Formation Of Magnetic Polarons Research Articles

A variational study of the self-trapped magnetic polaron formation in double-exchange model

We study the formation of self-trapped magnetic polaron (STMP) in an antiferro/ferromagnetic double-exchange model semi-analytically by variational solutions. It is shown that the Jahn–Teller effect is not essential to the STMP formation and the STMP forms in the antiferromagnetic material within the region of the order of the lattice constant. We also confirm that no ground state STMP exists in the ferromagnetic background, but the ground state bound MP could appear due to the impurity potential.

Controlling magnetic moment and its fluctuations in individual semimagnetic quantum dots with different exchange interactions

The influence of exchange interaction between exciton and magnetic impurity spins on magnetic moment and its fluctuations in semimagnetic quantum dots has been investigated with the use of individual dot magnetophotoluminescence technique. In quantum dots with strong exchange interaction, both the polarization of magnetic ions and magnetic fluctuations in a dot are highly influenced by the formation of exciton magnetic polaron. In contrast, in the quantum dots with weak interaction, the localized exciton acts as a perfect noninvasive probe: it allows one to analyze the quantum-dot magnetic moment and its fluctuations with negligibly small influence on the dot magnetization. Numerical values of exchange magnetic field and magnetic polaron energy are obtained and analyzed for both types of dots.

Optical studies of zero-field magnetization of CdMnTe quantum dots: Influence of average size and composition of quantum dots

We show that through the resonant optical excitation of spin-polarized excitons into CdMnTe magnetic quantum dots (QD), we can induce a macroscopic magnetization of the Mn impurities. We observe very broad (4-meV linewidth) emission lines of single dots, which are consistent with the formation of strongly confined exciton magnetic polarons. Therefore, we attribute the optically induced magnetization of the magnetic dots to the formation of spin-polarized exciton magnetic polarons. We find that the photoinduced magnetization of magnetic polarons is weaker for larger dots which emit at lower energies within the QD distribution. We also show that the photoinduced magnetization is stronger for quantum dots with lower Mn concentration, which we ascribe to weaker Mn–Mn interaction between the nearest neighbors within the dots. Due to particular stability of the exciton magnetic polarons in QDs, where the localization of the electrons and holes is comparable to the magnetic exchange interaction, this optically induced spin alignment persists to temperatures as high as 160K.

Evaluation of evidence for magnetic polarons inEuB6

Spin flip Raman scattering measurements on the semi-metal ${\mathrm{EuB}}_{6}$ show the appearance of a Stokes' shift above the ferromagnetic critical temperature. This has been interpreted as arising from the formation of magnetic polarons. However, this data contains a previously unremarked puzzle, in that the energy scale turns out to be considerable lower than expected based on reliable estimates of the exchange interaction mediated by electrons. We propose the Stokes' shift is due to the much smaller on-site coupling of holes with the local spins.

Magnetic polaron conduction in the colossal magnetoresistance materialFe1−xCdxCr2S4

The magnetotransport properties of the spinel ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}{\mathrm{Cr}}_{2}{\mathrm{S}}_{4}$ have been studied. We found that the magnetic polarons dominate the conduction at temperatures above the Curie temperature ${\mathrm{T}}_{c}.$ Upon substitution of Fe by Cd, the carrier density decreases, and the magnetoresistance increases. As a result, the magnetic polarons become more stable, in agreement with the theoretical predictions of Majumdar and Littlewood for the magnetoresistance in low carrier density ferromagnets. The evolution of magnetic polarons in ${\mathrm{CdCr}}_{2}{\mathrm{S}}_{4}$ has been studied with electron spin resonance (ESR) measurements. As the temperature increases, the peak-to-peak linewidth $\ensuremath{\Delta}{H}_{\mathrm{pp}}$ decreases in a broad temperature range, providing direct evidence for the existence of magnetic polarons. The analysis of the ESR spectra reveals the existence of two temperature scales, which are related to the evolution of the magnetic polarons. The first temperature, denoted as ${T}_{p},$ corresponds to the formation of magnetic polarons. The second temperature, denoted as ${T}^{*},$ can be related to the temperature where correlations among the magnetic polarons occur.

