T. Stubb

Free-carrier absorption of radiation in magnetic semiconductors due to spin-disorder scattering

The free-carrier absorption in the case of spin-disorder scattering is calculated using the density matrix method developed by Kohn and Luttinger (1957). A quantum mechanical equation is derived and then solved by iterations to lowest order. The absorption coefficient alpha at various frequencies is calculated for non-degenerate and degenerate ferromagnetic semiconductors. alpha shows anomalous behaviour at the frequency corresponding to the splitting of the conduction band into spin-up and spin-down sub-bands.

Anomalous Magnetic Field Dependence of Charge Carrier Density in Ferromagnetic Semiconductors

This paper reports calculations of temperature and magnetic field dependent thermal and optical activation energies of a shallow donor state and the energy of the conduction band edge in a ferromagnetic semiconductor. The formation of the bound magnetic polaron (BMP), i.e., a magnetically polarized cluster associated with the donor electron, is taken into account. The solution of a set of coupled equations for the energy of a donor electron and for the local non-uniform magnetization around the donor center indicates that the activation energies have their maxima near the Curie temperature and decrease with the application of a magnetic field. This decrease leads to a strong magnetic field dependence of the charge carrier density nc explains well the giant negative magnetoresistance of EuSe observed experimentally at low temperatures.

Instability of Homogeneous State in Magnetic Semiconductors

The instability of the homogeneous state in a ferromagnetic semiconductor is studied. The electronic part of the free energy is determined using Thomas-Fermi statistical model and the magnetic part is calculated by the molecular field approximation including the RKKY-interaction. The inhomogeneity consists of a small magnetically polarized region with a high electron density surrounded by a less polarized positively charged depletion layer. The inhomogeneous state is found to be stable in a relatively broad temperature range around the Curie temperature at low and intermediate doping densities. The stability range shrinks in an applied magnetic field. At fields exceeding about 3 T or at doping densities larger than 1021 cm-3 the inhomogeneous state is no more stable.

Transport properties of EuO at ferromagnetic resonance

Some transport properties of the magnetic semiconductor EuO have been measured at the ferromagnetic resonance (FMR). A static voltage appeared when the contacts on the sample were unsymmetrially located with respect to the external magnetic field. The induced static field was linearly proportional to the microwave power, the static electric field/microwave power ratio being 5×10−4 V/W mm. A change in sign of the static voltage was found when the angle between external magnetic field and microwave magnetic field was changed through 90 degree. To explain the appearance of the static voltage two models have been analyzed, electrodynamic interaction and magnon drag. The electrodynamic interaction model seems to fit better. A decrease in the sample resistivity at FMR was also observed, the change being 6 per cent.

Microwave Conductivity Dependence of Ferromagnetic Resonance Linewidth in Magnetic Semiconductors

Ferromagnetic and paramagnetic resonance linewidth ΔB has been measured in single crystals of as-grown and annealed EuSe in the liquid helium temperature range. A standard microwave spectrometer operating at K-band frequencies was used. The polished spherical samples were oriented so that the (110) plane contained both the mw and static magnetic fields. The measured large paramagnetic linewidth ~ 1400 G, on which annealing had no effect, is explained solely on the basis of spin-spin interactions. A further conclusion is that the non-classical dipolar and quadrupolar mechanisms are not important in EuSe. In the critical temperature range 4-12 K an exchange narrowing of ΔB, typical for ferromagnets, was found in annealed samples, which were electrically insulating. On the other hand, in the as-grown samples, which had a high microwave conductivity, the ferromagnetic linewidth showed the opposite behaviour, i.e., it increased largely with decreasing temperature being approximately 3000 G at 2.8 K. This exceptionally broad line-width can be explained by an indirect spin-lattice relaxation of magnons due to charge carriers. This effect is proportional to the microwave conductivity σmw of the sample and hence it has the same annealing dependences of ΔB and the dependence on the sample size. In annealed samples surface pit scattering of magnons and 3-magnon processes dominate at low temperatures.

