Fig. 2

a Magnetoresistance of CeIn₃ at 600 mK for fields up to 92 T along the directions [100], [110], and [111]. While for both the [110] (blue) and [111] (red) directions a break in slope (marked by arrows) indicates the destruction of the AFM order at a critical field H _c ≈ 60 T, the AFM phase exists up to substantially larger fields H _c  ≈ 80 T along the [100] direction (black). b Calculated crystal field-level spectrum of CeIn₃ for fields along [100] and [111]. For H//[100] the upper energy level of the field-split ground-state doublet and the lowest-energy state of the upper quartet (bold lines) anticross in the field range where the critical field anisotropy appears. The overlap of each wavefunction with the ground-state doublet in zero field \(\left( {{W_{{\Gamma _7}}} \equiv {{\left\| {\left\langle {\Gamma _7^1|\Psi } \right\rangle } \right\|}^2} + {{\left\| {\left\langle {\Gamma _7^2|\Psi } \right\rangle } \right\|}^2}} \right)\) is shown with the color scale. For H//[100] the two lowest-energy states retain the orbital character of the zero field Γ₇ doublet (green) up to ≈40 T. Above 40 T the orbital character of the upper energy state of the field-split doublet obtains some Γ₈ character (purple). Similar mixing is not appreciable for H//[111] because the lowest-energy state of the quartet is the eigenstate of (J ^x + J ^y + J ^z)/\(\sqrt 3\) with eigenvalue 3/2. This state and its time-reversed partner (−3/2) cannot mix with any of the other four states because they transform differently under a ±2π/3 rotation about the [111] axis