Crystallographically Amorphous Ferrimagnetic Alloys: Comparing a Localized Atomistic Spin Model with

Experiments

MMM, Scottsdale, AZ Oct/Nov MMM, Scottsdale, AZ Oct/Nov 20112011

T. Ostler, R. F. L. Evans and R. W. ChantrellDept. of Physics, The University of York, York, United Kingdom.

U.Atxitia and O. Chubykalo-FesenkoInstituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, Madrid, Spain.

R. AbrudanExperimentalphysik IV, Ruhr-Universität Bochum, Bochum, Germany

F. RaduHelmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Berlin, Germany

A. Tsukamoto and A. ItohCollege of Science and Technology, Nihon University, Funabashi, Chiba, Japan.

I. Radu, A. Kirilyuk, Th. Rasing and A. V. KimelRadboud University Nijmegen, Institute for Molecules and Materials, Nijmegen, The Netherlands.

Stanciu et al. Phys. Rev. Lett. 99, 047601 (2011).

Motivation/Aims Recent interest in switching in ferrimagnetic (GdFeCo) materials.

Switching mechanisms not well understood.

Aim: to develop a time-resolved model of ferrimagnet that can look at processes on the atomistic level.

To parameterise exchange and anisotropy for amorphous systems for a range of stoichiometries via ab-initio methods is computationally very expensive.

Overview

• Numerical model.

• Temperature dependent magnetisation (LLG and experiment).

• Curie and compensation point (MF, LLG and experiment).

• Coercivity (LLG and experiment).

• Effect of TM-RE exchange (LLG).

• Summary and outlook.

Numerical Model• Energetics of system described by Hamiltonian:

Dynamics of each spin given by Landau-Lifshitz-Gilbert Langevin equation.

Moments defined through the fluctuation dissipation theorem as:

Effective field given by:

• GdFeCo is amorphous.

• In numerical model we allocate Gd and Fe spins randomly on closed packed lattice to required composition.

• Exchange parameters paremeterised on experimental observations

JFe-Fe >0 (ferromagnetic)

JFe-Gd>0 (antiferromagnetic)

JGd-Gd<0 (ferromagnetic)

• Model features local moment variation Fe< Gd.

Fe

Gd

Atomic Level Macrospin

Numerical Model

Temperature Dependent Magnetisation

Used model to calculate temperature dependent magnetisation for a range of RE concentrations.

As amount of Gd increases, the more the Gd-Gd and Fe-Gd interaction becomes important, reducing the Curie temperature.

XMCD measurements of the temperature dependence of both the Fe and Gd magnetisation.

By “tuning” the model to temperature dependent magnetisation seen experimentally, the temperature dependence of the magnetisation can be reproduced in the model.

XMCD

Figures from Ostler et al. Phys. Rev. B 84, 024407 (2011).

LLG

Compensation point

Curie and Compensation points: MF, LLG and Experiments.

Adapted Mean Field model allows calculation of Curie temperatures and magnetisation compensation temperatures.

Mean Field and numerical model Curie temperatures agree very well.

Experimental (red triangles), numerical (blue circles) and Mean Field (dashed line) compensation temperatures agree (Tcomp).

Figures from Ostler et al. Phys. Rev. B 84, 024407 (2011).

Coercivity• Measured coercivity shows “diverging” behaviour at magnetisation compensation

point.

• Qualitatively similar behaviour in numerical model.

Experiment LLG

Figures from Ostler et al. Phys. Rev. B 84, 024407 (2011).

Affect of TM-RE Exchange Changing TM-RE exchange affects both equilibrium and non-equilibrium properties.

Increasing TM-RE exchange changes temperature dependence of magnetisation.

Increased Curie temperature.

Figures from Ostler et al. Phys. Rev. B 84, 024407 (2011).

Direct affect on longitudinal relaxation time.

Speeds up dynamics in Gd sub-lattice by almost an order of magnitude.

Increasing exchange

Increasing exchange

Summary

• Developed a model for an amorphous TM-RE ferrimagnetic system based on experimental observations of both the Fe and Gd sublattices.

• Fitted exchange parameters based on the experimental measurements.

• Compared the numerical results to mean field and experimental data.

• Numerically studied how the longitudinal relaxation time decreases with increasing TM-RE antiferromagnetic exchange interaction.

• With this model we can now perform time-resolved simulations and compare with experimental results (for an example of the application of this model please come along to ED03 on Wednesday).

Acknowledgements

This work has been supported by the EU FP7 programme [Grants No. NMP3-SL-2008- 214469 (UltraMagnetron), No. 214810 (FANTOMAS), and Grant No. 226716].

Grants No. MAT2007-66719-C03-01, FIS2010-20979-C02-02 and No. CS2008-023 from the Spanish Ministry of Science and Education.

Financial support from the European COST Action P-19 is also gratefully acknowledged, as well as De Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).

Radu et al. Nature 472, 205-208 (2011).