---
title: Disordered Perovskite BaCu1/3Ta2/3O3
url: https://www.emergentmind.com/topics/disordered-perovskite-bacu-_-1-3-ta-_-2-3-o-_3
type: topic
---

# Disordered Perovskite BaCu1/3Ta2/3O3

BaCu$_{1/3}$Ta$_{2/3}$O$_3$ (BCTO) is a three-dimensional disordered perovskite quantum magnet where magnetic Cu$^{2+}$ ($S = 1/2$) and non-magnetic Ta$^{5+}$ ions randomly occupy the B-sublattice of a pseudo-cubic ABO$_3$ unit cell in a 1:2 ratio. The random yet anti-clustered arrangement of B-site cations results in a structurally constrained distribution of magnetic exchange interactions. This scenario generates a quantum ground state composed of random spin singlets with a broad but bounded exchange spectrum, distinct from the conventional infinite-randomness fixed point associated with random-singlet phases [2601.17455].

## 1. Crystallography and Local Structure

Synchrotron X-ray diffraction (XRD) analyses show that BCTO crystallizes predominantly in a tetragonal perovskite lattice (P4/mmm, with a minority P4mm phase), with $c/a \approx 1$. Ba$^{2+}$ exclusively occupies the A-site. In both phases, Cu$^{2+}$ and Ta$^{5+}$ ions are distributed randomly over the B-site, resulting in nearly linear B–O–B superexchange paths (bond angle $\approx$ 180°). The minority P4mm phase features a slight B-site off-centering, resulting in minor additional broadening of exchange couplings.

X-ray absorption spectroscopy (XAS) at the Cu K- and Ta L$_{III}$-edges confirms the formal valences of the transition-metal cations. Extended X-ray absorption fine structure (EXAFS) measurements reveal that CuO$_6$ octahedra are strongly Jahn–Teller distorted with four short Cu–O$_1$ bonds ($R_{\rm CuO_1}=2.03(1)$ Å) and two long Cu–O$_2$ bonds ($R_{\rm CuO_2}=2.32(1)$ Å), whereas TaO$_6$ octahedra are nearly regular ($R_{\rm TaO}=1.98(1)$ Å). Coordination statistics demonstrate significant local chemical ordering: each Cu on average is neighbored by about $N_{\rm Cu-Ta} \approx 5.6$ Ta ions and $N_{\rm Cu-Cu} \approx 0.4$ Cu ions at the next B-site shell; Ta sites have $N_{\rm Ta-Cu} \approx 2.9$ and $N_{\rm Ta-Ta} \approx 3.1$. This chemical short-range order suppresses extended Cu–O–Cu superexchange networks and thus large magnetic cluster formation [2601.17455].

## 2. Magnetic Hamiltonian and Distribution of Exchange Interactions

At low temperatures, where no magnetic long-range order or spin freezing is observed down to 0.1 K, the effective low-energy physics is described by a random-bond spin-$1/2$ Heisenberg Hamiltonian,
$$
H = \sum_{\langle i,j\rangle} J_{ij}\, \mathbf{S}_i \cdot \mathbf{S}_j - g\mu_B \sum_i \mathbf{H} \cdot \mathbf{S}_i,
$$
where the sum runs over Cu–O–(Ta–O–)…–O–Cu exchange paths of varying length. The hetero-atomic local order and suppressed Cu clustering produce a broad yet intrinsically bounded distribution $P(J)$ of exchange constants, with multiple peaks corresponding to direct Cu–O–Cu, Cu–O–Ta–O–Cu (one intervening Ta), and longer exchange pathways involving two or more Ta ions.

The distribution $P(J)$ is empirically reconstructed from thermodynamic and magnetic data using a sum of log-normal components:
$$
P(J) = \sum_{k=1}^K w_k \frac{1}{J\,\sigma_k \sqrt{2\pi}} \exp \left[-\frac{(\ln J - \ln J_{0k})^2}{2\sigma_k^2} \right], \quad \sum_k w_k = 1,
$$
where $J_{0k}$, $\sigma_k$, and $w_k$ parameterize each log-normal peak, representing distinct exchange pathways. $P(J)$ remains finite as $J \to 0$, indicating the absence of truly vanishing exchange scales [2601.17455].

