Current-induced Heating

Application of a current to observe spin-torque effects, e.g. domain wall motion, is also connected with a rise of the temperature in the sample due to Ohmic heating. This effect is more pronounced if very thin Si3N4

membranes are required for transmission electron microscopy (TEM) be-cause the heat transport is rather poor. First, the 50 nm-thick membrane does not conduct the heat as well as the bulk material such as a silicon wafer which is hundreds of micrometers thick. Second, the heat conduc-tivity of Si3N4 is one order of magnitude worse than e.g. silicon. Due to the large pulse length, the conductivity rather than the heat capacity dominates the thermal properties since thermalization takes place within a few nanoseconds. On the one hand, this allows one the investigation of the influence of heating on the spin structure. On the other hand, heat-ing might render the observation of the current-induced spin torque ef-fect using TEM techniques difficult. While off-axis electron holography (section 3.3), which requires time-consuming data processing, reveals de-tailed information about the spin structure, Fresnel imaging (section 3.2) is much easier but yields only indirect information; the type and the po-sition of domain walls can be obtained and in contrast, one can conclude the direction of the vortex circulation (chirality). Samples consisting of

Figure 6.2: (From [HKK⁺07]) (a),(d),(g) Schematic spin structures, (b),(e),(h) Fresnel images and (c),(f),(i) off-axis holograms of multivortex walls, whereby (i) is a simulated image. The red (solid) and blue (dotted) circles indicate positions of opposite-sign mag-netic charge accumulation. The black and white contrast in the schematic drawings corresponds to overfocus Fresnel images and for simplicity the vortex cores are drawn in the center of the wire. The images show (a)-(c) a 2AP domain wall, (d)-(f) a 3AP domain wall and (g)-(i) a 2P domain wall. The contrast appearing at the sample edge is omitted in the schematic images.

four Py zigzag wires with 240 - 560 nm linewidth and 12 - 34 nm thickness were fabricated as described in section 2.3.4. Depending on the geometry of the wires, after initialization with an external magnetic field, vortex or transverse walls were observed. Then 10µs long rectangular current pulses were applied because the wires cannot sustain the necessary cur-rent densities for longer periods of time without being damaged struc-turally. The observed changes of the spin structure are described in the following.

6.3.1 Transformation of the Spin Structure

When current pulses are injected, the temperature in the wire rises signif-icantly due to the Joule heating [YSJ06]. When monitoring the resistance of the wire in a comparable setup, Togawa et al. [TKH⁺06] found evi-dence that Joule heating above the Curie temperature is possible. This

large thermal energy due to the current pulses makes it possible to over-come even high energy barriers.

Besides transformation of transverse walls into vortex walls as de-scribed in sections 6.2, more complicated domain wall types were ob-served; two vortices with antiparallel chirality (Fig. 6.2(a)-(c)), three vor-tices with alternating chirality (Fig. 6.2(d)-(f)), and two vorvor-tices with par-allel chirality (Fig. 6.2 (g)-(i)). Other higher order vortex spin structures occurred less often. The more complicated structures allow an increase in the separation between same sign stray field sources (marked with cir-cular frames in Fig. 6.2(a),(d),(g)) or allow flux closure through the ini-tialization of opposite sign stray field sources, thus decreasing the stray field. At the same time an energy barrier to nucleate a vortex has to be overcome [LBB⁺06a]. After some current pulses with a certain strength (0.69to2.88×10¹¹A/m²) the vortex walls irreversibly transformed into more complicated spin structures, i.e. on applying further current pulses it did not revert back to the initial spin state.

Thus the explanation for the multitude of observed domain wall types is as follows: besides the initial vortex state there are several energetically lower-lying multivortex states, which are separated from each other by energy barriers. Some of these states have the same energy for symmetry considerations, e.g. domain walls with reversed chiralities, but in general their energies vary. Due to the strong heating, transitions between the dif-ferent states are possible and the energy barriers separating the difdif-ferent wall types lead to the fact that different spin structures can be observed at room temperature.

6.3.2 Domain Wall Motion due to Heating

In addition to a change in the spin structure, thermally activated domain wall motion can occur. For this, pinning at edge roughness, which holds the domain walls in place, has to be overcome. Contrary to unidirectional movement due to the spin torque, this random motion is bidirectional.

The threshold current densities for movement are lower than those

re-ported for the spin torque effect [YON⁺04, KJA⁺05, KVB⁺05, KLH⁺06].

The measured current density is between 0.71× 10¹¹A/m² and 2.91× 10¹¹A/m² and is of the same magnitude as needed to switch between different spin configurations. This indicates that it is not a spin torque effect that is observed, but rather a thermally induced effect. Differences arise between samples with varying wire dimensions due to the better heat dissipation for a wire with a proportionally larger interface with the substrate [YSJ06].

