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arXiv:cond-mat/0003147 · Physical review. B, Condensed matter

Evidence of quantum criticality in the doped Haldane system Y2BaNiO5

C. Payen, Étienne Janod, K. Schoumacker, C. D. Batista, K. Hallberg, Armando A. Aligia

Published Aug 1, 2000• 24 citations
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Abstract

Experimental bulk susceptibility $\ensuremath{\chi}(T)$ and magnetization $M(H,T)$ of the $S=1$ Haldane chain system doped with nonmagnetic impurities, ${\mathrm{Y}}_{2}{\mathrm{BaNi}}_{1\ensuremath{-}x}{\mathrm{Zn}}_{x}{\mathrm{O}}_{5}$ $(x<~0.08),$ are analyzed. A numerical calculation for the low-energy spectrum of noninteracting open segments describes well experimental data above 4 K. Below 4 K, we observe power-law behaviors $\ensuremath{\chi}(T)\ensuremath{\sim}{T}^{\ensuremath{-}\ensuremath{\alpha}}$ and $M(H,T)\ensuremath{\sim}{T}^{1\ensuremath{-}\ensuremath{\alpha}}{f}_{\ensuremath{\alpha}}(H/T),$ with $\ensuremath{\alpha}(<1)$ depending on the doping concentration x. This observation suggests the appearance of a gapless quantum phase due to a broad distribution of effective couplings between the dilution-induced moments.

