  Cubic f-electron compounds commonly exhibit highly anisotropic magnetic phase
diagrams consisting of multiple long-range ordered phases. Field-driven
metamagnetic transitions between them may depend not only on the magnitude, but
also on the direction of the applied magnetic field. Examples of such behavior
are plentiful among rare-earth borides, such as RB$_6$ or RB$_{12}$ ($R$ = rare
earth). In this work, for example, we use torque magnetometry to measure
anisotropic field-angular phase diagrams of La-doped cerium hexaborides,
Ce$_{1-x}$La$_x$B$_6$ ($x$ = 0, 0.18, 0.28, 0.5). One expects that
field-directional anisotropy of phase transitions must be impossible to
understand without knowing the magnetic structures of the corresponding
competing phases and being able to evaluate their precise thermodynamic energy
balance. However, this task is usually beyond the reach of available
theoretical approaches, because the ordered phases can be noncollinear, possess
large magnetic unit cells, involve higher-order multipoles of 4f ions rather
than simple dipoles, or just lack sufficient microscopic characterization. Here
we demonstrate that the anisotropy under field rotation can be qualitatively
understood on a much more basic level of theory, just by considering the
crystal-electric-field scheme of a pair of rare-earth ions in the lattice,
coupled by a single nearest-neighbor exchange interaction. Transitions between
different crystal-field ground states, calculated using this minimal model for
the parent compound CeB6, possess field-directional anisotropy that strikingly
resembles the experimental phase diagrams. This implies that the anisotropy of
phase transitions is of local origin and is easier to describe than the ordered
phases themselves.
