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# Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet

## Abstract

The anomalous thermodynamic properties of the paradigmatic frustrated spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLH) has remained an open topic of research over decades, both experimentally and theoretically. We further the theoretical understanding based on the recently developed, powerful exponential tensor renormalization group method on cylinders and stripes in a quasi-one-dimensional (1D) setup, as well as a tensor product operator approach directly in 2D. The observed thermal properties of the TLH are in excellent agreement with two recent experimental measurements on the virtually ideal TLH material $${\mathrm{Ba}}_{8}{\mathrm{CoNb}}_{6}{\mathrm{O}}_{24}$$. Remarkably, our numerical simulations reveal two crossover temperature scales, at $${T}_{l}/J{\sim}0.20$$ and $${T}_{h}/J{\sim}0.55$$, with $J$ the Heisenberg exchange coupling, which are also confirmed by a more careful inspection of the experimental data. We propose that in the intermediate regime between the low-temperature scale $${T}_{l}$$ and the higher one $${T}_{h}$$, the "rotonlike" excitations are activated with a strong chiral component and a large contribution to thermal entropies. Bearing remarkable resemblance to the renowned roton thermodynamics in liquid helium, these gapped excitations suppress the incipient $${120}^{{\circ}}$$ order that emerges for temperatures below $${T}_{l}$$.

- Authors:

- Beihang Univ., Beijing (China). Dept. of Physics. Key Lab. of Micro-Nano Measurement-Manipulation and Physics
- Beihang Univ., Beijing (China). Dept. of Physics. Key Lab. of Micro-Nano Measurement-Manipulation and Physics; Ludwig Maximilian Univ. of Munich (Germany). Munich Center for Quantum Science and Technology (MCQST). Arnold Sommerfeld Center for Theoretical Physics (ASC). Center for NanoScience (CeNS)
- Ludwig Maximilian Univ. of Munich (Germany). Munich Center for Quantum Science and Technology (MCQST). Arnold Sommerfeld Center for Theoretical Physics (ASC). Center for NanoScience (CeNS)
- Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Condensed Matter Physics and Materials Science; Ludwig Maximilian Univ. of Munich (Germany). Munich Center for Quantum Science and Technology (MCQST). Arnold Sommerfeld Center for Theoretical Physics (ASC). Center for NanoScience (CeNS)
- Beihang Univ., Beijing (China). Dept. of Physics. Key Lab. of Micro-Nano Measurement-Manipulation and Physics. International Research Inst. of Multidisciplinary Science

- Publication Date:

- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States)

- Sponsoring Org.:
- National Natural Science Foundation of China (NNSFC); Fundamental Research Funds for the Central Universities (China); German Research Foundation (DFG); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1515152

- Alternate Identifier(s):
- OSTI ID: 1506155

- Report Number(s):
- BNL-211618-2019-JAAM

Journal ID: ISSN 2469-9950

- Grant/Contract Number:
- SC0012704; 11504014; 11834014; 11874078; EXC-2111–390814868; WE4819/3-1; WE4819/2-1

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 14; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Chen, Lei, Qu, Dai-Wei, Li, Han, Chen, Bin-Bin, Gong, Shou-Shu, von Delft, Jan, Weichselbaum, Andreas, and Li, Wei. Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet. United States: N. p., 2019.
Web. doi:10.1103/PhysRevB.99.140404.
```

```
Chen, Lei, Qu, Dai-Wei, Li, Han, Chen, Bin-Bin, Gong, Shou-Shu, von Delft, Jan, Weichselbaum, Andreas, & Li, Wei. Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet. United States. doi:10.1103/PhysRevB.99.140404.
```

```
Chen, Lei, Qu, Dai-Wei, Li, Han, Chen, Bin-Bin, Gong, Shou-Shu, von Delft, Jan, Weichselbaum, Andreas, and Li, Wei. Wed .
"Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet". United States. doi:10.1103/PhysRevB.99.140404.
```

```
@article{osti_1515152,
```

title = {Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet},

author = {Chen, Lei and Qu, Dai-Wei and Li, Han and Chen, Bin-Bin and Gong, Shou-Shu and von Delft, Jan and Weichselbaum, Andreas and Li, Wei},

abstractNote = {The anomalous thermodynamic properties of the paradigmatic frustrated spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLH) has remained an open topic of research over decades, both experimentally and theoretically. We further the theoretical understanding based on the recently developed, powerful exponential tensor renormalization group method on cylinders and stripes in a quasi-one-dimensional (1D) setup, as well as a tensor product operator approach directly in 2D. The observed thermal properties of the TLH are in excellent agreement with two recent experimental measurements on the virtually ideal TLH material ${\mathrm{Ba}}_{8}{\mathrm{CoNb}}_{6}{\mathrm{O}}_{24}$. Remarkably, our numerical simulations reveal two crossover temperature scales, at ${T}_{l}/J{\sim}0.20$ and ${T}_{h}/J{\sim}0.55$, with $J$ the Heisenberg exchange coupling, which are also confirmed by a more careful inspection of the experimental data. We propose that in the intermediate regime between the low-temperature scale ${T}_{l}$ and the higher one ${T}_{h}$, the "rotonlike" excitations are activated with a strong chiral component and a large contribution to thermal entropies. Bearing remarkable resemblance to the renowned roton thermodynamics in liquid helium, these gapped excitations suppress the incipient ${120}^{{\circ}}$ order that emerges for temperatures below ${T}_{l}$.},

doi = {10.1103/PhysRevB.99.140404},

journal = {Physical Review B},

number = 14,

volume = 99,

place = {United States},

year = {2019},

month = {4}

}

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