Fluctuation Effects on the Quadrupolar Ordering in Magnetic Field

TL;DR

This paper investigates how magnetic fields influence quadrupolar ordering, revealing that weak fields suppress fluctuations and raise transition temperatures, with significant entropy effects even without Kondo interactions.

Contribution

It introduces an effective medium theory to analyze fluctuation effects on quadrupolar ordering under magnetic fields, highlighting competing influences on transition behavior.

Findings

Magnetic field suppresses fluctuations quadratically, increasing transition temperature.

Fluctuation effects reduce entropy release at ordering to about half of ln 4.

Weak magnetic fields enhance quadrupolar ordering by diminishing fluctuations.

Abstract

Effects of magnetic field on the quadrupolar ordering are investigated with inclusion of fluctuation of order parameters. For the simplest model with the nearest-neighbor quadrupolar interaction, the transition temperature and the specific heat are derived by the use of the recently proposed effective medium theory. It is shown that magnetic field H has two competing effects on the quadrupolar ordering; one is to encourage the ordering by suppressing the fluctuation among different components of order parameters, and the other is to block the ordering as in antiferromagnets. The former is found to be of order H^2 and the latter of order H^4. Hence the fluctuation is suppressed for weak fields, and the transition temperature increases with magnetic field. The fluctuation effect is so strong that the entropy released at the quadrupolar ordering is only about half of the full value ln 4 even without the Kondo effect.