Dynamics in magneto-optical properties of digital magnetic Zn 1− xCd xSe quantum wells

We have studied dynamics in magneto-optical properties of digital magnetic Zn 1− x Cd x Se quantum wells (QWs). Various types of MnSe layers were digitally doped in the Zn 1− x Cd x Se QWs. The giant Zeeman shift energy and the field-induced enhancement of the photoluminescence (PL) intensity of excitons depend on the digital-doping profile. This can be attributed to the spatial overlap of the exciton wavefunction with the 0.5 monatomic-thick effective paramagnetic layers at the interfaces between the antiferromagnetic MnSe layers and non-magnetic Zn 1− x Cd x Se layers. The exciton magnetic polaron (MP) formation energy as large as 18.6 meV is observed in time-resolved PL spectra for the digital magnetic QWs. The MP formation energy and time are also affected by the digital-doping profile.

磁性イオンを希薄ドープした半導体量子ナノワイヤ中のスピン制御

We have studied anisotropic exchange interaction in (CdTe)0.5 (Cd0.75Mn0.25Te)0.5 tilted superlattices fabricated by fractional monolayer growth onto a 1° off vicinal surface of Cd0.74Mg0.26Te (001). The (CdTe)0.5(Cd0.75Mn0.25Te)0.5 tilted superlattices have been confirmed by polarized photoluminescence to be equivalent to compositionally modulated quantum wires consisting of CdTe-rich and Cd0.75Mn0.25Te-rich wires. The Stokes shift for the CdTe-rich wires is remarkable at less than 10K. The large Stokes shift is due to exciton-magnetic polaron formation and non-magnetic localization. The exciton magnetic polaron formation is a result of the exchange interaction between excitons and Mn ions. The exchange interaction causes the large Zeeman shift of the CdTe-rich wires. The Zeeman shift depends on the direction of the magnetic field in the (001) plane; the Zeeman shift in the magnetic field parallel to the wire direction is smaller than that in the perpendicular field. We demonstrate reorientation of hole spins in the parallel magnetic field by polarized magneto-photoluminescence measurements. The reorientation of the hole spins causes the valence-band mixing, which results in the small Zeeman shift in the parallel magnetic field.

Spin dynamics of excitons and magnetic ions in Cd1−xMnxTe/Cd1−yMgyTe quantum wells

Dynamical processes of spin systems of exciton and magnetic ions in diluted magnetic semiconductor quantum wells were studied by using transient pump-and-probe absorption spectroscopy technique. Bleaching of the spin-down exciton absorption peak appeared with a red shift of 10meV within the lifetime of the pump created excitons, indicating the excitonic magnetic polaron formation due to the s,p–d exchange interaction between excitons and Mn ions. After the excitons recombine, induced absorption at the spin-aligned region of the magnetic ion matrix, which is left by the excitonic magnetic polaron, was observed with and without magnetic fields. These induced absorption signals arose from the local fields projected by the Mn spins that enhanced or suppressed Zeeman splitting of exciton. The decay times of these induced absorption peaks are longer than 3ns, implying the long-lived spin polarization of the Mn ions. From the energy splitting of the induced absorption peaks, the local field strength of 2.5T was extracted.

Structural and magneto‐optical studies on multiple quantum dots containing magnetic semiconductors

We have fabricated single and multi-layer self-assembled quantum dot (QD) systems based on CdSe/ZnSe combination, including magnetic semiconductors (DMSs). Transmission electron microscopy (TEM) images shows that magnetic QDs are formed within the CdMnSe layer, and they are vertically correlated in multi-layer quantum dot systems. Magneto-optical experiments were also carried out on those structures. The PL energy from multi-layer QDs appears at a lower energy than that emitted by a single QD layer, suggesting that there exists electronic coupling between the QD layers. When an external magnetic field is applied, the PL peaks from QDs both in single-layer and in multi-layer form exhibit a large intensity enhancements and energy shifts, a behavior that is typical for many low dimensional systems involving DMSs. The observed weak PL energy dependence in low magnetic fields can be understood in terms of magnetic polaron formation in these DMS QD systems. We also discuss statistical magnetic fluctuations in these systems, as revealed by PL line narrowing in a magnetic field.

FMR probing of ‘spontaneous’ and Ru-doping induced ferromagnetism in Sm 0.2Ca 0.8Mn 1− xRu xO 3 ( x≤0.08) manganites

The FMR spectra of electron-doped Sm 0.2Ca 0.8Mn 1− x Ru x O 3 (0≤ x≤0.08) system are measured and analyzed in the temperature interval 100≤T≤320 K, including all critical points of magnetic transitions. It is shown that the origin of macroscopic magnetization in the parent Sm 0.2Ca 0.8MnO 3 and Ru-doped compounds is essentially different. The bound magnetic polarons formation at temperatures below the Neel point is suggested to be responsible for the appearance of a minute ‘spontaneous’ magnetic moment in Sm 0.2Ca 0.8MnO 3. Doping with Ru induces formation of ‘conventional’ ferromagnetic phase in antiferromagnetic matrix. Such a phase is characterized by a Curie temperature, which is higher than the Neel temperature of the matrix. Magnetic phase diagrams of Sm 0.2Ca 0.8Mn 1− x Ru x O 3 determined by ferromagnetic resonance and dc magnetic measurements are discussed.

