NQR and NMR spectra in the odd-parity multipole material CeCoSi
Megumi Yatsushiro, Satoru Hayami
Abstract
We study theoretically 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 a Co nucleus generated from electronic origin multipole moments of the Ce ion in 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 global inversion symmetry. We mainly examine the 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 (${x}^{2}\ensuremath{-}{y}^{2}$)-type antiferroquadrupole structure, and a $z$-type electric dipole order with a staggered ($3{z}^{2}\ensuremath{-}{r}^{2}$)-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.