Fig. 5: Onset of hyperbolicity and magnetic order.
From: Hyperbolic exciton polaritons in a van der Waals magnet
a Schematic of intralayer ferromagnetic correlations (dotted lines) aligning in-plane \({{{{{\rm{Cr}}}}}}\) spins (arrows) below a critical temperature \({T}_{C}=160{{{{{\rm{K}}}}}}\). b Interlayer correlations below the bulk Néel temperature (\({T}_{N}=132{{{{{\rm{K}}}}}}\)) order CrSBr into an A-type antiferromagnet (AFM) with ferromagnetic van der Waals layers of alternating spin (arrows). c Real \(b\)-axis permittivity \({\varepsilon }_{1}\) near \({T}_{N}\) and \({T}_{C}\) from fits in Supplementary Fig. 11. CrSBr becomes hyperbolic, \({\varepsilon }_{1} \, < \, 0\) (white), below \({T}_{C}\); and the hyperbolic band broadens with decreasing temperature. d Measured spectral weight (black crosses) of the CrSBr exciton (inset shows integral of real optical conductivity \({\sigma }_{1}\)) increases rapidly with the onset of magnetic order at \({T}_{C}\) and plateaus below \({T}_{N}\). Orange line is a guide to the eye. Solid gray lines show \({{{{{\rm{QS}}}}}}G\hat{W}\) theory predicting enhancement in exciton oscillator strength going from paramagnetic (PM) to AFM states. e \({{{{{\rm{QS}}}}}}G\hat{W}\) electronic band structure in AFM (left) and PM (right) phases. Colored bands (orange) show the distribution of exciton spectral weight across various valence and conduction band states. Magnetic disordering in the PM phase leads to electron localization and reduced dispersion along \(\Gamma\)-Y (black arrow). f The probability of both electron (−) and hole (+) being on the same \({{{{{\rm{Cr}}}}}}\) site increases due to electron localization in PM phase.
