Dilution-Controlled Quantum Criticality in Rare-Earth Nickelates

A microscopic model for the diluted spin-mixed compounds $(R_x{\mathrm{Y}}_{1-x}{)}_2{\mathrm{B}\mathrm{a}\mathrm{N}\mathrm{i}\mathrm{O}}_5$ ($R=\mathrm{\text{magnetic}}$ rare earth) is studied using quantum Monte Carlo simulations. The ordering temperature is shown to be a universal function of the impurity concentration $x$ and the intrinsic Ni-chain correlation length. An effective model for the critical modes is derived. The possibility of a quantum critical point driven by the rare-earth concentration and the existence of a quantum Griffiths phase in the high dilution limit is investigated. Several possible experimental approaches to verify the results are put forward.

Figure 1

(a) Critical temperature $T_c$ as a function of the correlation length in the independent ITF chain ${\xi }_{\mathrm{c}\mathrm{h}}$, for different concentrations of $R$ using a periodic dilution pattern and $J_c=0.2$. The dashed line indicates the value of the gap of the independent chain ($k_B=\hslash =1$). This energy scale separates the two completely different behaviors at $T_c={\Delta }_{\mathrm{c}\mathrm{h}}$ showing that the 1D features of the gapped chains survive even at the critical point. (b) Universal dependence of the critical temperature on the dimensionless variable $x{\xi }_{\mathrm{c}\mathrm{h}}$ at high dilutions. The dashed line is a fit to $T_c(x=1)$ using 2D ANI with $J_{\parallel }=J{\overline{S}}^2$ and$J_{\perp }=\kappa J_c{\overline{S}}^2(\kappa =2.25)$. The thick solid line corresponds to the same model with $J_{\parallel }={\rho }_0\exp (-1/x{\xi }_{\mathrm{c}\mathrm{h}})$ with ${\rho }_0=1.15J$ and $J_{\parallel }=0.13J$. Inset: $T_c(x{\xi }_{\mathrm{c}\mathrm{h}})$ for 2D ANI with $J_{\parallel }=\rho (x,{\xi }_{\mathrm{c}\mathrm{h}}){\overline{S}}^2,J_{\perp }={\overline{S}}^2$ with $\rho (x,{\xi }_{\mathrm{c}\mathrm{h}})$ being the stiffness of the independent ITF chain.

Figure 2

Finite-size analysis of the order parameter in the vicinity of the critical point for $J_c=0.1$, $\Gamma =1.25$, $x=0.5$, and $T_c=0.13$ in the randomly diluted system. Here the data collapse is achieved with $\beta =\frac{1}{8}$ and $\nu =1$, the exponents of the 2D Ising model.

Figure 3

(a) Critical temperature $T_c(x)$ as for Hamiltonians (1, 2) with different model parameters. A randomly diluted pattern is used in all the cases. The arrows show the value of the inverse correlation length for each model. (b) Generic zero-temperature phase diagram of the randomly diluted system described in the text. The paramagnetic (PM) region is a Griffiths-McCoy region. Note that the phase boundary of the ordered phase approaches ${\Gamma }_{\mathrm{e}\mathrm{f}\mathrm{f}}=0$ at $x=0$ with an essential singularity. The value of ${\Gamma }_c$ corresponds to the quantum critical point (QCP) of the pure system (see the text).