Magneto-photoluminescence studies of diluted magnetic semiconductor type-II quantum wells ZnMnSe/ZnSSe

Magneto-photoluminescence (PL) has been studied in type II Zn 1− x Mn x Se/ZnS y Se 1− y multiple quantum wells (QWs) with the Mn content x between 0.03 and 0.15. Two PL lines are observed in the samples with x equal to 0.05 and 0.15. The lines are attributed to the excitons of two different types, coexisting in the QWs. At least one of them is associated with the formation of an exciton magnetic polaron.

Magneto-Transport Properties of p-Type Zn1−xMnxTe:N Grown by MBE

The magneto-transport properties of nitrogen-doped p-Zn1−xMnxTe films grown by MBE were studied, with an emphasis on the dependence on the Mn composition and the hole concentration. The Mn composition x and hole concentration p were varied in the range of x = 0.026–0.068 and p = 8.2 × 1018–2.6 × 1019 cm−3. In the measurement of magnetoresistance (MR), a large negative component was observed at low temperatures. In the dependence on the Mn composition, it was found the magnitude of the negative component of MR became larger and survived up to higher temperatures in the sample with a higher Mn composition. The observed negative MR is attributed to the localization of holes due to the magnetic polaron formation. The origin of the dependence on the Mn composition is discussed.

Magnetic and lattice polaron in the Holsteint−Jmodel

We investigate the interplay between the formation of lattice and magnetic polaron in the case of a single hole in the antiferromagnetic background. We present an exact analytical solution of the Holstein-t-J model in infinite dimensions. Ground state energy, electron-lattice correlation function, spin bag dimension as well as spectral properties are calculated. The magnetic and hole-lattice correlations sustain each other, i.e. the presence of antiferromagnetic correlations favors the formation of the lattice polaron at lower value of the electron-phonon coupling while the polaronic effect contributes to reduce the number of spin defects in the antiferromagnetic background. The crossover towards a spin-lattice small polaron region of the phase diagram becomes a discontinuous transition in the adiabatic limit.

Nano-Optics on Individual Quantum Objects - From Single to Coupled Semiconductor Quantum Dots

Some recent highlights of our optical studies on single and coupled semiconductor quantum dots are reviewed. In the first part, we concentrate on the role of spins and spin-spin interaction in nonmagnetic and magnetic single quantum dots. In the case of strictly resonant excitation of the ground state in self-assembled CdSe/ZnSe quantum dots, we find an exciton spin relaxation time, which exceeds the recombination lifetime significantly. Linear polarization has to be used for these experiments, as the electron-hole exchange interaction lifts the spin degeneracy and the eigenstates are linear combinations of spin-up and spin-down excitons. In a magnetic quantum dot, the exchange interaction between carrier spins and the spins of magnetic ions is shown to be responsible for giant magneto-optical effects. We demonstrate the formation of zero-dimensional magnetic polarons and we succeeded in measuring the magnetization on a scale of a few nanometers using the characteristic photoluminescence signal of individual quantum dots as experimental monitor. The second part is devoted to pairs of single quahtum dots. On one hand, single exciton tunneling within an individual quantum dot pair is demonstrated studying single pairs of vertically correlated strain-induced and self-organized quantum dots. On the other hand, we show that in a pair of lithographically defined single dots with strongly different g-factors the energy spacing between the dot ground states can be tuned in an external magnetic field by about 10 meV, giving access to a controlled coupling between two individual quantum dots.

