Magnetic energies of single submicron permalloy rectangles determined via magnetotransport

We have investigated the magnetic properties of single submicron permalloy rectangles with a thickness of 20 nm and an aspect ratio of 2:1 via anisotropic magnetoresistance (AMR). Preparation and investigation via magnetotransport are performed in situ in ultrahigh vacuum. The field-dependent magnetization behavior of the two generic cases with the magnetic field applied perpendicular and parallel to the long axis of the rectangles is studied. Due to the high sensitivity of our setup, single field sweeps are sufficient to obtain magnetoresistance curves of structures with dimensions as small as $600\times 300{\text{nm}}^2$. To link features of the AMR to changes in the micromagnetic states, the remanent state has been investigated via scanning electron microscopy with polarization analysis. Our main result is that the energy density of micromagnetic states can be obtained from the hard-axis magnetization behavior. It is demonstrated that a C/S state can be distinguished from a Landau state and the energy difference between both states is determined.

Figure 1

(Color online) Microsized circuits for magnetoresistance measurements. (a) Sketch of the measurement principle. The tungsten tip can be moved by a micromanipulator to contact the circuit within the framed region. The approach is monitored via SEM. The current is driven from the tip to the film crossing a small ferromagnetic rectangle within the gap of the yoke-shaped frame. (b) SEM micrograph of two microsized circuits with different orientations of the ferromagnetic rectangles (4) with respect to the field direction (arrow). The rectangles of size $800\times 400{\text{nm}}^2$ are surrounded by paramagnetic material (5), which has been created by ${\text{Ga}}^{+}$ ion bombardment out of the ferromagnetic film (1). The dark gray parts (2, 3), where the metal has been totally removed by sputtering, are electrically insulating.

Figure 2

(Color online) Resistance versus field curves. (a) MR measurement of a paramagnetic gap. An SEM micrograph of the microsized circuit is shown as inset. (b) MR measurements of the film system. The measurements are performed on a macroscopic wire with dimensions of $l=6\text{mm}$ and $w=0.5\text{mm}$. The current is driven through the whole wire while the voltage drop along 4 mm is measured. The magnetic field is applied in the film plane perpendicular ($H\perp j$) and parallel ($H\parallel j$) to the current direction, respectively. At low fields the AMR dominates due to magnetization reversal processes. At high fields the isotropic negative MR dominates, which is due to the decrease in spin-wave density on field increase.

Figure 3

(Color online) Resistance versus field curves for rectangles with long axis parallel to the field direction. The easy-axis loops for rectangles of size (a) $1000\times 500$, (b) $800\times 400$, and (c) $600\times 300{\text{nm}}^2$ are plotted. The geometry of the measurement is given as inset.

Figure 4

(Color online) Cartoon of supposed magnetization behavior for fields applied along the easy axis. The domain structures at zero and small positive fields are SEMPA micrographs. The magnetization orientation is color coded according to the given color wheel.

Figure 5

(Color online) Resistance versus field curves for rectangles with short axis parallel to the field direction. The hard-axis loops for rectangles with dimensions of (a) $1000\times 500$, (b) $800\times 400$, and (c) $600\times 300{\text{nm}}^2$ are shown. The geometry of the measurement is given as inset. The dashed lines show parabolic fits which indicate (coherent) magnetization rotation during the reversal process.

Figure 6

(Color online) Cartoon of supposed magnetization behavior for fields applied along the hard axis. The domain structure at zero field is a SEMPA micrograph. The magnetization orientation is color coded according to the given color wheel.

Figure 7

Anisotropies for different sizes of Py rectangles. The open symbols represent calculated shape anisotropy and calculated energy density differences between the hard-axis saturated state and certain domain structures given as labels in the plot. The filled symbols have been obtained by fitting a uniaxial behavior to the hard-axis curves from Fig. 5.