# Field-Induced Switching of Ferro-Quadrupole Order Parameter in PrTi2Al20

## TL;DR

This study reveals magnetic-field-induced phase transitions in the ferro-quadrupole order of PrTi2Al20, showing how external fields can switch quadrupole states and influence electron hybridization, with implications for understanding quadrupole interactions.

## Contribution

It demonstrates field-induced switching of ferro-quadrupole order parameters and provides a symmetry-based theoretical explanation for these transitions in PrTi2Al20.

## Key findings

- Discontinuous switching of quadrupole order parameters under magnetic fields.
- Violation of proportionality between NMR Knight shift and magnetic susceptibility.
- Significant influence of quadrupole order on conduction-f electron hybridization.

## Abstract

We report magnetic-field-induced first-order phase transitions in the ferro-quadrupole (FQ) ordered state of PrTi2Al20, in which non-Kramers Pr3+ ions with two 4f electrons have a non-magnetic Gamma3 doublet ground state in the cubic Td crystalline electric field. For magnetic fields along [111], 27Al-NMR and magnetization experiments reveal Qz \propto 3z2-r2 type FQ order below 2 K independent of field strength. Magnetic fields along [001] or [110], however, induce discontinuous switching of order parameters within the two dimensional space spanned by Qz and Qx \propto x2-y2 at small field values less than a few tesla. A symmetry-based theoretical analysis shows that the transitions can be caused by competition between the magnetic Zeeman interaction and anisotropy in the quadrupole-quadrupole interactions, if the latter dominates over the former in low fields and vice versa in high fields. Furthermore, striking violation of proportionality between NMR Knight shift and magnetic susceptibility is observed in the symmetry-broken FQ phases, indicating significant influence of FQ order on the hybridization between conduction and f electrons, which in turn mediates the RKKY-type quadrupole interaction causing the FQ order. This feedback effect may be a specific feature of quadrupole orders not commonly observed in magnetic phase transitions and play a key role for inducing the discontinuous transitions.