# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1703.07190