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Random singlet physics in exchange disordered 2D triangular YbCu $_{1.14}$ Se $_2$

Although YbCu $_{1.14}$ Se $_2$ lacks magnetic order, significant structural disorder prevents a quantum spin liquid ground state, leading instead to a universal 2D random singlet phase characterized by a distribution of singlet formations.

Original authors: Caitlin S. T. Kengle, Sean M. Thomas, Roman Movshovich, Shengzhi Zhang, Eun Sang Choi, Minseong Lee, Priscila F. S. Rosa, Allen O. Scheie

Published 2026-03-02

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Original authors: Caitlin S. T. Kengle, Sean M. Thomas, Roman Movshovich, Shengzhi Zhang, Eun Sang Choi, Minseong Lee, Priscila F. S. Rosa, Allen O. Scheie

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: When a Perfect Dance Floor Gets Crowded

Imagine a giant, perfectly flat dance floor where dancers (atoms) are supposed to hold hands and spin in a specific, chaotic pattern. Physicists have been looking for a special kind of dance called a Quantum Spin Liquid (QSL).

In a QSL, the dancers never settle down into a rigid line or a static pose, even when the music stops (the temperature gets near absolute zero). Instead, they keep jiggling and entangling with each other in a weird, fluid state. This is a "holy grail" of physics because it could lead to super-fast quantum computers.

However, finding a real material that does this is incredibly hard. It's like trying to get a perfect dance floor, but the floor is slightly uneven, or there are random holes in it. Usually, these imperfections ruin the dance, causing the dancers to freeze up in a messy pile (a "spin glass") instead of doing the fluid QSL dance.

The Experiment: YbCu1.14Se2

The scientists in this paper studied a material called YbCu1.14Se2. Think of this material as a triangular dance floor made of Ytterbium (Yb) atoms.

The Plan: They hoped this material would be a perfect QSL.
The Problem: The dance floor wasn't perfect. There were extra Copper (Cu) atoms hanging around where they shouldn't be, creating a "disordered" environment. It's like having random furniture scattered on the dance floor.

What They Found: The "Random Singlet" Party

Instead of finding the perfect Quantum Spin Liquid, they found something else interesting. They discovered that the material didn't freeze into a solid block, nor did it stay perfectly fluid. Instead, it formed a Random Singlet Phase.

Here is the best way to visualize this:

The Analogy of the "Couples" vs. The "Crowd"

The Ideal QSL: Imagine a crowd of people where everyone is holding hands with everyone else simultaneously in a giant, complex web. No one is paired off; the whole group is one big, entangled unit.
The Spin Glass (The Failure): Imagine the music stops, and everyone just freezes in place, bumping into their neighbors randomly. Nothing moves.
The Random Singlet (What they found): Imagine the music is playing, but because the floor is messy, people can't hold hands with everyone. Instead, they start pairing up with whoever is closest to them.
- Some pairs are very close and hold hands tightly (strong bonds).
- Some pairs are far apart and hold hands loosely (weak bonds).
- These pairs form randomly across the floor. They are "frozen" in their pairs, but the pairs themselves are constantly fluctuating.

The scientists found that the "messy" copper atoms in the material forced the Ytterbium atoms to pair up randomly. This created a state that isn't a perfect QSL, but it's also not a boring frozen block. It's a frozen network of random couples.

The Evidence: How They Knew

The team used three main tools to figure this out, which we can think of as checking the "temperature" and "energy" of the dance floor:

The Thermometer (Magnetic Susceptibility): They measured how the material reacted to magnets. They saw a tiny "bump" at a very low temperature (0.1 Kelvin). This is like seeing the dancers finally stop moving and freeze into their random pairs.
The Calorie Counter (Specific Heat): They measured how much heat the material could hold. A normal solid usually follows a predictable curve. This material, however, showed a "sub-linear" curve.
- The Metaphor: Imagine a bucket filling with water. Usually, the water level rises in a straight line. Here, the water level rose, but it started to flatten out weirdly. This specific shape told them the energy wasn't coming from a solid block or a fluid, but from a distribution of different-sized pairs (some tight, some loose).
The Crystal Scanner (X-ray): They looked at the atoms and confirmed that the Copper atoms were indeed scattered randomly, creating the "messy floor" that forced the random pairing.

