Shape-dependent exchange bias effect in magnetic nanoparticles with core-shell morphology

We study the low-temperature isothermal magnetic hysteresis of cubical and spherical nanoparticles with ferromagnetic-core/antiferromagnetic-shell morphology, in order to elucidate the sensitivity of the exchange bias effect to the shape of the particles and the structural imperfections at the core-shell interface. We model the magnetic structure using a classical Heisenberg Hamiltonian with uniaxial anisotropy and simulate the hysteresis loop using the metropolis Monte Carlo algorithm. For nanoparticles with geometrically sharp interfaces, we find that cubes exhibit a higher coercivity and lower exchange bias field than spheres of the same size. With increasing interface roughness, the shape dependence of the characteristic fields gradually decays, and eventually, the distinction between cubical and spherical particles is lost for moderately rough interfaces. The sensitivity of the exchange bias field to the microstructural details of the interface is quantified by a scaling factor ($b$) relating the bias field to the net moment of the antiferromagnetic shell $(H_{\mathrm{eb}}=b{M}_{\mathrm{AF}}+H_o)$. Cubical particles exhibit a lower sensitivity to the dispersed values of the net interfacial moment.

Figure 1

Midplane of a cubical ($C58$) and a spherical ($S710$) particle with rough interfaces. Roughness dispersion is $\sigma =0.5a$ in both cases.

Figure 2

Dependence of low-temperature ($T={10}^{-3}$) coercivity (top) and exchange bias field (bottom) of cubical and spherical particles on the rotation angle ($\varphi$) of the underlying SC lattice about the crystallographic axis [001].

Figure 3

Low-temperature ($T={10}^{-3}$) hysteresis loops of cubical and spherical particles with rough interfaces. Error bars arise from configurational averaging over the interface disorder.

Figure 4

Dependence of coercivity on interface roughness at a low temperature ($T={10}^{-3}$).

Figure 5

Dependence of exchange bias field on interface roughness at a low temperature ($T={10}^{-3}$).

Figure 6

Scaling behavior of the exchange bias field with the net magnetic moment of the AF shell for spherical and cubical nanoparticles with rough interfaces. Data in each case are selected from an assembly of $N_s=150–200$ noninteracting nanoparticles with interface roughness in the range $\sigma =0.05-0.20$. The slopes of the least squares fits, shown by straight lines, are $b\left(S58\right)=0.039(\pm 2\%), b\left(C58\right)=0.008(\pm 11\%)$, and $b\left(C58r\right)=0.017(\pm 6\%)$