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(a) Schematic of spin arrangements in magnetic phases exhibiting spontaneous magnetization: ferrimagnetism, canted-spin magnetism, and ferromagnetism. (b) Basic crystal structure with monoclinic P121/c1 symmetry and FM spin orientation of lightly doped perovskite manganite LSMO at x = 1/8 below 187 K revealed by Li et al. by neutron diffraction analysis. 17 The directions in parentheses are described in a pseudocubic perovskite setting. The spin orientation changes from the b axis to the c axis in the b-c plane with increasing temperature; the estimated values of φ are ∼0.3° at 5 K, ∼12.0° at 100 K, and ∼59.7° at 170 K.
Variation in in-plane magnetization in the 180° domain structure of the FM LSMO at 100 K with external magnetic field normal to the sample plane. (a) Overfocused Lorentz image with Δf = −300 μm at 0 Oe. (b) Underfocused Lorentz image with Δf = 300 μm at 0 Oe. (c) In-plane magnetization at 0 Oe analyzed by the TIE method using the images in (a) and (b). The colors and arrows represent the direction and magnitude of magnetization (see the color wheel). (d)–(f) In-plane magnetization at (d) 1.5 kOe, (e) 2.9 kOe, and (f) 3.6 kOe obtained by analysis. The magnitude is reduced in the additional domains shown by triangles. The magnetization in these domains has large perpendicular components.
(a) Variation in in-plane magnetization in the serpentine-like domain structure at 100 K with the perpendicular magnetic field (−1.5 kOe, 0 Oe, and 1.5 kOe). (b) Lorentz images with Δf = −300 μm at 100 K for magnetic fields of −2.8–2.8 kOe, where the green rectangles show the area analyzed in (a). The domains indicated by arrows are deteriorated by the fields, resulting in nanoscale elliptical magnetic bubbles shown by triangles. The inset shows a schematic of the formation of magnetic bubbles, where the signs “+” and “−” denote that the magnetization is along the + k and − k directions, respectively, and the angle θ is estimated to be approximately 33°.
(a) Lorentz images with Δf = −300 μm at 100 K showing extinction of magnetic bubbles at 3.6 kOe and the sample thickness profile measured by EELS. The letters a-e represent some of the positions where the thickness was measured. (b) Values of I s −2 (I s: saturation magnetization) and d (diameter of magnetic bubbles) of the FM insulating phase of LSMO and other bubble materials: ferrimagnetic iron-garnets R 3(Fe,M)5O12 and spin-canted orthoferrites RFeO3 (a: Y1.8Eu0.2Gd0.5Tb0.5Al0.6Fe4.4O12, b: Y2GdAl0.8Fe4.2O12, c: EuEr2Ga0.7Fe4.3O12, d: Eu1.5Gd1.5Al0.5Fe4.5O12, e: Eu2ErGa0.7Fe4.3O12, f: Gd0.95Tb0.75Er1.3Al0.5Fe4.5O12, g: Eu1.9Gd1.1Al0.5Fe4.5O12, h: PrGd2Ga0.5Fe4.5O12, i: Gd2.34Tb0.66Fe5O12, j: Er2TbAl1.1Fe3.9O12, k: Sm0.55Tb0.45FeO3, l: Sm0.6Er0.4FeO3). 3,4
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