## This content will become publicly available on October 25, 2020

# Bose-Einstein condensation of triplons close to the quantum critical point in the quasi-one-dimensional spin-$$\frac{1}{2}$$ antiferromagnet $$\mathrm{NaVOPO_4}$$

## Abstract

Structural and magnetic properties of a quasi-one-dimensional spin-$$\frac{1}{2}$$ compound $$\mathrm{NaVOPO_4}$$ are explored by x-ray diffraction, magnetic susceptibility, high-field magnetization, specific heat, electron spin resonance, and $$\mathrm{^{31}P}$$ nuclear magnetic resonance measurements, as well as complementary *ab initio* calculations. Whereas magnetic susceptibility of $$\mathrm{NaVOPO_4}$$ may be compatible with the gapless uniform spin chain model, detailed examination of the crystal structure reveals a weak alternation of the exchange couplings with the alternation ratio $α ≃ 0.98$ and the ensuing zero-field spin gap $$Δ_0/k_B ≃ 2.4 K$$ directly probed by field-dependent magnetization measurements. No long-range order is observed down to 50 mK in zero field. However, applied fields above the critical field $$H_{c1} ≃ 1.6 T$$ give rise to a magnetic ordering transition with the phase boundary $$T_N ∝(H - H_{c1})^{\frac{1}{Φ}}$$, where $Φ ≃ 1.8$ is close to the value expected for Bose-Einstein condensation of triplons. Finally, with its weak alternation of the exchange couplings and small spin gap, $$\mathrm{NaVOPO_4}$$ lies close to the quantum critical point.

- Authors:

- Indian Inst. of Science Education and Research, Pune (India). School of Physics
- Max Planck Inst. for Chemical Physics, Dresden (Germany)
- Helmholtz-Zentrum Dresden-Rossendorf, Dresden (Germany). Dresden High Magnetic Field Lab. (HLD-EMFL)
- Kyushu Univ., Fukuoka (Japan). Dept. of Applied Quantum Physics, Faculty of Engineering; Iowa State Univ., Ames, IA (United States). Dept. of Electrical and Computer Engineering
- Iowa State Univ., Ames, IA (United States). Dept. of Electrical and Computer Engineering
- Univ. of Augsburg (Germany). Inst. of Physics, Center for Electronic Correlations and Magnetism

- Publication Date:

- Research Org.:
- Ames Laboratory (AMES), Ames, IA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1572382

- Report Number(s):
- IS-J 10064

Journal ID: ISSN 2469-9950; PRBMDO

- Grant/Contract Number:
- 37(3)/14/26/2017-BRNS; AC02-07CH11358

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 100; 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

```
Mukharjee, Prashanta K., Ranjith, K. M., Koo, B., Sichelschmidt, J., Baenitz, M., Skourski, Y., Inagaki, Y., Furukawa, Y., Tsirlin, A. A., and Nath, R. Bose-Einstein condensation of triplons close to the quantum critical point in the quasi-one-dimensional spin-$\frac{1}{2}$ antiferromagnet $\mathrm{NaVOPO_4}$. United States: N. p., 2019.
Web. doi:10.1103/PhysRevB.100.144433.
```

```
Mukharjee, Prashanta K., Ranjith, K. M., Koo, B., Sichelschmidt, J., Baenitz, M., Skourski, Y., Inagaki, Y., Furukawa, Y., Tsirlin, A. A., & Nath, R. Bose-Einstein condensation of triplons close to the quantum critical point in the quasi-one-dimensional spin-$\frac{1}{2}$ antiferromagnet $\mathrm{NaVOPO_4}$. United States. doi:10.1103/PhysRevB.100.144433.
```

```
Mukharjee, Prashanta K., Ranjith, K. M., Koo, B., Sichelschmidt, J., Baenitz, M., Skourski, Y., Inagaki, Y., Furukawa, Y., Tsirlin, A. A., and Nath, R. Fri .
"Bose-Einstein condensation of triplons close to the quantum critical point in the quasi-one-dimensional spin-$\frac{1}{2}$ antiferromagnet $\mathrm{NaVOPO_4}$". United States. doi:10.1103/PhysRevB.100.144433.
```

```
@article{osti_1572382,
```

title = {Bose-Einstein condensation of triplons close to the quantum critical point in the quasi-one-dimensional spin-$\frac{1}{2}$ antiferromagnet $\mathrm{NaVOPO_4}$},

author = {Mukharjee, Prashanta K. and Ranjith, K. M. and Koo, B. and Sichelschmidt, J. and Baenitz, M. and Skourski, Y. and Inagaki, Y. and Furukawa, Y. and Tsirlin, A. A. and Nath, R.},

abstractNote = {Structural and magnetic properties of a quasi-one-dimensional spin-$\frac{1}{2}$ compound $\mathrm{NaVOPO_4}$ are explored by x-ray diffraction, magnetic susceptibility, high-field magnetization, specific heat, electron spin resonance, and $\mathrm{^{31}P}$ nuclear magnetic resonance measurements, as well as complementary ab initio calculations. Whereas magnetic susceptibility of $\mathrm{NaVOPO_4}$ may be compatible with the gapless uniform spin chain model, detailed examination of the crystal structure reveals a weak alternation of the exchange couplings with the alternation ratio $α ≃ 0.98$ and the ensuing zero-field spin gap $Δ_0/k_B ≃ 2.4 K$ directly probed by field-dependent magnetization measurements. No long-range order is observed down to 50 mK in zero field. However, applied fields above the critical field $H_{c1} ≃ 1.6 T$ give rise to a magnetic ordering transition with the phase boundary $T_N ∝(H - H_{c1})^{\frac{1}{Φ}}$, where $Φ ≃ 1.8$ is close to the value expected for Bose-Einstein condensation of triplons. Finally, with its weak alternation of the exchange couplings and small spin gap, $\mathrm{NaVOPO_4}$ lies close to the quantum critical point.},

doi = {10.1103/PhysRevB.100.144433},

journal = {Physical Review B},

number = 14,

volume = 100,

place = {United States},

year = {2019},

month = {10}

}

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