Micromagnetic simulation study of a disordered model for one-dimensional granular perovskite manganite oxide nanostructures

Chemical techniques are an efficient method to synthesize one-dimensional perovskite manganite oxide nanostructures with a granular morphology, that is, formed by arrays of monodomain magnetic nanoparticles. Integrating the stochastic Landau-Lifshitz-Gilbert equation, we simulate the dynamics of a simple disordered model for such materials that only takes into account the morphological characteristics of their nanograins. We show that it is possible to describe reasonably well experimental hysteresis loops reported in the literature for single ${\mathrm{La}}_{0.67}{\mathrm{Ca}}_{0.33}{\mathrm{MnO}}_3$ nanotubes and powders of these nanostructures, simulating small systems consisting of only 100 nanoparticles.

Figure 1

Sketch of the model. Each nanograin (sphere) of radius $r$ is separated from its first neighbors by a distance $d_{ij}=2r$ and has associated both a magnetization vector ${\mathbf{M}}_i$ and a random oriented uniaxial anisotropy axis ${\mathbf{n}}_i$. In the figure the external field $\mathbf{H}$ is applied along the $x$ axis.

Figure 2

Hysteresis loops calculated for SNs of size $N=100$, with their anisotropy axis vectors oriented at random (black open symbols) and aligned along the $x$ axis (red closed symbols). Squares and circles stand for curves with and without dipolar interactions, respectively. The continuous thick line corresponds to the hysteresis loop for the RSW model.

Figure 3

Hysteresis loops calculated for five different SNs of size (a) $N=10$ and (b) $N=100$.

Figure 4

Hysteresis loops for one SN of size $N=100$, calculated for three different values of $\varphi$ as indicated. The continuous thick line corresponds to the hysteresis loop for the RSW model.

Figure 5

Hysteresis loops calculated for (a) an EANs and (b) an ERONs of sizes $N=100$. The continuous thick line corresponds to the hysteresis loop for the RSW model.

Figure 6

Coercive field versus $R$ for both an EANs and an ERONs. Inset shows the same information for the remanent magnetization. Dashed and dotted curves are fits to Eq. (12). The continuous thick line both in the main panel and inset are, respectively, the curves of $h_c$ and $m_r$ as functions of $R$ for an assembly of noninteracting nanograins with their easy axes randomly oriented in space.

Figure 7

Experimental hysteresis loop for two single magnetically isolated LCMO nanotubes (black spheres) [16], along with simulation curves calculated for (a) different diameters $d$ (with $K$ constant) and for (b) different values of $K$ (with $d$ constant), as indicated.

Figure 8

Experimental hysteresis loops for (a) two single magnetically isolated LCMO nanotubes and for (b) a powder of this material [16], along with simulation curves calculated using the parameters $K_0=2.5\times {10}^4$ J/${\mathrm{m}}^3$ and $\mathrm{\Delta }K=2.0\times {10}^4$ J/${\mathrm{m}}^3$.