Disordered Quantum Ground State in Perovskites

• Disordered quantum ground states are defined by quenched disorder in magnetic lattices that leads to a finite, bounded distribution of exchange interactions, precluding conventional long-range order.
• Magnetic measurements reveal a Curie–Weiss response with a power-law divergence and scaling collapse in magnetization, indicating robust quantum fluctuations down to sub-Kelvin temperatures.
• The distributed-exchange-dimer model captures key experimental signatures such as Schottky-like peaks and partial entropy recovery, suggesting tunability of quantum phases in perovskite systems.

A disordered quantum ground state is a quantum magnetic state that emerges in systems where the underlying lattice is subject to quenched disorder, leading to a broadly distributed but finite set of magnetic exchange interactions. In such systems, randomness is not merely a perturbation but an essential structural feature that fundamentally reshapes the low-temperature magnetic properties, often precluding conventional long-range order or simple spin-glass behavior. Disordered quantum ground states provide a distinct platform for studying the interplay between randomness, quantum fluctuations, and dimensionality, resulting in exotic emergent phenomena such as random-singlet phases and departures from known universality classes (Mahapatra et al., 24 Jan 2026).

1. Structural Foundations and Disorder Mechanisms

In BaCu$_{1/3}$Ta$_{2/3}$O$_3$ (BCTO), a representative three-dimensional perovskite, the presence of disorder stems from the random occupation of the pseudo-cubic B-sites by Cu$^{2+}$ (S = 1/2) and Ta$^{5+}$ ions in a 1:2 ratio. High-resolution synchrotron X-ray diffraction (XRD) establishes two closely related tetragonal variants (P4/mmm and P4mm), differentiated primarily by minor B-site off-centering in P4mm. In both, Ba$^{2+}$ occupies the central A-site, while Cu/Ta atoms are distributed statistically on cube corners, resulting in a nearly cubic unit cell with $c/a\approx1$.

Extended X-ray absorption fine-structure (EXAFS) experiments at the Cu K-edge and Ta L$_3$-edge provide local insight. The CuO$_6$ site is Jahn–Teller distorted (four short Cu–O bonds at $R\approx2.03$ Å and two long at $R\approx2.30$ Å), while the TaO$_6$ octahedron is nearly regular ($R\approx1.98$ Å). EXAFS coordination analysis reveals “chemical-ordering” — around each Ta, neighboring Cu and Ta atoms are nearly equally probable ($N_{\mathrm{Ta-Cu}}\approx2.9$, $N_{\mathrm{Ta-Ta}}\approx3.1$), but Cu atoms predominantly neighbor Ta ($N_{\mathrm{Cu-Ta}}\approx5.6$, $N_{\mathrm{Cu-Cu}}\approx0.4$). This motif suppresses direct Cu–O–Cu superexchange in favor of Cu–O–Ta–O–Cu and longer exchange paths and prevents proliferation of arbitrarily weak Cu–Cu bonds, structurally enforcing a finite minimum spacing in the magnetic network (Mahapatra et al., 24 Jan 2026).

2. Magnetic Properties and Absence of Order

Magnetic susceptibility $\chi(T)$ measurements in BCTO, down to 0.1 K and up to 9 T, show no anomalies indicative of long-range magnetic order or spin-glass freezing. Above 3 K, the data adhere to a Curie–Weiss law with $\mu_{\mathrm{eff}} = 1.85\,\mu_B$ (characteristic of $S=1/2$) and $\theta_{CW}\approx -35$ K. Zero-field-cooled and field-cooled susceptibility curves are indistinguishable, confirming the absence of conventional spin freezing.

For $T<10$ K, $\chi(T)$ diverges as $\chi(T)\propto T^{-\gamma}$ with $\gamma\approx0.67$ down to approximately 4 K. In applied fields, both $\chi$ and magnetization $M(H,T)$ obey the “random singlet” $M[H,T]$-scaling, exhibiting a collapse when plotted as $(\mu_0 H)^{\gamma}\chi$ versus $T/\mu_0 H$ or $M/T^{1-\gamma}$ versus $H/T$. This scaling behavior is emblematic of a disordered quantum ground state with significant randomness in exchange interactions (Mahapatra et al., 24 Jan 2026).

3. Distribution of Exchange Couplings and Theoretical Modeling

The absence of long-range order is accompanied by a broad, non-singular distribution $P(J)$ of exchange couplings $J$. Heat capacity data show a Schottky-like peak in $c_p/T$ at low temperature, shifting with applied magnetic field. Integrating the extracted magnetic component $c_{\mathrm{mag}}(T)$ up to ~20 K recovers only approximately $0.4\,R\,\ln2$ of magnetic entropy, indicating that about 60% of spin-1/2 degrees of freedom remain unquenched by 0.1 K.

