Magnetization plateau observed by ultrahigh-field Faraday rotation in the kagome antiferromagnet herbertsmithite

To capture the high-field magnetization process of herbertsmithite ${[\mathrm{ZnCu}}_3{\left(\mathrm{OH}\right)}_6{\mathrm{Cl}}_2]$, Faraday rotation (FR) measurements were carried out on a single crystal in magnetic fields of up to 190 T. The magnetization data evaluated from the FR angle exhibited a saturation behavior above 150 T at low temperatures, which was attributed to the 1/3 magnetization plateau. The overall behavior of the magnetization process was reproduced by theoretical models based on the nearest-neighbor Heisenberg model. This suggests that herbertsmithite is a proximate kagome antiferromagnet hosting an ideal quantum spin liquid in the ground state. A distinguishing feature is the superlinear magnetization increase, which is in contrast to the Brillouin function-type increase observed by conventional magnetization measurements and indicates a reduced contribution from free spins located at the Zn sites to the FR signal.

Figure 1

Magnetic sublattice of herbertsmithite. Red spheres represent ${\mathrm{Cu}}^{2+}$ ions, and red-blue spheres disordered sites with mixed occupancy of ${\mathrm{Cu}}^{2+}$ and ${\mathrm{Zn}}^{2+}$. Red and grey sticks represent the kagome net intra- and interplane bonds with the disordered sites (${\mathrm{Zn}}^{2+}$/${\mathrm{Cu}}^{2+}$), respectively.

Figure 2

Evolution of Faraday rotation angle with magnetic field at the temperatures of 6 K (pale blue) and 10 K (pale red). The red and blue solid lines are results of polynomial fitting to the data at 6 and 10 K, respectively. The magnetic field was applied along the [101] axis of the herbertsmithite crystal. The dashed line indicates the position of the magnetization plateau starting from $B_p\sim 150\mathrm{T}$.

Figure 3

Local coordination environment of Cu sites. (a) Cu on a kagome plane, and (b) of a disordered site at an interlayer between kagome planes.

Figure 4

Comparison of normalized FR data with theoretical calculations: normalized FR data at 6 K (blue) and 10 K (red), magnetization data measured by induction method (thin black) [43], calculation of $S=1/2$ Heisenberg kagome antiferromagnet by tensor network (PEPS) [42] (purple dotted line) and exact diagonalization (ED) [47] (dashed sky blue), and $S=1/2$ Heisenberg kagome antiferromagnet with random interaction by exact diagonalization (EDR) [26] (green circle with line). The FR data are normalized by the NN interaction and the FR at the full magnetization, which are assumed to be 250 K and 90°, respectively.