Why Does This Matter?

You might ask, "If they didn't find the Quantum Spin Liquid, why is this paper important?"

It's important because it suggests a universal rule.

The scientists realized that many materials that failed to be Quantum Spin Liquids (because they were too messy) might actually all be doing this same "Random Singlet" dance.

It's like finding that every time you try to build a perfect sandcastle and the wind ruins it, the sand doesn't just fall apart; it forms a specific, predictable pile.
This "Random Singlet" state is a new kind of quantum matter. It has strong quantum connections (entanglement) but is driven by disorder.

The Takeaway

The paper concludes that while YbCu1.14Se2 isn't the "perfect" Quantum Spin Liquid they were hoping for, it is a perfect example of a 2D Random Singlet Phase.

It teaches us that even when nature is messy and disordered, it doesn't just give up. Instead, it finds a new, complex way to organize itself. This "failed" state might actually be a new chapter in physics, showing us that disorder can create its own unique, exotic quantum world.

1. Problem Statement

Quantum Spin Liquid (QSL) phases are theoretically predicted ground states for geometrically frustrated magnets (such as the triangular lattice Heisenberg antiferromagnet) where magnetic order is suppressed by quantum fluctuations, resulting in long-range entanglement without symmetry breaking. However, experimentally realizing QSLs is challenging because real materials often contain structural defects and disorder. These imperfections typically disrupt the delicate QSL ground state, leading to "failed QSLs" that exhibit spin-glass behavior or magnetic ordering instead.

The central question addressed by this work is: What is the nature of the ground state in frustrated triangular lattice materials where disorder prevents a true QSL but also prevents conventional magnetic ordering? The authors investigate whether these "failed QSLs" belong to a distinct universality class, specifically the 2D Random Singlet (RS) phase.

2. Methodology

The authors synthesized and characterized the candidate material YbCu $_{1.14}$ Se $_2$ , a compound featuring a 2D triangular lattice of magnetic Yb $^{3+}$ ions separated by non-magnetic Cu/Se layers.

Synthesis: Single crystals were grown using the self-flux technique. The resulting stoichiometry was found to be YbCu $_{1.14}$ Se $_2$ , indicating an excess of Copper (Cu) compared to the ideal stoichiometric YbCuSe $_2$ .
Structural Characterization: Single-crystal X-ray diffraction (SC-XRD) was performed to determine the crystal structure, lattice parameters, and site occupancies. Precession imaging was used to check for vacancy ordering.
Bulk Measurements:
- Magnetic Susceptibility: Measured from 2 K to 350 K (DC) and down to ultra-low temperatures (AC susceptibility) to detect magnetic ordering or glassy freezing.
- Specific Heat: Measured from 10 K down to 30 mK using both a PPMS (with $^3$ He insert) and a dilution refrigerator. Data was analyzed to separate phonon, nuclear Schottky, and magnetic contributions.
- Resistivity: Measured to confirm the electronic state (semiconducting vs. metallic).
Theoretical Modeling: A phenomenological model was developed where the specific heat is calculated by summing the contributions of a distribution of $S=1/2$ singlet-triplet gaps ( $w(\Delta)$ ). This model links the low-temperature specific heat behavior directly to the distribution of exchange interactions.

3. Key Results

Structural Properties

Crystal Structure: The material crystallizes in the hexagonal $P\bar{3}m1$ space group. The magnetic Yb ions form a perfect 2D triangular lattice.
Disorder: The Cu site (Wyckoff position 2d) shows a partial occupancy of 56.6%, significantly deviating from the ideal 50% expected for stoichiometric YbCuSe $_2$ . Crucially, X-ray diffraction shows no ordering of Cu vacancies, implying a random distribution of disorder. This creates a random landscape of magnetic exchange interactions between Yb ions.
Electronic State: Despite the excess Cu, the material remains a semiconductor with an activation gap of ~307 meV, ruling out metallic screening effects.

