Electrically driven singlet-triplet transition in triangulene spin-1 chains

Department of Physics of Complex Systems, Eötvös Loránd University

MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and  Economics

László Oroszlány 

The Team

Gabriel Martinez

Oviedo

Amador Garcia Fuente

Oviedo

László Szunyogh

BME

Jaime Ferrer

Oviedo

Haldane's conjecture and the AKLT model

\displaystyle \hat H = {\color{red}J} \left (\sum_p \vec{S}_p \cdot \vec{S}_{p+1} + {\color{red}\beta} (\vec{S}_p \cdot \vec{S}_{p+1})^2 \right )

BL-BQ model

\displaystyle \hat H = \sum_p \vec{S}_p \cdot \vec{S}_{p+1} + \frac{1}{3} (\vec{S}_p \cdot \vec{S}_{p+1})^2

Affleck, Kennedy, Lieb, Tasaki Phys. Rev. Lett. 59, 799 (1987)

\displaystyle H=\sum_p \vec{S}_p\cdot\vec{S}_{p+1}

\(S=\frac{1}{2}\rightarrow\) gapless

\(S=1\rightarrow\) gapped

F. D. M. Haldane Phys. Rev. Lett. 50, 1153 (1983)

How to realize S=1 and the Haldane phase

Renard, Regnault, Verdaguer, in

Magnetism: Molecules to Materials I: Models and Experiments

  • inelastic neutron-scattering experiments on bulk samples
  • interchain interaction
  • anisotropy

Magnetism at the zig-zag edge

ribbon width

gap [eV]

Magda et al. Nature 514, 608 (2014)

Mapping total energy to simple spin cahin

O. V. Yazyev and M. I. Katsnelson,

Phys. Rev. Lett. 100,047209 (2008).

spin-wave stiffness:

2100 meVÅ\(^2\)

exchange constant:

105 meV

Socio-scientific interlude

vs.

SKKR

+ Wannier90

Zig-zag ribbon with SIESTA

\( D_{Yazyev}=2108 meVA^2 \)

\(\updownarrow\)

\( D_{edge}=2308 meVA^2 \)

\( D_{half}=3406 meVA^2 \)

  

Phys. Rev. B 99, 224412 (2019)

https://github.com/oroszl/nojij

Can we realize with S=1 with carbon?

Su, Telychko, Song, Lu Angewandte Chemie 59 7658 (2020)

YES!

E. Lieb,

Phys. Rev. Lett. 62  1201 (1989)

Making a chain!

Mishra et al. Nature 598, 287 (2021).

fit to BL-BQ model:

J=18 \mathrm{meV}\, ,\beta=0.09

Ab initio spin model parameters

\displaystyle \delta E_{nm} = -\frac{1}{\pi} \int \mathrm{Im} \mathrm{Tr} [G\delta V_n G \delta V_m] \mathrm{d}E \rightarrow \mathbb{E}_{nm}\, \delta\mathbf{S}_n\cdot\delta\mathbf{S}_m
\mathbb{E}_{nm}=J_{nm}\,\left(\,1+2\,\beta_{nm}\left(\mathbf{S}_n\cdot\mathbf{S}_m\right)\,\right)
J_{nm} = \left(\mathbb{E}_{nm}^{FM}+ \mathbb{E}_{nm}^{AFM}\right)/2\\\,\\ \beta_{nm} = \dfrac{1}{2}\,\dfrac{\mathbb{E}_{nm}^{FM}- \mathbb{E}_{nm}^{AFM}}{\mathbb{E}_{nm}^{FM}+\mathbb{E}_{nm}^{AFM}}
\displaystyle \hat H = \sum_{nm} {\color{red}J_{nm}} \left (\vec{S}_n \cdot \vec{S}_{m} + {\color{red}\beta_{nm}} (\vec{S}_n \cdot \vec{S}_{m})^2 \right )

DFT through

Dimer Infinite chain Experiment
17.7 meV 19.75 meV 18 meV
0.03 0.05 0.09

The proof of the pudding

\( \beta \)

\( J \)

Singlet-Triplet qubit

M. D. Shulman, O. E.  Dial, S. P. Harvey,H. Bluhm, V. Umansky, A. Yacoby; Science 336, 202 (2012)

Singlet-Triplet qubit in an S=1 chain

B. Jaworowski, N. Rogers, M. Grabowski, P. Hawrylak Sci. Rep. 7, 5529 (2017)

Singlet-Triplet transition in odd-length chains

Singlet-Triplet transition through mechanical distortions

But there is a dipole!

Singlet-Triplet transition through electric field

Thank You for your attention!

 arXiv:2207.13683

Phys. Rev. B 107, 035432 (2023)
\displaystyle \hat H = \sum_{nm} {\color{red}J_{nm}} \left (\vec{S}_n \cdot \vec{S}_{m} + {\color{red}\beta_{nm}} (\vec{S}_n \cdot \vec{S}_{m})^2 \right )