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Quantum critical point in CuGeO3 doped with magnetic impurities

Using high frequency (up to 450 GHz) ESR and low temperature specific heat measurements we find that insertion of 1% Fe and 2% Co damps spin-Peierls and Neel transitions and for T<30K gives rise to onset of a quantum critical behaviour characteristic for a random dimer Griffiths phase.

Most of the available data for doped inorganic spin-Peierls compound CuGeO 3 correspond to the limit of weak disorder when density of states have a pseudogap [1,2]. In the oppposite case of a strong disorder the situation is expected to change dramatically: the ground state of CuGeO 3 should be a Griffiths phase (GP) which thermodynamic properties are controlled by relatively rare spin clusters correlated more strongly than average [3,4]. In this case density of states becomes gapless and diverges at ǫ=0: ρ(ǫ)∝|ǫ| −α [1]. As a consequence the temperature dependences of magnetic susceptibility χ and magnetic contribution to specific heat c m for Cu 2+ spin-Peierls chains acquire the forms [3,4] where α<1. As long as T =0 becomes singular or critical point, the aforementioned situation may be described in terms of quantum critical (QC) behaviour [3].
The experimental information about feasibility of the QC point in CuGeO 3 is very limited [5]. The aim of the present work consists in providing possible evidence of onset of the QC point in CuGeO 3 doped with magnetic impurities Co and Fe.
Single crystals of CuGeO 3 doped with 1% of Fe (S=1) and 2% of Co (S=3/2) impurities have been grown using self-flux method. The quality of crystals was controlled by X-ray and Raman scattering data [6]. Magnetic properties of the samples in the temperature range 1.7-300K have been studied by high (up to 450 GHz) frequency ESR technique [2] for B a geometry. Specific heat for the temperature interval 6-20K was studied with the help of low temperature small sample relaxation calorimeter.
Doping of CuGeO 3 with magnetic impurities causes (i) rapid damping of the spin-Peierls transition and (ii) onset of a strong paramagnetic background [7]. Therefore the deriving of the effects of doping on Cu 2+ S=1/2 chains in convenient magnetisation measurements requires ad hoc assumptions about background behaviour [7]. This difficulty overcomes in ESR experiment, where magnetic impurity in CuGeO 3 matrix and Cu 2+ chains modified by impurity gives rise to a different absorption lines [8].
Typical magnetoabsorption spectra for CuGeO 3 :Co and CuGeO 3 :Fe at helium temperatures are shown in Fig.1. For the Co-doped sample spectrum is formed by two broad lines which becomes resolved for frequencies ν>100 GHz. The spectrum of Fe-doped sample is characterised by a single resonance. The reso- nant fields B res for all modes presented in Fig.1 are found to vary linearly with frequency B res ∼ν. This result suggests that the observed magnetoabsorption features correspond to different ESR modes rather than coexistence of the ESR and antiferromagnetic resonance [1].
The analysis of the g-factor values together with the frequency and temperature dependences of the linewidth [2] have allowed to attribute the high field resonances with g≈2.15 to ESR on disordered Cu 2+ chains and the low field resonance with g≈4.7 for CuGeO 3 :Co to ESR on Co 2+ impurity in CuGeO 3 matrix (Fig.1). A strong g-factor renormalisation for the Co-doped sample may reflect formation of the impurity spin clusters [8].
As long as the integrated intensity of the ESR line in the region of linear response is proportional to magnetic susceptibility it was possible to subtract contributions of Cu 2+ chains and Co 2+ impurities unambiguously and find χ(T ) dependence for both contributions from the spectra taken at different temperatures (Fig.2). The correctness of the χ(T ) evaluation from ESR spectra has been checked by measurements of the static susceptibility for Co-doped sample by vibrating sample magnetometer. We found that sum of χ(T ) for Cu 2+ and Co 2+ resonances represents the integral static susceptibility of the sample within the error of less than 5%.
Quantitative analysis of χ(T ) data for doped Cu 2+ chains indicates that Eq.(1) holds for T <30K (curves 1 and 2 in Fig.2) and the power law provides reasonable description of experimental data. The best fit was obtained using index values α =0.36±0.03 and α =0.69±0.04 for Fe-doped and Co-doped crystals respectively. In contrast to the magnetic properties of Cu 2+ chains, the susceptibility for Co 2+ impurity is better fitted by Curie-Weiss law, χ∼1/(T -Θ), with characteristic temperature Θ =-2.8K (Fig.2, curve 3) corresponding to antiferromagnetically interacting Co 2+ impurities. For doped Cu 2+ chains it is visible that for magnetic impurities studied spin-Peierls and Neel transitions are already damped.
The observation of the power asymptotics of χ(T ) in the absence of any type of long range magnetic order for the wide range 1.7<T <30K (where temperature varies more than 15 times) agrees with the theoretical predictions [3,4] for the QC point. An additional argument in favour of proposed interpretation follow from specific heat data for CuGeO 3 :Fe. It was found [2] that magnetic contribution c m follows power law with the index α =0.37±0.03 which coincide within experimental error with the value obtained from magnetic susceptibility.
In conclusion, we provide possible experimental evidence that doping of CuGeO 3 with magnetic impurities Co and Fe induces a strong disorder limit and low temperature T <30K ground state may become a GP. A magnetic structure  of the clusters in GP, including the possibility of the predicted in [9] random dimer phase, is a subject of future investigations.