Direct observation of competition between charge order and itinerant ferromagnetism in the van der Waals crystal ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$

The interplay of symmetry-breaking ordered states, such as superconductivity, charge density waves, magnetism, and pseudogaps, is a fundamental issue in correlated systems. Periodic modulation and antiferromagnetism often coexist in the proximity of phase diagram region in high-$T_c$ superconductors. It is also worth noting that different order states appear in a situation on comparable temperature scales, so these orders are intertwined and competing on the same footing. The magnetism of vdW material ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$, with one of the highest reported bulk Curie temperatures, is found to be sensitive to thermal history and external magnetic field. However, the temperature-dependent magnetization with two characteristic points still lacks a unified picture to describe it. Using angle-resolved photoemission spectroscopy, scanning tunneling microscopy, magnetic property measurements, and first-principles calculations, the complex yet intriguing magnetic behaviors are gradually unveiled. A competition mechanism between charge order and ferromagnetism is proposed and firmly observed by experimental measurements. As the ferromagnetic order strengthens at low temperature, the charge order will be suppressed. Exchange splitting in itinerant ferromagnetism plays a significant role in the temperature evolution of band structure and causes a Lifshitz transition, which provides more control means to realize novel devices at room temperature.

Figure 1

(a) Schematic of ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$ crystal structure with Fe-Ge-Te slab stacked along $c$ axis, where Fe(1) and Ge are split sites that allow for local atomic order and disorder. (b) Atomic-resolution topography STM image ($V_b=-10$ mV, $I_t=-100$ pA) of ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$ cleavage plane indicated by the red arrow in (a). Line profile along the white dashed line indicates the Te-Te interval 0.41 nm. (c) The $dI/dV$ conductance map ($V_b=-50$ mV, $I_t=-100$ pA) of ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$. (d) The corresponding fast Fourier transform (FFT) image of (c), where the white and yellow dotted circles in the FFT image indicate the $1\times 1$ and $\sqrt{3}a\times \sqrt{3}aR{30}^{\circ }$ structures, respectively. (e) Temperature-dependent magnetization curves for $H\parallel ab$ at different field indicated by the colors. (f) Temperature-dependent phase diagram of ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$ crystal in different magnetic fields.

Figure 2

ARPES band mapping at 30 K and DFT band calculations for ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$. (a) Photoemission intensity map at the $E_F$ in $k_x\text{−}{k}_y$ plane at 30 K, and the orange hexagon indicates the Brillouin zone (BZ) boundary. The ARPS spectra taken on a nearly stoichiometric single crystal of ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$ ($x=0.22$). (b) The calculated FSs at $k_z=0$ plane and the high-symmetry points are presented in (d). (c) The calculated band structures along the high-symmetry lines, and the magnetic moments are given by $M\parallel c$. The calculated Fe $3d$ orbital contributions is imposed on (c). (d) The BZ of ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$ with the high-symmetry points and lines indicated. (e)–(f) and (g)–(h): The photoemission intensity and their second derivative of the intensity plots along the $\mathrm{\Gamma }$-K-M direction and the K-M-K direction, respectively.

Figure 3

Temperature dependence of the band structure. (a) Photoemission intensity map at $E_F$ in $k_x\text{−}{k}_y$ plane at 150 K. (b)–(c): The intensity maps along the cut 3 and cut 4 indicated in (a), and the shallow electron-like band feature originated from the charge order is labeled ${\gamma }^{*}$. (d)–(j): Temperature dependence of the band structure along the $\mathrm{\Gamma }$-K-M direction from $T=150\mathrm{K}$ to 30 K. The electron-like band ${\gamma }^{*}$ is indicated by the red arrows. (k) Temperature-dependent MDCs extracted from (d)–(j) at the binding energy $-0.1\mathrm{eV}$, indicated by the dashed line in (j).

Figure 4

Temperature dependence of the EDC peaks. (a) ARPES core level spectrum shows clear Fe $3p$, Te $4d$, and Ge $3d$ peaks with the decrease of temperature at $h\nu =200\mathrm{eV}$. (b) Temperature dependence of the EDCs at $\mathrm{\Gamma }$ divided by Fermi-Dirac distribution function. (c) The energy gap defined as the peak positions indicated by the black arrow in (b) at the corresponding temperature. The thermal fluctuation is indicated by the error bars. (d) Temperature dependence of the normalized EDCs at $M$, and the temperature-dependent shift of the peaks indicated by the black arrow nearing the $E_F$ is magnified.

Figure 5

Band folding along the $K-\mathrm{\Gamma }-K$ in ${\mathrm{Fe}}_{5-x}{\mathrm{GeTe}}_2$ and the reconstruction of Brillouin zone. (a) The band dispersion obtained from DFT calculation along the high-symmetry line $K-\mathrm{\Gamma }-K$ with the moments $M\parallel c$, and the band along the $\mathrm{\Gamma }-K$ from the charge order are superimposed, indicated by the orange lines. (b) The blue and gray hexagons represent the BZ of the primitive cell and superlattice of $\sqrt{3}a\times \sqrt{3}aR{30}^{\circ }$ periodicity, respectively.