# Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals

## Abstract

Liquid crystals are widely known for their facile responses to external fields, which forms a basis of the modern information display technology. However, switching of molecular alignment field configurations typically involves topologically trivial structures, although singular line and point defects often appear as short-lived transient states. Here, we demonstrate electric and magnetic switching of nonsingular solitonic structures in chiral nematic and ferromagnetic liquid crystals. These topological soliton structures are characterized by Hopf indices, integers corresponding to the numbers of times that closed-loop-like spatial regions (dubbed “preimages”) of two different single orientations of rod-like molecules or magnetization are linked with each other. We show that both dielectric and ferromagnetic response of the studied material systems allow for stabilizing a host of topological solitons with different Hopf indices. Furthermore the field transformations during such switching are continuous when Hopf indices remain unchanged, even when involving transformations of preimages, but discontinuous otherwise.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Colorado, Boulder, CO (United States)

- Sponsoring Org.:
- USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

- OSTI Identifier:
- 1417234

- Alternate Identifier(s):
- OSTI ID: 1511027

- Grant/Contract Number:
- ER46921; SC0010305

- Resource Type:
- Published Article

- Journal Name:
- Proceedings of the National Academy of Sciences of the United States of America

- Additional Journal Information:
- Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 115 Journal Issue: 5; Journal ID: ISSN 0027-8424

- Publisher:
- Proceedings of the National Academy of Sciences

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; three-dimensional soliton; self-assembly; ferromagnetism; chirality

### Citation Formats

```
Tai, Jung-Shen B., Ackerman, Paul J., and Smalyukh, Ivan I. Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals. United States: N. p., 2018.
Web. doi:10.1073/pnas.1716887115.
```

```
Tai, Jung-Shen B., Ackerman, Paul J., & Smalyukh, Ivan I. Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals. United States. doi:10.1073/pnas.1716887115.
```

```
Tai, Jung-Shen B., Ackerman, Paul J., and Smalyukh, Ivan I. Wed .
"Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals". United States. doi:10.1073/pnas.1716887115.
```

```
@article{osti_1417234,
```

title = {Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals},

author = {Tai, Jung-Shen B. and Ackerman, Paul J. and Smalyukh, Ivan I.},

abstractNote = {Liquid crystals are widely known for their facile responses to external fields, which forms a basis of the modern information display technology. However, switching of molecular alignment field configurations typically involves topologically trivial structures, although singular line and point defects often appear as short-lived transient states. Here, we demonstrate electric and magnetic switching of nonsingular solitonic structures in chiral nematic and ferromagnetic liquid crystals. These topological soliton structures are characterized by Hopf indices, integers corresponding to the numbers of times that closed-loop-like spatial regions (dubbed “preimages”) of two different single orientations of rod-like molecules or magnetization are linked with each other. We show that both dielectric and ferromagnetic response of the studied material systems allow for stabilizing a host of topological solitons with different Hopf indices. Furthermore the field transformations during such switching are continuous when Hopf indices remain unchanged, even when involving transformations of preimages, but discontinuous otherwise.},

doi = {10.1073/pnas.1716887115},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

number = 5,

volume = 115,

place = {United States},

year = {2018},

month = {1}

}

DOI: 10.1073/pnas.1716887115

*Citation information provided by*

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Web of Science

#### Figures / Tables:

*A*) and Solomon links (4$^2_1$) (

*B*) with linking numbers matching their

*Q*= 1 (

*A*) and

*Q*= 2 (

*B*) Hopf indices. Since the direct (ϕ) and inverse (ϕ

^{−1}) stereographic projections relatemore »

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*