Experimental Verification of Theoretical Relations for the Domain Structure of Uniaxial Ferromagnets

Abstract

Precise measurements of stripe domain periods and of bubble domain collapse field in two garnets over a wide thickness range are reported along with a comparison with existing theories and attempts to determine from them the material parameters. Domain periods obey the Kittel half-power law in an intermediate sample thickness range, increase more steeply at larger sample thickness in accordance with the Szymczak theory, and also increase with decreasing sample thickness (below a 'critical' value) as earlier predicted by MAlek and Kamberskjr. The correction to the Kittel law derived by Kooy and Em, which affects the determination of the characteristic material length and the wall energy, is supported by the presented results of micromagnetic calculations. contrary to earlier micromagnetic results by Blake et al. The bubble collapse fields fit well the Thiele theory with micromagnetic corrections reported by Blake et al. Genaue Messungen der Streifendomanenperioden und der Kollapsfelder von Zylinderdomanen in zwei Granatproben in einem weiten Schichtdickenbereich werden vorgelegt, zusammen mit einem Vergleich mit existierenden Theorien und einem Versuch, aus ihnen die Materialparameter zu bestimmen. Die Domiinenperioden folgen dem Kittelschen Wurzelgesetz im mittleren Schichtdickenbereich, nehmen bei grof5eren Schichtdicken entsprechend der Theorie von Szymczak steiler zu, und nehmen auch bei abnehmenden Schichtdicken (unter einer ,kritischen' Dicke) zu, wie von PIiIBlek und Kamberskjr vorhergesagt. Die von Kooy und Enz abgeleitete Korrektur des Kittelschen Gesetzes, die die Bestimmung der charakteristischen Materiallange und der Wandenergie beeinfluBt, wird durch die Ergebnisse mikromagnetischer Rechnungen unterstiitzt, im Gegensatz zu friiheren Ergebnissen von Blake et al. Die Kollapsfelder der Zylinderbereiche stimmen mit der Thiele-Theorie mit den mikromagnetischen Korrekturen von Blake et al. gut uberein.

Room-temperature antiskyrmions and sawtooth surface textures in a non-centrosymmetric magnet with S4 symmetry

“…It has been known since 1960's that as the crystal thickness increases, magnetic domains at the surface become more complex, and show corrugations and even fractalizations to further screen the surface magnetic charges on larger scales [26−30]. Such wavy or branched flower-like domain textures have been observed in a broad range of uniaxial ferromagnets such as Co [26,28], Nd-Fe-B alloys [26,30,31], hexagonal ferrites [28,32] and garnet ferrites [29]. In spite of such a long history of domain wall physics over 60 years, the anisotropic sawtooth pattern governed by 4 ̅ symmetry as observed in this antiskyrmion material has never been reported so far, and thus must be exclusively attributed to the anisotropic DMI in the S4 crystal lattice.…”

Theory of magnetic domains in uniaxial thin films

“…The Kittel model is limited to systems with small quality ratios. However, in many strongly anisotropic materials Q is large and no critical thickness is observed [4,18,23]. [6,7], it separates the homogeneous state without domains from the weak stripe phase.…”

“…We adopt a sinewave magnetization profile in the wall and we take into account the magnetostatic interaction between the top and bottom surfaces of the film. Our model applies to hexagonal Co, for which a critical thickness between 25 nm [15,16] and 40 nm [17] has been reported, as well as to materials with high magneto-crystalline anisotropy, such as FePd(001) or garnet films [4,17,18]. Another possible application concerns ferromagnetic thin films of Mn 5 Ge 3 that were recently synthesized [19,20].…”

Magnetic-domain structure of Nd2Fe14B permanent magnets

“…However, investigations were limited by using the magneto-optic Faraday and Kerr effect in the past 12,13 and type-I contrast in SEM more recently. [14][15][16] Measurement in domain size using TEM can provide high spatial resolution for a range of thickness through which electrons can penetrate, although determining the thickness of a TEM sample is not trivial. 17 Figure 1͑a͒ is a Lorentz image revealing the configuration of magnetic domains from a Nd 2 Fe 14 B single crystal with its surface normal near the ͓001͔ easy axis.…”