The spinel compounds ${\mathrm{MnSc}}_2{X}_4$ are highly frustrated and candidate materials for vortex-like 3 q magnetic states, such as skyrmions, with propagation vectors in the [111] plane. Because of the strong magnetoelastic coupling, we could extract a refined magnetic $(H,T)$ phase diagram for ${\mathrm{MnSc}}_2{\mathrm{S}}_4$ from ultrasound and dilatometry measurements. We found a variety of magnetic phases, including the skyrmion phase, which is stable down to lowest temperatures. In comparison, we investigated ${\mathrm{MnSc}}_2{\mathrm{Se}}_4$, having a larger distance between the magnetic ${\mathrm{Mn}}^{3+}$ ions using the same methods. Unlike in ${\mathrm{MnSc}}_2{\mathrm{S}}_4$, we found no skyrmion phase and overall a lack of sharp anomalies indicative of phase transitions, neither in dilatometry nor ultrasound nor in specific heat and ac-susceptibility data. Motivated by our findings, we performed model calculations, which reproduced the experimentally observed magnetostriction and specific-heat results reasonably well.

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• Frustrated magnetism
• Magnetic phase transitions
• Magnetostriction
• Skyrmions
• Mean field theory
• Monte Carlo methods
• Thermodilatometry
• Ultrasound techniques