Comparison of $S=0\mathrm{}$ and $S=\frac{1}{2}$ impurities in the Haldane chain compound ${\mathrm{Y}}_2{\mathrm{BaNiO}}_5$

We present the effect of Zn $\mathrm{}(S=0\mathrm{})\mathrm{}$ and Cu $\mathrm{}(S=1/2\mathrm{})\mathrm{}$ substitution at the Ni site of $S=1\mathrm{}$ Haldane chain compound ${\mathrm{Y}}_2{\mathrm{BaNiO}}_5.$ ${}^{89}\mathrm{Y}$ nuclear-magnetic resonance (NMR) allows us to measure the local magnetic susceptibility at different distances from the defects. The ${}^{89}\mathrm{Y}$ NMR spectrum consists of one central peak and several less intense satellite peaks. The central peak represents the chain sites far from the defect. Its shift measures the uniform susceptibility, which displays a Haldane gap $\Delta \approx 100\mathrm{K}$ and it corresponds to an antiferromagnetic (AF) coupling $J\approx 260\mathrm{K}$ between the nearest neighbor Ni spins. Zn or Cu substitution does not affect the Haldane gap. The satellites, which are evenly distributed on the two sides of the central peak, probe the antiferromagnetic staggered magnetization near the substituted site. The spatial variation of the induced magnetization is found to decay exponentially from the impurity for both Zn and Cu for $T>\mathrm{}50\mathrm{}\mathrm{K}.$ Its extension is found identical for both impurities and corresponds accurately to the correlation length $\xi \mathrm{}\left(T\right)\mathrm{}$ determined by Monte Carlo simulations for the pure compound. In the case of nonmagnetic Zn, the temperature dependence of the induced magnetization is consistent with a Curie law with an “effective” spin $S=0.4\mathrm{}$ on each side of Zn. This staggered effect is quantitatively well accounted for in all the explored range by quantum Monte Carlo (QMC) computations of the spinless-defect-induced magnetism. In the case of magnetic Cu, the similarity of the induced magnetism to the Zn case implies a weak coupling of the Cu spin to the nearest-neighbor Ni spins. The slight reduction of about $20-30\%$ of the induced polarization with respect to Zn is reproduced by QMC computations by considering an antiferromagnetic coupling of strength $J^{\prime }=0.1J-0.2J$ between the $S=1/2\mathrm{}$ Cu spin and nearest-neighbor Ni spin. Macroscopic susceptibility measurements confirm these results as they display a clear Curie contribution due to the impurities nearly proportional to their concentration. This contribution is indeed close to that of two spin half for Zn substitution. The Curie contribution is smaller in the Cu case, which confirms that the coupling between Cu and near-neighbor Ni is antiferromagnetic.