NQR and NMR spectra in odd-parity multipole material CeCoSi

TL;DR

This paper provides a theoretical analysis of NQR and NMR spectra in CeCoSi, revealing how odd-parity multipoles from various ordered states cause distinct spectral splittings, aiding experimental identification of these multipoles.

Contribution

It introduces a theoretical framework for understanding NQR and NMR spectral splittings caused by odd-parity multipoles in CeCoSi, highlighting their dependence on different multipole orders and magnetic fields.

Findings

Different odd-parity multipoles cause unique spectral splittings.

Only the xy-type electric toroidal quadrupole shows NQR spectral splitting.

Spectral splittings depend on the type of multipole order and magnetic field.

Abstract

We theoretically study NQR and NMR spectra in the presence of odd-parity multipoles originating from staggered antiferromagnetic and antiferroquadrupole orderings. For the $f$-electron metal, CeCoSi, which is a candidate hosting odd-parity multipoles, we derive an effective hyperfine field acting on Co nucleus generated from electronic origin multipole moments at Ce ion under zero and nonzero magnetic fields. We elucidate that emergent odd-parity multipoles give rise to sublattice-dependent spectral splittings in NQR and NMR through the effective hyperfine coupling in the absence of the global inversion symmetry. We mainly examine behaviors of the NQR and NMR spectra in three odd-parity multipole ordered states: a $y$-type magnetic toroidal dipole order with a staggered $x$-type antiferromagnetic structure, an $xy$-type electric toroidal quadrupole order with a staggered $x^2-y^2$-type antiferroquadrupole structure, and a $z$-type electric dipole order with a staggered $3z^2-r^2$-type antiferroquadrupole structure. We show that different odd-parity multipole orders lead to different field-dependent spectral splittings in NMR, while only the $xy$-type electric toroidal quadrupole order exhibits the NQR spectral splitting. We also present possible sublattice-dependent spectral splittings for all the odd-parity multipole orders potentially activated in low-energy crystal-field levels, which will be useful to identify odd-parity order parameters in CeCoSi by NQR and NMR measurements.