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The tetragonal intermetallic compound EuAl$_{4}$ hosts an exciting variety of low temperature phases. In addition to a charge density wave below 140 K, four ordered magnetic phases are observed below 15.4 K. Recently, a skyrmion phase was proposed based on Hall effect measurements under a $c$-axis magnetic field. We present a detailed investigation of the phase transitions in EuAl$_{4}$ under $c$-axis magnetic field. Our dilatometry, heat capacity, DC magnetometry, AC magnetic susceptibility, and resonant ultrasound spectroscopy measurements reveal three magnetic phase transitions not previously reported. We discuss what our results reveal about the character of the magnetic phases. Our first key result is a detailed $H \parallel [001]$ magnetic phase diagram mapping the seven phases we observe. Second, we identify a new high-field phase, phase VII, which directly corresponds to the region were skyrmions have been suggested. Our results provide guidance for future studies exploring the complex magnetic interactions and spin structures in EuAl$_{4}$., 20 pages, 15 figures

Background : The emergence of hyperon degrees of freedom in neutron star matter has been associated to first order phase transitions in some phenomenological models, but conclusions on the possible physical existence of an instability in the strangeness sector are strongly model dependent. Purpose : The purpose of the present study is to assess whether strangeness instabilities are related to specific values of the largely unconstrained hyperon interactions, and to study the effect of the strange meson couplings on phenomenological properties of neutron stars and supernova matter, once these latter are fixed to fulfill the constraints imposed by hypernuclear data. Method : We consider a phenomenological RMF model sufficiently simple to allow a complete exploration of the parameter space. Results : We show that no instability at supersaturation density exists for the RMF model, as long as the parameter space is constrained by basic physical requirements. This is at variance with a non-relativistic functional, with a functional behavior fitted through ab-initio calculations. Once the study is extended to include the full octet, we show that the parameter space allows reasonable radii for canonical neutron stars as well as massive stars above two-solar mass, together with an important strangeness content of the order of 30\%, slightly decreasing with increasing entropy, even in the absence of a strangeness driven phase transition. Conclusions : We conclude that the hyperon content of neutron stars and supernova matter cannot be established with present constraints, and is essentially governed by the unconstrained coupling to the strange isoscalar meson., 13 pages, 8 figures

International audience; Background: The advent of new dedicated experimental programs on hyperon physics is rapidly boosting the field, and the possibility of synthetizing multiple strange hypernuclei requires the addition of the strangeness degree of freedom to the models dedicated to nuclear structure and nuclear matter studies at low energy. Purpose: We want to settle the influence of strangeness on the nuclear liquid-gas phase transition. Because of the large uncertainties concerning the hyperon sector, we do not aim at a quantitative estimation of the phase diagram but rather at a qualitative description of the phenomenology, as model independent as possible. Method: We analyze the phase diagram of low density matter composed of neutrons, protons and $\Lambda$ hyperons using a Relativistic Mean Field (RMF) model. We largely explore the parameter space to pin down generic features of the phase transition, and compare the results to ab-initio quantum Monte Carlo calculations. Results: We show that the liquid-gas phase transition is only slightly quenched by the addition of hyperons. Strangeness is seen to be an order parameter of the phase transition, meaning that dilute strange matter is expected to be unstable with respect to the formation of hyper-clusters. Conclusions: More quantitative results within the RMF model need improved functionals at low density, possibly fitted to ab-initio calculations of nuclear and $\Lambda$ matter.