Spin-phonon coupling and high-pressure phase transitions of $R\mathrm{Mn}{\mathrm{O}}_3$ ($R=\mathrm{Ca}$ and Pr): An inelastic neutron scattering and first-principles study

We report inelastic neutron scattering measurements over 7–1251 K in $\mathrm{CaMn}{\mathrm{O}}_3$ covering various phase transitions, and over 6–150 K in $\mathrm{PrMn}{\mathrm{O}}_3$ covering the magnetic transition. The excitations around 20 meV in $\mathrm{CaMn}{\mathrm{O}}_3$ and at 17 meV in $\mathrm{PrMn}{\mathrm{O}}_3$ at low temperatures are found to be associated with magnetic origin. We observe coherent magnetic neutron scattering in localized regions in reciprocal space and show it to arise from long-range correlated magnetic spin-waves below the magnetic transition temperature ($T_{\mathrm{N}}$) and short-range stochastic spin-spin fluctuations above $T_{\mathrm{N}}$. In spite of the similarity of the structure of the two compounds, the neutron inelastic spectrum of $\mathrm{PrMn}{\mathrm{O}}_3$ exhibits broad features at 150 K unlike well-defined peaks in the spectrum of $\mathrm{CaMn}{\mathrm{O}}_3$. This might result from the difference in the nature of interactions in the two compounds (magnetic and Jahn-Teller distortion). Ab initio phonon calculations have been used to interpret the observed phonon spectra. The ab initio calculations at high pressures show that the variations of Mn-O distances are isotropic for $\mathrm{CaMn}{\mathrm{O}}_3$ and highly anisotropic for $\mathrm{PrMn}{\mathrm{O}}_3$. The calculation in $\mathrm{PrMn}{\mathrm{O}}_3$ shows the suppression of Jahn-Teller distortion and simultaneous insulator-to-metal transition. It appears that this transition may not be associated with the occurrence of the tetragonal phase above 20 GPa as reported in the literature, since the tetragonal phase is found to be dynamically unstable, although it is found to be energetically favored over the orthorhombic phase above 20 GPa. $\mathrm{CaMn}{\mathrm{O}}_3$ does not show any phase transition up to 60 GPa.

Figure 1

The neutron inelastic spectra of $\mathrm{CaMn}{\mathrm{O}}_3$ at low temperatures, the data were summed over (a) $Q=0.5–7{\AA }^{-1}$ and (b) $Q=4–7{\AA }^{-1}$, respectively. The peak at $\sim 20\mathrm{meV}$ is due to spin-wave excitations, not due to phonons ($1\mathrm{meV}=8.0585\mathrm{c}{\mathrm{m}}^{-1}$).

Figure 2

The $(Q,E)$ contour plot of $S(Q,E)$ data for $\mathrm{CaMn}{\mathrm{O}}_3$ at $T=7\mathrm{K}$ measured at SEQUOIA with incident neutron energy of 110 meV is shown at the top. Strong intensity excitations at low temperatures (7 and 110 K) below $E=20\mathrm{meV}$ and $Q=3.5{\AA }^{-1}$ are due to magnetic spin-wave excitations. The excitations around 30, 45, 55, 60, 65, 70, and 90 meV are due to phonons (their intensities increase with increasing $Q$).

Figure 3

Top panel: The $(Q,E)$ contour plot of $S(Q,E)$ spectra for $\mathrm{CaMn}{\mathrm{O}}_3$. Bottom panel: Temperature-dependent neutron inelastic spectra of $\mathrm{CaMn}{\mathrm{O}}_3$ summed over various $Q$ range. Bottom right panel: Temperature-dependent neutron elastic spectra $S\left(Q\right)$ of $\mathrm{CaMn}{\mathrm{O}}_3$.

Figure 4

The temperature dependence (above 300 K) of the neutron inelastic spectra of $\mathrm{CaMn}{\mathrm{O}}_3$, the data were summed over (a) $Q=0.5–7{\mathrm{A}}^{-1}$ and (b) $Q=4–7{\mathrm{A}}^{-1}$, respectively.

Figure 5

Top panel: Temperature-dependent neutron inelastic spectra of $\mathrm{PrMn}{\mathrm{O}}_3$ summed over various $Q$ range. Bottom panel: Contour plot of $S(Q,E)$ spectra for $\mathrm{PrMn}{\mathrm{O}}_3$ measured at 6 K (right) and 150 K (left). A dispersed spin-wave excitation is clearly seen below 20 meV and $1.5{\mathrm{A}}^{-1}$ at 6 K. In 150 K spectra, weakly dispersed magnetic excitation around 15 meV is observed.

