Frustration induced dimensional reduction and coexistence of long and short-range magnetic order in NdCl 3

arXiv:2607.17995 · cond-mat.str-el, cond-mat.mtrl-sci · Submitted 2026-07-20 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "Frustration induced dimensional reduction and coexistence of long and short-range magnetic order in NdCl 3".

Kai: The gist The phenomenon of frustration greatly enriches the accessible physics of quantum magnets in NdCl3 by inducing dimensional reduction and causing a coexistence of long and short-range magnetic order.

Mira: First, who's behind it and why it matters.

Paper summary: Kai: So, we're looking at this paper, "Frustration induced dimensional reduction and coexistence of long and short-range magnetic order in NdCl three" by Zoghlin, Stone, Garlea, Frontzek, Christianson, and May <ref:2607.17995#pg3>. The main idea here is that frustration in this material leads to a kind of dimensional reduction and causes both short-range and long-range magnetic order to exist at the same time.

Mira: Right. It claims that this frustration enriches the physics because it sets up these conditions for coexistence, which is what they call quasi-one-dimensional, short-range antiferromagnetic order being the origin of a broad peak in the heat capacity and magnetic susceptibility >

Lev: From an experimental standpoint, if we're looking at real hardware, this means we're dealing with something where the physics isn't just simple bulk behavior but something highly structured along certain directions >

Kai: Exactly. The bulk measurements show two transitions at TN1 = two hundred seventy mK and TN2 = one hundred eighty mK, and most of the magnetic entropy above TN1 shows up as this broad peak around T* ≈ four hundred fifty mK > <ref:2607.17995#pg1,transitions at TN1 = 270 mK and TN2 = 180 mK>

Mira: And what's interesting is that single crystal elastic neutron scattering confirms that this broad peak is actually caused by quasi-one-dimensional, short-range, antiferromagnetic order >

Lev: That tells us the magnetic correlations are really constrained in space, which is crucial for how we might model this on a real quantum computer architecture >

Kai: Below TN1 there are these magnetic Bragg peaks with a propagation vector of k = (zero zero one/two), and then this diffuse scattering keeps going between TN2 and TN1 > <ref:2607.17995#pg1,k = (0 0 1/2>

Mira: That persistent diffuse scattering in that intermediate regime, between TN2 and TN1, is what points to the coexistence of short and long-range order >

Lev: If you were trying to run an error correction protocol here, having this mix of orders means the dynamics would be incredibly complex, with different correlation lengths depending on which way you look >

Kai: Then below TN2, we see these magnetic Bragg peaks get stronger without changing the k-vector, and the diffuse scattering just vanishes completely >

Mira: That disappearance of the diffuse scattering indicates that full long-range order has been achieved in that specific regime >

Lev: But there's a caveat here, though. The paper mentions that the refined magnetic structure they found from those Bragg peak intensities looks nonphysical, and the true magnetic ground state is still open question >

Kai: That’s a big thing for us because it means we can't just take their structural picture at face value yet >

Mira: It suggests that while they have identified the tendencies, pinning down the exact nature of that ordered magnetic ground state is still a challenge for them >

Lev: And that feeds into what we need to build. If the structure isn't perfectly clear, how do we design an error correction scheme robust enough to handle whatever this frustrated system actually is?

Kai: So, looking at the title of "Frustration induced dimensional reduction and coexistence of long and short-range magnetic order in NdCl three" what does that tell us about the bigger picture > <ref:2607.17995#pg3>

Mira: It tells us that frustration isn't just a simple complication; it actively shapes the dimensionality of the magnetic interactions, forcing a state where different types of order live together >

Lev: For error correction, that means we can't treat this as one uniform system; we have to account for these different correlation lengths and ordering regimes simultaneously >

Kai: It also points toward how material properties are dictated by the underlying crystal structure, specifically those quasi-one-dimensional aspects of NdCl three > <ref:2607.17995#pg3>

Mira: And the implication for condensed matter physics is that frustration is a powerful tool to generate complex magnetic phases with long-range order that aren't easily found in simpler models >

Lev: From an experimental standpoint, it means we need techniques sensitive enough to resolve these competing orders, like the neutron scattering they used >

Kai: So, what does this all mean for us when we think about building quantum hardware or studying complex spin systems?

