Mean-field Study of Antiferromagnetic and Antiferroquadrupolar Orderings in Tetragonal CeCoSi

TL;DR

This study uses mean-field calculations to explore the stability and origins of antiferromagnetic and antiferroquadrupolar orderings in CeCoSi, revealing how interactions influence phase transitions and order parameters.

Contribution

It demonstrates that antiferroquadrupolar interactions can induce quadrupolar order in tetragonal systems without orbital degeneracy, clarifying the phase transition sequence in CeCoSi.

Findings

Antiferroquadrupolar interactions can renormalize CEF level splitting.

The stability of magnetic and quadrupolar states under magnetic fields is analyzed.

Behavior of susceptibilities helps identify the order parameter.

Abstract

We investigate the stability of the multipolar orderings in $f$-electron material CeCoSi based on a self-consistent mean-field calculation for the effective localized model. This material has two ordered phases in the temperature-pressure phase diagram: the antiferromagnetic phase and the nonmagnetic phase, the latter of which has been suggested to be an antiferroquadrupolar phase. Meanwhile, the origin of the antiferroquadrupolar phase has been unclear, since a quadrupole degree of freedom is present only between the ground-state level and highly separated excited-state level under a tetragonal crystalline electric field (CEF), whose energy scale is much larger than the transition temperature. To understand the sequence of the phase transition from the paramagnetic phase, antiferroquadrupolar phase, and antiferromagnetic phase when decreasing the temperature, we examine the important interaction parameters in the effective localized model. We clarify that the $3z^2-r^2$-type of the antiferroquadrupolar interactions can renormalize the CEF level splitting, which assists a quadrupolar ordering even in a tetragonal system without orbital degeneracy. Moreover, the stability of the antiferroquadrupolar and antiferromagnetic states in a magnetic field and the behavior of the magnetic/quadrupolar susceptibility are also presented for the information to identify the unknown order parameter in the nonmagnetic ordered phase.