Spontaneous Ferromagnetism Induced Topological Transition in ${\mathrm{EuB}}_6$

The interplay between various symmetries and electronic bands topology is one of the core issues for topological quantum materials. Spontaneous magnetism, which leads to the breaking of time-reversal symmetry, has been proven to be a powerful approach to trigger various exotic topological phases. In this Letter, utilizing the combination of angle-resolved photoemission spectroscopy, magneto-optical Kerr effect microscopy, and first-principles calculations, we present the direct evidence on the realization of the long-sought spontaneous ferromagnetism induced topological transition in soft ferromagnetic ${\mathrm{EuB}}_6$. Explicitly, we reveal the topological transition is from $Z_2=1$ topological insulator in paramagnetic state to $\chi =1$ magnetic topological semimetal in low temperature ferromagnetic state. Our results demonstrate that the simple band structure near the Fermi level and rich topological phases make ${\mathrm{EuB}}_6$ an ideal platform to study the topological phase physics.

Figure 1

(a) Crystal structure and (b) bulk and (001)-projected surface BZs of ${\mathrm{EuB}}_6$. (c) Calculated band structure of ${\mathrm{EuB}}_6$ in its paramagnetic state without SOC. The valence band and conduction band with opposite parity near $E_F$ are labeled as ${\mathrm{\Gamma }}_3^{-}$ and ${\mathrm{\Gamma }}_3^{+}$, respectively. Here the lattice constant $a=4.1851\AA$ and $u=0.200$ are used, determined directly from the fitting of XRD data. (d) Enlargement of the band crossing at $Z(X,Y)$ point. (e) Schematic plot of emergent topological phases with TRSB in centrosymmetric 3D systems. “$+$” and “$-$” represent even and odd parity of corresponding band, and “$\uparrow$” and “$\downarrow$” represent spin-up and spin-down, respectively. Black bands are spin degenerated bulk bands, while red and blue bands are spin-up and spin-down branches, respectively. DNLSM (Dirac nodal line semimetal): without considering SOC, the spin degenerated conduction and valence band crossing with each other gives rise to the fourfold degenerate nodal line.

Figure 2

(a) Sketch plot of the Eu termination surface. (b)(I),(II) Photoemission intensity plots along $\overline{\mathrm{\Gamma }}-\overline{X}$ at different time after sample cleaved on the Eu termination surface. The probing photons are of 71 eV. (c) Energy distribution curve (EDCs) along the corresponding dashed lines in (b). (d) Photoemission intensity map on the $k_x–k_z$ plane taken at $E_F$. Inset is the corresponding intensity map for the band SS2 [for details, see (i) and (j)]. (e) Sketch plot of the B termination surface. (f) (I),(II) ARPES intensity plots along $\overline{\mathrm{\Gamma }}–\overline{X}$ at different time after sample cleaved on the B termination. Photons are of 71 eV. (g) EDCs along the corresponding dashed lines in (f). (h) Photoemission intensity map on the $k_x–k_z$ plane taken at $E_F$ with the photon-energy range from 40 to 136 eV. The inner potential of 15 eV was determined to match the periodicity along $k_z$. Inset is the intensity map taken at $E_F-0.2$ eV for the dashed square containing the $Z$ point, suggesting the 3D character of the valence band. (i) Photoemission intensity map on the $k_x–k_y$ plane of the Eu termination surface with an energy window of 50 meV. $\overline{\mathrm{\Gamma }}$, $\overline{X}$, and $\overline{M}$ represent high-symmetry points in the projected two-dimensional BZ. (j),(k) Photoemission intensity plots of the Eu termination surface along $\overline{\mathrm{\Gamma }}–\overline{X}$ and $\overline{M}–\overline{X}$, respectively. (l) Intensity plots on the B termination surface along the $\mathrm{\Gamma }–X$ direction with the photon energy 130 eV at 4.9 K. (m) Intensity plots on the B termination surface along the $T–Z$ direction at 4.9 K with the photon energy 103 eV.

Figure 3

(a) Photoemission intensity plots at different temperatures along the $T–Z$ direction, which are also following the chronological order. Symbols “$+$” and “$-$” in (VI) indicate even and odd parity of occupied bands at $Z$, respectively. The probing photons are of 103 eV. (b),(c) Photoemission intensity plot and corresponding momentum distribution curves taken in the PM state along $T–Z$. OP represents the band overlap region. (d),(e) The same as (b) and (c), but taken in the FM state. (f),(g) Photoemission intensity plots taken along $\mathrm{\Gamma }-X$ in the PM and FM states. The probing photons are of 130 eV.