Origin of the charge gap in LaMnPO

We present high temperature inelastic neutron scattering and magnetic susceptibility measurements of the antiferromagnetic insulator LaMnPO that are consistent with the presence of two-dimensional magnetic correlations up to a temperature $T_{\text{max}}\approx 700\text{K}\gg T_N=375$ K, the Néel temperature. Optical transmission measurements show the $T=300$ K direct charge gap $\Delta =1$ eV has decreased only marginally by 500 K and suggest it decreases by only 10% at $T_{\text{max}}$. Density functional theory and dynamical mean-field theory calculations reproduce a direct charge gap in paramagnetic LaMnPO only when a strong Hund's coupling $J_H=0.9$ eV is included, as well as on-site Hubbard $U=8$ eV. Our results show that LaMnPO is a Mott-Hund's insulator, in which the charge gap is rather insensitive to antiferromagnetic exchange coupling.

Figure 1

(a) Wave-vector $q$ dependence of the scattered neutron intensity $S(\mathbf{q},\mathit{E})$ for constant energy transfer $E=5$ meV at indicated temperatures $T$. Solid lines are fits as described in the main text. Inset: $T$ dependence of the spatial correlation length $\xi$ in units of the lattice constant $a$, for $E=5$ meV (), 10 meV (red ), and 15 meV (green ). (b) Magnetic susceptibility $\langle \chi \rangle$ of a collection of single crystals (red ) $\langle \chi \rangle =2/3\left({\chi }_{ab}\right)+1/3\left({\chi }_c\right)$, where ${\chi }_{ab}$ (green ) and ${\chi }_c$ (blue ) were measured with a 1 T field applied in the $ab$ plane and $c$ plane, respectively. The magnetic susceptibility at high temperatures was measured on a powder sample (red ). Orbital susceptibility ${\chi }_{\text{orb}}=1.7\times {10}^{-4}$ mu/mol Mn is subtracted from all data. Dashed lines indicate the Néel temperature $T_N$ and mean-field ordering temperature $T_{\text{max}}$. (c) The dynamic susceptibility ${\chi }^{\prime \prime }(q,E)=S(q,E)[1-exp(-E/k_{B}T)]$ measured at 5 K. (d) $E$ cuts near the (100) AF zone center summed over the indicated ranges. Solid lines are fits to the sum of two Lorentzians. Inset: $\Delta q$, measured relative to $q_{100}$, for different $E$. The solid line is a theoretical expression for $\epsilon \left(q\right)$ in the $\Gamma -X$ direction, with $S{J}_1=34$ meV. Error bars are smaller than points. (e) $E$ cut near (210) averaged on the interval 40–50 meV. The solid lines are the resolution-convoluted intensities expected from a powder-averaged Heisenberg model for $S{J}_1=18$ meV (black), 34 meV (blue), 48 meV (red). (f) Left: Calculations of $\epsilon \left(q\right)$ along different directions in reciprocal space for indicated values of $J_2/J_1$. Right: Comparison of the experimental density of states (DOS) (green shaded area) to the powder average of $\epsilon \left(q\right)$ for values of $J_2/J_1$ indicated. The low energy part of the DOS is attributed to phonons.

Figure 2

(a) ${[\text{log}\left(\text{transmission}\right)/\text{wave}\text{number}]}^2$ at $T=295$ K (black), 325 K (red), 350 K (green), 380 K (cyan), 425 K (brown), 450 K (navy blue), 500 K (purple). Dashed lines are fits to the 295 and 500 K data as described in the text. Inset: Transmission data for 295 K (black) and 500 K (purple). (b) The temperature dependence of the experimental direct gap $\Delta$ (), $\Delta$ in the AF and PM states determined from DFT + DMFT calculations (green ), and the experimental AF correlation length $\xi$.

Figure 3

Density functional theory + dynamical mean-field theory (DFT + DMFT) calculations of the band structure of LaMnPO . (a) Paramagnetic (PM) state with Hubbard $U=10$ eV and Hund's $J_H=0$ eV. (b) PM state with $U=8$ eV and $J_H=0.9$ eV. (c) Antiferromagnetic (AF) state with $U=8$ eV and $J_H=0.9$ eV. (d) Spectral function $A(k,\omega )$ at high symmetry points for the calculations shown in (b) and (c). Triangles indicate the peak position of $A(k,\omega )$.