10.2.3 Elliptical Particles with Contact Faces

Finally the influence of contact faces, which is necessary for electrical contact in MR experiments, between the particles has been investigated. This contact causes exchange coupling of the magnetization of the particles and has a strong influence on the domain patterns.

First, a rather large contact face of $50 \times 10 \mathrm{nm}$ between the elliptical particles was assumed. The demagnetization curves in Fig. 10.9 show, that the switching field of the particles with initially parallel magnetization is reduced by more than 50%. For the particles with initially antiparallel magnetization we find a new behavior: The exchange coupling of the particles overrides the shape anisotropy and causes the formation of domains which extend over several particles. The equilibrium magnetization distributions are given in Fig. 10.10.

Figure 10.9: Demagnetization curves for a chain of elliptical particles with (``touch.'' - $50 \times 10$ nm) and without (``isol.'') contact faces with parallel and antiparallel initial magnetization.

Figure 10.10: Equilibrium magnetization distribution in zero field of a chain of 6 elliptical particles with a contact area of $50 \times 10$ nm.

[Initially antiparallel magnetization.]

[Initial magnetization parallel to the chain axis.]

However, if we reduce the size of the contact faces to $10 \times 10 \mathrm{nm}$ we can ``pin'' these domain walls (we should rather call it an area of transition of the magnetization, since it is strictly speaking not a domain wall) at the contact faces. The demagnetization curves for these small contact faces in comparison with isolated particles are given in Fig. 10.11. A comparison of the demagnetization curves between small and large contact faces is given in Fig. 10.13. The magnetization distribution in equilibrium is shown in Fig. 10.12. If the particles are initially magnetized parallel to the chain axis, the exchange coupling is still strong enough to suppress the spontaneous formation of the antiparallel pattern (cf. Fig. 10.12(b)). When the external field is switched on, the magnetization of the inner particles rotates homogeneously into the direction of the external field.

Figure 10.11: Demagnetization curves for a chain of elliptical particles with (``touch.'' - $10 \times 10$ nm) and without (``isol.'') contact faces with parallel and antiparallel initial magnetization.

Figure 10.12: Equilibrium magnetization distribution in zero field of a chain of six elliptical particles with a contact area of $10 \times 10$ nm.

[Initially antiparallel magnetization.]

[Initial magnetization parallel to the chain axis.]

Figure 10.13: Demagnetization curves for a chain of elliptical particles with $10 \times 10$ nm and $50 \times 10$ nm contact faces with parallel and antiparallel initial magnetization.