Impact of core-shell dipolar interaction on magnetic phases of spherical core-shell nanoparticles

Abstract

We show that confinement in small volumes affects the interplay of exchange and dipolar interactions and the magnetic phases of hard and soft spherical core-shell nanoparticles. Large variations in the magnetization of thin shells may occur due to the core dipolar field gradient within the shell. The reversal field is tunable by the trends imposed by the dipolar and core-shell interface exchange energies. We show, for instance, that the reversal field of a CoFe 2 O 4 (30 nm)@MnFe 2 O 4 (6 nm) particle ranges from 15.5 kOe for antiferromagnetic coupling down to 2.5 kOe for ferromagnetic coupling.

Non-Exchange Bias in Binary Nanoparticle Systems

“…(with k B the Boltzmann constant, 𝑀 𝑆 the saturation magnetization, V the particle volume and φ the particle packing fraction) for either soft-soft, hard-hard and soft-hard combination 39 affects the strong intraparticle exchange-coupling (i.e., the exchange bias) of the Co-doped particles, the latter having a much larger associated energy 26 , i.e., the ratio T ex /T dd (where the temperature T ex is proportional to the exchange-coupling energy at the interface, 𝐸 𝐸𝑋 = 𝐻 𝐵 𝑉 𝐹𝑖𝑀 𝑀 𝑆 2 ), is much larger than unity for small particles (as it is the case here). The exchange stiffness constant Aex for the corresponding ferrites (~10 -12 ) 44 is 2 orders of magnitude larger than the dipolar stiffness Adip extracted from the random anisotropy model (~10 -14 ) for the present systems 35 , confirming that the exchange energies involved are much higher 45,46 . Indeed, a bibliographic study presented in the SI (Supplementary Section 5) shows that T ex T dd ≫ 1 in all the nanoparticle systems considered, but those exhibiting very low exchange bias fields 26,39,47,48 .…”

High-energy product SmCo5@Fe core-shell nanoparticles

“…For each value of the external field H , the core-shell magnetization pattern is found using a self-consistent algorithm [11][12][13][14]. The magnetization mj is adjusted to be parallel to the effective magnetic field (H j eff = −(1/M S )(∂E/∂ mj ), so that for each one of the cells the torque is smaller than 10 −17 erg.…”

“…The core dipolar field of spherical hard-soft core-shell nanoparticles is easily predictable. The large core anisotropy favors a core uniform magnetization state in the demagnetization quadrant and qualifies the core as a stable dipolar field source at the shell [14]. Furthermore, materials with very high magnetocrystalline anisotropy, such as FePt, SmCo 5 , and Nd 2 Fe 14 B, allow producing hard-soft core-shell nanoparticles with a wide range of core diameter values, starting with a few nanometers diameter core hard material nanoparticles [2].…”

“…On the other hand, the core-shell dipolar interaction may compete with the interface exchange energy [14]. The longranged dipolar field produced by the core in the shell is opposite to the core magnetization, except for the shell region near the poles of the core, and may produce nonuniform phases, as shown in Fig.…”

“…The anisotropic nature of the core dipolar field is a major issue for choosing the optimum value of the shell thickness δ * for a given value of the core diameter. HSCS nanoparticles may exhibit large variations in the magnetization of thin shells, due to the core dipolar field gradient within the shell [14].…”