[Paper Review] Resonant state selection in synthetic ferrimagnets

Ben F. Koop, Yu. I. Dzhezherya+4 more|arXiv (Cornell University)|Feb 26, 2013

Magnetic properties of thin films25 references3 citations

TL;DR

This paper demonstrates deterministic ground state selection in synthetic ferrimagnets (SFi) by exploiting magnetic asymmetry from thickness imbalance and asymmetric field biasing, enabling tunable splitting of optical spin-resonance modes. By applying a uniform external field, the system's magnetic phase space is reversibly tuned between antiferromagnetic and ferrimagnetic behavior, allowing selective excitation of one antiparallel ground state via frequency-selective resonant microwave driving.

ABSTRACT

Resonant activation of a synthetic antiferromagnet (SAF) is known to result in a dynamic running state, where the SAF's symmetric spin-flop pair continuously rotates between the two antiparallel ground states of the system, with the two magnetic moments in-phase in the so-called acoustical spin-resonance mode. The symmetry of an ideal SAF does not allow, however, to deterministically select a particular ground state using a resonant excitation. In this work, we study asymmetric SAF's, or synthetic ferrimagnets (SFi), in which the two magnetic particles are different in thickness or are biased asymmetrically with an external field. We show how the magnetic phase space of the system can be reversibly tuned, post-fabrication, between the antiferro- and ferri-magnetic behavior by exploiting these two asymmetry parameters and applying a uniform external field. We observe a splitting of the optical spin-resonance for the two ground states of the SFi system, with a frequency spacing that can be controlled by a quasistatic uniform external field. We demonstrate how the tunable magnetic asymmetry in SFi allows to deterministically select a particular ground state using the splitting of the optical spin-resonance. These results offer a new way of controlling the magnetic state of a spin-flop bilayer, currently used in such large scale applications as magnetic memory.

Motivation & Objective

• To overcome the non-deterministic switching in symmetric synthetic antiferromagnets (SAFs) by introducing magnetic asymmetry.
• To enable post-fabrication, reversible tuning of the magnetic behavior between SAF-like and SFi-like states using an external uniform field.
• To achieve deterministic selection of a specific antiparallel ground state in a spin-flop bilayer via controlled optical spin-resonance splitting.
• To develop a method for deducing individual asymmetry contributions (thickness and field biasing) post-fabrication in SFi systems.

Proposed method

• Engineered magnetic asymmetry in synthetic ferrimagnets (SFi) via thickness mismatch (t₁ ≠ t₂) and asymmetric fringing fields (H₁^m ≠ H₂^m) from the reference layer.
• Applied a quasistatic uniform external field Hₓ along the easy axis to tune the double-well potential symmetry and control resonance splitting.
• Used micromagnetic modeling and analytical solutions of the effective damping and resonance frequency equations to predict stability boundaries.
• Solved the critical amplitude condition Ω_eff^a = 0 from Eq. (S15) to determine the threshold for instability in each AP state, leading to a cubic equation for A_c.
• Derived the critical frequency Ω_c from the effective frequency shift, accounting for asymmetry and microwave amplitude.
• Mapped switching and spin-flop fields using the Hessian determinant condition (Eq. S16) to extract thickness and field bias parameters from measured hysteresis.

Experimental results

Research questions

• RQ1 Can magnetic asymmetry in synthetic ferrimagnets enable deterministic selection of a specific antiparallel ground state?
• RQ2 How does an external uniform field tune the symmetry of the magnetic double-well potential in SFi systems?
• RQ3 What is the relationship between resonance frequency splitting and the applied external field in asymmetric SFi structures?
• RQ4 Can post-fabrication asymmetry parameters (thickness and field biasing) be quantitatively deduced from hysteresis and resonance measurements?
• RQ5 What is the frequency-amplitude regime in which only one AP state is stable due to asymmetry-induced resonance splitting?

Key findings

• The optical spin-resonance splits into a doublet in asymmetric SFi systems, with a frequency spacing controllable via a uniform external field.
• A critical microwave amplitude A_c ≈ 0.34 (A_c² = 0.118) was determined, below which one AP state becomes unstable while the other remains stable.
• The critical frequency Ω_c was derived as Ω_o²(1 - 3A_c²/4)/(1 + 5A_c²/4), enabling frequency-selective excitation for state selection.
• The spin-flop field H_sf was identified as the point where one potential minimum vanishes, transitioning the system to a scissor state.
• The thickness difference |t₁ - t₂| was extracted from switching field differences, yielding |t₁ - t₂| = (H₁⁺ - H₁⁻ - H₂⁺ + H₂⁻)/(n_y - (1 + r_x)n_x) × b/(8πM_S).
• The sum of internal field biases H₁^m + H₂^m was determined from the average of switching fields, H₁^m + H₂^m = - (H₁⁺ + H₁⁻ + H₂⁺ + H₂⁻)/2.