Pérez N, Guardia P, Roca A G, Morales M P, Serna C J, Iglesias O, Bartolomé F, García L M, Batlle X, Labarta A
Departament de Física Fonamental and Institut de Nanociència i Nanotecnologia IN2UB, Universitat de Barcelona, Martíi Franqués 1, E-08028 Barcelona, Catalonia, Spain.
Nanotechnology. 2008 Nov 26;19(47):475704. doi: 10.1088/0957-4484/19/47/475704. Epub 2008 Oct 30.
The effect of surface anisotropy on the distribution of energy barriers in magnetic fine particles of nanometer size is discussed within the framework of the Tln(t/τ(0)) scaling approach. The comparison between the distributions of the anisotropy energy of the particle cores, calculated by multiplying the volume distribution by the core anisotropy, and of the total anisotropy energy, deduced by deriving the master curve of the magnetic relaxation with respect to the scaling variable Tln(t/τ(0)), enables the determination of the surface anisotropy as a function of the particle size. We show that the contribution of the particle surface to the total anisotropy energy can be well described by a size-independent value of the surface energy per unit area which permits the superimposition of the distributions corresponding to the particle core and effective anisotropy energies. The method is applied to a ferrofluid composed of non-interacting Fe(3-x)O(4) particles of 4.9 nm average size and x about 0.07. Even though the size distribution is quite narrow in this system, a relatively small value of the effective surface anisotropy constant K(s) = 2.9 × 10(-2) erg cm(-2) gives rise to a dramatic broadening of the total energy distribution. The reliability of the average value of the effective anisotropy constant, deduced from magnetic relaxation data, is verified by comparing it to that obtained from the analysis of the shift of the ac susceptibility peaks as a function of the frequency.
在Tln(t/τ(0))标度方法的框架内，讨论了表面各向异性对纳米尺寸磁性细颗粒中能垒分布的影响。通过将体积分布乘以核心各向异性来计算颗粒核心的各向异性能量分布，并通过推导磁弛豫主曲线相对于标度变量Tln(t/τ(0))来得出总各向异性能量分布，二者之间的比较使得能够确定作为颗粒尺寸函数的表面各向异性。我们表明，颗粒表面对总各向异性能量的贡献可以通过单位面积表面能的尺寸无关值来很好地描述，这允许叠加对应于颗粒核心和有效各向异性能量的分布。该方法应用于由平均尺寸为4.9 nm且x约为0.07的非相互作用Fe(3 - x)O(4)颗粒组成的铁磁流体。尽管该系统中的尺寸分布相当窄，但有效表面各向异性常数K(s) = 2.9 × 10^(-2) erg cm^(-2)的相对较小值会导致总能量分布显著变宽。通过将从磁弛豫数据推导的有效各向异性常数的平均值与从交流磁化率峰值随频率变化的分析中获得的值进行比较，验证了该平均值的可靠性。
