Tunable exchange bias-like effect in patterned hard-soft 2D lateral composites
with perpendicular magnetic anisotropy
Magnetic properties of amorphous NdCo thin films
In a magnetic film, the strength of the perpendicular magnetic anisotropy (PMA) can be
estimated as the ratio between the out-of-plane anisotropy energy density and the film shape
anisotropy [1], leading to the definition of a quality parameter Q=KN/2πMS2, where KN and MS
are the PMA energy density and saturation magnetization of the material, respectively. In this
framework, we can define as strong PMA materials, those that present a Q > 1 value, while Q <
1 represents materials with a weak PMA. In this latter case, a special kind of magnetic stripe
domains appear, the so called “weak” magnetic stripe domains, where the magnetization
presents a stripe pattern as sketched in Fig. A: parallel stripe domains appear with periodically
oscillating out-of-plane magnetization component separated by Bloch walls (i.e. with in-plane
magnetization pointing along the wall) [1]. The Bloch character of domain walls in weak stripe
patterns leads to a link between in-plane magnetization and stripe domain direction: the in-plane
magnetization component is always aligned with the stripes direction [1].
Fig. A: Scheme of a weak magnetic stripe domain magnetization configuration representing
one period of the magnetization structure. The XY plane defines the in-plane directions.
The above defined magnetization configuration, introduces two important points: first, the
system’s magnetic behavior is strongly dependent on the film thickness [1] because of the
competition between PMA and film shape anisotropy; and second, the appearance of a
unidirectional in-plane magnetic anisotropy, defined as “rotatable anisotropy” [2, 3],that is
dependent onthe last saturating field. The first point leads to the introduction of a critical
thickness parameter which defines the minimum film thickness needed to allow the formation of
weak stripe domains [1], thus, above the critical thickness, the system presents an out-of-plane
magnetic behavior, and below it, an in-plane behavior is dominant, as illustrated in Fig. 1(c) of
the manuscript. When the system presents weak stripe domains (i.e. it is above the critical
thickness) and a strong enough magnetic field is applied in an in-plane direction, the stripe
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domains are removed, and therefore, the sample magnetization is aligned with the field. If the
field intensity is decreased, the nucleation point for the magnetic stripe domains is reached.The
stripe domains are formed with their in-plane magnetization component aligned with the field.
In the remanent state, the system will present a pattern of parallel stripes, which have been
oriented by the direction of the last saturating magnetic field [1]. Due to the periodic oscillation
of the magnetization along the out-of-plane and around the fixed in-plane directions (last
saturating applied field direction), the magnetization configuration is stabilizedin sense and
direction leading to the unidirectional rotatable anisotropy.
In this framework, our thin films of amorphous Nd-Co alloyswith typically KN≈1x106 erg/cm3
and MS≈1000 emu/cm3, lead to a Q≈0.16 [4-7],presenting thus weak PMA and all the
characteristics mentioned above.
References:
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