Magnetic Phase Diagram of ErB$_4$ as Explored by Neutron Scattering

The tetragonal $4f$-electron intermetallic ErB$_4$ is characterized by strong Ising anisotropy along the tetragonal $c$ axis. The magnetic moments on the erbium sites can be mapped onto a Shastry-Sutherland (SSL) lattice resulting in geometrical frustration. At zero magnetic field ErB$_4$ exhibits collinear columnar antiferromagnetic (CAFM) order below $T_\text{N} = 15.4$ K. In the presence of a magnetic field parallel to the $c$ axis, ErB$_4$ exhibits a plateau at $1/2$ of the saturation magnetization $M_\text{S}$, which arises at a spin flip transition at $H_1$ $=$ 1.9 T. Fractional magnetization plateaus and other exotic spin phases are a well-established characteristic feature of frustrated spin systems. Monte Carlo simulations propose that ErB$_4$ is an ideal candidate to feature a spin supersolid phase in close vicinity of $H_1$ between the CAFM and $M/M_\text{S}=1/2$ plateau (HP) phase. Here we combine single-crystal neutron diffraction and inelastic neutron scattering to study the magnetic phase diagram and the crystal electric field (CEF) ground state of ErB$_4$. Our measurements as a function of magnetic field find no signature of the spin supersolid phase but allow us to determine the magnetic structure of the HP phase to be of the uuud type consistent with an Ising material. The magnetic moment $\mu_{\mathrm{CEF}}$ $=$ 8.96 $\mu_B$ expected from the CEF configuration determined by our inelastic neutron scattering measurements is also consistent with the ordered moment observed in neutron diffraction showing that the moments are fully ordered and close to the Er$^{3+}$ free ion moment (9.6 $\mu_B$).