Figure 6

The variation of integrated intensity of the excitation for $\mathrm{CaMn}{\mathrm{O}}_3$ (energy range = 15–21 meV) (left side panel) and $\mathrm{PrMn}{\mathrm{O}}_3$ (energy range = 13–19 meV) (right side panel) at different temperature. The magnetic form factor for $\mathrm{M}{\mathrm{n}}^{3+}$ and $\mathrm{M}{\mathrm{n}}^{4+}$ are computed using the analytical relation and shown as a continuous line. To compare the energy dependence of the dispersive magnetic modes with expectations for single-mode spin-wave excitations, intensity of dispersive magnetic modes is scaling by a constant factor.

Figure 7

Extracted magnetic contributions (intensity difference between low $Q$ and high $Q$) in neutron inelastic spectra of $\mathrm{CaMn}{\mathrm{O}}_3$ and $\mathrm{PrMn}{\mathrm{O}}_3$ at temperatures below $T_{\mathrm{N}}$ from polycrystalline samples.

Figure 8

Comparison between the experimental ($T=300\mathrm{K}$) and calculated neutron inelastic spectra of $\mathrm{CaMn}{\mathrm{O}}_3$ using (a) LDA and (b) GGA. Experimental data are summed over $4–7{\AA }^{-1}$. The phonon calculations are carried out in the FRM configuration. The calculated phonon spectra have been convoluted with a Gaussian of FWHM of 4.5 meV to account for the effect of energy resolution in the experiment.

Figure 9

Comparison between the experimental ($T=150\mathrm{K}$) and calculated phonon spectra in $\mathrm{PrMn}{\mathrm{O}}_3$. Experimental data are summed over $4–7{\AA }^{-1}$. The phonon calculations are carried out in the FRM configuration in the GGA.

Figure 10

Comparison of the calculated long-wavelength phonon frequencies (in FRM structures and using GGA) with the available data in literature. The references for reported experimental and calculated optical long-wavelength data are as Raman experimental data (red squares; Ref. [57] for $\mathrm{CaMn}{\mathrm{O}}_3$; Ref. [32] for $\mathrm{PrMn}{\mathrm{O}}_3$), first-principles DFT calculation (blue circles; Ref. [33] for $\mathrm{CaMn}{\mathrm{O}}_3$), IR experimental data (blue stars; Ref. [58] for $\mathrm{CaMn}{\mathrm{O}}_3$ and $\mathrm{PrMn}{\mathrm{O}}_3$), and lattice dynamical calculation using potential model (black inverted triangles; Ref. [58] for $\mathrm{CaMn}{\mathrm{O}}_3$; Ref. [32] for $\mathrm{PrMn}{\mathrm{O}}_3$).

Figure 11

Pressure dependence of the calculated pseudocubic lattice parameters (in FRM structures and using GGA) for (a) $\mathrm{CaMn}{\mathrm{O}}_3$ and (b) $\mathrm{PrMn}{\mathrm{O}}_3$ compared to reported experimental data for $\mathrm{CaMn}{\mathrm{O}}_3$ [59] and $\mathrm{PrMn}{\mathrm{O}}_3$ [13], respectively. Pressure dependence of Mn-O bond length and distortion of $\mathrm{Mn}{\mathrm{O}}_6$ octahedra as calculated are shown in (c) $\mathrm{CaMn}{\mathrm{O}}_3$ and (d) $\mathrm{PrMn}{\mathrm{O}}_3$, respectively.

Figure 12

(a) Enthalpy difference ($\mathrm{\Delta }H$) between the orthorhombic (Pnma) and tetragonal ($I4/mcm$) phases of $\mathrm{PrMn}{\mathrm{O}}_3$ as calculated using ab initio DFT calculation (in FRM structures and using GGA). The computed phonon dispersion relations for $\mathrm{PrMn}{\mathrm{O}}_3$ in tetragonal phase at $P=30\mathrm{GPa}$ is shown in (b).

Figure 13

(a) The calculated partial phonon density of states of various atoms in $\mathrm{CaMn}{\mathrm{O}}_3$ with in LDA and GGA approximations. (b) The calculated partial density of states of $\mathrm{CaMn}{\mathrm{O}}_3$ in various configurations within GGA. The energies of unstable modes in PNM-GGA are plotted as negative energies.

Figure 14

The calculated partial phonon density of states of various atoms in $\mathrm{PrMn}{\mathrm{O}}_3$. The phonon calculations are carried out in the FRM configuration in the GGA.

Figure 15

Computed phonon dispersion relations for $\mathrm{CaMn}{\mathrm{O}}_3$ (left panel) and $\mathrm{PrMn}{\mathrm{O}}_3$ (right panel) using GGA in cubic phase.

Figure 16

The displacements pattern of unstable mode at the $R$ point in the cubic phase.