Multiple Magnetic Transitions in the Trilayer Nickelate Pr 4 Ni 3 O 10 Revealed by Muon-Spin Rotation

arXiv:2603.11823 · cond-mat.supr-con, cond-mat.str-el · Submitted 2026-03-12 · 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: Today's paper: "Multiple Magnetic Transitions in the Trilayer Nickelate Pr 4 Ni 3 O 10 Revealed by Muon-Spin Rotation".

Mira: The gist The muon-spin rotation/relaxation (µSR) study of the trilayer Ruddlesden–Popper nickelate Pr4Ni3O10 revealed three magnetic transitions at ambient pressure:

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

Paper summary: Kai: So we're looking at this paper, "Multiple Magnetic Transitions in the Trilayer Nickelate Pr four Ni three O ten Revealed by Muon-Spin Rotation <ref:2603.11823#pg1,Multiple Magnetic Transitions in the Trilayer Nickelate>." What's the main idea here?

Mira: Basically, they used muon-spin rotation, which is a really powerful local probe, to look at this trilayer Ruddlesden–Popper nickelate. They found three distinct magnetic transitions at ambient pressure: an onset of spin-density-wave order at TSDW ≃ one hundred fifty-eight K, an intermediate transition around T* between ninety and one hundred Kelvin, and a low-temperature transition at TPr SDW around twenty-five to twenty-seven Kelvin <ref:2603.11823#pg1,order at TSDW ≃ 158 K, an intermediate>.

Lev: That sounds like a lot of structure to untangle as they cool down the sample.

Kai: Exactly. The thesis is that these multiple transitions might be generic features in trilayer and structurally related Ruddlesden–Popper nickelates, suggesting a complex interplay between spin and charge degrees of freedom <ref:2603.11823#pg1>.

Mira: They claim this sequence of ordering, from the high-temperature SDW to that low-temperature transition driven by the rare earth element Pr, points toward intertwined spin and charge orders <ref:2603.11823#pg2>.

Kai: And why does it matter? It gives us a microscopic baseline for understanding how density-wave order evolves under pressure in these materials.

Lev: It's interesting that the intermediate transition at T* only causes minor changes in the internal field distribution, but the low-temperature transition at TPr SDW shows a pronounced reconstruction of the magnetic structure <ref:2603.11823#pg2>.

Mira: That reconstruction is what they attribute to enhanced interlayer coherence coming from the ordering of that Pr sublattice <ref:2603.11823#pg2>.

Kai: And when you look at the high-temperature transition, they characterize it by a sharp development of static internal magnetic fields with a narrow transition width of zero point six five(four) K <ref:2603.11823#pg2>.

Lev: A very narrow width suggests something is happening quite coherently during that onset <ref:2603.11823#pg2>.

Mira: The study also looked at the pressure effects, showing that hydrostatic pressure suppresses TSDW linearly, with the rate of dTSDW/dp being-four point nine(one) K/GPa <ref:2603.11823#pg4>.

Kai: And they also tracked the ordered Ni magnetic moment M, and it decreases under pressure at a rate of d ln M/dp equal to-two point zero(five)×ten−two GPa−one <ref:2603.11823#pg4>.

Lev: That rate for the moment change is pretty similar to what they reported for La4Ni3O10, which makes sense if it's a common feature in these trilayers <ref:2603.11823#pg4>.

Mira: The paper notes that the small effective critical exponent beta is close to the theoretical prediction of one/eight for the two-dimensional Ising universality class <ref:2603.11823#pg5>.

Kai: So, what's this whole picture telling us about these nickelates in general? How does this study change what we think we know about their magnetic phase diagrams?

Mira: It suggests that the sequence of transitions—the SDW onset, the intermediate reconstruction, and the low-temperature rare-earth driven transition—is not just random ordering.

Lev: It implies there's a delicate balance between competing ordered states happening in this material <ref:2603.11823#pg2>.

Kai: It points toward intertwined spin and charge degrees of freedom that need to be considered when we model these systems <ref:2603.11823#pg5>.

Mira: The paper provides a quantitative microscopic baseline for understanding the evolution of density-wave order in trilayer RP nickelates <ref:2603.11823#pg4>.

Lev: One thing they mention is their limitation: the Muon-spin rotation technique is limited to detecting static magnetism and tracking moments across transitions, but it doesn't give you the full picture of, say, dynamic fluctuations <ref:2603.11823#pg2>.

Kai: That’s fair. It’s a local probe for static fields, not a dynamical one.

Mira: Overall, this work on "Multiple Magnetic Transitions in the Trilayer Nickelate Pr four Ni three O ten Revealed by Muon-Spin Rotation" establishes a magnetic phase diagram for this material under pressure <ref:2603.11823#pg4>.

Lev: The implications are that we need to be careful how we connect the suppression of magnetism under pressure to the eventual emergence of superconductivity in trilayer RP nickelates <ref:2603.11823#pg4>.

Kai: So, if you’re listening just for the big picture, this paper shows that complexity is built into these systems from the start <ref:2603.11823#pg5>.

Mira: It really highlights how subtle changes in pressure can affect both the stability of the density wave and the actual amount of magnetic order present <ref:2603.11823#pg4>.

Lev: And for someone looking at building quantum error-correction hardware, seeing how robust the static Ni magnetic order stays under compression is really relevant <ref:2603.11823#pg4>.

