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Page 8 of 10 Ge et al. Microstructures 2023;3:2023026 https://dx.doi.org/10.20517/microstructures.2023.13

Therefore, in our material, we may explain the origin of the domain microstructure as follows. Since the
temperature during crystal growth is below T , ferroelectric domains are to be expected, and ideally, they
c
would assume a form to minimise the competing ferroelectric/ferroelastic/electrostatic energy components
of the system. In thin film growth, it is well established that domain microstructures may evolve during film
deposition and, in turn, can influence growth morphology . Therefore, in our case of single-crystal
[39]
[38]
BiFeO growth, we may expect regions with positive and negative surface charges that have an effect on
3
domain structure and subsequent growth. Importantly, Li showed that nonstoichiometric monolayers
[29]
may form on polarisation-up, negatively charged BiFeO growth surfaces. They found that as growth
3
progresses, a region with polarisation pointing towards the growth surface may, therefore, reach a critical
negative charge, causing the incorporation of FeO octahedra at the crystal surface and producing
6
nonstoichiometric monolayers of the defective material. They also showed that the negative charge induces
[32]
and pins head-to-head polarisation . It seems plausible that a similar mechanism is responsible for the
head-to-head domain walls that we observe. On a (hhl) growth surface, the FeO octahedra would form
6
edge-sharing chains along [1 0], partly defining the orientation of the wall. These negatively-charged defects
stabilise the 180° domain walls and perpetuate incorporation of FeO octahedra in the next monolayer of
6
crystal growth. It is not clear if the (112) plane makes the best match of their structure to the adjacent R3c
BFO or whether this habit plane is a result of the asymmetrical surface charge where the domain wall
intersects the surface, which may vary with, for example, the growth rate. An array of such structures can
only exist with a further reversal of polarisation between them, and tail-to-tail 180° domain walls are the
most efficient way of achieving this. The presence of the sawtooth walls is thus topologically necessary. It
has been shown that unpinned 180° domain walls are expected to develop a crenellated structure to balance
polarisation and electrostatic energy [40,41] . The crenellated structure of these walls indicates that they are not
pinned in the same way as the flat walls, and a very recent study of these tail-to-tail walls indicates that they
[18]
are, to some extent, mobile when an electric field is applied, while head-to-head flat walls are immobile .
This is in good agreement with our measurements of P hysteresis, which gave essentially no signal,
s
indicating that the flat walls are completely pinned. It is commonly observed that measurements of P in
s
bulk BiFeO crystals are usually an order of magnitude smaller than in thin films, even though our
3
-2
measured δ vectors at the atomic scale are similar, equivalent to P approximately 100 μC cm . While this
s
FB
batch of material now dominates high-resolution structural studies of bulk BiFeO 3 [16,17] , there is nothing in
the proposed origin of the domain structure that would indicate it to be specific to these particular crystals.
On a macroscopic scale, the deviation from perfect stoichiometry is miniscule; approximating the defects as
sheets of Bi with 50% occupancy, a spacing of 100 nm gives a Fe excess of only approximately 0.2 at.%,
meaning that they are unlikely to be avoided by changes in starting composition.

CONCLUSIONS
Periodic domain structures in single crystal BiFeO have been re-investigated. Our results show that all
3
domain walls are of 180°-type, alternating between flat head-to-head and sawtooth tail-to-tail walls. We
focus on the flat walls here, finding that they have an orientation close to (112) and a polarisation reversal
that occurs over only approximately 1 nm, significantly less than seen in other charged domain walls in
BiFeO . They are locally nonstoichiometric, with an atomic reconstruction of roughly a unit cell in
3
thickness, similar to that seen in planar defects in thin film BiFeO and related materials. The reconstructed
3
region contains edge-sharing FeO octahedra that produce a rigid-body shift of half a unit cell and a
6
negative charge density that induces head-to-head polarisation. We propose that the periodic domain
structure forms during crystal growth in regions where negative surface charges exceed a critical value,
causing the incorporation of FeO octahedra that is perpetuated and becomes self-organised as growth
6
proceeds. The reconstruction and local charge strongly pin head-to-head 180° domain walls, explaining the
poor response of these BiFeO single crystals in measurements of polarisation. Avoiding their formation is,
3