Kinetic Exchange between the Conduction Band Electrons and Magnetic Ions in Quantum-Confined Structures

Abstract

We provide an experimental evidence and a theoretical substantiation for a strong reduction of the s-d exchange interaction between electrons and Mn-ion spins with increasing degree of the confinement in nanostructures of diluted magnetic semiconductors. By spin-flip Raman scattering a strong (up to 25%) reduction of the exchange parameter is observed in ͑Cd, Mn͒Te͑͞Cd, Mn, Mg͒Te quantum well structures. As a responsible mechanism we suggest switching-on of the kinetic exchange for the conduction electrons with finite k vectors. Quantitative agreement between experimental data and calculations is achieved. PACS numbers: 75.30.Et, 71.70.Ej, 75.50.Pp, 78.20.Ls Semimagnetic or diluted magnetic semiconductors (DMS) are known for their giant magneto-optical effects originating in a strong sp-d exchange interaction between the band electrons and the magnetic (e.g., Mn) ions. Incorporation of semimagnetic layers in quantum-confined heterostructures opened new possibilities for the "spin splitting engineering" [1]. In this context, in addition to a magnetic field, temperature, and Mn molar fraction dependences, also the confinement energy and the size quantization became means of an effective tuning of the spin splittings. While a precise tuning of the spin splitting is of great significance for future-spin-dependent electronics, it is already now of obvious importance in, e.g., studies of samples with zero g-factor in the fractional quantum Hall regime [2]. Also, exciting physical phenomena have been reported recently for semimagnetic heterostructures: coherent spin excitations [3,4], magnetic polaron formation [5], and ferromagnetic hole alignment in p-type doped structures [6].For the electrons from the vicinity of the conduction band edge the exchange interaction with the localized d electrons of magnetic ions is described by the Hamiltonian:where the parameter of the s-d exchange interaction a is positive. In the case of the holes, the exchange energy has the same form but the parameter of p-d exchange interaction b , 0. In Eq. (1) s and r are the spin (total angular momentum in the case of the holes) and coordinate operators of a carrier, and S i and R i are the total spin and coordinate of the ith magnetic ion. A positive sign of a results from the direct (or potential) exchange of the conduction band electron with the d electrons of Mn ions. The negative sign of b is due to a dominant role of the kinetic exchange [7] which occurs because of possible transitions to virtual states in the d shell [8].A possibility of a modification of the exchange parameters under quantum-confined conditions has been recognized already with the first semimagnetic semiconductor quantum wells (QWs) studied. However, experimental evidences showing unambiguously such a modification of the exciton Zeeman splitting, i.e., of ͑a 2 b͒, have been found only recently [9]. A special design of the QW structures was crucial for the latter studies since one had to rule out effects related to a modification of magnetic properties at the magneti...

Luminescence of Cd0.7Mn0.3Te crystals in magnetic field: Linewidth, Landau quantization, and carrier effective mass

“…The reduction of exchange constant α was observed in samples with reduced dimensionality [9] when the decrease of α by 25% was found for QWs of 4.5 nm width. But our experimental results do not confirm the trend of exchange constants' reduction.…”

Orbital pathways for Mn2+-carriersp−dexchange in diluted magnetic semiconductor quantum dots

“…[1][2][3][32][33][34][35][36] Whereas the general features of sp-d exchange appear to translate across length scales, specific contrasts have been emphasized in some cases. 12,13,[36][37][38][39][40] Most prominently, a strong quantum-confinement-induced change in the fundamental nature of the conduction-band-electron ( e CB − ) -Mn 2+ exchange (s-d exchange) interaction has been described both theoretically 36,37 and experimentally. 37,[41][42][43][44][45] According to k·p-model descriptions of Mn at finite k vectors.…”

Optical probing of the spin state of a single magnetic impurity in a self-assembled quantum dot

“…Since many semiconductors efficiently emit and absorb light, the spin states of electrons and magnetic impurities can be manipulated optically by using circularly-polarized light pulses 4 . In diluted magnetic semiconductors such as bulk crystals, quantum wells and dots, photo-generated excitons interact with a large collection of spins of Mn impurities and therefore a large number of degrees of freedom becomes involved 5,6,7,8,9,10,11 . In these systems, it is challenging to address individual spins of Mn atoms.…”