# Magnetic memory effect in ensembles of interacting anisotropic magnetic nanoparticles

## TL;DR

This study investigates how the organization geometry of anisotropic ZnFe₂O₄ nanoparticles influences magnetic memory effects and spin-glass behavior, revealing that hollow core arrangements enhance memory due to increased frustration and anisotropy.

## Contribution

It provides new insights into the role of nanoparticle organization geometry on magnetic memory and spin-glass phases in anisotropic magnetic nanoparticle ensembles.

## Key findings

- Hollow core ensembles show stronger magnetic memory effects than compact ensembles.
- Presence of cluster spin-glass phase confirmed by dynamic scaling models.
- Hollow core geometry results in higher coercivity and lower blocking temperature.

## Abstract

We explore the influence of demagnetization interaction on magnetic memory effect by varying organization geometry of anisotropic ZnFe$_2$O$_4$ nanoparticles in an ensemble. The static and dynamic behaviour of two differently organized ensembles, compact ensemble (CE) and hollow core ensemble (HCE), are extensively studied by both dc and ac susceptibility, magnetic memory effect and spin relaxation. The frequency-dependence peak shifting of freezing temperature in both the systems is analyzed properly with the help of two dynamic scaling models: Vogel-Fulcher law and power law. Presence of cluster spin-glass phase is reflected from Vogel-Fulcher temperature $T_0$ $\simeq$ 142.58 K for CE, $\simeq$ 97 K for HCE and characteristic time constant $\tau_0$ $\simeq$ $8.85\times10^{-9}$ s for CE, $\simeq$ $3.8\times10^{-10}$ s for HCE; along with $\delta$T$_{Th}$ $\sim$ 0.1 for CE and 0.2 for HCE. The power law fitting with dynamic exponent $zv'$ = 6.2 $\pm$ 1.1 for CE, 6.3 $\pm$ 0.5 for HCE and single spin flip $\tau^*$ $\simeq$ $7.7\times10^{-11}$ s for CE, $\simeq$ $1.3\times10^{-10}$ s for HCE provide firm confirmation of cluster spin-glass phase. The progressive spin freezing across multiple metastable states with prominent memory effects is reflected in both the systems via nonequilibrium dynamics study. The hollow core geometry with anisotropic nanoparticles on surface with closer proximity leads to complex anisotropy energy landscape with enhanced demagnetizing field resulting highly frustrated surface spins. As a consequence, more prominent magnetic memory effect is observed in HCE with higher activation energy, reduced blocking temperature and enhanced coercivity than that of CE.