Origin of Thickness Dependent Spin Reorientation Transition

of B2 Type FeCo Alloy Films

Dongyoo Kim

Applied Materials Physics, Department of Materials Science and Engineering,

Royal Institute of Technology, Stockholm, Sweden.

KU = 700 ~ 800 µeV/atomMS = 2.1 µB/atom

Chemical composition : 0.55 ≤ x ≤ 0.65

Tetragonal distortion : 1.2 ≤ c/a ≤ 1.25

Introduction

about 15 MLs

SRT at 15 ML

Introduction

Introduction

Giant MCA Energy

Tetragonal distortion

ChemicalComposition

To account SRT of FeCo films at 15 ML We have considered film structures.

MCA of bulk FeCo cannot explain SRT of FeCo at 15 ML.

We calculated FeCo film with coverage of 6, 8, 10, 12, 14, and 16 ML thickness

Purposes

FLAPW method(Full potential linearized augmented plane wave)

Exchange correlation potential : GGA

Spherical harmonics (lmax ) : 8

Energy cut-offs : 225 Ry and 13.7 Ry

Muffin-tin radius of Fe and Co atoms : 2.2 a.u.

Lattice Constant: 2.866 Å (experimental value, [PRB, 64, 132102 (2001)])

K-points: 420 points

<Calculated Systems>

Calculation Method

The optimized atomic structure in verticaldirection Force and total energy minimization procedure.

Calculated interlayer distance (in Å)

Thin Thick

Structural Features

c/a = 1.07

Calculated spin magnetic moment (in µB) in MT region.

Magnetic Moment

Magnetization

Linearly increasing Ms

MAE in Thin Film Structures

EMCA = E// – E ㅗE ㅗ

E//

MAE = EMCA - ESh

About 15 ML

Magnetic Anisotropy Energy

EMCA = E// – E ㅗPositive value: Perpendicular MCA

Negative value: in-plane MCA

Esh = ½ µ0Ms2

EMCA = Torque method [1]

[1] X. D. Wang, R. Q. Wu, D. S. Wang, A. J. Freeman, Phys, Rev, B 54, 61 (1996)

MCA Energy in Thin Film Structures

E ㅗ

E//

K = KV + 2KS/dKV : Volume contributions KS : Surface contributions d : Film thickness

[J. Hong, et. al, PRL, 92, 147202 (2004)]

Kv = 67.04 µeV/atom

Ks = 594.7 µeV/atom

Kv = 142.42 µeV/atom

Ks = 132.61 µeV/atom

~ 90 ML=

K = KV + 2KS/d

Magnetic Anisotropy Energy15 ML

Average Esh

[FeCo(3ML) /Pt(7ML)]23

MCA Energy – FeCo (3ML)

Kv = 142.42 µeV/atom

Ks = 132.61 µeV/atom

Cal: EMCA = 227.82 µeV/atom at FeCo(3ML)Exp: EMCA = (208±14) µeV/atom at FeCo(3ML)

MCA Energy – FeCo (3ML)

K = KV + 2KS/dK = KV + 2KS/d

Summary

We have investigated the thickness dependent magnetic anisotropy of B2 FeCo Films.

FeCo films show perpendicular MCA, but MCA energy rapidly decrease as the film thickness increase.

The crossover of shape and MCA energies occurs at approximately 15 ML thickness. This agrees well with many experimental observations.

The competition of shape and MCA energies can nicely account for universal behavior of thickness dependent SRT of FeCo alloy films

Thank You