlita M, Grill R, Hlídek P, Zvára M, Döhler G H, Malzer S and Byszewski M 2005 Phys. Rev. B 72 165314theory

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, invited chapter in the book "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, NY. Editors: Alfred Ruyter and Harper O'Mahoney, in press

C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131

Question:

What about Β // in spintronics?

- 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

Doping = introduction of impurities, on purpose

Host crystals, doping, impurities

Εικόνα από Ohno, Science 281 (1998) 951

☺ DMS = dilute magnetic semiconductor, a semiconductor doped with (dilute) magnetic

impurities

Εικόνες από MacDonald Schiffer Samarth, Nature Materials 4 (2005) 195

Spintronics = spin + electronics: use

carrier charge as well as spin

Carriers (holes, electrons)

induce ferromagnetism!

DMS:Electric field

control of

ferromagnetism.

αλλάζει βρόγχος

υστέρησης

Figure from Ohno, J. Crystal Growth 251 (2003) 285

“M

”

αλλάζουμετάση πύλης

αλλάζει συγκέντρωση

οπών

Mn σε ημιαγωγούς III-V

Εικόνα από Jungwirth et al., Rev. Mod. Phys. 78 (2006) 809

Αντικατάσταση MnGa

(καλό => οπές κ εντοπισμένες μαγνητικές ροπές

GaAs

Ενδοπλεγματικό MnI

(κακό! διπλός δότης)

Αντικατάσταση AsGa antisite (κακό! Διπλός δότης)

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 Cd, Zn, Mg

VI Se, Te

π.χ.. n- ή p- DMS ZnSe / Zn1-x-yCdxMnySe / ZnSe QWs

Η παρουσία μαγνητικών προσμίξεων αυξάνει το spin-splitting των φορέων, Uοσ

.

)(2 0

**

Sdspce

o SBJyNm

mgU

Όρος Zeeman

Tk

nnSJSBg

B

updowndspBMn 2

)()( rr

Όρος ανταλλαγής σπιν-σπιν μεταξύs- (p-) ηλεκτρονίων ζώνης αγωγιμότητας (σθένους)

και d- ηλεκτρονίων των κατιόντων Μn

(I) Χαμηλές θερμοκρασίες

Μέγιστο spin-splitting~ 1/3 της ασυνέχειας ζώνης αγωγιμότητας

(II) Υψηλότερες θερμοκρασίες.

Το spin-splitting μικραίνει Αυξάνεται η συνεισφορά των φορέων μειονότητας

Μηχανισμός ανάδρασης λόγω ndown

(r) - nup

(r).

Θεωρία μέσου

πεδίου

C. Simserides, Phys. Rev. B 69, 113302 (2004) C. Simserides, Phys. Rev. B 75 (2007) 195344

s

upsdowns

N

NN ,,

Ns = Ns,up + Ns,down (επιφανειακές συγκεντρώσεις)

Σπιν πόλωσηΓια ηλεκτρόνια ζώνης αγωγιμότητας

Απλά κβαντικά φρέατα με μαγνητικές προσμίξεις στη ζώνη αγωγιμότητας υπό παράλληλο μαγνητικό

πεδίο (μη κλιμακοειδής DOS)

• ταλάντωση της M (ΕΑΝ ισχυρός ανταγωνισμός χωρικού και μαγνητικού εντοπισμού)

• Αλλαγές στις φυσικές ιδιότητες π.χ.

• Εντροπία, S

• Πληθυσμοί σπιν-υποζωνών και σπιν-πόλωση

• Εσωτερική ενέργεια, U, και Ελεύθερη ενέργεια, F

• Μαγνήτιση, M

(I) Χαμηλές θερμοκρασίες.

Μέγιστο spin-splitting,~ 1/3 της ασυνέχειας ζώνης αγωγιμότητας

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).

Απλά κβαντικά φρέατα με μαγνητικές προσμίξεις στη ζώνη αγωγιμότητας υπό παράλληλο μαγνητικό

πεδίο (μη κλιμακοειδής DOS)

C. Simserides, Phys. Rev. B 75 (2007) 195344

(II) Υψηλότερες θερμοκρασίες.

Σχετική επίδραση όρου Zeeman – όρου ανταλλαγής

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.

Figure from Prinz, Science 282 (1998) 1660

- If MFM ↑↑ spin-dependent scattering minimized,lowest resistance

alternatingFerromagnetic (FM) -

nonmagnetic (NM) layers

The directions of MFM manipulated by external magn. fields.

Devices operate at relatively small magnetic fields and at room temperature.

- read heads in modern hard drives- random access memory (RAM)

- If MFM ↑↓, spin-dependent scattering maximized, highest resistance.

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