Author Correction: The anisotropic field of ensemble coding

In the original version of this Article a Data and Code Availability section was omitted. It has now been included and states.

Pure electromagnetic-gravitational interaction in Hořava–Lifshitz theory at the kinetic conformal point

We introduce the electromagnetic-gravitational coupling in the Hořava–Lifshitz framework, in $$3+1$$3+1 dimensions, by considering the Hořava–Lifshitz gravity theory in $$4+1$$4+1 dimensions at the kinetic conformal point and then performing a Kaluza–Klein reduction to $$3+1$$3+1 dimensions. The action of the theory is second order in time derivatives and the potential contains only higher order spacelike derivatives up to $$z=4$$z=4, z being the critical exponent. These terms include also higher order derivative terms of the electromagnetic field. The propagating degrees of freedom of the theory are exactly the same as in the Einstein–Maxwell theory. We obtain the Hamiltonian, the field equations and show consistency of the constraint system. The conformal kinetic point is protected from quantum corrections by a second class constraint. At low energies the theory depends on two coupling constants, $$\beta $$β and $$\alpha $$α. We show that the anisotropic field equations for the gauge vector is a deviation of the covariant Maxwell equations by a term depending on $$\beta -1$$β-1. Consequently, for $$\beta =1$$β=1, Maxwell equations arise from the anisotropic theory at low energies. We also prove that the anisotropic electromagnetic-gravitational theory at the IR point $$\beta =1$$β=1, $$\alpha =0$$α=0, is exactly the Einstein–Maxwell theory in a gravitational gauge used in the ADM formulation of General Relativity.

Anomalous anisotropic behaviour of spin-triplet proximity effect in Au/SrRuO3/Sr2RuO4 junctions

Spin-polarized supercurrents can be generated with magnetic inhomogeneity at a ferromagnet/spin-singlet-superconductor interface. In such systems, complex magnetic inhomogeneity makes it difficult to functionalise the spin-polarized supercurrents. However, spin-polarized supercurrents in ferromagnet/spin-triplet-superconductor junctions can be controlled by the angle between magnetization and spin of Copper pairs (d-vector), that can effectively be utilized in developing of a field of research known as superconducting spintronics. Recently, we found induction of spin-triplet correlation into a ferromagnet SrRuO3 epitaxially deposited on a spin-triplet superconductor Sr2RuO4, without any electronic spin-flip scattering. Here, we present systematic magnetic field dependence of the proximity effect in Au/SrRuO3/Sr2RuO4 junctions. It is found that induced triplet correlations exhibit strongly anisotropic field response. Such behaviour is attributed to the rotation of the d-vector of Sr2RuO4. This anisotropic behaviour is in contrast with the vortex dynamic. Our results will stimulate study of interaction between ferromagnetism and unconventional superconductivity.