Abstract
The self-organization of strongly interacting electrons into superlattice structures underlies the properties of many quantum materials. How these electrons arrange within the superlattice dictates what symmetries are broken and what ground states are stabilized. Here we show that cryogenic scanning transmission electron microscopy (cryo-STEM) enables direct mapping of local symmetries and order at the intra-unit-cell level in the model charge-ordered system Nd1/2Sr1/2MnO3. In addition to imaging the prototypical site-centered charge order, we discover the nanoscale coexistence of an exotic intermediate state which mixes site and bond order and breaks inversion symmetry. We further show that nonlinear coupling of distinct lattice modes controls the selection between competing ground states. The results demonstrate the importance of lattice coupling for understanding and manipulating the character of electronic self-organization and that cryo-STEM can reveal local order in strongly correlated systems at the atomic scale.
Highlights
The self-organization of strongly interacting electrons into superlattice structures underlies the properties of many quantum materials
The modulation is unidirectional, some regions of the sample exhibit bidirectional modulations. These might arise from the coexistence of small charge-order domains within a single crystal twin or from the presence of crystalline twins that establish the direction of the charge-order wavevector. By mapping both the charge order and the crystalline order parameters, we find that the orthogonal charge-order domains are coupled to crystalline twins in the sample (Supplementary Fig. 3)
While we have focused on the X1 displacements so far, the low-temperature phase may contain additional structural responses that are allowed by symmetry (Fig. 4a)
Summary
The self-organization of strongly interacting electrons into superlattice structures underlies the properties of many quantum materials. An alternative bond-centered state has been proposed[21]; in this case, a charge modulation does not occur so the superlattice is generated from orbital ordering (Fig. 1d). Manganite compounds exhibit large interactions between the lattice and the electronic degrees of freedom, and so most experimental proposals for site- or bond-centered charge-order models have relied on obtaining the average lattice distortions and crystal symmetry[19,21].
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