Author Affiliations
1School of Physics and Electronic Science, Hunan University of Science and Technology, Xiangtan 411201, China2School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, Chinashow less
Fig. 1. Typical spin topology defects in magnetic materials: (a) Domain wall
[42]; (b) flux-closure pattern
[42]; (c) vortex
[43]; (d) anti-vortex
[43]; (e) center-divergent pattern
[43]; (f) center-convergent pattern
[43]; (g) meron
[43,70]; (h) skyrmion
[43,70].
Fig. 2. Typical polar topologies in ferroelectric materials: (a) Polar vortex in nanodisks
[22,71]; (b) polar vortex in nanorods
[22,71]; (c) polar vortex in nanodots
[74]; (d) vortex in BTO nanoislands
[75]; (e) vortex domain in PZT nanodots
[28]; (f) anti-vortex domain in BFO films
[76,77]; (g) center-divergent domain in BFO films
[76-78]; (h) flux-closure pattern in BTO crystal
[64,79]; (i), (j) center-divergent (convergent) domain in BFO nanoislands
[29-31].
Fig. 3. Mobility of flux-closed topological domains in ferroelectric materials: (a) Bundles-like domain structures at the edges of the PZNPT single crystal lamella
[26]; (b) approach, coalesce and separate of the vertices after delivery of a prepoling field pulse
[27].
Fig. 4. Conductivity of polar topological domains in ferroelectric thin films. Creation (a) and conductivity (b) of the flux-closure domain in BFO films
[65,66]; (c) flux- closure domain and center-divergent (convergent) domain in BiFeO
3 films and (d) their conductivity
[24,68].
Fig. 5. Observation of the polar topological domains in ferroelectric thin films: (a) Flux-closure domains in ferroelectric PZT
[34]; (b) vortex domains in ferroelectric BFO ultrathin films
[82]; (c) flux-closure domains in ferroelectric BFO ultrathin films
[37].
Fig. 6. Observation of the polar bubble-like domains in ferroelectric thin films: (a) Polar bubble domains in PZT thin films; (b) structure of the bubble domains; (c) merging and coarsening of the polar bubble domains
[83]; (d) erasuring and recreation of the polar bubble domains
[84].
Fig. 7. Polar topological domains in PTO/STO superlattices: (a) Flux-closure domain arrays in a PTO/STO superlattices on GdScO
3 substrate
[35]; (b) polar vortex domain arrays in PTO/STO superlattices on DSO substrate
[39,90]; (c) a calculated phase diagram for PTO
m/STO
n illustrating the length scales within which different topological states can be stabilized
[40]; (d) polar skyrmion bubbles in a PTO/STO superlattices on STO substrate
[41].
Fig. 8. Topological mixed phase structure and field control in ferroelectric superlattice: (a) Lateral piezoresponse force studies revealing the distribution of
a1/
a2 and vortex phases
[95]; (b) dark field TEM image showing ferroelectric vortices and
a1/
a2-domain coexistence
[96]; (c) phase field model of the
a1/
a2-domain/vortex boundary
[96]; (d) reversible electric-field control of ferroelectric and vortex phases
[95,97]; (e) temperature-dependent synchrotron X-ray diffraction on reversible switching of ferroelectric and vortex phases
[95,97]; (f) reversible sub-picosecond optical pulses control of ferroelectric mixture and supercrystal structure
[95,97].
Fig. 9. Topological mixed phase structure and field control in ferroelectric superlattice: (a) Theoretical guidelines to create polar skyrmions
[98]; (b) topoligical transition between polar vortex and skyrmion in ferroelectric nanocomposites
[88]; (c) phase field model of the topoligical transition between polar vortex and skyrmion in ferroelectric PTO/STO superlattices
[58]; (d) manipulating topological transformations of polar vortices in ferroelectric superlattices
[99].