A “distributed-exchange-dimer” model rationalizes these results, representing the system as an ensemble of antiferromagnetic dimers with a broad but bounded distribution of $J$, plus a fraction $f\approx4\%$ of free spins. Here, $P(J)$ is modeled as a sum of $K$ weighted log-normal components: $$P(J) = \sum_{k=1}^K w_k \left[\frac{1}{J\sigma_k\sqrt{2\pi}}\right] \exp\left\{-\frac{(\ln J - \ln J_{0k})^2}{2\sigma_k^2}\right\}$$ with $\sum_k w_k = 1$. Joint fits to susceptibility, magnetization, and specific heat reveal $P(J)$ spans more than two decades in $J$:

• Dominant peak near $J\approx4$ K (Cu–O–Ta–O–Cu paths)
• Higher energy shoulder at $J\sim70$ K (direct Cu–O–Cu)
• Low-energy tail for $J<0.1$ K (longer Cu–O–(Ta–O)$_n$–Cu)
• Importantly, $P(J)$ remains finite as $J\rightarrow0$ rather than showing the $J^{-\gamma}$ divergence of the infinite-randomness fixed point (Mahapatra et al., 24 Jan 2026).

4. Deviation from Infinite-Randomness Fixed Point Phenomenology

Canonical random-singlet (RS) phases—encountered on one-dimensional chains and highly frustrated lattices—are governed by an infinite-randomness fixed point, leading to a power-law divergence $P(J)\propto J^{-\gamma}$ as $J\to0$, with $\gamma\approx0.67$ for the present case. These phases display divergent low-$T$ susceptibilities and sublinear heat capacity exponents, $c_{\mathrm{mag}}(T)\propto T^{1-\gamma}$ (i.e., $T^{0.33}$), and scaling of $(\mu_0 H)^{\gamma}c_p/T$ versus $T/\mu_0 H$.

In BCTO, while intermediate-$T$ susceptibility and $M[H,T]$ scaling reflect RS-like physics, at the lowest energies the bounded $P(J)$ produces a crossover in $c_{\mathrm{mag}}(T)$ to an approximately linear-in-$T$ regime, inconsistent with infinite-randomness behavior. This departure arises from the structural constraints discussed above, which cut off the low-$J$ tail and inhibit the proliferation of arbitrarily weak singlets. The resulting disordered quantum ground state thus resides in an intermediate regime between pure RS and conventional magnetism, defined by finite density of weak bonds and unique thermodynamic signatures (Mahapatra et al., 24 Jan 2026).

5. Experimental Signatures and Data Synthesis

The defining experimental signatures of this bounded-disorder quantum ground state include:

• Absence of magnetic order or glassiness down to 0.1 K
• Overlapping zero-field-cooled and field-cooled $\chi(T)$ curves
• Intermediate-$T$ power-law divergence in $\chi(T)\propto T^{-\gamma}$
• $M[H,T]$ scaling collapse for both $\chi$ and $M$
• Broad, field-dependent Schottky-like peaks in $c_p/T$ at low $T$
• Magnetic entropy recovery limited to $\sim$40% of $R\ln2$ up to 20 K
• Crossover of $c_{\mathrm{mag}}(T)$ to linearity at lowest $T$ (not obeying RS scaling)

The bounded distribution $P(J)$ supports these phenomena and is required to fit all experimental thermodynamic and magnetic data (Mahapatra et al., 24 Jan 2026).

6. Broader Implications and Prospects for Tunability

Disordered quantum ground states of this type indicate that three-dimensional disordered perovskites—where local structural motifs limit the extent of exchange randomness—enable realization of novel quantum phases distinct from both glassy and pure RS behaviors. By tuning B-site disorder, chemical constituents, strain, or ordering patterns (e.g., exploring A Cu$_{1/3}$M$_{2/3}$O$_3$ with M = Nb, Sc, etc.), it is possible to engineer specific $P(J)$ profiles, systematically navigating the parameter space between bounded and scale-free randomness.

Such tunability positions disordered perovskite magnets as prime platforms for investigating disorder-driven quantum phenomena and testing the limits of random-singlet criticality in higher spatial dimensions. Extensions to related ABO$_3$ frameworks with half-occupied spin-1/2 sublattices hold potential for uncovering further varieties of bounded-$P(J)$ quantum ground states, thereby enhancing the understanding of quantum magnetism under structural randomness (Mahapatra et al., 24 Jan 2026).