Magnetic and Thermodynamic Properties

Absence of Long-Range Order: No sharp anomalies indicative of long-range magnetic ordering were observed in susceptibility or specific heat down to 30 mK.
Spin Glass Freezing: AC susceptibility measurements revealed a frequency-dependent peak at $T_f \approx 0.1$ K, characteristic of spin-glass freezing. However, the freezing temperature is two orders of magnitude lower than the exchange energy scale (Weiss temperature $\Theta_W \approx -17$ K), suggesting strong quantum dynamics persist well above the freezing point.
Specific Heat Behavior:
- The magnetic specific heat ( $C_{mag}$ ) exhibits sub-linear behavior ( $C/T$ decreases with increasing $T$ ) from 0.5 K to 5 K.
- This behavior contradicts standard models: it is not consistent with 2D bosonic magnons ( $C \propto T^2$ ) nor a Fermi surface ( $C \propto T$ ).
- The integrated magnetic entropy recovers approximately 80% of $R \ln(2)$ above $T_f$ , indicating that the ground state is not a simple frozen glass with residual entropy.
Absence of 1/3 Magnetization Plateau: Unlike other triangular QSL candidates (e.g., AYbSe $_2$ ), YbCu $_{1.14}$ Se $_2$ lacks the characteristic 1/3 magnetization plateau in field-dependent susceptibility, signaling a departure from the ideal Heisenberg model due to disorder.

The Random Singlet Model

The authors successfully modeled the specific heat data using a distribution of singlet-triplet gaps.
The data is best fit by a triangular distribution of gaps $w(\Delta)$ , where the density of pairs decreases linearly as the gap energy increases.
The mean singlet-triplet gap is $\langle \Delta \rangle \approx 1.20$ meV (13.9 K), consistent with the Weiss temperature.
The model predicts that as $T \to 0$ , $C/T \propto w(u_0 k_B T)$ . The linear slope observed in $C/T$ vs. $T$ directly maps to the triangular distribution of exchange energies caused by the random Cu vacancies.

4. Key Contributions

Identification of a 2D Random Singlet Phase: The paper provides strong evidence that YbCu $_{1.14}$ Se $_2$ realizes a 2D Random Singlet phase rather than a QSL or a conventional spin glass. The disorder-induced randomness in exchange interactions leads to a frozen network of singlets with a broad distribution of energy scales.
Phenomenological Link between Disorder and Thermodynamics: The authors establish a rigorous mathematical link showing that the low-temperature specific heat ( $C/T$ ) directly reflects the distribution of singlet gaps ( $w(\Delta)$ ). This allows experimentalists to "read" the disorder landscape from thermodynamic data.
Universality in Disordered Frustrated Systems: The results in YbCu $_{1.14}$ Se $_2$ are strikingly similar to YbMgGaO $_4$ and YbZnGaO $_4$ . The authors argue that these "failed QSLs" may not be distinct anomalies but rather members of a universal class of 2D random singlet states formed when disorder destroys the QSL state in frustrated lattices.
Clarification of the Ground State: The study resolves the ambiguity of the ground state in this material, demonstrating that while it exhibits glassy freezing at ultra-low temperatures, the dominant physics at higher energies is governed by quantum entanglement and random singlet formation.

5. Significance

This work fundamentally shifts the perspective on "failed" QSL candidates. Instead of viewing structural disorder merely as a nuisance that ruins the QSL state, the authors propose that disorder can drive the system into a distinct, robust quantum phase: the 2D Random Singlet phase.

Theoretical Impact: It supports theoretical predictions that disorder in frustrated lattices (triangular, Kagome, honeycomb) can stabilize a random singlet ground state with non-trivial quantum entanglement, distinct from simple spin glasses.
Experimental Guidance: The paper provides a diagnostic framework (specifically the sub-linear specific heat and the $C/T$ vs. $T$ slope) for identifying random singlet physics in other disordered quantum magnets.
Material Science: It highlights the critical role of stoichiometry and site disorder in determining the ground state of quantum materials, suggesting that controlling disorder might be a pathway to engineering specific quantum phases.

In conclusion, YbCu $_{1.14}$ Se $_2$ serves as a prototype for understanding how disorder transforms frustrated quantum magnets, revealing a universal 2D random singlet phase that bridges the gap between ideal QSLs and disordered spin glasses.