Microstrain induced deviation from N\'eel's 1/d behaviour: Size-dependent magnetization in Bi1-xCaxFe1-yTiyO3-delta nanoparticles

TL;DR

This study reveals how microstrain influences the size-dependent magnetization in Bi1-xCaxFe1-yTiyO3-delta nanoparticles, deviating from Nél's traditional 1/d behavior, with implications for magnetic and ferroelectric properties.

Contribution

It introduces an empirical model linking magnetization to particle size and microstrain, highlighting the complex interplay affecting magnetic behavior in doped nanoparticles.

Findings

Magnetization deviates from 1/d dependence due to microstrain effects.

A critical size (~35 nm) marks a rapid increase in magnetization.

Large magnetodielectric response (~9.5%) observed in optimized samples.

Abstract

Magnetization of antiferromagnetic nanoparticles is known to generally scale up inversely to their diameter (d) according to N\'eel's model. Here we report a deviation from this conventional linear 1/d dependence, altered significantly by the microstrain, in Ca and Ti substituted BiFeO3 nanoparticles. Magnetic properties of microstrain-controlled Bi1-xCaxFe1-yTiyO3-delta (y = 0 and x = y) nanoparticles are analyzed as a function of their size ranging from 18 nm to 200 nm. A complex interdependence of doping concentration (x or y), annealing temperature (T), microstrain (epsilon) and particle size (d) is established. X-ray diffraction studies reveal a linear variation of microstrain with inverse particle size, 1/d nm-1 (i.e. epsilon.d = 16.5 nm.%). A rapid increase in the saturation magnetization below a critical size dc ~ 35 nm, exhibiting a (1/d)^alpha (alpha ~ 2.6) dependence, is attributed to the influence of microstrain. We propose an empirical formula M is proportional to (1/d)epsilon^beta (beta ~ 1.6) to highlight the contributions from both the size and microstrain towards the total magnetization in the doped systems. The magnetization observed in nanoparticles is thus, a result of competing magnetic contribution from the terminated spin cycloid on the surface and counteracting microstrain present at a given size. Large magnetodielectric response of ~ 9.5 % is observed in spark plasma sintered pellets with optimal size and doping concentration, revealing a strong correlation between magnetic and ferroelectric order parameters.