Evidence for Ferromagnetic Clusters in the Colossal-Magnetoresistance Material ${\mathrm{EuB}}_6$

We combined scanning tunneling microscopy and locally resolved magnetic stray field measurements on the ferromagnetic semimetal ${\mathrm{EuB}}_6$, which exhibits a complex ferromagnetic order and a colossal magnetoresistance effect. In a zero magnetic field, scanning tunneling spectroscopy visualizes the existence of local inhomogeneities in the electronic density of states, which we interpret as the localization of charge carriers due to the formation of magnetic polarons. Micro-Hall magnetometry measurements of the total stray field emanating from the end of a rectangular-shaped platelike sample reveals evidence for magnetic clusters also in finite magnetic fields. In contrast, the signal detected below the faces of the magnetized sample measures a local stray field indicating the formation of pronounced magnetic inhomogeneities consistent with large clusters of percolated magnetic polarons.

Figure 1

(a) Topography of ${\mathrm{EuB}}_6$ over an area of $10\mathrm{nm}\times 10\mathrm{nm}$ ($V=-0.2\mathrm{V}$, $I_{sp}=0.5\mathrm{nA}$). Inset: cubic crystal structure of ${\mathrm{EuB}}_6$. (b) Height scans along the lines marked in (a). (c),(e) Maps of local conductance $g(V)=dI(V,\overrightarrow{r})/dV$ at $V=-24\mathrm{mV}$ over an area of $20\mathrm{nm}\times 20\mathrm{nm}$ obtained at 5.6 K (c) and 20 K (e). At 5.6 K, the ${\mathrm{EuB}}_6$ surface is nearly homogeneously conducting, while at 20 K local inhomogeneities are clearly visible. (d),(f) $\mathrm{d}I(V)/\mathrm{d}V$-spectra averaged within areas marked in (c) and (e), respectively, by rectangles of corresponding colors. In (d), a curve averaged over the total area is also included. The local inhomogeneities are most pronounced at $V=-24\mathrm{mV}$, dashed lines in (d) and (f).

Figure 2

(a) Temperature-dependent magnetic stray field $⟨B_z⟩$ vs $T$ (solid lines) detected at cross $A$ (see schematics in the inset) in external magnetic fields $B_{\mathrm{ext}}\ge 10\mathrm{mT}$. Dashed lines are three-parameter fits of a mean-field magnetization model, Eqs. (1) and (2), as described in the text. Fit parameters (b) saturation stray field ${⟨B_z⟩}_{\mathrm{sat}}\propto M_s$ and cluster size $\mu /{\mu }_B$, and (c) transition temperature $T_C$ in dependence on $B_{\mathrm{ext}}$ compared to $T_{c_2}$ as determined from the peak in the derivative of the $⟨B_z⟩(T)$ curves shown in (a).

Figure 3

(a),(b) Total and local magnetic stray fields detected at crosses $A$ and $B$, respectively, as contour plots $⟨B_z⟩(T,B)$. Red lines are selected curves $⟨B_z⟩(B_{\mathrm{ext}},T=\text{const})$. (c) Field-sweep data of cross $B$ in a wider field range at various constant temperatures. (d) Enlarged diagram of selected temperatures showing the occurrence of the characteristic peak below $T_{c_1}$.