High Resolution Polar Kerr Effect Studies of Cs3Sb5 and ScV6Sn6 Below the Charge Order Transition

TL;DR

This work tests for spontaneous TRSB via the polar Kerr effect in CsV$_3$Sb$_5$ and ScV$_6$Sn$_6$ across their CDW transitions using high-sensitivity Zero-Area Sagnac Interferometers at $1550$ nm and $830$ nm. Across both wavelengths and both materials, no spontaneous Kerr rotation is detected down to about $50$ nrad in zero field, though field-induced Kerr signals align with Pauli susceptibility expectations; the CDW transitions are clearly witnessed in the optical volume by coherent reflection measurements. Uniaxial strain does not induce a Kerr signal, placing stringent limits on hidden flux-ordered states and challenging theories predicting large TRSB Kerr effects in these kagomé systems. Overall, the results constrain orbital flux-phase scenarios and refine the understanding of TRSB in CsV$_3$Sb$_5$- and ScV$_6$Sn$_6$-based CDW materials, with implications for related TRSB claims in Kagomé lattices.

Abstract

We report high resolution polar Kerr effect measurements on CsV3Sb5 and ScV6Sn6 single crystals in search for signatures of spontaneous polar Kerr effect (PKE) below the charge order transitions of these materials. Utilizing two separate zero-area loop Sagnac interferometers operating at 1550 nm and 830 nm wavelengths, we studied the temperature dependence of possible PKE after training with magnetic field. While a finite field Kerr measurement yielded optical rotation expected from the Pauli susceptibility of the itinerant carriers, no signal was detected at zero-field to within the noise floor limit of the apparatus of below $\sim$100 nanoradians. Simultaneous coherent reflection measurements confirm the sharpness of the charge order transition in the same optical volume as the Kerr measurements. Application of strain to reveal a hidden flux-ordered magnetic state did not result in a finite Kerr effect.

Figures (7)

• Figure 1: Corner-sharing triangles of vanadium atoms constitute the Kagomé lattice planes of CsV$_3$Sb$_5$ (left) and ScV$_6$Sn$_6$ (right). Side views highlight the relative displacement of the vanadium and Sn planes in ScV$_6$Sn$_6$. Shaded area corresponds to the rhombus- shaped unit cell.
• Figure 2: Experimental setup. a) Schematic of the Zero-Area Loop Sagnac Interferometer system. Light emitted from a SLED is polarized (P), then going through a circulator (C) and vertically polarized in (P). Half waveplate rotates the polarization at 45$^\circ$ and only the vertical component is modulated at the electro-optic modulator (EOM) at frequency $\omega$, controlled by a function generator (FG). Upon exiting the EOM, the two, now incoherent components (marked as "1" and "2", are launched into the two axes of a polarization maintaining (PM). The two beams enter the probe end optics assembly (enlarged within the dashed-lined ellipse), where a quarter waveplate (QWP) transforms the two linear polarizations into right and left circular polarizations. Upon reflection from the sample the two beams exchange circular polarization role. In the presence of birefringent these polarizations become slightly elliptical, and in the presence of TRSB a non reciprocal phase shift, $\Delta\phi_{nr}$ is acquired. Moving back in the same optical path, the two beams coherently combine at the detector and the output signal is analyzed to extract $\theta_K=\Delta\phi_{nr}$. b) Top shows two ways of mounting of a CsV$_3$Sb$_5$ crystal either flat on the cold plate or over a trench, affixed at one side only, while bottom shows a photo of a mounted sample over a trench.
• Figure 3: Polar Kerr Effect measurements at 1550 nm wavelength: a,b) on CsV$_3$Sb$_5$ , and c,d) on ScV$_6$Sn$_6$ . Measurements in magnetic field (panels (a and (c)) track the transition with signal of order of the respective Pauli susceptibility Saykin2023. Zero-field warmup measurements after training the sample in a field while cooling it through the CDW transition (panels (a and (c)) Show no evidence for a spontaneous Kerr effect (see text). Dashed lines in panels (b) and (d) track the DC component of the reflectivity (in arbitrary units) measured simultaneously with the PKE, which reaffirms that the optical volume that we test indeed undergo the CDW transition.
• Figure 4: Polar Kerr Effect measurements at 830 nm wavelength: a,b) on CsV$_3$Sb$_5$ , and c,d) on ScV$_6$Sn$_6$ . Similar to Fig. \ref{['1550']}, measurements in magnetic field (panels (a and (c)) track the transition with signal of order of the respective Pauli susceptibility Saykin2023. Zero-field warmup measurements after training the sample in a field while cooling it through the CDW transition (panels (a and (c)) Show no evidence for a spontaneous Kerr effect (see text). Dashed lines in panels (b) and (d) track the DC component of the reflectivity (in arbitrary units) measured simultaneously with the PKE, which reaffirms that the optical volume that we test indeed undergo the CDW transition.
• Figure 5: Kerr signal in strained CsV$_3$Sb$_5$ at 1550 nm. a) Kerr effect measured in an applied field of 50 mT, yielding similar Kerr signal to previous in-field measurements. b) Zero-field warmup measurements after training in a field of 50 mT showing no discernible strain-induced signal through the CDW transition. c) CsV$_3$Sb$_5$ crystal cut and mounted onto the strain cell. Crystal dimensions 2mm$\times$1.2mm. Arrow marks the $a$-direction of the crystal in the cell (see Fig. \ref{['structure']}.)