Mira: It means that understanding how frustration can lead to this kind of coexistence helps us design materials where we can engineer specific types of magnetic phases for our experiments >

Lev: And it gives us a template for what kinds of complexity to expect when we try to map real physical systems onto a quantum simulation platform >

Conclusion: Kai: So, to wrap up this paper, we're looking at how frustration in NdCl3 creates this weird mix of magnetic orders that are both short and long-range simultaneously >

Mira: Exactly. The authors are saying that this frustration acts like a kind of dimensional reduction on the magnetic interactions, which is what drives all these competing behaviors >

Lev: From an error correction standpoint, that means we can't assume a uniform system; you're dealing with different correlation lengths depending on the direction you look >

Kai: Right. And this coexistence is key because it complicates how we try to model quantum states in hardware >

Mira: It changes the physics because it shows that these complex magnetic phases aren't just theoretical curiosities, they can actually form in real materials with specific crystal structures >

Lev: So when you look at the implications for building a system, it means you have to design your error correction protocol to handle these different ordering regimes >

Kai: Because if we can't get that structure right, or if the frustration is too strong, we might miss the actual physics happening on the chip >

Mira: The real thing is that this paper shows how material properties are dictated by those underlying crystal structures in a way that simple models just don't capture >

Lev: It suggests that for complex quantum magnets, you need experimental techniques sensitive enough to probe all these different ordering tendencies at once >

Kai: So the big picture here is frustration isn't just noise; it’s a very active ingredient in creating magnetic phases that are fundamentally more complex than we might initially think >

Materials Science & Technology Division, Oak Ridge National Laboratory

cond-mat.str-el, cond-mat.mtrl-sci

Submitted: 2026-07-20

Updated: 2026-10-08

Comments: 15 pages, 6 figures, 2+A1 tables, with supplemental material

DOI: 10.1103/1b93-8m54

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 66/100

The gist: The gist The phenomenon of frustration greatly enriches the accessible physics of quantum magnets in NdCl3 by inducing dimensional reduction and causing a coexistence of long and short-range magnetic

Key concepts

Frustration
Frustration occurs when competing magnetic interactions prevent the system from achieving a simple, low-energy ground state. In this case, the competing exchange interactions in NdCl3 cause the system to adopt complex behaviors like dimensional reduction and the coexistence of different types of magnetic order rather than a single simple pattern.
Coexistence of Orders
This means that at certain temperatures, two different types of magnetic ordering—short-range (local) and long-range (system-wide)—exist simultaneously within the material. The paper observed this between $T_{N2}$ and $T_{N1}$, suggesting that the magnetic structure is complex, involving both local correlations and larger ordered domains.
Quasi-one-dimensional Order
This describes a magnetic arrangement where the interactions are much stronger along one direction (like the c-axis) compared to others. The diffuse scattering results confirm that this quasi-1D, short-range antiferromagnetic order is responsible for the broad features observed in heat capacity and susceptibility above $T_{N1}.

Terminology

Summary

The gist The phenomenon of frustration greatly enriches the accessible physics of quantum magnets in NdCl3 by inducing dimensional reduction and causing a coexistence of long and short-range magnetic order.

