Anomalous Phonon Lifetime Shortening in Paramagnetic CrN Caused by Spin-Lattice Coupling: A Combined Spin and Ab Initio Molecular Dynamics Study

We study the mutual coupling of spin fluctuations and lattice vibrations in paramagnetic CrN by combining atomistic spin dynamics and ab initio molecular dynamics. The two degrees of freedom are dynamically coupled, leading to nonadiabatic effects. Those effects suppress the phonon lifetimes at low temperature compared to an adiabatic approach. The dynamic coupling identified here provides an explanation for the experimentally observed unexpected temperature dependence of the thermal conductivity of magnetic semiconductors above the magnetic ordering temperature.

Figure 1

(a) Thermal conductivities of CrN [5] and MgO [6] compared to (b) averaged phonon lifetimes obtained by DLM-AIMD, ASD-AIMD and nonmagnetic AIMD. (c) CrN spectral density of the transversal acoustic phonon at the $L$ point at $T=300\mathrm{K}$ and (d) $T=1000\mathrm{K}$. Shaded areas indicate the corresponding nonfitted spectral densities.

Figure 2

Representation of the combined ASD-AIMD approach: After a preequilibration, a subsequent scheme of ASD and AIMD runs are performed. At each step, the actual spin state $\{\mathbf{S}\}$ and the actual atomic positions $\{\mathbf{R}\}$ serve as input of the following AIMD and ASD calculation, respectively. Within each coupled step, the atoms and spins propagate for 1 fs in total.

Figure 3

Two dimensional probability diagrams of Cr-Cr nearest neighbor pairs with respect to their spin orientation. The spin orientation is given by the dot products of the two spin vectors in a pair [1 (-1) corresponds to the ferro- (antiferro-) magnetic coupling]. The diagrams are plotted for different temperatures and methods: (a) DLM-AIMD at $T=300\mathrm{K}$, (b) ASD-AIMD at $T=300\mathrm{K}$, (c) DLM-AIMD at $T=1000\mathrm{K}$, and (d) ASD-AIMD at $T=1000\mathrm{K}$. The red lines show the linear regression between distances and spin orientations.

Figure 4

Spin pair autocorrelation functions of CrN at $T=300\mathrm{K}$ (a) and $T=1000\mathrm{K}$ (b) obtained from ASD (fixed lattice), ASD on a pre-calculated DLM-AIMD vibrating lattice (dynamic lattice) and ASD-AIMD (coupled dynamics).