Observation of hidden altermagnetism in Cs$_{1-δ}$V$_2$Te$_2$O

Abstract

Altermagnets are characterized by anisotropic band/spin splittings in momentum space, dictated by their spin-space group symmetries. However, the real-space modulations of altermagnetism are often neglected and have not been explored experimentally. Here we combine neutron diffraction, angle-resolved photoemission spectroscopy (ARPES), spin-resolved ARPES and density functional theory to demonstrate that Cs$_{1-δ}$V$_2$Te$_2$O realizes a spatially modulated form of altermagnetism, i.e., hidden altermagnetism. Such a state in Cs$_{1-δ}$V$_2$Te$_2$O results from its G-type antiferromagnetism and two-dimensional electronic states, allowing for the development of spatially alternating altermagnetic layers, whose local spin polarizations are directly verified by spin-resolved ARPES measurements. Our experimental discovery of hidden altermagnetism broadens the scope of unconventional magnetism and opens routes to exploring emergent phenomena from real-space modulations of altermagnetic order.

Figures (3)

• Figure 1: Magnetic ground state and calculated electronic structure of Cs$_{1-\delta}$V$_2$Te$_2$O. (a) Crystal structure. (b) Temperature-dependent magnetic susceptibility. (c,d) Two possible AFM states with lowest energies: C-type (c) and G-type AFM (d). The corresponding symmetry operations are indicated. (e,f) Calculated spin-resolved band structures for C-type (e) and G-type AFM (f). (g,h) Neutron diffraction intensity maps in the $[H0L]$-plane at 300 K (g) and at 5 K (h). Magnetic peaks with half-integer $L$ are indicated in (h) using white arrows. (i,j) Temperature dependence of the $\mathbf{Q}=(0,-1,\frac{5}{2})$ (i) and $(0,-1,\frac{1}{2})$ (j) magnetic peaks.
• Figure 2: Electronic structure and temperature evolution of Cs$_{1-\delta}$V$_2$Te$_2$O from ARPES. (a,b) The $k_x$-$k_y$ FS taken with 44 eV photons at T = 20 K (a) and 310 K (b), respectively. The calculated Fermi contours at $k_z$ = 0 (white curves) are overlaid on the right half. (c) A three-dimensional view of the calculated FS corresponding to the G-type AFM. (d) The photon-energy-dependent scan at $E_F$ along $\bar{M}-\bar{X}-\bar{M}$. (e,f) Energy-momentum cuts along $\bar{M}-\bar{X}-\bar{M}$ at T = 20 K (e) and 295 K (f), respectively. The calculated band structures for the G-type AFM and nonmagnetic states (black dashed curves) are overlaid on the right half. (g) Temperature-dependent MDCs at $E_F$ along $\bar{M}-\bar{X}-\bar{M}$, taken with 21.2 eV photons. Original data can be found in Fig. S5 supplementary.
• Figure 3: Detecting the local spin polarization by spin-resolved ARPES. (a) A schematic of hidden altermagnetism in Cs$_{1-\delta}$V$_2$Te$_2$O. (b) Local spin signals, detected by spin-resolved ARPES, decay exponentially with $z$ and oscillate due to hidden altermagnetism. (c,d) Projected spin polarization and orbital weight of the calculated bands at the A (c) and B (d) sectors. (e) Calculated two-dimensional FS for the A sector. (f) Geometry of the spin-resolved ARPES measurement. The spin polarization along $z$, $S_z$, is equal to $S_{x'}$/sin($\theta$), where $S_{x'}$ is the effective spin polarization along $x'$ measured by spin-resolved ARPES. (g,h) Spin-up (g) and spin-down (h) ARPES spectra corresponding to $S_{x'}$. The spin-resolved DFT calculation is overlaid in (g). The momentum cut is along $\bar{X}-\bar{M}$ as indicated in (e). Blue and red curves in (c-e,g) correspond to spin up and down, respectively. (i) The spin-resolved MDCs obtained from (g,h), integrated over the white dashed rectangle defined in (h). Insets are zoom-in view of the $\alpha$ and $\gamma$ bands, respectively. The much weaker intensity on the left side is caused by the detector inhomogeneity. (j) The extracted momentum-dependent spin polarization $S_z$ from (i).