Polarizability of shallow donors in EuSe

Abstract Permittivity measurements at a microwave frequency 24 GHz have been made on n-type EuSe at low temperatures 4.2–77 K after various annealing times. Consideration of different models for annealing dependent permittivity leads to the polarizability of Se vacancy defects as the most likely explanation. Donor polarizability α d = 3.2 × 10 6 A 3 is found and further an estimation for electron effective mass m ∗ = 0.28m 0 .

Microwave Conductivity of EuO and EuSe

The conductivity and dielectric constant have been measured in the temperature range 1.7 to 300 K. Three samples have been studied: unannealed and annealed EuSe and unannealed EuO . At room temperature the microwave conductivity is ∼10−1, 8.0·10−3 and 1.4·10−3 (Ωcm)−1 respectively, the corresponding dc‐conductivities being 3·10−1, ∼10−5 and 10−7 (Ωcm)−1. The strong temperature dependence of the dc‐conductivity is not seen in the microwave conductivity. The dielectric constants obtained from the same measurements are 24.0 and 12.1 for EuO and EuSe respectively. The strong frequency dependence of conductivity can possibly be explained by a hopping mechanism, which could depend on temperature and magnetic order.

Resistivity Decrease Due to Ferromagnetic Resonance in EuO

The d.c. transport properties of EuO at ferromagnetic resonance (FMR) have been studied in the liquid helium temperature range at 24 GHz microwave frequency in samples with d.c. resistivities ρd.c. (4.2 K) = 103-106 Ω-cm. A decrease in ρd.c. was found at FMR. This decrease was largest in a sample with ρd.c. (4.2 K) = 3.3 × 104 Ω-cm and it was strictly proportional to the microwave power absorbed by the sample. The experimental results are explained on the basis of the spin energy transfer model in which two different electronic systems, that is, the localized 4f-electrons being responsible for the FMR and mobile band electrons contributing to the resistivity are assumed. The microwave energy absorbed by 4f-electrons is transferred to the free charge carriers through their mutual interactions and it turns out to give an increase in the kinetic energy of carriers and accordingly an increase in their mobilities. This model explains reasonably well the order of magnitude of the observed changes in ρd.c. and gives an estimate for the energy relaxation time of carriers τ = 3.0 × 10-13 s.

Contribution to the Theory of Magnetoelectric Effect in Magnetic Semiconductors

A generation of a d.c. electric field at ferromagnetic resonance or the magnetoelectric effect in magnetic semiconductors is studied theoretically in the whole magnon wave vector space. The magnetoelectric effect in the classical regime kl 1 are calculated. All the calculated static electric fields are compared with experimental results. At low-microwave power levels the non-linear electrodynamic interaction due to a mixing of the oscillating magnetization (k = 0) and the induced electric field seems to dominate the magnetoelectric effect. In some cases the classical drag effect may also be significant. At sufficiently high power levels the quantum mechanical magnon drag can make the largest contribution. It is shown that in the magnon drag effect the induced static electric field is proportional to the damping coefficient of magnons.

Self-consistent Ground State of Trigonal Tellurium

The purpose of the present paper is to report our non-relativistic Xα calculations of trigonal Te. In the self-consistent (SC) symmetrized OPW (SOPW) method used [1] both the valence states represented by SOPWs and the core states are included in the SC iteration. The only parameters entering into our calculations are the lattice constants a=0.44572 nm, u=0.11736 nm, c=0.5929 nm and the Xα-parameter α. Our SC α=1 band structure is quite similar to the SC pseudopotential one [2], Our bands are characteristically ∼0.2 eV broader and the gaps about the same amount narrower. Our rough α=2/3 density of states (DOS) histogram has two s, two p-bonding and one broader p-non-bonding peaks in agreement with earlier experience [2,4,5].