Bulk Characterization Findings

** The low-temperature heat capacity reveals two magnetic transitions at TN1 = 270 mK and TN2 = 180 mK, with much of the magnetic entropy released above TN1, manifesting as a broad peak centered at T∗ ≈ 450 mK Single crystal elastic neutron scattering reveals highly anisotropic magnetic diffuse scattering above TN2, confirming that quasi-one-dimensional, short-range, antiferromagnetic order is the origin of the broad peak in the heat capacity Magnetic Bragg peaks characterized by a ⃗k = (0 0 1/2) propagation vector emerge below TN1 Interestingly, the magnetic diffuse scattering persists for TN2 < T < TN1, indicating a regime of coexisting short and long-range order A Curie-Weiss fit of dc magnetization data collected on a powdered single crystal between T = 4 K – 50 K gave ΘC−W = -1.37(3) K and µef f = 3.55(1) µB/Nd Magnetization versus field measurements (Fig. 3b,c) confirm that the easy axis of magnetization is along the c-axis At T = 0.42 K the ratio of the magnetization at H = 60 kOe for the field parallel and perpendicular to the [0 0 1] (M = 2.22 µB/Nd and M⊥ = 1.13 µB/Nd, respectively) is M / M⊥ ≈ 1.97, similar to the ratio g/g⊥ = 2.267(1) Two clear features are visible in the ac susceptibility data (Fig. 3d): a broad maximum close to T∗ and a kink at TN2 For the higher energy mode a clear decrease in intensity as a function of Q⃗ is also observed, as expected for a CEF mode Calculations of the phonon spectra with the INSPIRED software package indicate that a phonon overlaps with the lower energy CEF mode, causing the observed nonmonotonic dependence of the intensity on Q⃗ (Fig. 4e, left) The previous optical measurements established a CEF level scheme composed of five doublets consistent with the Kramers nature of the Nd3+ ion with J = 9/2 The observation of two CEF modes in the INS data is consistent with this level scheme, as we would not necessarily expect to be able to resolve the two modes of each pair separately We also observe a higher energy mode at ∆E = 253(1) meV using Ei = 500 meV (Fig. 4f) We identify this as the first intermultiplet transition (J = 9/2 → 11/2) based on the observed decrease in intensity with Q⃗ and its consistency with the previous optical measurements [12, 13] We identify this as the first intermultiplet transition (J = 9/2 → 11/2) based on the observed decrease in intensity with Q⃗ and its consistency with the previous optical measurements [12, 13]> The magnetic diffuse scattering is much narrower along the (0 0 L) direction than the (H H¯ 0) direction We extract the real space magnetic correlation lengths associated with this diffuse magnetic scattering by fitting cuts through the (-1.2 1.2 0.5) position – highlighted by the orange square in Fig. 5c to a Lorentzian line-shape (Fig. 5f) The correlation length is x1/e, defined as the 1/e decay length of the Fourier transform of the Lorentzian line-shape x1/e = 31(3) A along (˚ H H¯ 0) and x1/e = 180(11) A along (0˚ 0 L)> The intermediate regime is defined by the emergence of new Bragg peaks at (H H L¯) positions with integer H and half-integer L These new Bragg peaks with half-integer L decrease in intensity with increased Q⃗; this, in addition to the observed Tdependence, confirms they stem from magnetic order The fully ordered regime at T = 45 mK (Fig. 5) the magnetic diffuse scattering disappears entirely and only the same AFM Bragg peaks which marked the emergence of the intermediate regime remain The refined AFM magnetic structure which best captures the observed magnetic Bragg peak intensities appears nonphysical, and the true magnetic ground state remains an open question In order to refine the Nd Biso value was generally unstable, resulting in negative values or very large error bars, so this was fixed to a small, physically reasonable value (0.

Improvements for AI systems

  1. textbfPrecision in Magnetic Structure Solution via Symmetry Exploration: The improved AI can rigorously test magnetic space group solutions using both standard refinement methods (MSG approach) and advanced irrep-based analysis (irep-based approach). This addresses the ambiguity of whether a refined structure is a true magnetic ground state by systematically checking if the solution is robust against inappropriate symmetry constraints, as demonstrated by comparing results from P63/m, P¯3, and P3 space groups in Appendix A.

  2. textbfCharacterization of Frustration-Driven Dimensional Reduction: The system can be specifically trained to correlate experimental features (e.g., quasi-1D behavior) with the underlying exchange interaction network (e.g., the dominance of JNN is effectively enhanced because the tendency toward AFM correlations along the c-axis frustrates the FM JNNN). This allows it to move beyond simple observation to a mechanistic understanding of how frustration induced dimensional reduction manifests in materials like NdCl3.

  3. textbfModel Comparison for Coexistence Regimes: The improved system can be used to quantitatively assess the coexistence of short and long-range order in the intermediate regime by analyzing the temperature dependence of magnetic Bragg peak intensities versus correlation length analysis derived from diffuse scattering (The correlation length is x1/e, defined as the 1/e decay length of the Fourier transform of the Lorentzian line-shape). This allows for a more nuanced quantification of partially disordered antiferromagnetism.

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