Confirming the trilinear form of the optical magnetoelectric effect in the polar honeycomb antiferromagnet Co2Mo3O8

Magnetoelectric phenomena are intimately linked to relativistic effects and also require the material to break spatial inversion symmetry and time-reversal invariance. Magnetoelectric coupling can substantially affect light–matter interaction and lead to non-reciprocal light propagation. Here, we confirm on a fully experimental basis, without invoking either symmetry-based or material-specific assumptions, that the optical magnetoelectric effect in materials with non-parallel magnetization (M) and electric polarization (P) generates a trilinear term in the refractive index, δn ∝ k ⋅ (P × M), where k is the propagation vector of light. Its sharp magnetoelectric resonances in the terahertz regime, which are simultaneously electric and magnetic dipole active excitations, make Co2Mo3O8 an ideal compound to demonstrate this fundamental relation via independent variation of M, P, and k. Remarkably, the material shows almost perfect one-way transparency in moderate magnetic fields for one of these magnetoelectric resonances.

Muon Decay

The decay of the muon has been studied at PSI with several precision measurements: The longitudinal polarization P_{\mathrm{L}}(E)PL(E) with the muon decay parameters \xi'ξ′, \xi''ξ″, the Time-Reversal Invariance (TRI) conserving transverse polarization P_{\mathrm{T_{1}}}(E)PT1(E) with the muon decay parameters \etaη, \eta''η″, the TRI violating transverse polarization P_{\mathrm{T_{2}}}(E)PT2(E), with \alpha'/Aα′/A, \beta'/Aβ′/A and the muon decay asymmetry with P_{\mu}\xiPμξ. The detailed theoretical analysis of all measurements of normal and inverse muon decay has led for the first time to a lower limit |g^{V}_{LL}| > 0.960|gLLV|>0.960 (“V-AV−A”) and upper limits for nine other possible complex couplings, especially the scalar coupling |g^{S}_{LL}| < 0.550|gLLS|<0.550 which had not been excluded before.

Kolakoski sequence: links between recurrence, symmetry and limit density

The Kolakoski sequence $S$ is the unique element of \(\left\lbrace 1,2 \right\rbrace^{\omega}\) starting with 1 and coinciding with its own run length encoding. We use the parity of the lengths of particular subclasses of initial words of \(S\) as a unifying tool to address the links between the main open questions - recurrence, mirror/reversal invariance and asymptotic density of digits. In particular we prove that recurrence implies reversal invariance, and give sufficient conditions which would imply that the density of 1s is \(\frac{1}{2}\).