Microscopic and Macroscopic Signatures of Antiferromagnetic Domain Walls

Magnetotransport measurements on small single crystals of Cr, the elemental antiferromagnet, reveal the hysteretic thermodynamics of the domain structure. The temperature dependence of the transport coefficients is directly correlated with the real-space evolution of the domain configuration as recorded by x-ray microprobe imaging, revealing the effect of antiferromagnetic domain walls on electron transport. A single antiferromagnetic domain wall interface resistance is deduced to be of order $5\times {10}^{-5}\mu \Omega {\mathrm{cm}}^2$ at a temperature of 100 K.

Figure 1

Schematic AF domain structure in Cr. Only one of the two possible spin polarizations $\mathbf{S}$ is illustrated for each $Q$ domain; hence we show only one of the four types of boundary that are possible between this pair of $Q$ vectors. The rotations ${\widehat{\eta }}_S$ and ${\widehat{\eta }}_Q$ (defined in the text) that characterize the domain wall are collinear for this particular domain wall realization. In reciprocal space the gapped and ungapped Fermi surfaces are shown in red and blue, respectively. The electron Fermi surface centered at the middle of the Brillouin zone and the hole surface centered at the corner of the zone are connected by the nesting vector $\mathbf{Q}$. Only the magnetic bands are shown for clarity.

Figure 2

(a) Superposition of actual sample wired for electrical measurements with a typical $Q$-domain image to scale, permitting direct comparison of the length scales involved. Domain wall motion, such as that seen in Figs. 3, 4, is significant on the length scale of the current paths. (b) Difference between the longitudinal resistivities $\Delta \rho \equiv {\rho }_{xx}-{\rho }_{yy}$ showing thermal hysteresis and clear evidence for domain rearrangement with changes in temperature. Residual ($T=10\mathrm{K}$) and room temperature ($T=300\mathrm{K}$) resistivities are 0.24 and $11.70\mu \Omega \mathrm{cm}$, respectively. The ($x$, $y$) coordinates are defined by the sample geometry.

Figure 3

Thermal hysteresis of the Hall coefficient measured on a sub-mm Cr crystal. Images are maps of microprobe diffraction intensity from one of three $Q$-domain types; diffraction is from the charge-density wave satellite at (0, 0, 2 $-2\delta$), and therefore is sensitive only to domains with $\mathbf{Q}\parallel [001]$. Beam spot size is $300\times 600{\mathrm{nm}}^2$, sample face is (111), x-ray energy is 11.6 keV, and the penetration length is $\approx 1.5\mu \mathrm{m}$. Images are taken at 50 K and 200 K within a thermal cycle between 50 K and 300 K. Color bar indicates diffraction intensity in counts/sec; multiplication factors of $2\times {10}^4$ and ${10}^4$ should be used for the 50 K and 200 K images, respectively. Images at the same $T$ show the same sample area, but for different $T$ the areas imaged are different.

Figure 4

Hall coefficient around a nested temperature loop, showing persistence of hysteresis. Images are maps of microprobe diffraction intensity from one $Q$-domain type, taken at 110 K within a thermal cycle between 110 K and 170 K. Diffraction is from the magnetic satellite at (0, 1, $\delta$); below $T_{\mathrm{SF}}$ entire $Q$ domains with $\mathbf{Q}\parallel [001]$ diffract at this position [3]. Beam spot size is $300\times 600{\mathrm{nm}}^2$, sample face is (111), x-ray energy is 5.8 keV, and the penetration length is $\approx 2\mu \mathrm{m}$. Color bar indicates diffraction intensity in counts/sec. Images show the same sample area.