Visualization of ferromagnetic domains in $\mathrm{Er}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ single crystals: Weak ferromagnetism and its coexistence with superconductivity

The magnetic flux structure in the basal plane, (001), of single crystals of superconducting $\mathrm{Er}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ was studied by high resolution Bitter decoration at temperatures below $T_c$ (superconducting transition) and/or $T_N$ (antiferromagnetic transition). Two sets of domain boundaries, in {110} and {100} planes, were observed. The temperature range in which the {100} domain boundaries were observed coincides with the weak ferromagnetic (WFM) ordering in this material. On the other hand, the {110} twin boundaries—the antiferromagnetic domain boundaries—were observed below $T_N$. For comparison, $\mathrm{Tb}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$, the related compound with higher magnetic ordering temperatures but no superconductivity, was also studied. The possibility of interpretation of {100} boundaries as Bloch domain walls in the weakly ferromagnetic phase, for $T<T_{\mathit{WFM}}<T_N$ $\left(\mathrm{Tb}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}\right)$ or $T<T_{\mathit{WFM}}<T_N<T_c$ $\left(\mathrm{Er}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}\right)$, is discussed.

Figure 1

Bitter decoration pattern on a $\mathrm{Tb}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ single crystal cooled down to $T_1=4.2\mathrm{K}$ in a magnetic field of $H=1.1\mathrm{kOe}$ and decorated at $T_d\approx 7\mathrm{K}$. Magnetic particles (bright dots) arranged along the ⟨100⟩ direction indicate the WFM domain boundaries, whereas segregation of magnetic particles along the ⟨110⟩ direction indicates the AFM twin boundaries.

Figure 2

Bitter decoration pattern on a twin-boundaries-free region of a $\mathrm{Er}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ single crystal cooled down to $T_1=1.8\mathrm{K}$ in a magnetic field of $H=20\mathrm{Oe}$ and decorated at $T_d\approx 4\mathrm{K}$. The vortex arrays (bright dots) are arranged along the ⟨100⟩ direction. Inset: Fourier transform of the image.

Figure 3

Upper panel: illustration of the protocols used in the low temperature experiment. Path (a): cooling down to $T_1$ below $T_{\mathit{WFM}}$, $T_d$ slightly above $T_{\mathit{WFM}}$. Path (b): both $T_1$ and $T_d$ above $T_{\mathit{WFM}}$ but below $T_N$. Lower panel: example of experimental time-temperature trace. $T_{\mathit{max}}\approx 3.2\mathrm{K}$ corresponds to the heating by unscreened radiation from the filament before deposition of the magnetic particles; $T_d^a$ is an extrapolated temperature of the buffer He gas at the moment of the end of the heating.

Figure 4

Bitter decoration pattern on an $\mathrm{Er}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ single crystal (sample I) obtained after field cooling in an applied field $H$, using experimental protocols (a) $T_1=1.8\mathrm{K}$, $T_d=2.6\mathrm{K}$, and $H=15\mathrm{Oe}$ [panel (a)] and (b) $T_1=4.2\mathrm{K}$, $T_d=5.5\mathrm{K}$, and $H=20\mathrm{Oe}$ [panel (b)]. Inset of panels (a) and (b): Fourier transform of the image from the left side of the pattern showing a feature along [010] in panel (a) and hexagonal order of vortices in panel (b).

Figure 5

Bitter decoration pattern on an $\mathrm{Er}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ single crystal (sample II) obtained after field cooling in applied field $H$, using experimental protocols (a) $T_1=1.6\mathrm{K}$, $T_d=4.2\mathrm{K}$, and $H=20\mathrm{Oe}$ [panel (a)] and (b) $T_1=4.2\mathrm{K}$, $T_d=5.5\mathrm{K}$, and $H=20\mathrm{Oe}$ [panel (b)].