2022
DOI: 10.1038/s41467-022-29764-w
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Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice

Abstract: Topology, an important branch of mathematics, is an ideal theoretical tool to describe topological states and phase transitions. Many topological concepts have found their physical entities in real or reciprocal spaces identified by topological invariants, which are usually defined on orientable surfaces, such as torus and sphere. It is natural to investigate the possible physical realization of more intriguing non-orientable surfaces. Herein, we show that the set of spin-induced ferroelectric polarizations in… Show more

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Cited by 10 publications
(6 citation statements)
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“…For some classical literature that presents more interesting properties in particular of the Roman surface, see Clebsch [31], Cayley [32], Lacour [33] and Hilbert and Cohn-Vossen [34, §46]. Very recently, the possibility of physically realizing the Roman surface by a spin-induced polarization vector in a particular cubic crystal was reported in Liu et al [35]. The example of the Roman surface as the degeneracy region for v = 0 in a tetrahedron graph clearly shows that while an individual ground-state density does not need to reflect the symmetry of the system, the whole degeneracy region does.…”
Section: Further Classification and Examples For Density Regionsmentioning
confidence: 99%
“…For some classical literature that presents more interesting properties in particular of the Roman surface, see Clebsch [31], Cayley [32], Lacour [33] and Hilbert and Cohn-Vossen [34, §46]. Very recently, the possibility of physically realizing the Roman surface by a spin-induced polarization vector in a particular cubic crystal was reported in Liu et al [35]. The example of the Roman surface as the degeneracy region for v = 0 in a tetrahedron graph clearly shows that while an individual ground-state density does not need to reflect the symmetry of the system, the whole degeneracy region does.…”
Section: Further Classification and Examples For Density Regionsmentioning
confidence: 99%
“…A-site-ordered quadruple perovskite oxides with the chemical formula of AA′ 3 B 4 O 12 have attracted much attention for their fascinating structural and physical properties, such as a giant dielectric constant, magnetoelectric multiferroicity, negative thermal expansion, , magnetoresistance (MR), , highly efficient catalysis, , etc. In such a specially ordered structure, three-quarters of the A-site is replaced by a transition metal A′ with a strong Jahn–Teller effect like Cu 2+ or Mn 3+ .…”
Section: Introductionmentioning
confidence: 99%
“…On the other hand, three-quarter A-site cations can be substituted by small-size Jahn–Teller active ions such as Mn 3+ (t 2g 3 e g 1 ) and Cu 2+ (t 2g 6 e g 3 ), which tends to form a square-coordinated unit. , As a result, A-site ordered quadruple perovskites (QPs) with the chemical formula AA’ 3 B 4 O 12 with heavily tilted BO 6 octahedra can be formed, and intriguing physical properties can therefore be expected. For example, typical QPs such as CaCu 3 Ti 4 O 12 with a large dielectric constant, LaCu 3 Fe 4 O 12 exhibiting intermetallic charge transfer and unusual negative thermal expansion properties, and multiferroic in RMn 3 Cr 4 O 12 (R = rare earth element and Bi) have been extensively studied. One can suppose that the above two kinds of site orderings can be combined to design new materials of both A- and B-site ordered QPs with the chemical formula AA’ 3 B 2 B’ 2 O 12 .…”
Section: Introductionmentioning
confidence: 99%