# Charge Transfer Effect under Odd-Parity Crystalline Electric Field: Divergence of Magnetic Toroidal Fluctuation in $\beta$-YbAlB$_4$

## TL;DR

This paper theoretically reveals that odd-parity crystalline electric fields in $eta$-YbAlB$_4$ induce magnetic toroidal fluctuations that diverge at the quantum critical point, linking charge transfer and critical fluctuations.

## Contribution

It introduces a minimal model showing how odd-parity CEF causes magnetic toroidal fluctuations to diverge at the valence quantum critical point.

## Key findings

- Magnetic toroidal fluctuations diverge at the quantum critical point.
- Charge transfer between 4f and 5d states is driven by Coulomb repulsion.
- Onsite 4f-5d Coulomb interaction causes simultaneous divergence of MT and electric dipole fluctuations.

## Abstract

A novel property of the quantum critical heavy fermion superconductor $\beta$-YbAlB$_4$ is revealed theoretically. By analyzing the crystalline electronic field (CEF) on the basis of the hybridization picture, odd parity CEF is shown to exist because of sevenfold configuration of B atoms around Yb, which breaks the local inversion symmetry. This allows onsite admixture of 4f and 5d wavefunctions with a pure imaginary coefficient, giving rise to the magnetic toroidal (MT) degree of freedom. By constructing a realistic minimal model for $\beta$-YbAlB$_4$, we show that onsite 4f-5d Coulomb repulsion drives charge transfer between the 4f and 5d states at Yb, which makes the MT fluctuation as well as the electric dipole fluctuation diverge simultaneously with the critical Yb-valence fluctuation at the quantum critical point of the valence transition.