Constantinos Simserides Institute of Materials Science, NCSR Demokritos, Athens, Greece Two-dimensional carriers under in-plane magnetic field: novel phenomena NN09, Thessaloniki, Greece, July 2009

quantum wells, QWs Host crystals: III-V (e.g. GaAs), II-VI (e.g. CdTe) conduction band or valence band ☺ heterostructure QW (Ga,Al)As/GaAs/(Ga,Al)As conduction band minimum (Ga,Al)As conduction band minimum GaAs Barrier conduction band minimum (Ga,Al)As NO applied fields, NO dopants conduction band offset

(Ga,Al)As/GaAs/(Ga,Al)As heterostructure QW (Ga,Al)As conduction band minimum (Ga,Al)As conduction band minimum GaAs conduction band minimum 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) 5131–5141 C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney, ISBN: 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]

Quasi two-dimensional carriers - Hamiltonian 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: 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) 5131–5141 C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney, ISBN:

Quasi two-dimensional carriers: density of states (DOS) Limit B → 0 or very narrow QWs E i ( k x ) = E i + ħ 2 k x 2 /(2 m * ) DOS regains its step-like form Limit of a simple saddle point, E i ( k x ) = E i – ħ 2 k x 2 /(2 n * ), ( n * > 0) DOS deviates logarithically -ln|ε-E i |ρ(ε)ρ(ε) DOS deviates from the well-known step-like form C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131 C. Simserides, Physica E 21 (2004) 956 C. Simserides, Phys. Rev. B 69 (2004) 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. E iσ ( k x ) must be self-consistently calculated. The k x -dependence increases the numerical cost by

Quasi two-dimensional carriers: Thermodynamic properties population internal energy entropy free energy magnetization C. Simserides, Phys. Rev. B 69 (2004) C. Simserides, J. Phys.: Condens. Matter 21 (2009)

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:

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:

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:

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:

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:

Entirely orbital Thermodynamic properties of quasi two-dimensional carriers under parallel magnetic field C. Simserides, J. Phys.: Condens. Matter 21 (2009) The magnetic susceptibility χ m = ∂M/∂H oscillates between 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

change DOS => oscillation of M Principal thermodynamic properties (IV) Increasing the magnitute of the system, S minimum increases. (I) Depopulation of E 1 (k x ) MAX “cohesion” (II) MIN “cohesion”: occupied E 0 (k x ) splits in two parts ~ |k x | ≈ 0 (III) minima move apart χ m = ∂M/∂H between 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 Θεωρία Peierls R 1933 Z. Phys Πείραμα Wilde M A, Schwarz M P, Heyn C, Heitmann D, Grundler D, Reuter D and Wieck A D 2006 Phys. Rev. B

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) 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) 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: C. Simserides, J. Phys.: Condens. Matter 21 (2009)

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: Depopulation of E 1 (k x ) for Β ~ 13 T

Β // in magnetoresistance O. N. Makarovskii, L. Smrčka, P. Vašek, T. Jungwirth, M. Cukr, and L. Jansen, PRB 62 (2000) Experimentally: - min of resistance (R xx ): step in DOS at E F (= subband depopulation) - max of resitance (R xx ): van Hove singularity in DOS at E F

Β // in photoluminescence (PL): N-type kink Huang D and Lyo S K 1999 Phys. Rev. B Orlita M, Grill R, Hlídek P, Zvára M, Döhler G H, Malzer S and Byszewski M 2005 Phys. Rev. B theory experiment

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] 3d 5 4s 2 ) 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” αλλάζουμε τάση πύλης αλλάζει συγκέντρωση οπών

Mn σε ημιαγωγούς III-V Εικόνα από Jungwirth et al., Rev. Mod. Phys. 78 (2006) 809 Αντικατάσταση Mn Ga (καλό => οπές κ εντοπισμένες μαγνητικές ροπές GaAs Ενδοπλεγματικό Mn I (κακό! διπλός δότης) Αντικατάσταση As Ga 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 / Zn 1-x-y Cd x Mn y Se / ZnSe QWs

Η παρουσία μαγνητικών προσμίξεων αυξάνει το spin-splitting των φορέων, U οσ. Όρος Zeeman Όρος ανταλλαγής σπιν-σπιν μεταξύ s- (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 n down (r) - n up (r). Θεωρία μέσου πεδίου C. Simserides, Phys. Rev. B 69, (2004)C. Simserides, Phys. Rev. B 75 (2007) N s = N s,up + N s,down (επιφανειακές συγκεντρώσεις) Σπιν πόλωση Για 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, (2004)

Magnetization considerable fluctuation of M (if vigorous competition between spatial and magnetic confinement) Magnetization fluctuation: 5 A/m (as adding 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) (II) Υψηλότερες θερμοκρασίες. Σχετική επίδραση όρου Zeeman – όρου ανταλλαγής

C. Simserides, Phys. Rev. B 75,

Quasi-two-dimensional carriers in dilute-magnetic-semiconductor quantum wells under in-plane magnetic field

Conduction band –valence band (bulk) From Winkler,

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)

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) If M FM ↑↑ spin-dependent scattering minimized, lowest resistance alternating Ferromagnetic (FM) - nonmagnetic (NM) layers The directions of M FM 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 M FM ↑↓, 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