Competition between Electron–Phonon and Spin–Phonon Interaction on the Band Gap and Phonon Spectrum in Magnetic Semiconductors - Angel T. Apostolov; Iliana N. Apostolova; Julia M. Wesselinowa (Applied Sciences, 2024)
Using the microscopic s-f model and Green’s function theory, we study the temperature dependence of the band gap energy <semantics>Eg</semantics> and the phonon energy <semantics>ω</semantics> and damping <semantics>γ</semantics> of ferro- and antiferromagnetic semiconductors, i.e., with different signs of the s-f interaction constant I. The band gap is a fundamental quantity which affects various optical, electronic and energy applications of the materials. In the temperature dependence of <semantics>Eg</semantics> and the phonon spectrum, there is a kink at the phase transition temperature <semantics>TC</semantics> or <semantics>TN</semantics> due to the anharmonic spin–phonon interaction (SPI) R. Moreover, the effect of the SPI R and electron–phonon interaction (EPI) A on these properties is discussed. For <semantics>I>0,R>0</semantics>, <semantics>Eg</semantics> decreases with increasing SPI and EPI, whereas for <semantics>I<0,R>0</semantics>, there is a competition; <semantics>Eg</semantics> increases with raising the EPI and decreases for enhanced SPI. For <semantics>R<0</semantics>, in both cases, the SPI and EPI reduce <semantics>Eg</semantics>. The magnetic field dependence of <semantics>Eg</semantics> for the two signs of I and R is discussed. The SPI and EPI lead to reducing the energy of the phonon mode <semantics>ω</semantics> = 445 cm−1 in EuO (<semantics>I>0</semantics>, <semantics>R<0</semantics>), whereas <semantics>ω</semantics> = 151 cm−1 in EuSe (<semantics>I>0</semantics>, <semantics>R>0</semantics>) is enhanced with increasing EPI and reduced with SPI. Both the SPI and EPI lead to an increasing of the phonon damping in EuO and EuSe. The results are compared with the existing experimental data.