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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.
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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
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about 15 MLs
SRT at 15 ML
Introduction
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Introduction
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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
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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.
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Calculated interlayer distance (in Å)
Thin Thick
Structural Features
c/a = 1.07
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Calculated spin magnetic moment (in µB) in MT region.
Magnetic Moment
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Magnetization
Linearly increasing Ms
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MAE in Thin Film Structures
EMCA = E// – E ㅗE ㅗ
E//
MAE = EMCA - ESh
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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)
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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)]
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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
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[FeCo(3ML) /Pt(7ML)]23
MCA Energy – FeCo (3ML)
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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
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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
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Thank You