Zero-field quantum criticality and the role played by the mutual interactions in paramagnets

The phenomenon of quantum criticality [1] has been intensively explored by the scientific community and represents a current hot topic of research. In the case of a magnetic-field-induced quantum phase transition (QPT), the paradigm is the one-dimensional Ising model under transverse magnetic field [2], where a magnetic-driven QPT takes place when the applied transverse field overcomes the exchange coupling constant. Some of the fingerprints to probe magnetic-field-induced quantum criticality is the divergence and sign-change of the magnetic Grüneisen parameter $\Gamma_{mag}$ upon crossing a critical magnetic field $B_c$ [3]. In this contribution, we cover two topics: i) we employ $\Gamma_{mag}$ to explore a quantum critical-like behavior in model systems, such as the Brillouin-like paramagnet, a modified Brillouin function taking into account a zero-field splitting originated from spin-orbit interactions, and the one-dimensional Ising model under longitudinal magnetic field [4]. Our results show that such models present an intrinsic zero-field quantum-critical-like behavior ($B_c$ = 0 T), being that the spin-orbit interactions shift the enhancement of $\Gamma_{mag}$ to higher temperatures; ii) we unveil the key role played by mutual interactions in the regime of ultra-low temperatures ($T$ $<$ 6 mK) and vanishing external magnetic field [5]. Usually, such interactions are neglected because they are very small when compared, for instance, with the thermal energy, but rigorously speaking they are always present in real paramagnets. We demonstrate that a genuine zero-field quantum phase transition is prevented to occur in real paramagnets. This is due to the fact that even for vanishing external magnetic field there is always a remaining finite local magnetic field $B_{loc}$ ($\sim$ 0.01 T) originated from dipolar magnetic interactions between adjacent magnetic moments. We discuss unprecedented aspects emerging from the mutual interactions.

[1] S. Sachdev, Quantum Phase Transitions, Cambridge University Press, Cambridge, U.K., (2001).
[2] J. Wu, L. Zhu, and Q. Si, Journal of Physics: Conference Series $\textbf{273}$, 012019 (2011).
[3] P. Gegenwart, Philosophical Magazine $\textbf{97}$, 3415 (2017).
[4] G. O. Gomes, L. Squillante, A. C. Seridonio, A. Ney, R. E. Lagos, and M. de Souza, Physical Review B $\textbf{100}$, 054446 (2019).
[5] L. Squillante, I. F. Mello, G. O. Gomes, A. C. Seridonio, R. E. Lagos-Monaco, H. E. Stanley, and M. de Souza, Scientific Reports $\textbf{10}$, 7981 (2020).

E-mail for corresponding author: [email protected]