Fractional Magnetization Plateaus and Magnetic Order in the Shastry-Sutherland Magnet ${\mathrm{TmB}}_4$

We investigate the phase diagram of ${\mathrm{TmB}}_4$, an Ising magnet on a frustrated Shastry-Sutherland lattice, by neutron diffraction and magnetization experiments. At low temperature we find Néel order at low field, ferrimagnetic order at high field, and an intermediate phase with magnetization plateaus at fractional values $M/M_{\mathrm{sat}}=1/7,1/8,1/9,\dots$ and spatial stripe structures. Using an effective $S=1/2$ model and its equivalent two-dimensional fermion gas we suggest that the magnetic properties of ${\mathrm{TmB}}_4$ are related to the fractional quantum Hall effect of a 2D electron gas.

Figure 1

(a) The phase diagram of ${\mathrm{TmB}}_4$ as derived from magnetization data for $B\parallel (001)$ (full symbols). (b) Magnetization at $T=2\mathrm{K}$ (open squares) and $T=3\mathrm{K}$ (open circles). The arrows indicate the direction of the field change. The inset in (b) gives an overview towards high field: lines are measured data, full circles are calculated using the high temperature approximation. The magnetic field data are corrected for demagnetization.

Figure 2

The magnetic structure of Ising spins in ${\mathrm{TmB}}_4$ in the tetragonal plane. For clarity only the domains along the $a$ direction are drawn. Red circles or blue circles indicate up or down moments, the different surface colors indicate the periodicity of the various stripe structures. The labels (i)–(iii) refer to the phase identification in Fig. 1a. In (i) the position of the ${\mathrm{Tm}}^{3+}$ ions in the tetragonal plane is expanded with the SS bonds marked in red. Note the almost identical length of exchange paths $J_1$ and $J_2$.

Figure 3

(a) and (b) show the neutron diffraction pattern in the tetragonal plane $q=(h,k,0)$ [with wave vectors $h,k$ in reciprocal lattice units (RLU)] for the intermediate and the plateau phase, respectively. The figures share the intensity color code given in (a). For the indexing of the AFM peaks see the text. The powder lines arise from aluminum in the “Orange” cryostat (a) and the “VM3” magnet cryostat [13] used for experiments in a field (b).