DOI
10.1103/physrevb.62.2998

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Experimental bulk susceptibility \ensuremathχ(T)\ensuremath{\chi}(T)\ensuremathχ(T) and magnetization M(H,T)M(H,T)M(H,T) of the S=1S=1S=1 Haldane chain system doped with nonmagnetic impurities, Y2BaNi1\ensuremath−xZnxO5{\mathrm{Y}}_{2}{\mathrm{BaNi}}_{1\ensuremath{-}x}{\mathrm{Zn}}_{x}{\mathrm{O}}_{5}Y2​BaNi1\ensuremath−x​Znx​O5​ (x< 0.08),(x<~0.08),(x< 0.08), are analyzed. A numerical calculation for the low-energy spectrum of noninteracting open segments describes well experimental data above 4 K. Below 4 K, we observe power-law behaviors \ensuremathχ(T)\ensuremath∼T\ensuremath−\ensuremathα\ensuremath{\chi}(T)\ensuremath{\sim}{T}^{\ensuremath{-}\ensuremath{\alpha}}\ensuremathχ(T)\ensuremath∼T\ensuremath−\ensuremathα and M(H,T)\ensuremath∼T1\ensuremath−\ensuremathαf\ensuremathα(H/T),M(H,T)\ensuremath{\sim}{T}^{1\ensuremath{-}\ensuremath{\alpha}}{f}_{\ensuremath{\alpha}}(H/T),M(H,T)\ensuremath∼T1\ensuremath−\ensuremathαf\ensuremathα​(H/T), with \ensuremathα(<1)\ensuremath{\alpha}(<1)\ensuremathα(<1) depending on the doping concentration x. This observation suggests the appearance of a gapless quantum phase due to a broad distribution of effective couplings between the dilution-induced moments.
Experimental bulk susceptibility X(T) and magnetization M(H,T) of the S=1-Haldane chain system doped with nonmagnetic impurities, Y2BaNi1-xZnxO5 (x=0.04,0.06,0.08), are analyzed. A numerical calculation for the low-energy spectrum of non-interacting open segments describes very well experimental data above 4 K. Below 4 K, we observe power-law behaviors, X(T)=T^-alpha and M(H,T)/T^(1-alpha)=f(alpha,(H/T)), with alpha (<1) depending on the doping concentration x.This observation suggests the appearance of a gapless quantum phase due to a broad distribution of effective couplings between the dilution-induced moments.
We present the effect of Zn (S=0)(S=0)(S=0) and Cu (S=1/2)(S=1/2)(S=1/2) substitution at the Ni site of S=1S=1S=1 Haldane chain compound Y2BaNiO5.{\mathrm{Y}}_{2}{\mathrm{BaNiO}}_{5}.Y2​BaNiO5​. 89Y{}^{89}\mathrm{Y}89Y nuclear-magnetic resonance (NMR) allows us to measure the local magnetic susceptibility at different distances from the defects. The 89Y{}^{89}\mathrm{Y}89Y 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 $\ensuremath{\Delta}\ensuremath{\approx}100\mathrm{K}$ and it corresponds to an antiferromagnetic (AF) coupling $J\ensuremath{\approx}260\mathrm{K}$ 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>50K.T>50\mathrm{K}.T>50K. Its extension is found identical for both impurities and corresponds accurately to the correlation length $\ensuremath{\xi}(T)$ 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=0.4S=0.4S=0.4 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 $20\ensuremath{-}30%$ of the induced polarization with respect to Zn is reproduced by QMC computations by considering an antiferromagnetic coupling of strength ${J}^{\ensuremath{'}}=0.1J\ensuremath{-}0.2J$ between the S=1/2S=1/2S=1/2 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.
Open segments of S=1S=1S=1 antiferromagnetic spin chains are studied at finite temperatures and fields using continuous time quantum Monte Carlo techniques. By calculating the resulting magnetization profiles for a large range of chain lengths with fixed field and temperature we reconstruct the experimentally measured NMR spectrum of impurity doped ${\mathrm{Y}}_{2}{\mathrm{BaNi}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{O}}_{5}.$ For temperatures above the gap the calculated NMR spectra are in excellent agreement with the experimental results, confirming the existence of S=1/2S=1/2S=1/2 excitations at the end of open S=1S=1S=1 chain segments. At temperatures below the gap, neglecting interchain couplings, we still find well defined peaks in the calculated NMR spectra corresponding to the S=1/2S=1/2S=1/2 chain end excitations. At low temperatures, interchain couplings could become important, resulting in a more complicated phase.
Using the density matrix renormalization-group technique, we calculate the impurity energy levels for two different effective models of off-chain doping for quasi-one-dimensional Heisenberg chain compound Y2BaNiO5:{\mathrm{Y}}_{2}{\mathrm{BaNiO}}_{5}:Y2​BaNiO5​: ferromagnetic bond doping and antiferromagnetic site spin-1/2 doping. Thresholds of the impurity strength for the appearance of localized states are found for both models. However, the ground-state and low-energy excitations for weak impurity strength are different for these two models and the difference can be detected by experiments.
We present a static, model-independent, experimental determination of the spin-spin correlation length $\ensuremath{\xi}$ in a quantum spin system. This is achieved in the doped Haldane (i.e., S=1S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1S=1 Heisenberg antiferromagnetic) chain ${\mathrm{Y}}_{2}{\mathrm{BaNi}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{O}}_{5}$ by 89Y{}^{89}\mathrm{Y}89Y NMR imaging of the staggered magnetization induced around the Mg impurities (i.e., chain boundaries) by a magnetic field. The magnitude of this magnetization is found to decay exponentially, with $\ensuremath{\xi}$ equal to the theoretical prediction for an infinite S=1S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1S=1 chain and the staggered magnetic moment at the edge site showing the Curie behavior of an effective S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=1/2 spin.
Using an impurity density-matrix renormalization-group scheme, we establish a reliable picture of how the low-lying energy levels of an S=1S=1S=1 Heisenberg antiferromagnetic chain change quantitatively upon bond doping. An impurity state gradually occurs in the Haldane gap as ${J}^{\ensuremath{'}}<J$, while it appears only if $\frac{{J}^{\ensuremath{'}}}{J}>{\ensuremath{\gamma}}_{c}$ with $\frac{1}{{\ensuremath{\gamma}}_{c}}=0.708$ as ${J}^{\ensuremath{'}}>J$. The spin polarization in the impurity state shows a localization-delocalization transition at ${\ensuremath{\gamma}}_{c}$. The system is nonperturbative as $1<~\frac{{J}^{\ensuremath{'}}}{J}<~{\ensuremath{\gamma}}_{c}$. It can explain the appearance of a new state in the Haldane gap recently observed experimentally on ${\mathrm{Y}}_{2\ensuremath{-}x}{\mathrm{Ca}}_{x}\mathrm{BaNi}{\mathrm{O}}_{5}$ [J.F. DiTusa et al., Phys. Rev. Lett. 73, 1857 (1994)].