## 3. Magnetic and Thermodynamic Properties

Magnetic susceptibility $\chi(T)$ measured at fields $0.1$–$9$ T exhibits no evidence of long-range magnetic ordering or spin freezing down to $0.1$ K. At $T \gtrsim 50$ K, a Curie–Weiss fit gives an effective moment $\mu_{\rm eff} = 1.85(5)\,\mu_B$ and Weiss temperature $\theta_{\rm CW} = -35(10)\,$K—consistent with isolated Cu$^{2+}$ spins coupled antiferromagnetically. Below $10$ K, $\chi(T)$ displays a weak power-law divergence, $\chi(T) \propto T^{-\gamma}$, with $\gamma \approx 0.67$ in the range $4\,{\rm K} \gtrsim T \gtrsim 1\,{\rm K}$, and $M[H,T]$–scaling is observed for both susceptibility and isothermal magnetization $M(H)$, characteristic of systems with a broad distribution of energy scales.

Heat-capacity measurements $c_p(T, H)$ down to $0.1$ K reveal a broad Schottky-like anomaly. After subtracting the phonon contribution, the magnetic specific heat $c_{\rm mag}/T$ deviates from the $T^{-(1-\gamma)}$ prediction of the infinite-randomness random-singlet scenario. Instead, for $T \ll 1$ K, $c_{\rm mag}(T) \propto T$ (a Sommerfeld-like linear term) and scaling is absent. Integration of $c_{\rm mag}/T$ from $0.1$ to $20$ K yields a recovered entropy $\Delta S_{\rm mag} \approx 0.4\,R\ln2$, indicating 60% of Cu spins remain dynamic at the lowest measured temperature [2601.17455].

## 4. Distributed-Exchange Dimer plus Orphan Model

A combined quantitative fit to susceptibility, magnetization, and specific-heat data is achieved using a “distributed-exchange dimer plus orphan” model. In this description, a small fraction $f \approx 0.04$ of Cu spins act as free (orphan) monomers, while the majority form antiferromagnetic dimers whose exchange strength is drawn from the empirically reconstructed $P(J)$. The model employs standard expressions for the susceptibility and Schottky anomaly of $S=1/2$ dimers and monomers and achieves a global rms deviation $\lesssim 3\%$ across all magnetic field and temperature data sets.

This approach accommodates the residual Curie tail in $\chi(T)$, the linear-in-$T$ low-temperature specific heat, and the observed entropy recovery profile. The small orphan-spin fraction accounts for the nuclear Schottky contribution and matches the suppression of large-scale Cu–O–Cu networks indicated by local structure analysis [2601.17455].

## 5. Ground State and Theoretical Implications

In many random quantum magnets, especially in one dimension or highly frustrated lattices, strong-disorder renormalization group (RSRG) theory predicts flow to an infinite-randomness fixed point, resulting in a scale-free singlet-bond distribution,
$$
P_{\rm IRFP}(J) \propto J^{-\gamma}, \quad 0 < \gamma < 1,
$$
along with thermodynamic singularities $\chi \propto T^{-\gamma}$ and $c_{\rm mag} \propto T^{1-\gamma}$. In contrast, in BCTO, the disorder is unfrustrated and constrained by the structural and chemical correlations between Cu and Ta ions. The consequence is a bounded $P(J)$, finite as $J \to 0$, with peaks near $0.1$ K (long exchange paths), $4$ K (paths with one Ta), and $70$ K (direct Cu–O–Cu). This prevents flow to an infinite-randomness fixed point.

At the lowest temperatures, the specific heat recovers to a linear $T$ dependence and scaling collapses in $c_p$ are lost, consistent with a finite-randomness regime. Approximately 60% of magnetic entropy remains unquenched at $0.1$ K, supporting the presence of a highly dynamic singlet network rather than a frozen or ordered state [2601.17455].

## 6. Broader Context and Relevance

The results place BaCu$_{1/3}$Ta$_{2/3}$O$_3$ within a new category of three-dimensional quantum magnets in which "structurally constrained" randomness creates a broad yet bounded distribution of magnetic interactions. No magnetic ordering or spin freezing is found despite a Cu-site occupancy above the percolation threshold for the cubic lattice. The system provides an archetype for experimentally realizing a random quantum singlet ground state not governed by the infinite-randomness scenario, but by a finite-randomness RG flow. A plausible implication is the engineering of quantum spin liquid–like ground states via controlled disorder and cation ordering, providing an alternative to magnetic frustration as a route to quantum-disordered phases. This scenario may be relevant for other structurally disordered oxides and points to new experimental strategies for exploring three-dimensional disordered quantum magnetism [2601.17455].

Source: https://www.emergentmind.com/topics/disordered-perovskite-bacu-_-1-3-ta-_-2-3-o-_3