 # Uniform Mode in a nanoparticle Imagine we have a rectangular shape...

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Uniform Mode in a nanoparticle Imagine we have a rectangular shaped nanoparticle. There is an applied magnetic field, Ho, in the Z direction Z Ho x y In an object where all the edges are about the same size, we have to consider demagnetizing fields in each direction. Let these demagnetizing fields be parameterized by Nx, Ny, and Nz Hdemag-x = (4xNx) Mx Hdemag-y = (4xNy) My Hdemag-z = (4xtN2) M2 Use the magnetic equation of motion dM = - Ivl M X dt The effective field is the sum of the applied field and all the demagnetizing fields. Assume that there is a Ho in the Z direction and the magnetization is mostly saturated in the Z. direction, but that there can be small dynamic values for Mx and My a) Find the frequency of the "uniform mode" in the nanoparticle in terms of Nx, Ny, Nz, M and Ho. b) Let's do some examples. Suppose Nx = Ny = 1/2 and N2 = 0. What physical shape do you think this corresponds to? Find the frequency as a function of Ho and make a general plot (Use M = 1.7 kG) How does this compare to the case of a thin film? (make a plot) c) Suppose we have Nx = Ny = 1/4 and N2 = 1/2. Find the frequency as a function of Ho and make a general plot using M = 1.7 kG. Is there a critical value of Ho? What does it correspond to physically

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