Zigzag domain boundaries in magnetostrictive Fe-Ga alloys

A recent development in magnetic materials research on a non-Joulian magnetostriction phenomenon [H. D. Chopra and M. Wuttig, Nature 521, 340 (2015)] highlights peculiar cellular magnetic domains with zigzag boundaries in Fe-Ga alloys. The cause of zigzag boundaries of cellular domains is attributed to hypothetical charge density waves beyond classical magnetic domain theory. In this paper, we report observations in Fe-Ga alloys of zigzag boundaries that form conventional stripe domains. The responses of stripe domains to external magnetic fields are observed, and the behaviors of zigzag boundaries are examined, which are further compared with those in cellular domains. It shows that both cellular and stripe domains and the constituent zigzag boundaries in magnetostrictive Fe-Ga alloys can be explained well by classical magnetic domain theory, without resorting to theory based on hypothetical charge density waves. In particular, our findings provide convincing evidence that zigzag boundaries in Fe-Ga alloys are conventional V lines commonly observed in cubic magnetic crystals like Fe-Si alloys. The intricate cellular domain structure is shown to correlate with the simple stripe domain structure in terms of zigzag V lines and flux-closure surface domains.

Figure 1

Comparison between two contrasting models for zigzag domain boundaries in Fe-Ga alloys: (a) charge density wave model (reproduced with permission, Ref. [6]), and (b) V-line model [8]. In the V-line model, a zigzag boundary is the intersection of closure domains at the surface; red and green arrows correspond to [001] and $\left[00\overline{1}\right]$ subsurface perpendicular domains, respectively.

Figure 2

Zigzag boundaries in as-grown Fe-8.5 at. % Ga single crystal. (a) Stripe domains observed on the (001) surface with a zoomed-in portion showing the zigzag boundary. (b) Interpretation of the stripe domain pattern with zigzag boundaries by the V-line model.

Figure 3

Responses of zigzag boundaries of stripe domains to a [001] magnetic field in Fe-8.5 at. % Ga single crystal. (a) The same contrast of V1+ and V1− boundaries at $H^{\mathrm{ex}}=0$. (b) Enhancing of V1+ and fading of V1− boundaries at $H^{\mathrm{ex}}=8\mathrm{kA}/\mathrm{m}$. (c) Enhancing of V1+ boundaries, reappearing of V1− boundaries, and emerging of spike domains at $H^{\mathrm{ex}}=52\mathrm{kA}/\mathrm{m}$.

Figure 4

Schematic illustration of spike domains on the (001) surface because of the formation of [001] domains within the V-shaped surface closure domains ([010] or $\left[0\overline{1}0\right]$) under a perpendicular [001] magnetic field. These [001] domains facilitate the [001] field-driven growth of basic perpendicular [001] domains (orange color under zero field) and shrinkage of basic perpendicular $\left[00\overline{1}\right]$ domains (green color under zero field).

Figure 5

Schematic illustration of spikes on the (001) surface within (a) [010] parent domain and (b) $\left[0\overline{1}0\right]$ parent domain. A spike alone would create magnetic charges at its base if the underneath perpendicular domain were not present.

Figure 6

Responses of zigzag domain boundaries and formations of spikes in Fe-8.5 at. % Ga single crystal under a magnetic field $H^{\mathrm{ex}}=70\mathrm{kA}/\mathrm{m}$ along (a) [001] (out of the surface) and (b) $\left[00\overline{1}\right]$ (into the surface), respectively. (a′) and (b′) Schematics of two branches of pointing-left/pointing-right spikes, subsurface perpendicular magnetizations (red and green arrows) beneath the spike bases, and distinct contrasts (enhancing and fading) of zigzag V1+ and V1− boundaries in (a) and (b).

Figure 7

Spike clusters formed under a magnetic field of 70 kA/m along [001]. They exhibit newly formed (a) single zigzag boundary and (b) double zigzag boundaries, which are highlighted with white dashed line loops. (a′) and (b′) Schematics of the magnetic domain structures corresponding to (a) and (b).

Figure 8

Schematics of moth domain structure on a slightly misoriented (001) surface of Fe-12.8 at. % Si bulk crystal (reprinted figure with permission from Ref. [13]).

Figure 9

(a) V-line model of cellular domains in Fe-Ga alloys [8]. Predicted responses of V lines under magnetic field along (b) [001] (out of the surface) and (c) $\left[00\overline{1}\right]$ (into the surface).

Figure 10

Three-dimensional (3D) views of the V-line model of cellular domains in Fe-Ga alloys (reproduced with permission from Ref. [16]). (a) Top view with zigzag V-lines and side view with closure domains. (b) Wedge-shaped surface domains shown separately must elastically deform to fit into the space above and between the internal perpendicular basic domains. The magnetization is shown by arrows and the strain state by filled colors.

Figure 11

Responses of cellular domains on the (001) surface in quenched Fe-18.07 at. % Ga single crystal to perpendicular magnetic fields: (a) 0 G, (b) 8 kA/m along [001] (out of the surface), and (c) 8 kA/m along $\left[00\overline{1}\right]$ (into the surface).