Exchange Interactions In Magnetic Semiconductors Research Articles

Magnetic neutron diffraction under pressures up to 43 GPa. Study of the EuX and GdX compounds

We present some recent results on magnetic neutron studies at pressures above 40 GPa. We used diamond and sapphire anvil pressure cells for low temperature neutron studies and a powder diffractometer specialized for high pressure studies. Focusing systems and low-background conditions allowed us to study samples with volumes as small as 0.001 mm3 in a diamond anvil cell at a pressure of 50 GPa. This technical progress allowed us to obtain new results in studies of “textbook” magnetic insulators EuX (X = S, Se, Te) and GdX (X = As, Sb, Bi). We found new magnetic phases. In the Eu-chalcogenides we observed a strong anion-dependent increase of the ferromagnetic exchange with decreasing lattice constant. In contrast, in the GdX compounds the antiferromagnetic order remains stable up to a pressure of 43 GPa. We show the importance of our results to understand the origin of indirect exchange interactions in magnetic semiconductors with well localized magnetic shells.

Superexchange in insulators and semiconductors: II. The range of the exchange interaction

In this paper we discuss the range of exchange interactions in magnetic semiconductors. It is shown that the range depends strongly on the energy required to excite an electron from the fully occupied valence band to the empty magnetic d orbitals. The range of the exchange interaction and of the spin-density distribution is the same when this excitation energy is large. It is found that kinetic exchange and correlation exchange are the dominant contributions. The usual perturbation theory breaks down when the dp excitation energy becomes of the order of the band width. In this case one has to calculate the exchange interaction in a more rigorous way. This limit is discussed using two-particle Green functions. It is found that these results deviate strongly from the ones obtained using perturbation theory. We derive a path model from an analysis of the effective transfer between two magnetic orbitals. Such a model can explain the long-range exchange interactions reported in the last decades in a large number of magnetic semiconductors and semimagnetic semiconductors. This path model can explain the anisotropy of long-range spin-density distributions found in doped semiconductors.

Indirect Exchange in Semiconductors

The effect of intervalley transitions on the indirect exchange interaction in magnetic semiconductors is considered. Using second-order perturbation theory, we derive an expression for the spin-spin coupling energy in terms of the susceptibility $\ensuremath{\chi}({\mathbf{R}}_{12})$ for one valley. When the spins are located on lattice sites and a local $s\ensuremath{-}f$ exchange interaction is used, the coupling energy reduces to a particularly simple form. Calculations are based on a two-valley model, for simplicity. The resulting coupling is used to study the ferromagnetic spin wave spectrum for a lattice of spins. The latter quantity is shown to be especially sensitive to the ratio of the Fermi wave number to the separation of valley minima.

Indirect Exchange in Many-Valley Semiconductors

The effect of intervalley transitions on the indirect exchange interaction in magnetic semiconductors is considered. Using second-order perturbation theory, we derive an expression for the spin-spin coupling energy in terms of the susceptibility χ(R12) for one valley. When the spins are located on lattice sites, and a local s-f exchange interaction is used, the coupling energy reduces to a especially simple form. Calculations are based on a two-valley model, for simplicity. The resulting coupling is used to study the paramagnetic Curie temperature and ferromagnetic spin-wave spectrum for a lattice of spins. The latter quantity is shown to be especially sensitive to the ratio of Fermi wavenumber to the separation of valley minima. The paramagnetic Curie temperature θ is shown to be independent of the direction and of the valley separation. Using the number of valleys as a parameter, we have fit the variation of θ with concentration in EuxGd1−xSe and EuxGd1−xTe. In this way we obtain four for the valley number in Se and sixteen for the case of Te.