Physics

Dr. Anup Kumar Bera
BARC, Mumbai

Abstract :

The confinement of quasi particles, a well-known phenomenon in particle physics [1], can also be realized in a condensed matter system [2,3]. In particle physics, baryons and mesons are produced by the confinement of quarks, where quarks are bound together by a strong interaction (gauge field) that grows stronger with increasing distance and, therefore, the quarks never exist as individual particles.  The condensed matter analogue, confinement of magnetic quasiparticles (spinons) can be illustrated in a quasi-one-dimensional spin-1/2 chains.

We demonstrate experimentally such spinon confinement in the model quasi-1D spin-1/2 XXZ antiferromagnet SrCo₂V₂O₈. The compound SrCo₂V₂O₈ belongs to the general family SrM₂V₂O₈ (M = Ni, Co and Mn) [4-12], having 1D spin chains of magnetic M²⁺ ions along the  c axis. In the pure 1D magnetic state of SrCo₂V₂O₈ (above the T_N =5 K; 3D AFM ordering temperature) a spin flip creates two spinon excitations [particles with fractional spin (S=1/2) in contrast to the magnons have integer spin (S=1)]. These two spinons can propagate along the chain independently by subsequent spin flips without any cost of energy [4, 10]. However, below the T_N (in the 3D long-range AFM state), two spinons are bound together by weak interchain interactions [9, 10]. The interchain interactions play the role of an attractive potential (equivalent to the gauge field in quark confinement), proportional to the distance between spinons, and result into the confinement of spinons into bound pairs.

Under an external magnetic field, the long range AFM order is destroyed above a critical field (H_c =3.8 T @ 1.5 K) and the system enters into a gapless critical regime. In the quantum critical regime, for the first time, we have experimentally observed “Bethe strings” [12], exotic states of strongly bound electron spins.

References

1. T. Muta, Foundations of Quantum Chromodynamics (World Scientific, Singapore, 1987).
2. B. Lake, A. M. Tsvelik, S. Notbohm, D. A. Tennant, T. G. Perring, M. Reehuis, Ch. Sekar, G. Krabbes, and B. Büchner, Nature Physics, 6, 50 (2010).
3. R. Coldea, D. A. Tennant, E. M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer, Science, 327, 177 (2010).
4. A. K. Bera, B. Lake, F. H. L. Essler, L. Vanderstraeten, C. Hubig, U. Schollwock, A. T. M. N. Islam, A. Schneidewind, and D. L. Quintero-Castro, Phys. Rev. B 96, .054423 (2017).
5. A. K. Bera, B. Lake, A. T. M. N. Islam and A. Schneidewind,
   Phys. Rev. B (rapid comm.), 92, 060412(R) (2015)
6. A. K. Bera, B. Lake, A. T. M. N. Islam, O. Janson, H. Rosner, A. Schneidewind, J. Park, E. Wheeler, and S. Zander, Phys. Rev. B  91, 144414 (2015).
7. A. K. Bera, B. Lake, W.-D. Stein, and S. Zander, Phys. Rev. B 89, 094402 (2014).
8. A. K. Bera, B. Lake, A. T. M. N. Islam, B. Klemke, E. Faulhaber, and J. M. Law,
   Phys. Rev. B 87, 224423 (2013).
9. A. K. Bera and Yusuf, Phys. Rev. B 86, 024408 (2012).
10. Z. Wang, M. Schmidt, A. K. Bera, B. Lake, A. Loidl, J. Deisenhofer,
    Phys. Rev. B (rapid comm.) 91, 140404(R) (2015).
11. Z. Wang, M. Schmidt, A. K. Bera, A. T. M. N. Islam, B. Lake, A. Loidl, and J. Deisenhofer,
    Phys. Rev. B 87, 104405 (2013).
12. Z. Wang, J. Wu, W. Yang, A. K. Bera, D. Kamenskyi, A. T. M. N. Islam, S. Xu, J. M. Law, B. Lake, C. Wu, and A. Loidl, Nature 554, 219 (2018).