An explanation to spin reorientation of 𝘊𝘰𝘗𝘵/𝘈𝘭𝘕 multilayers using Heisenberg Hamiltonian with third-order perturbation

Abstract

Thin film magnetism has become a dominant research area in present science and technology. This field received further attentions with the present competitiveness. 𝘊𝘰𝘗𝘵 is one common member of the family of ferromagnetic thin film researching. In our project, easy axis orientation of 𝘊𝘰𝘗𝘵/𝘈𝘭𝘕 multilayer thin films was investigated using Heisenberg Hamiltonian with third-order perturbation. The experimental data of out-plane spin reorientation temperatures (SRT) for thicknesses of 4 nm, 6 nm and 8 nm which contained ~11, 16 and 21 layers respectively and each of ~3.784 Å individual thickness were found as 484 K, 453 K and 584 K respectively. There are seven unknown parameters in the currently considering Hamiltonian equation. Explicitly, they are J, ω, Dm⁽²⁾, Dm⁽⁴⁾, Hᵢₙ , Hₒᵤₜ and Kₛ which denote exchange interaction, strength of long range dipole interaction, second order and fourth order anisotropy, in-plane internal field, out-of-plane internal field and stress induced anisotropy factor. J = 10⁻³⁰ J, ω = 10⁻³⁵ J, Dm⁽²⁾ = 10⁻²⁷ J, Dm⁽⁴⁾ = 10⁻²⁵ J, Hᵢₙ = 10⁻²⁷ A m⁻¹ , Hₒᵤₜ = 10⁻³⁰ Am⁻¹ and Kₛ = 10⁻²⁸ J were found to be the values corresponding to the SRT of 484 K for film with 11 layers. The values obtained were J = 10⁻⁴⁴ J, ω = 10⁻³⁴ J, Dm⁽²⁾ = 10⁻²⁶ J, Dm⁽⁴⁾ = 10⁻²⁵ J, Hᵢₙ = 10⁻²⁶ A m⁻¹ , Hₒᵤₜ = 10-32 A m⁻¹ and Kₛ = 10⁻²⁸ J in order to get SRT of 453 K for film with 16 layers. Later J = 10⁻⁴⁴ J, ω = 10-34 J, Dm⁽²⁾ = 10⁻²⁶ J, Dm⁽⁴⁾ = 10⁻²⁵ J, Hᵢₙ = 10-54 A m⁻¹ , Hₒᵤₜ = 10-30 A m⁻¹ and Kₛ = 10⁻⁸⁰ J were the resulted values corresponding to SRT of 584 K for film with 21 layers. As the next part, characteristics of each of seven parameters for 𝘊𝘰𝘗𝘵 layers were studied using the Heisenberg Hamiltonian. What mainly identified was that the SRT did not respond to the parameters J, Dm⁽⁴⁾ and Hᵢₙ; but all the others responded in unique proportions. Among varying parameters, SRT decreased with ω, Hₒᵤₜ and Ks. However, Dm⁽²⁾ responded in the opposite way, 𝘪.𝘦. SRT showed an apparent increment with increasing Dm⁽²⁾ values.