Reference no: EM132460719
Question 1: Regarding special relativity, the electromagnetic interaction can he formulated as - ρΦ - j.A. Under the functional variation A → A + δA, the electromagnetic energy ∈ = ∫dVΨ* H^Ψ with H^ = ((P^) - qA^)/2m + gμB/h S^.B becomes ∈ → ∈ + δ∈ with δ∈ = ∫dVj.δA, from which we can easily identify the form of the total current j. Please verify that j is composed of the transport current (independent of magnetic effects), the diamagnetic current (proportional to A), and the magnetization current (proportional to ∇ x M).
Question 2: Find the continuum form of the Dzyaloshinskii-Moriya (DM) interaction for:
(a) Bulk inversion symmetry breaking Dij = α r^ij
(b) Interfacial inversion (mirror) symmetry breaking Dij = βz^ x r^ij
Question 3: Consider an ensemble of independent magnetic particles, where each has a total angular momentum of J = 1 and Lande factor g = 2. The system is subject to a uniaxial anisotropy kmz2 and has a uniform density of n.
(1) Under a magnetic field B applied along the z direction, find the paramagnetic susceptibility Xz(T) for k > 0 (hard axis) and k < 0 (easy axis), respectively.
(2) Sketch Mz(T, B)/Ms, as a function of B for fixed T and a few different values of k. Explain the pattern change you find.
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