Real Space Imaging of Spin Polarons in Zn-Doped ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$

We report on the real space profile of spin polarons in the quasi-two-dimensional frustrated dimer spin system ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$ doped with 0.16% of Zn. The ${}^{11}\mathrm{B}$ nuclear magnetic resonance spectrum exhibits 15 additional boron sites near nonmagnetic Zn impurities. With the help of exact diagonalizations of finite clusters, we have deduced from the boron spectrum, the distribution of local magnetizations at the Cu sites with fine spatial resolution, providing direct evidence for an extended spin polaron. The results are confronted with those of other experiments performed on doped and undoped samples of ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$.

Figure 1

${}^{11}\mathrm{B}$ NMR spectrum at $T=1.6\mathrm{K}$ and $B=6.615\mathrm{T}$. The black arrows mark the position of the reference line (zero internal field). Fifteen additional lines named ${\mathrm{B}}_1$ to ${\mathrm{B}}_{15}$ have been resolved. Note that ${\mathrm{B}}_1$ is about twice as intense as ${\mathrm{B}}_2$, and that ${\mathrm{B}}_{12}$ (shaded in blue) is also about twice as intense as ${\mathrm{B}}_{11}$ (shaded in orange).

Figure 2

Real space sketch of the spin polaron formed around a Zn impurity (cross). The up (down) arrows on the Cu sites represent the spin moments parallel (antiparallel) to the external field. The length of the arrow is proportional to $|⟨S_z⟩|$ as calculated on a 36-site cluster with $J^{\prime }/J=0.67$. The numbers show the assignment of the B sites to the NMR lines of Fig. 1 deduced from the analysis described in the text. Primed numbers have been used when different sites are assigned to the same line. The other B sites have very small internal field.

Figure 3

(a) Main hyperfine couplings between a Cu spin and the B nuclei in the same layer ($A_1$ and $A_2$) or in the neighboring layers ($A_3$ or $A_4$). (b) Quadrupolar splitting ${\nu }_Q$ for B sites near a Zn impurity. (c) Dependence on $\alpha =J^{\prime }/J$ of the local magnetization calculated with exact diagonalizations on a 32-site cluster (open symbols) and 36-site cluster (solid symbols).

Figure 4

(a) $B_{\mathrm{int}}$ at the B sites calculated by using the spin density distribution with $\alpha =0.665$ for 36 sites (upper panel) and $B_{\mathrm{int}}$ deduced from experiment (lower panel). The data near $B_{\mathrm{int}}=0\mathrm{T}$ are expanded in Fig. 4. The thickness of the lines in the lower panel indicates the half width at the half maximum of the corresponding peaks of the NMR spectrum. In the calculated histograms, red solid lines correspond to B sites in the layer of the Zn impurity, green dotted (blue dashed) lines to B in the adjacent layer above (below) the impurity, and the height is proportional to the number of B sites having exactly the same internal field (1 or 2).