Sometimes, especially for moving single vortex walls, the available energy is not sufficient to fully depin the domain wall. Then a wall is ob-served which as a whole is still pinned but the central intensity dot, mark-ing the center of the vortex, moves from one position to the other. Because the outer parts of the wall are pinned by edge roughness while the vortex center is held in place by structural defects, e.g. holes, this yields infor-mation about the relative strengths of these two pinning mechanisms and pinning by edge roughness prevails.

Another special case of thermally activated motion is a repeated jump-ing between two particular positions in the wire when injectjump-ing pulses.

In this case the potential landscape for the domain wall is apparently a local multi-well potential, whereby the separating barrier is overcome by thermal excitations due to Joule heating by the current pulses.

6.3.3 Vortex Annihilation

Domain walls within a wire can interact as follows: when a new domain wall is nucleated in the neighborhood of an existing one, its chirality will prefer to be antiparallel to the one of its neighbor. If the walls consist of more than one vortex, the core which is closest to the other wall is af-fected by the interaction. A similar effect was observed in the thinnest wire when two vortex walls came close to each other. If they have oppo-site chirality, they will attract each other once depinned by current pulses.

The motion is still random but has a strong unidirectional component.

The walls will move towards each other until they finally annihilate. If

Figure 6.3: (From [HKK⁺07]) (a) The spins in the domain between the vortex wall can rotate continuously, while in (b) they face an increasing exchange energy the closer the two walls are to each other.

by contrast two walls of parallel chirality come within a certain distance towards each other there is a repulsive force. Even for much higher pulses than usually needed to depin domain walls, there will be no further mo-tion towards each other. This can be understood when taking into ac-count the spin structure (Fig. 6.3). While for vortices with opposite chi-rality the magnetization between the two walls can continuously rotate because spins at both sides of the domain are parallel, this is not possible for vortex walls with the same sense of rotation. Here the magnetization cannot rotate continuously, but will face an increasing exchange energy, which will stabilize the configuration, prevent a further approach and hinder the ultimate annihilation.

6.3.4 Structural Changes by Heating

If pulses are injected which are 10 % or more above the current density usually needed to induce wall motion, even structural changes can be in-duced locally. The first observable consequence is the formation of a very long vortex chain (Fig. 6.4(c)). Second, in-focus images of the crystalline wire structure reveal a clear difference seen before and after the pulses (Fig. 6.4(a),(b)). The crystallites within the wire, which appear as dark spots in Fig. 6.4(b), have considerably grown in size. The usual size of

Figure 6.4: (From [HKK⁺07]) In-focus image of (a) an as-grown wire and (b) the wire after the structural change. (c) Magnetic induction of the region pictured in (b). (d) Holographic magnetic image of the changed wire after remagnetization, (e) after one current pulse and (f) after another three pulses. The left image in (d),(e),(f) shows the same region pictured in (b),(d).

crystallites in Py is between 5 and 10 nm [VABR06], now they are found to be up to 20 times this size. Third, the magnetic structure change is permanent and not reversible by remagnetization. Figs. 6.4(d)-(f) show a pulse experiment after the structural change has happened. After remag-netization, an initial vortex wall is nucleated in the kink as before and the adjacent wire, where the vortex chain was observed, is single domain until the next kink (Fig. 6.4(d)). After one pulse with the usual depinning current density, the domain wall just moves out of the kink and out of the field of view (Fig. 6.4(e)). After another three pulses the wire has a similar spin structure as before remagnetizing (Fig. 6.4(c),(f)). Above all, the re-sistance of the total sample rises by about 6 % compared to the as-grown wire.

The nucleation of chains of vortices can be explained if the sample is heated above the Curie temperature and becomes paramagnetic. Simu-lations have shown that a multivortex state is formed after cooling down (not shown). The strong heating leads to a recrystallization that changes the sizes of the crystallites and perhaps leads to oxidation and / or inter-mixing with the Au capping layer, which could explain the higher

resis-Figure 6.5: (From [JKB⁺07]) Permalloy wire width: 580 nm, thickness: 12 nm. Pulses with a current density of 7×10¹¹A/m² are applied. The Fresnel images are acquired in the alphabetical order with one 10 s pulse between the adjacent pictures. (a-d) High resolution images of the same vortex wall that have moved in the direction of the electron flow from position (a-d) as indicated above during five consecutive pulses. Here, no change of the vortex circulation direction is observed. (e-h) Back and forth movement of the vortex domain wall with changes of the vortex circulation direction (seen as contrast reversal) due to heating effects.

tance.

There is an additional indication that the effects presented so far are truly of thermal origin. When increasing the pulse length, smaller cur-rent densities are needed to trigger the various effects. Thermal effects are statistical events and as such a longer period of heating and stronger pulses, i.e. more heating, increases the probability for them to take place.

Thus for longer pulses, smaller current densities are sufficient to obtain the same probability for an event to take place.