Dynamic spin freezing and magnetic memory effect in ensembles of interacting anisotropic magnetic nanoparticles

We explore the dependence of the magnetic memory effect on demagnetizing interactions by considering two differently organized ensembles of anisotropic ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ nanoparticles: a compact ensemble (CE) and a hollow core ensemble (HCE). The dynamic magnetic behavior is extensively investigated by performing ac susceptibility, magnetic memory measurements, and dc magnetic aging protocols. The frequency dependence of the freezing temperature is analyzed with the help of two dynamic scaling models: the Vogel-Fulcher (VF) model and the power-law model. Both the systems exhibit a cluster spin-glass phase, as realized from the Mydosh parameter, VF temperature, relaxation time for single spin flip, and critical exponent. The progressive spin freezing is ensured by multiple intermediate metastable states and significant memory effects in both the systems. The presence of hollow core geometry with highly interacting surface nanoparticles and partially aligned magnetic easy axes leads to a complex anisotropic energy landscape in HCE. As a consequence, prominent magnetic memory effect is observed in HCE along with higher activation energy, reduced blocking temperature, and enhanced coercivity compared to CE.

Figure 1

HRTEM micrographs of (a, b, c) CE and (d, e, f) HCE.

Figure 2

PXRD pattern of (a) CE, (b) HCE showing SAXS and MSANS intensity profiles with log-norm fitting by using the SASfit software package, (c) CE, (d) HCE showing particle size distribution of both CE and HCE, (e) primary nanoparticles from SAXS, and (f) secondary ensembles from SANS.

Figure 3

($\mathrm{a})\delta M$ plots of CE and HCE systems. (b, c) Irreversible susceptibility plots for (b) CE and (c) HCE.

Figure 4

Zoomed probe field dependent magnetization of (a) CE and (b) HCE. Inset (i): Field dependent magnetization of (a) CE and (b) HCE. Inset (ii): LAS fitting of (a) HC and (b) HCE at experimental data of 5 K.

Figure 5

Temperature-dependent magnetization plot of (a) CE and (b) HCE. Inset: Curie-Weiss (CW) law fitting.

Figure 6

In-phase ac susceptibility at applied field $H_{\text{dc}}$ = 0 kOe with $H_{\text{ac}}$ = 10 Oe. Inset: Out-of-phase ac susceptibility of (a) CE and (b) HCE.

Figure 7

Fitting of critical slowing down model. Inset (i): Arrhenius law fitting of (a) CE and (b) HCE. Inset (ii): VF law fitting of (a) CE and (b) HCE.

Figure 8

(a) In-phase ac susceptibility at applied field $H_{\text{dc}}$ = 1 kOe with $H_{\text{ac}}$ = 10 Oe; the inset shows out-of-phase ac susceptibility. (b) Power law; the inset shows VF law fitting. (c) In-phase ac susceptibility at three different magnetic fields for system HCE.

Figure 9

(a, c) FC memory effect for the system (a) CE and (c) HCE. (b, d) Temperature derivative of the FC warming curve of (b) CE and (d) HCE. (e, f) ZFC memory effect of (e) CE and (f) HCE.

Figure 10

(a, b) Magnetic relaxation measurements using ZFC protocol for (a) CE and (b) HCE. (c, d) Continuation of the relaxation trend with stretched exponential function fitting for (c) CE and (d) HCE.

Figure 11

Schematic on easy axis arrangement in the ensemble: CE (left) and HCE (right).