Correlation between spin-phonon coupling and the magnetoelectric properties of ${\text{EuMnO}}_3$ and ${\text{GdMnO}}_3$ were investigated using ceramic samples in this work. The experimental results evidence a stronger spin-phonon coupling in ${\text{GdMnO}}_3$ than in ${\text{EuMnO}}_3$, as well as a clear anomaly in the phonon contribution for the dielectric constant. This anomaly is located at the paramagnetic-incommensurate antiferromagnetic phase-transition temperature of ${\text{GdMnO}}_3$, corroborating the existence of a magnetoelectric effect in this system. The absence of the magnetoelectric effect in ${\text{EuMnO}}_3$ is due to the existing disorder revealed in this compound by the striking thermal metastability and the large decrease in the activation energy associated with the dielectric relaxation processes. This kind of behavior has no counterpart in ${\text{GdMnO}}_3$. In fact, it has been confirmed that the existence of spin-phonon coupling is not a sufficient condition for the existence of magnetoelectric property, and other mechanisms have to be considered in order to understand the magnetoelectric properties.

When sound waves are taught at the secondary level, the speed of propagation of sound is one of the most important characteristics to be analyzed. However, it is very common in textbooks that the value of sound speed in air is considered constant regardless of the experimental conditions. The great question is that since sound is a mechanical wave, its speed is influenced by the medium of propagation and also by the temperature. In most cases, the techniques reported for that goal usually make use of expensive equipment and techniques that may not be affordable and/or easy to implement in schools, which is an experimental limitation for the teachers to show this influence on their students. In this work, we present a low-cost experimental apparatus, controlled by the open source electronic platform Arduino®, with which it is possible to determine the speed of propagation of sound as a function of the temperature for a short measuring region, thus enabling the students to verify experimentally this important feature of sound waves.

The result of additive colors is always fascinating to young students. When we teach this topic to 14- to 16-year-old students, they do not usually notice we use maximum light quantities of red (R), green (G), and blue (B) to obtain yellow, magenta, and cyan colors in order to build the well-known additive color diagram of Fig. 1. But how about using different light intensities for R, G, and B? What colors do we get? This problem of color mixing has been intensively discussed for decades by several authors, as pointed out by Ruiz's “Color Addition and Subtraction Apps” work and the references included therein. An early LED demonstrator for additive color mixing dates back to 1985, and apps to illustrate color mixing are available online. In this work, we describe an experimental setup making use of a microcontroller device: the Arduino Uno. This setup is designed as a game in order to improve students' understanding of color mixing.