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Hexagonal-to-orthorhombic structural transitions in RAl$_3$C$_3$ have beenstudied by X-ray diffraction for R=Yb, Tm, Er, Dy, and Lu. We report howorthorhombic domains are controlled by adjusting external magnetic fields. Itis shown that orthorhombic domains in RAl$_3$C$_3$ can be aligned by the fieldwhen the R ion is magnetic. It is also shown that a single-domain state can beswitched to another single-domain state by the field even in paramagneticstates with small induced moments. For R=Lu, however, it was not possible tochange the multidomain state by a field of up to 70 kOe. We discuss that domainselection and switching are caused by magnetic anisotropies in the orthorhombicphase of RAl$_3$C$_3$. We also propose an idea to explain the field-inducedantiferromagnetism revealed by Khalyavin et al. [Phys. Rev. B \textbf{87},220406 (2013)].

Structural Domain Switching by Magnetic Fields in RAl$_3$C$_3$ (R=Rare Earth)