Magnetization textures in NiPd nanostructures

We have observed peculiar magnetization textures in Ni${}_{80}$Pd${}_{20}$ nanostrips using three different imaging techniques: magnetic force microscopy, photoemission electron microscopy under polarized x-ray absorption, and scanning electron microscopy with polarization analysis. The appearance of diamondlike domains with strong lateral charges and of weak-stripe structures reveals the presence of both a transverse and a perpendicular anisotropy in these nanostructures. The anisotropy is seen to reinforce as temperature decreases, as testified by observations performed at 150 K. A thermal stress model with relaxation is proposed to account for these observations. Elastic calculations coupled to micromagnetic simulations support qualitatively this model.

Figure 1

MFM images of several NiPd nanostructures with 30 nm thickness: (a) 150-nm-wide and (b) 450-nm-wide nanostrip; (c) nanoring with 500 nm width and 5 $\mu$m diameter.

Figure 2

XMCD-PEEM images of four sets of 5-$\mu$m-long and 30-nm-thick structures, taken at room temperature (left column) and at low temperature ($\approx 150$ K, right column). Two series of widths are shown, namely, 1 to $0.85\mu$m [(a), (b), (e), (f)] and 0.6 to $0.45\mu$m [(c), (d), (g), (h)], both with a 50-nm step (see labels on the figures). Depending on the orientation of the nanostrips with respect to the trace of the x-ray incidence plane (shown by the double arrow), the transverse [(a), (c), (e), (g)] or longitudinal [(b), (d), (f), (h)] magnetization components are probed (as these two orientations correspond to different structures, the transverse and longitudinal images for the same nanostructure width can not, however, be combined). A distortion in the electron microscope of $\approx 6$ % in one direction affects the shape of the elements, and the points are defects in the imaging plate.

Figure 3

SEMPA imaging of 0.3-$\mu$m-wide and $\simeq 30-40$-nm-thick NiPd nanostrip: (a) SEM image; (b) and (c) $x$ and $y$ magnetization component distributions, respectively. The processed images from (b) and (c) are (d) color-coded reconstructed vector map of the in-plane magnetization (see color wheel for the direction coding), and (e) in-plane magnetization magnitude (left part of the image only). The image distortion due to drift while scanning is schematized in (a) by the slanted orientation of the short edge of the nanostrip.

Figure 4

SEMPA imaging of 0.5-$\mu$m-wide nanostrip of the same sample as in Fig. 3: (a) SEM image; (b) and (c) $x$ and $y$ magnetization component distributions, respectively; (d) color-coded reconstructed vector map of the in-plane magnetization (see color wheel for the direction coding); (e) arrow representation of the in-plane magnetization (magnified $1.5\times$ with respect to previous images), for the left part of the structure, on top of a background supplied by (c).

Figure 5

XMCD-PEEM images of two 0.9-$\mu$m-wide, 50-nm-thick NiPd nanostrips, in the transverse configuration at two temperatures: 300 K (a) and 150 K (b) and in the longitudinal configuration for the same temperatures (c), (d). Note that the same structure is observed in (a) and (b) and in (c) and (d).

Figure 6

MFM images of a 1-$\mu$m-wide NiPd nanostrip, with different thicknesses: (a) 30 nm, (b) 40 nm, and (c) 50 nm, showing the appearance of the weak-stripe domain structure. In (b), the largest internal contrast appears along the domain walls between transverse domains, and is probably linked to the wall structure [see Fig. 4b].

Figure 7

End-view cross-section representation of the thermal strain components in a 30-nm-thick and 500-nm-wide nanostrip calculated for an interfacial strain ${\epsilon }_0={10}^{-3}$ (corresponding to $\Delta T=92.5$ K for nickel), for an infinitely rigid substrate (for the meaning of axes, compare with Fig. 3). The displacements have been enhanced by a factor of 100 in order to be observable. The strain components are (a) the transverse strain ${\epsilon }_{yy}$, (b) the perpendicular strain ${\epsilon }_{zz}$, and (c) the shear strain ${\epsilon }_{yz}$. The color scale extends between $-{\epsilon }_0$ and ${\epsilon }_0$ for ${\epsilon }_{yy}$ and between $-{\epsilon }_1$ and ${\epsilon }_1$ for ${\epsilon }_{zz}$ and ${\epsilon }_{yz}$. A half cross section is represented because of symmetry. The anisotropy distribution is shown in (d), with arrows giving the easy axis direction and the gray levels coding the value of the transverse anisotropy, the color-code clipping values (evaluated with the nickel parameters) above 3 kJ/m${}^3$.

Figure 8

Same problem as in Fig. 7, but solved for a deformable Si substrate (treated as an isotropic medium with $E=185$ GPa and $\nu =0.26$) (Ref. 24). The substrate was an infinite parallelepiped with 1.5 $\mu$m edge size, with zero displacement boundary conditions applied at the three sides without structure.

Figure 9

Micromagnetic simulations of the equilibrium magnetization distribution (top view) in a 0.5-$\mu$m wide and 30-nm-thick nanostrip for different values of $\Delta T$ (computed with the parameters of nickel), using the anisotropy distribution shown in Fig. 7d: (a) $\Delta T=160$ K, (b) 250 K, (c) 260 K, (d) 270 K, and (e) 280 K. The mesh size is $5\times 5\times 5$ nm${}^3$, much below the exchange length ($\Lambda \approx 9.6$ nm). The grayscale represents the magnetization transverse component, at the sample surface. As the full equilibration of the weak-stripe domains (and of the number of transverse domains) requires an infinite number of iterations, the structures shown are meaningful locally, but maybe not globally.