Chapter 2 Fundamental aspects and theoretical Models
2.8. Surface effects
example of inducing the anisotropy in FM materials by field annealing. In the last case, the uniaxial anisotropy is induced by applying uniaxial stress (σ) in a ferromagnetic solid [KRON2003]. The magnitude of the stress-induced anisotropy is
=3
2 (2.39)
where, λS is the saturation magnetostriction. Both the single-ion and two-ion anisotropy contribute to the stress induced anisotropy. The highest values of uniaxial anisotropy are found in hexagonal and other uniaxial crystals. Smallest values are found in cubic alloys and amorphous ferromagnets.
2.7.4. Magnetostrictive anisotropy
Another important form of anisotropy in magnetic materials is due to magnetostriction, a change of volume of an isotropic crystal due to magnetic order. Magnetostriction relates the stress in a magnetic material to an anisotropy created by that stress. Figure 2.22 shows schematic views of bars with different applied stress conditions. If λ is positive, then application of a tensile stress to the bar creates an easy axis in the direction of the applied stress. If a compressive stress is applied, then the direction of the easy axis created will be perpendicular to the stress direction. On the other hand, if the magnetostriction constant for the material is negative, then the above phenomena would be reversed: a tensile stress will create an easy axis perpendicular to the stress direction and a compressive stress will create an easy axis in the direction of the applied stress.
feature of nanoparticles and their oxides, as reported by Sundaresan et al [SUND2006]. For example, nanoparticles of non-magnetic materials such as cerium oxide and aluminum oxide were found to display M-H loops at room temperature. Nanoparticles of metal nitrides, such as niobium nitride were also found to exhibit FM. Nanoparticles of some superconductors in the normal state were found to show FM. The smaller the nanoparticle, the larger is the FM. High field hysteresis and relaxation of the magnetization could result due to irreversible reorientations of the surface spins [KODA19991]. Nunes et al [NUNE1998] considered the structural relaxation of spinel ferrite nanoparticles using molecular dynamic modelling. They predicted non-uniform strains in the surface layers, with an average expansion of a few percent compared to bulk. They suggested that such an expansion might result in a stress-induced anisotropy field of up to 70 kOe, which could account for some of the anomalous magnetic behavior of ferrite nanoparticles. Kodama et al proposed that the canted spins in ferrite nanoparticles freeze into a spin glass-like phase at temperatures below 50 K [KODA1997, KODA19991, MORU2013]. Thus, the surface spins have multiple configurations for any orientation of the core magnetization. Nevertheless, several models such as two-sublattice model, multi-sublattice model [KODA1997] and core-shell model [TIWA2005, JAGO2009]
have been proposed by considering different types of particle interactions [MENE2010] on the complexity of the magnetic properties of NiO nanoparticles and the observed results were explained on the basis of competition among core size effects, surface anisotropy and interface interaction. The nature of temperature dependence of coercivity of such particles is strongly dependent on the particle size and the nature varies from linear behavior to non-linear behavior with decreasing particle size. Proenca et al [PROE2011] shown that the effective magnetic anisotropy increases with decreasing particle size and the number of uncompensated spins per nanoparticles was found to be proportional to ns1/3 (ns = total number of spins), indicating the random distribution on the nanoparticle surface. This leads to unidirectional anisotropy between ferromagnetically coupled uncompensated surface spins and AFM cores and provides additional pinning force resulting a shift of the hysteresis loop. Similarly, Duan et al [DUAN2012] reported that the larger saturation magnetization and coercivity in fine NiO nanoparticles is mainly resulting from the surface spins and explained using core-shell model.
It is well understood that the changes in the physical properties can be directly related to their microscopic origin and theoretical studies are required to confirm the surface effects. Several magnetic effects could also result from the finite size effect of nanoparticles. These could include:
(i) Random oriented uncompensated surface spins.
(ii) Canted spins.
(iii) Spin glass like behavior of the surface spins.
(iv) Magnetically dead layer at the surface.
(v) Enhancement of the magnetic anisotropy which result for surface anisotropy.
However, surface effects can lead to a decrease or an increase in the magnetization of the nanoparticle. It was reported that magnetization of oxide nanoparticles decreases up to creation size for some oxide nanoparticle [KODA19992]. On the other hand, the magnetization of some metallic nanoparticles (cobalt) was reported to increase [RESP1998]. The reduction of magnetization of oxide nanoparticles was attributed to the existence of a magnetically dead layer on the particle’s surface and the existence of canted spins or the existence of a spin glass- like behavior of the surface spins [KODA19992]. Several experimental studies reported an increase in the effective magnetic anisotropy due to surface effects [BODK1994, JAME2001, LUIS2002, JAME2004]. Computational studies also reported different anisotropy and magnetic moment at the surface of magnetic clusters embedded in matrices [XIEY2004]. Binns et al reported that both spin and orbital moments at the surface are different from those of the bulk counterparts using Synchrotron radiation [BINN2002]. These studies suggest that the total magnetization of the nanoparticle is composed of two components: a component due to the surface spins and a component due to the core of the particle. This led to the development of model of core-shell to describe interaction between the core and the shell. In nanoparticles of AFM or ferrimagnetic materials, this interaction occurs at the interface between the FM surface and AFM (or ferrimagnetic) core. In some FM nanoparticles, the surface of the metal usually oxidizes in air and forms an AFM metal-oxide shell around the FM metal core. Thus, there will be an interaction between the core and the shell, called exchange bias or exchange coupling, which provides an additional magnetic anisotropy to help aligning the FM spins in certain directions.
Core-shell exchange interaction and surface anisotropy were found to play significant roles in determining some magnetic properties of nanoparticles. The structural modifications at the boundaries of FM or ferrimagnetic nanoparticles, such as vacancies, broken bonds, may induce enough frustration, which leads to different canted magnetic structures [MAKO2009].
The canted surface spins may freeze giving rise to a glassy state at low temperatures. One of the important features characterizing the surface spin glass state in nanoparticles is the flattening of the field-cooled magnetization at low temperatures [LABA2005]. The main origin of spin glass-like behavior in nanoparticles could be due to strong inter-particle interactions or due to surface spin effects within individual particles.