Macrospin in ferromagnetic nanojunctions

Transformation of the domain structure of a cubic ferrimagnetic material at spontaneous spin flip of the easy magnetization axis

“…constant [7], we obtain that under condition (1), K eff → 0 and δ → ∞. In this case, the DS must be transformed due to the increased DB width, that is, in a certain temperature interval around T c , the domains of the old phase must disappear, and only after that the domains of the new magnetic phase must arise.…”

Effect of current on magnetization oscillations in the ferromagnet-antiferromagnet junction

“…This allows us to use the macrospin approximation described in detail in [9]. In this approximation, the magnetization varies only slightly over distances on the order of L AFM ; therefore, we can write (16) because the flux is zero at the interface with a nonmag netic layer closing the electric circuit, J M (L AFM ) = 0.…”

“…The details of such calculations can be found in our previous publi cations [9,25]. Here, we will write the result for the case when thickness L AFM of the antiferromagnetic layer is much smaller than spin diffusion length l for the direction of current corresponding to the electron flux from the ferromagnet to the antiferromagnet: (7) where is the equilibrium (for zero current) magne tization of conduction electrons, Δm is the nonequi librium correction produced by the current, = M/ is the unit vector in the direction of magneti zation of the ferromagnet, is the analogous vector for the ferromagnet, μ B is the Bohr magneton, e is the electron charge, τ is the electron spin relaxation time, and j is the current density.…”

“…Let us now formulate these boundary conditions for a junction of the FM-AFM type. The algorithm for deriving such boundary conditions was described in detail in [9]. It should be emphasized that we are speaking of condi tions that depend on the spin polarization of electrons.…”

“…In addition, the ferromagnetic resonance frequency is quite low in this case. In view of the above mentioned difficulties, other methods were also proposed for reducing the threshold (e.g., using a high spin injection level [8] or joint action of the external magnetic field and polar ization current [9,10]). The employment of ferromag net-antiferromagnet junctions, in which the ferro magnet (FM) serves as an injector of spin polarized electrons, and the antiferromagnetic (AFM) layer in an external magnetic field perpendicular to the easy axis may have a low magnetization because the mag netic sublattices are "canted," which facilitates the lowering of the threshold [11].…”