Magnetic polarons in weakly doped high-Tcsuperconductors

The formation of magnetic polarons in an antiferromagnetic medium is studied numerically in wide range of parameters with special attention to high-${T}_{c}$ superconductors. We consider a Hamiltonian describing $d\ensuremath{-}d$ exchange interactions between d spins of a finite Heisenberg antiferromagnet, $p\ensuremath{-}d$ interactions between a conducting hole p, and d spins, as well as kinetic energy of hole. The decoupling of orbital and spin degrees of freedom allows us to consider the spin Hamiltonian and kinetic energy separately. The spin Hamiltonian is solved exactly with use of the Lanczos method of diagonalization. We conclude that $p\ensuremath{-}d$ exchange interaction favors magnetic polarons localized on one site of the antiferromagnet. Adding the kinetic energy does not change essentially the phase diagram of magnetic polarons formation. For parameters relevant for high-${T}_{c}$ superconductors either a polaron localized on one lattice cell or a small ferron form. However, we find that the contribution of magnetic and phonon terms in the formation of a polaron in weakly doped high-${T}_{c}$ materials can be comparable.

Charge and spin inhomogeneous phases in the ferromagnetic Kondo lattice model

We study numerically the one-dimensional ferromagnetic Kondo lattice. This model is widely used to describe nickel and manganese perovskites. Due to the competition between double and super-exchange, we find a region where the formation of magnetic polarons induces a charge-ordered state. This ordering is present even in the absence of any inter-site Coulomb repulsion. There is an insulating gap associated to the charge structure formation. We also study the insulator-metal transition induced by a magnetic field which removes simultaneously both charge and spin ordering.

Correlation between exciton decay time and Stokes shift in digital magnetic heterostructures

The exciton recombination time and the exciton photoluminescence Stokes shift are systematically investigated in a set of CdTe/Cd 1 - x Mg x Te quantum-well samples containing MnTe layers with the thickness below or equal to 1 ML. Similar to diluted magnetic semiconductors, these digital magnetic heterostructures exhibit strongly magnetic-field-dependent photoluminescence lines which are inhomogeneously broadened. Both quantities under investigation depend on the Mn content, on the details of the Mn distribution within the quantum wells, and on the energy of detection. Three sets of samples are investigated: digital magnetic heterostructures containing four MnTe layers with equidistant spacing and various thickness of the MnTe layers, quantum wells containing 1-ML MnTe at various positions in the quantum well, and quantum wells containing in total 1-ML MnTe but distributed in the quantum well in different ways. For all samples, the exciton recombination time is strongly correlated to the Stokes shift. This correlation is caused by exciton localization, leading to a mixing of radiatively decaying states with small momentum with nonradiative states with large momentum. In our experiment, however, a linear dependence between the exciton decay time and the Stokes shift is observed, which is not yet explained by theory, to our knowledge. Although, the luminescence properties in semimagnetic semiconductors are affected by exchange interactions leading to the formation of magnetic polarons, this process can be ruled out as the origin of the observed correlation.

Dynamics of Zero-Dimensional Excitons in a Semimagnetic Environment

Time-resolved measurements on self-assembled CdSe/ZnMnSe quantum dots are presented. A rather long excitonic decay time of 580 ps is found which indicates a suppression of nonradiative recombination via the internal Mn2+ transition. The long excitonic lifetime allows for the formation of magnetic polarons, as evidenced by a transient redshift of the luminescence emission with a time constant of 125 ps. In a magnetic field, a decrease of the measured excitonic decay time is observed and a possible mechanism based on an interplay between bright and dark excitons is discussed.

Dynamics of Zero-Dimensional Excitons in a Semimagnetic Environment

Time-resolved measurements on self-assembled CdSe/ZnMnSe quantum dots are presented. A rather long excitonic decay time of 580 ps is found which indicates a suppression of nonradiative recombination via the internal Mn 2+ transition. The long excitonic lifetime allows for the formation of magnetic polarons, as evidenced by a transient redshift of the luminescence emission with a time constant of 125 ps. In a magnetic field, a decrease of the measured excitonic decay time is observed and a possible mechanism based on an interplay between bright and dark excitons is discussed.

Conductivity Control in Nitrogen‐Doped p‐Zn 1‐x Mn x Te and Magneto‐Transport Properties

p-doped Zn 1-x Mn x Te films were grown by MBE with nitrogen plasma as a dopant source. The highest hole concentration, which attained 4.5 × 10 20 cm -3 in ZnTe, exhibited decreasing tendency with the Mn composition x, but it kept the order of 10 19 cm -3 in the range of x < 0.1. In Zn 1-x Mn x Te with p = 1.5-4.8 × 10 19 cm -3 , the temperature dependence of the resistivity exhibited insulating behavior. In the magneto-transport measurement, a large negative magnetoresistance (MR) was observed at low temperatures below 4.2 K This was attributed to the localization of holes due to the magnetic polaron formation at zero field and its release under magnetic fields.