Influence of antiferromagnetic spin ordering on the far-infrared active optical phonon modes of $\alpha \text{−}\mathrm{Mn}\mathrm{Se}$

The effects of spin-phonon interaction and magnetic anisotropy on the temperature dependence of the infrared optical phonon modes in the antiferromagnetic $\alpha \text{−}\mathrm{Mn}\mathrm{Se}$ are investigated by use of Green’s function formalism within $1∕z$ perturbation framework. The renormalization effects are calculated explicitly as a function of temperature, phonon-phonon, and spin-phonon interaction constants. Temperature dependence of the renormalized LO phonon frequencies of the $F_{1u}$ infrared active and combinational phonon modes are calculated and compared with experimental data. We have shown that the inclusion of anisotropy is necessary in order to get a good quantitative agreement with the experiment.

Figure 1

(Color online) The fcc lattice of $\alpha \text{−}\mathrm{Mn}\mathrm{Se}$ in the antiferromagnetic phase with an arbitrary spin direction. Here, 1–12 are the labels for the nearest-neighbor ions and 13–18 are respective labels for the next-nearest neighbors.

Figure 2

The magnon-phonon interaction diagram.

Figure 3

The self-energy represented by four intersublattice pair-bubble parts.

Figure 4

(a) The visual survey of longitudinal optical phonon mode ${\Omega }_{01}$ and (b) combinational two-phonon mode ${\Omega }_{02}$ as a function of temperature. Squares with the error bars are the experimental results (Ref. 7), the full lines are our theoretical curves, whereas the triangles represent the residue of phonon hardening due to the phonon-phonon anharmonicity.