Ferromagnetic domain structures and spin configurations measured in doped manganite

We report on measurements of the spin configuration across ferromagnetic domains in ${\text{La}}_{0.325}{\text{Pr}}_{0.3}{\text{Ca}}_{0.375}{\text{MnO}}_3$ films obtained by means of low-temperature Lorentz electron microscopy with in situ magnetizing capabilities. Due to the particular crystal symmetry of the material, we observe two sets of independent ferromagnetic twin variants, one of which was pinned by crystallographic twinning. The spin orientation and configuration of the domains were measured quantitatively using electron diffraction and electron holography, and verified with structural modeling. The observed deviation of spin orientations from the expected $90°$ head-to-tail configuration across the domain walls was attributed to the variation in the domains’ aspect ratios as a result of the demagnetization field. Our study provides important insight on how the spin configuration coupled with the magnetic structure and the crystal symmetry might affect the magnetoresistivity under an applied magnetic field in a strongly correlated electron system.

Figure 1

Lorentz TEM images of LPCMO at 90 K. (a) Under-focus image, (b) over-focus image, and (c) in-focus image. The twin domain walls follow the crystallographic (101) twinning plane. (d) Schematic drawing of the local magnetic structure and crystal structure (enlarged part). The thick and thin black lines represent zigzag $\left(180°\right)$ and twin $\left(90°\right)$ domain walls, respectively. The twin ferromagnetic domains coincide with the crystal twinning lamellar structure of the sample.

Figure 2

(Color online) (a) The ED pattern of LPCMO at 90 K. Two boxed insets show the split intensity of transmitted beam and (101) Bragg reflection. (b) The magnetically split fine structure of transmitted beam, recorded using a large camera length of 15 m, shows two diffused lines of spotty intensities along the $q_y$ direction. Two related Foucault images (c) and (d) were taken with the diffraction aperture at positions A and B in (b), respectively. (e) Two nanobeam diffraction scans across the twin domain structure. The deviation of $\left(q_x,q_y\right)$ coordinates for diffraction spots versus scanning nanobeam position along $\left(x,y\right)$ coordinates, respectively, parallel (open squares) and perpendicular (solid squares) to the twin domain walls in LPCMO.

Figure 3

(Color online) (a) Reconstructed electron-optical phase shift $\phi \left(x,y\right)$ from off-axis electron hologram. (b) and (c), the two phase gradient components, are proportional to the $y$ and $x$ components of the local magnetic induction within the sample. (d) Profiles of $B_y$ and $B_x$ components extracted from the phase gradient.

Figure 4

(Color online) (a) Simulated Fresnel image for the zigzag and twin magnetic domain walls in LPCMO. (b) Wrapped phase map ($4\times$ amplified) $\phi \left(x,y\right)$ of the complex exit wave for the set of magnetic domains. [(c) and (d)] Projected magnetic induction maps for the two orthogonal components (c) $B_x\left(x,y\right)$ and (d) $B_y\left(x,y\right)$ within the sample, derived from the phase gradient. (e) Line profile of the phase shift across the dashed line in (b) showing the typical smoothed sawtooth function associated to realistic magnetic domains. (f) Simulated diffraction pattern showing the fine structure of the magnetically split Bragg spot obtained by the Fourier transform of exit wave function $\text{exp}\left[i\phi \left(x,y\right)\right]$. (g) Simulation of a nanobeam scan across the twin domains along the dashed line in (a), to be compared with the experimental data shown in Fig. 2e; the reciprocal coordinates and amplitudes of the diffraction spots resulting from the simulated $y$ scan show how the fine structure of the composite diffraction pattern shown in (h) [obtained by $90°$ rotation of (f)] may arise.

Figure 5

(a) Electron-optical phase shift, displayed as a cosine map, associated with a double set of twins (20 narrow domains with a 6:1 aspect ratio and two broader domains with aspect ratio of 3:1); (b) simulated diffraction pattern associated with the double set of twins; (c) phase derivative along the horizontal direction, related to the projected $B_y$ component; (d) phase derivative along the vertical direction, related to the projected $B_x$ component; and (e) vertical line profile across the $B_x$ map, proportional to the electron deflection.