First-principles study of vibrational and noncollinear magnetic properties of the perovskite to postperovskite pressure transition of ${\mathrm{NaMnF}}_3$

We performed a first-principles study of the structural, vibrational, electronic, and magnetic properties of ${\mathrm{NaMnF}}_3$ under applied isotropic pressure. We found that ${\mathrm{NaMnF}}_3$ undergoes a reconstructive phase transition at 8 GPa from the $Pnma$ distorted perovskite structure toward the $Cmcm$ postperovskite structure. This is confirmed by a sudden change of the Mn-F-Mn bondings where the crystal goes from corner-shared octahedra in the $Pnma$ phase to edge-shared octahedra in the $Cmcm$ phase. The magnetic ordering also changes from a $G$-type antiferromagnetic ordering in the $Pnma$ phase to a $C$-type antiferromagnetic ordering in the $Cmcm$ phase. Interestingly, we found that the high-spin $d$-orbital filling is kept at the phase transition which has never been observed in the known magnetic postperovskite structures. We also found a highly noncollinear magnetic ordering in the $Cmcm$ postperovskite phase that drives a large ferromagnetic canting of the spins. We discuss the validity of these results with respect to the $U$ and $J$ parameters of the $GGA+U$ exchange-correlation functional used in our study and conclude that large-spin canting is a promising property of the postperovskite fluoride compounds.

Figure 1

(a) Total energy of ${\mathrm{NaMnF}}_3$ as a function of the volume per atom for all different crystal structures. Cmcm and Pnma structures show the lowest-energy values for lower volumes. (b) $\Delta H/\mathrm{atom}$ as a function of external pressure in ${\mathrm{NaMnF}}_3$ structures. Pnma to Cmcm structural transition can be seen at the critical pressure of 8 GPa.

Figure 2

(a) Schematic view of the phase transition from Pnma to Cmcm. Na, Mn, and F atoms are represented in green, violet, and gray colors, respectively. The breaking of bondings for the transition from corner-shared to edge-shared octahedra can be appreciated. (b) Simulated XRD patterns for $Pnma$ and $Cmcm$ structures. The room-temperature $Pnma$ phase is in good agreement with the experimental reports (open triangles) [41, 42, 45]. (c) Octahedra tilt angle as a function of pressure in ${\mathrm{NaMF}}_3$. For $M$ = Zn, Ni, Co, and Mg, experimental results are taken from Yusa et al. [16]. All of these compounds present the transition from the Pnma to the Cmcm structures at a tilting angle close to ${25}^{\circ }$. Experimental results for ${\mathrm{NaMnF}}_3$ at low pressure were taken from Katrusiak et al. [49]. Full agreement between experimental (filled squares) and our theoretical calculations (empty squares) can be appreciated.

Figure 3

Vibrational behavior as a function of isotropic pressure for $Pnma$ and $Cmcm$ $pPv$. The open and filled symbols are the Raman and the infrared modes, respectively.

Figure 4

(a) Energy differences between the different magnetic orderings of the $pPv$ phase of ${\mathrm{NaMnF}}_3$ versus the $U$ parameter. (b) Sketch of the $F_z{C}_y$ and the $A_y{C}_z$ magnetic orderings in the $pPv$ phase of ${\mathrm{NaMnF}}_3$. For $U$ < 6.0 eV, the system exhibits an AFM + FM magnetic state with a high ferromagnetic canting. For $U$ > 6.0 eV, the system transits toward a canted AFM state with no weak FM.

Figure 5

Magnetic canting dependence as a function of $U$ and $J$ parameters for ${\mathrm{NaMnF}}_3$. Canting angle ($\phi$) varies from $0.{11}^{\circ }$ to $17.{94}^{\circ }$ when $U$ goes from 0.0 to 9.0 eV. The canting angle goes from $12.{07}^{\circ }$ to $3.{01}^{\circ }$ when $J$ varies from 0.0 to 1.0 eV.

Figure 6

Projected local density of states (LDOS) of the Cmcm phase of ${\mathrm{NaMnF}}_3$. A regular F-$p$ bonding Mn-$d$ antibonding is observed with small Mn:$3d$–F:$2p$ overlapping DOS is responsible for the small superexchange interaction present in ${\mathrm{NaMnF}}_3$.