Magnetodynamics of short nanoparticle chains

Abstract

In recent years, there has been increasing interest in the understanding and application of nanoparticle assemblies driven by external fields. Although these systems can exhibit marked transitions in behavior compared to non-interacting counterparts, it has often proven challenging to connect their dynamics with underlying physical mechanisms or even to verifiably establish their structure under realistic experimental conditions. We have studied colloidal iron oxide nanoparticles that assemble into ordered, few-particle linear chains under the influence of oscillating and pulsed magnetic fields. In this work, our goal has been to answer the following question: by what physical mechanisms does the magnetic switching of a linear chain evolve from the switching of its constituent particles? Cryo-TEM has been used to flash freeze and image the structures formed by oscillatory drive fields, and magnetic relaxometry has been used to extract the multiple time constants associated with magnetic switching of the short chains. Armed with the physical structure from microscopy and the field-dependent switching times from magnetic measurements, we have conducted extensive micromagnetic simulations, revealing probable physical mechanisms for each time constant regime spanning ~1 microsecond to 1 s in time. These types of magnetic nanomaterials have great potential for biomedical technologies, particularly magnetic particle imaging and hyperthermia, and rigorous elucidation of their physics will hasten their optimization.

Figures (7)

• Figure 1: AC magnetometry of strongly interacting "SI" ($\#$1, red) vs weakly interacting "WI" (Vivotrax, black) MNPs in response to a sinusoidal drive field at 10 kHz and 10 mT. (a) Voltage response amplitude (proportional to the time derivative of magnetization, Eq. \ref{['eq1']}, in arbitrary units) of the SI MNPs displays sharp narrow peaks relative to WI MNPs and a phase offset. (b) Fourier transform of (a) shows a significantly broader harmonic spectrum for the SI MNPs (red) compared to the WI MNPs (black). (c) TEM images of SI MNPs $\#$1. (d) TEM diameter distribution of 100 nanoparticles for the SI MNPs $\#$1 sample. (e) Dynamic light scattering (DLS) diameter distribution of nanoparticle solution for the SI MNPs $\#$1 sample. The dotted line is a fit to a log-normal distribution. (f) Table summarizing the size distribution of two SI MNPs systems in this work. The values for SI MNPs $\#$2 and additional physical characterization information can be found in our previous workAbel_2024. The DLS measurements do not include a standard deviation due to the presence of multiple aggregated populations.
• Figure 2: Threshold behavior of SI MNPs. Middle panel - Voltage response amplitude (arbitrary units) for four different MNPs at different AC field amplitudes and fixed frequency of 20 kHz. Only one (SI MNPs $\#$1, 15 nm) shows a threshold behavior marked at region "c" in the middle panel. VivoTrax (WI MNPs $\#$1) is an aggregate of single MNPs with diameter below 10 nm. Sub panels - comparison of the $m$ vs $H$ data for SI MNPs $\#$1 (15 nm, red) and VivoTrax (black) at the six different magnetic field points on the curve in the middle panel ("a" to "f" markers indicated by the gray arrows). The $m$ vs $H$ data are generally S-shaped for all fields for VivoTrax compared to the SI MNPs $\#$1, which shows an abrupt loop opening in the transition near the threshold field (region c).
• Figure 3: (a) Cryo-TEM flash-freeze plunger method. A manual plunger equipped with a tweezer holds the sample grid (green disc) and a drop of MNPs solution (blue circle). Panels (b) and (c) show images from Cryo-TEM measurements of SI MNPs $\#$2 with the magnetic ON and OFF, respectively. For the ON case, the AC magnetic field (250 Hz, 15 mT) is turned on for about 5 seconds prior to plunging the sample grid into the liquid nitrogen bath for flash cryo-freezing. The dashed ovals indicate MNP chains composed of individual MNPs (black dots). The yellow arrow in (b) points in the magnetic field direction. Panel (d) is a histogram for the distribution of chain lengths (in units of number of MNPs) at two concentrations $C_1$ and $C_2$, where $C_1 = 2C_2$. Here, the concentrations are $C_1 \approx 0.34$ mg/ml and $C_2 \approx 0.17$ mg/ml.
• Figure 4: MRX (pulsed) measurement. Time-dependent voltage response amplitude (arbitrary units) after turn-on of applied magnetic field of (a) WI MNPs $\#$1 (VivoTrax) and (b) SI MNPs $\#$1 at different field amplitudes. The data and corresponding fits using Eq. \ref{['eq3']} are indicated by data points and lines (solid/dashed), respectively. The inset in (a) shows the fitted amplitude and time constant for WI MNPs system. (c) and (d) show the fitted amplitudes and time constants, respectively, for the SI MNPs in (b). The solid lines in (c) and (d) are connecting lines for visual guide and not fits to the data. The "step $\#$" in the legend pertains to the three time constants in Eq. \ref{['eq3']}. Step $\#$2 shows the threshold behavior for the induced voltage (proportional to the magnetic response) and displays the largest decrease in the time constants with increasing magnetic field, indicating that it is the chain formation and spin-reversal avalanche step for the entire chain. This behavior of SI MNPs contrasts with the nearly linear field-dependence for the WI MNPs displayed in the inset of (a). (e) Remanence decay (voltage response) curves after applied field is turned off for SI MNPs $\#$1 at different initially applied magnetic fields from 9 mT to 17 mT (bottom to top). (f) Fitted decay time constants as a function of magnetic field. The fitting function is an single exponential with an offset. The increased remanence lifetime with increasing amplitude indicates a memory effect.
• Figure 5: Micromagnetic simulations of thermally activated Néel reversals for chains of four MNPs at temperature T = 290 K. Individual MNPs in the chain are 18 nm diameter spheres, with 2 nm spacing. Discretization cell size is 1 nm. Material parameters $M_s$ = 480 kA/m, A = 13.2 pJ/m, cubic anisotropy with K = -13.7 $kJ/m^3$ and damping coefficient $\alpha$ = 0.1, except as noted. (a) 12 iterations with reversing field $\mu_0 H$ = 18 mT. Applied field and chain axis parallel to $x$-axis. (b,c) Detail of a switching event with reversal field $\mu_0 H$ = 14 mT. At t = 22.5 ns the chain magnetization has just crossed over the energy barrier, and these curves show the tail of the reversal with the thermal field deactivated (i.e., T = 0 K). (b), (c) show the x- (resp. y-) magnetization component for each MNP individually (thin curves), along with the x-axis magnetization for the chain as a whole (thick purple curve). (d) Switching event times accumulated for 32 iterations at five different applied fields: $\mu_0 H$ = 30 mT (red triangles), 26 mT (gold circles), 22 mT (brown squares), 18 mT (blue asterisks), and 14 mT (green crosses and purple pluses). The curve trace marked by (+) has anisotropy $K$ = 0 $J/m^3$. Anisotropy for all others is cubic with $K$ = -13.7 $kJ/m^3$. Simulations extend to 1000 ns, but only the first 100 ns are presented for clarity. (e) Table of fitted constants for the 5 simulated iterations from (d). For each magnetic field, $\tau_N$ and the barrier height $E_b$ are fitted. The attempt time, $\tau_0$, is calculated using Eq. \ref{['eq4']}. Uncertainties determined from fits to the accumulated switching event statistics in (d) using the cumulative distribution function (CDF) are provided for energy barrier and attempt time constants.