Complete Multipole Basis Set for Single-Centered Electron Systems

Kusunose, Hiroaki; Oiwa, Rikuto; Hayami, Satoru

doi:10.7566/jpsj.89.104704

Cited by 56 publications

(45 citation statements)

References 31 publications

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“…Since it is predicted that the ferroic octupole order only appears when the spin chirality is negative 17 , the model calculation shows a complete correspondence between the presence of the XMCD signal and octupole order. In the XMCD experiment, although the direct detection of octuple may not be allowed, T z -mediated detection is proposed by recent theoretical investigations 18 , 22 .…”

Section: Resultsmentioning

confidence: 99%

“…Recently, a theoretical study suggests a possibility to detect the cluster magnetic octupole order by XMCD through the coupling between circular polarized X-ray and anisotropic magnetic dipole moment, which is known as the T z term 18 . Since both the magnetic dipole moment in XMCD and cluster magnetic octupole are arising from the spatial distribution of spin density, both of them can similarly be described as coupled operators of spin and quadratic moments 18 – 22 : the key point for the cluster multipole observation is the similarity of theoretical expression between the T z term and cluster magnetic octupole. Moreover, since the T z term is generally coming from the intra-atomic magnetic dipole moment, it is not detectable by the static magnetometry 23 , 24 .…”

Section: Introductionmentioning

confidence: 99%

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X-ray study of ferroic octupole order producing anomalous Hall effect

et al. 2021

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Recently found anomalous Hall, Nernst, magnetooptical Kerr, and spin Hall effects in the antiferromagnets Mn3X (X = Sn, Ge) are attracting much attention for spintronics and energy harvesting. Since these materials are antiferromagnets, the origin of these functionalities is expected to be different from that of conventional ferromagnets. Here, we report the observation of ferroic order of magnetic octupole in Mn3Sn by X-ray magnetic circular dichroism, which is only predicted theoretically so far. The observed signals are clearly decoupled with the behaviors of uniform magnetization, indicating that the present X-ray magnetic circular dichroism is not arising from the conventional magnetization. We have found that the appearance of this anomalous signal coincides with the time reversal symmetry broken cluster magnetic octupole order. Our study demonstrates that the exotic material functionalities are closely related to the multipole order, which can produce unconventional cross correlation functionalities.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

X-ray study of ferroic octupole order producing anomalous Hall effect

et al. 2021

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“…1(b) [60]. We adopt the lowest-rank multipoles from the four types of multipole expressions (electric, magnetic, electric toroidal, and magnetic toroidal) in each uniform and staggered order [67,68], as the multipoles with a different rank belong to the same irreducible representation in a lattice system. For the uniform componentX A +X B , cluster even-parity multipoles are defined as an electric monopoleQ (c) 0 when the local multipole X isQ 0 , three magnetic dipoles (M (c) x…”

Section: A Multipole Degrees Of Freedommentioning

confidence: 99%

NQR and NMR spectra in the odd-parity multipole material CeCoSi

Yatsushiro

Hayami

2020

Phys. Rev. B

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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 2type antiferroquadrupole structure. We show that different odd-parity multipole orders lead to different fielddependent 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 oddparity order parameters in CeCoSi by NQR and NMR measurements.

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“…Engineering asymmetric band deformations in the systems without P and T symmetries is important for nonreciprocal conductive phenomena irrespective of electrons and magnons. Meanwhile, the microscopic conditions have not been fully clarified yet, although active magnetic toroidal multipoles are necessary from the symmetry aspect [47,[83][84][85]. Recently, a useful framework to extract essential model parameters for the asymmetric band structure in the electron systems has been proposed on the basis of augmented multipoles [86].…”

Section: Introductionmentioning

confidence: 99%

Essential model parameters for nonreciprocal magnons in multisublattice systems

Hayami,

Matsumoto

2021

Preprint

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We theoretically investigate the microscopic conditions for emergent nonreciprocal magnons toward unified understanding on the basis of a microscopic model analysis. We show that the products of the Bogoliubov Hamiltonian obtained within the linear spin wave approximation is enough to obtain the momentum-space functional form and the key ingredients in the nonreciprocal magnon dispersions in an analytical way even without solving the eigenvalue problems. We find that the odd order of an effective antisymmetric Dzyaloshinskii-Moriya interaction and/or the even order of an effective symmetric anisotropic interaction in the spin rotated frame can be a source of the antisymmetric dispersions. We present possible kinetic paths of magnons contributing to the antisymmetric dispersions in the one-to four-sublattice systems with the general exchange interactions. We also test the formula for both ferromagnetic and antiferromagnetic orderings in the absence of spatial inversion symmetry.

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Complete Multipole Basis Set for Single-Centered Electron Systems

Cited by 56 publications

References 31 publications

X-ray study of ferroic octupole order producing anomalous Hall effect

X-ray study of ferroic octupole order producing anomalous Hall effect

NQR and NMR spectra in the odd-parity multipole material CeCoSi

Essential model parameters for nonreciprocal magnons in multisublattice systems

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