The reorientation temperature in ultrathin ferromagnetic films

Abstract

The reorientation temperature in ultrathin ferromagnetic films is studied within the framework of the many‐body Green function theory. The model Hamiltonian includes a Heisenberg term with the different surface exchange couplings with respect to the bulk one, a second‐order single‐ion anisotropy, and a transverse external magnetic field in the x‐direction. The single‐ion anisotropy term is treated by the generalized Anderson–Callen decoupling scheme. We investigate the reorientation temperature TR (a) as a function of the surface single‐ion anisotropic parameter K2,S(T → 0) for different: film thicknesses L, surface exchange coupling enhancements ΔS, transverse magnetic fields h and (b) as a function of the transverse magnetic field h for different: film thicknesses L, surface exchange coupling enhancements ΔS, surface single‐ion anisotropic parameters K2,S(T → 0).

Field‐induced magnetic reorientation in ultrathin ferromagnetic films: Phase diagrams

“…In this paper we extend our earlier investigation 8 of the reorientation temperature to the investigation of the reorientation magnetic field as a function of the surface single‐ion anisotropic parameter $K_{2,S} (T \to 0)$ for different film thicknesses L , surface exchange coupling enhancements, for different temperatures, and as a function of the temperature for different film thicknesses L .…”

“…2, 5, we obtain the following L coupled equations of motion for Green functions $\tilde {G}_{\mu \nu }^{(m)} ({\bf q},\Omega ) = J\langle S_j^{\tilde { + }} ;(S_k^{\tilde {z}} )^m S_k^{\tilde { - }} \rangle _\omega$ ( m is a positive integer number ($0 \leq m \leq 2S$ )) defined in the local reference frame: where the same notation as in Ref. 8 was used: …”

“…The components of the magnetizations per site $m_\mu ^x \equiv \langle S_\mu ^x \rangle$ and $m_\mu ^z \equiv \langle S_\mu ^z \rangle$ of each ML µ $(\mu = 1, \cdots ,L)$ in the fixed system ( x , y , z ) as a function of the reduced external magnetic field $\chi ^x \equiv h_0^x /J$ can then be calculated by using the eigenvector method 10 already applied in Ref. 4, 8 (see formulas (9), (19), (29), and (30) in Ref. 8).…”

Magnetic Reorientation in the Antiferromagnetic Bi-layer: Exchange Anisotropy Versus Single-Ion Anisotropy

“…The reorientation temperature in this case rapidly increases with the single-ion anisotropy parameter k 2 . The critical parameter k C 2 can be defined as the particular k 2 value at which the reduced reorientation temperature θ R1 is zero for a given value of the transverse magnetic field and it does not depend on film thickness [6]. We can therefore assume that the phase diagram in the plane (θ R1 , k 2 ) will be qualitatively similar to that shown in Fig.…”

The Reorientation Temperature in an Antiferromagnetic Monolayer

“…We now introduce sublattice indices (n, m) for the up (A) and down (B) spins. Four equations of motion for the Green functions (GF) in the local reference frame: We use the technique of the equation of motion for the Green functions within the usual random phase approximation (RPA) for the Green function appearing in the nonlocal exchange term and a generalized Anderson-Callen approximation developed by Schwieger et al [2] and applied to investigate the reorientation temperature in ferromagnetic films [5], in the local anisotropy term. After decoupling procedures for the Fourier components of the Green function G AA (ω, q) we have the following equation:…”