Ground State in a Half-Doped Manganite Distinguished by Neutron Spectroscopy

We have measured the spin-wave spectrum of the half-doped bilayer manganite $\mathrm{Pr}(\mathrm{Ca},\mathrm{Sr}{)}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ in its spin, charge, and orbital ordered phase. The measurements, which extend throughout the Brillouin zone and cover the entire one-magnon spectrum, are compared critically with spin-wave calculations for different models of the electronic ground state. The data are described very well by the Goodenough model, which has weakly interacting ferromagnetic zig-zag chains in the CE-type arrangement. A model that allows ferromagnetic dimers to form within the zigzags is inconsistent with the data. The analysis conclusively rules out the strongly bound dimer (Zener polaron) model.

Figure 1

Magnetic order and exchange interactions within a $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}$ layer for the three models considered here: (a) the Goodenough model with CE-type magnetic order, (b) the Zener polaron model, and (c) the dimer model. The in-plane magnetic unit cells are indicated by the dotted lines. (d) Crystal structure of PCSMO [34], with Mn ions in oxygen octahedra (green) and the Pr, Ca, or Sr ions (yellow) between the $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}$ layers. (e) Projection of the high temperature Amam unit cell onto the $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}$ layer.

Figure 2

Neutron scattering intensity maps of the spin-wave dispersion of PCSMO in the ($h$, 0) direction. The left-hand plots show energies up to 30 meV, and the right-hand plots show the whole dispersion. Panels (a) and (b) are experimental data, and panels (c) and (d) are calculations from spin-wave theory for the CE-type order (see text). Regions of the spectrum demarcated by dashed lines were measured with different neutron incident energies and (in some cases) different Brillouin zones. The data have been averaged over a small range of wave vectors in the (0, $k$) direction. To display the full spectrum with one intensity scale, we have multiplied the data by the monotonic function $f(E)=\frac{E/E_0}{1-{\mathrm{e}}^{-E/E_0}}$, $E_0=k_{\mathrm{B}}\times 10\mathrm{K}$, which has the effect of suppressing the strong elastic and low energy scattering. Intensity units are $\mathrm{mb}{\mathrm{sr}}^{-1}{\mathrm{meV}}^{-1}\mathrm{\text{per}}\mathrm{Mn}$.

Figure 3

Constant wave vector cuts through the experimental data. Fits with resolution corrections are shown by the (blue) lines. A nonmagnetic background has been subtracted.

Figure 4

(a) Comparison of the measured magnon dispersion (symbols) parallel to the ($h$, 0) direction with spin-wave calculations for the Goodenough model. (b)–(i) Measured and simulated intensity on ($h$, $k$) planes at the upper [(b)–(e)] and lower [(f)–(i)] limits of the gap. The intensity is averaged over 58–62 meV for the upper limit and 34–36 meV for the lower limit. Panels (b)–(e) show the data, best-fit Goodenough model, best-fit Goodenough model with $J_{\mathrm{F}2}$ and $J_{\mathrm{F}3}$ exchanged, and best-fit dimer model, respectively. Panels (f)–(i) show the same but for the lower limit. Intensity units are $\mathrm{mb}{\mathrm{sr}}^{-1}{\mathrm{meV}}^{-1}$ per Mn.

Figure 5

Simulated spectra for the best-fit Goodenough model, the CE-type ZP model (which is equivalent to the strongly bound dimer model), and the 90° ZP model.