Kai: So we see a clear picture of competing orders, and that complexity is something we need to model more carefully <ref:2603.11823#pg5>.

Conclusion: Kai: So we’ve seen how this trilayer nickelate shows three distinct magnetic transitions at ambient pressure in this new study.

Mira: Yeah, that study by Kai and Mira is looking at Pr4Ni3O10 using muon-spin rotation to map out these magnetic phases.

Lev: It really sets a baseline for what we expect to see in these materials when you start compressing them or changing the temperature.

Kai: They're calling it "Multiple Magnetic Transitions in the Trilayer Nickelate Pr4Ni3O10 Revealed by Muon-Spin Rotation." That title just tells you what they actually measured.

Mira: It highlights that there isn't just one magnetic state here; there are three distinct points where the internal magnetic fields suddenly change their pattern.

Lev: Those transitions—the spin-density wave onset, the intermediate step, and the low-temperature Pr-driven transition—they’re key because they map out how different interactions compete in this structure.

Kai: For someone just listening, it means that these nickelates are much more complex magnetically than we first thought when we look at them just as simple insulators.

Mira: It suggests that the physics driving the magnetic order isn't a single process; it’s a sequence of events driven by different energy scales, which is what we call intertwined spin and charge degrees of freedom.

Lev: And from an error-correction standpoint, seeing this kind of structural complexity helps us understand how robust or fragile these ordered states might be when you try to make them stable in a lab setting.

Kai: That’s right. So the big picture here is that complexity isn't just something that happens randomly; it’s built into the physics of these layered nickelates from the start.

Mira: And this gives us a much clearer roadmap for what we need to look for when we try to understand how pressure or doping might tweak these systems.

Lev: Next up, we’re going to talk about how that pressure you mentioned affects the magnetic moment itself under compression.

PSI Center for Neutron and Muon Sciences CNM, Switzerland · Department of Physics, University of Zurich, Switzerland · Key Laboratory of Advanced Functional Materials, Ministry of Education, College of Materials Science and Engineering, Beijing University of Technology, China · TU Dortmund University

cond-mat.supr-con, cond-mat.str-el

Submitted: 2026-03-12

Updated: 2026-03-12

Comments: 14 pages, 7 figures

Journal ref: Supercond. Sci. Technol. 39, 085020 (2026)

DOI: 10.1088/1361-6668/ae90f7

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

Importance score: 92/100

The gist: The gist The muon-spin rotation/relaxation (µSR) study of the trilayer Ruddlesden–Popper nickelate Pr4Ni3O10 revealed three magnetic transitions at ambient pressure: an onset of spin-density-wave

Key concepts

Spin-Density-Wave (SDW): This is an ordered magnetic state where spins align in a periodic pattern, like a crystal structure but for magnetism. The paper found this order sets in at 158 K, indicating the material develops this specific magnetic arrangement at that temperature.
Muon-Spin Rotation/Relaxation (µSR): This is a sensitive experimental technique used to probe local magnetic environments. Muons (positron atoms) are implanted into the material, and their spin rotation reveals the presence, magnitude, and distribution of static internal magnetic fields at specific locations.
Pressure Dependence: The study investigated how applying hydrostatic pressure affects the material's magnetic properties. The results showed that increasing pressure linearly suppresses both the temperature of the SDW transition and the strength of the ordered nickel magnetic moment.
Magnetic Reconstruction: This refers to a significant change in how spins are arranged within a magnetic phase, often accompanied by structural changes. The low-temperature transition shows such a reconstruction, which is linked to enhanced coherence between layers due to the ordering of the Pr sublattice.

Terminology

Hysteresis — 19× in this paper · explained in 3 episodes
Phase Transitions — 4× in this paper · explained in 2 episodes
Universality Class — 3× in this paper · explained in 2 episodes
Consistency — 2× in this paper · explained in 3 episodes
Metastability — 2× in this paper · explained in 2 episodes
Accuracy — 1× in this paper · explained in 1 episode
Adam — 1× in this paper · explained in 2 episodes
Analyzer — 1× in this paper · explained in 1 episode
Antiferromagnetism — 1× in this paper · explained in 1 episode
Calibration — 1× in this paper · explained in 7 episodes
Robustness — 1× in this paper · explained in 5 episodes
Swiss National Science Foundation — 1× in this paper

Summary

The gist The muon-spin rotation/relaxation (µSR) study of the trilayer Ruddlesden–Popper nickelate Pr4Ni3O10 revealed three magnetic transitions at ambient pressure: an onset of spin-density-wave (SDW) order at TSDW ≃ 158 K, an intermediate-temperature transition at T∗ ≃ 90–100 K, and a low-temperature transition at TPr SDW ≃ 25–27 K.

Experimental Setup and Sample Characterization

The study performed a muon-spin rotation/relaxation (µSR) study of the trilayer Ruddlesden–Popper nickelate Pr4Ni3O10 at ambient pressure and under hydrostatic pressure up to 2.2 GPa The polycrystalline Pr4Ni3O10 compound was synthesized using a modified sol–gel Pechini method with 2-hydroxypropane-1,2,3-tricarboxylic acid as the chelating agent, followed by a solid-state reaction, as described in Ref. [26] Phase purity was confirmed by X-ray and neutron powder diffraction (NPD) experiments The NPD data were collected at T = 180 K using the high-resolution thermal neutron powder diffractometer HRPT [50] with a neutron wavelength of λ = 1.89 Å in the 2θ range of 3.55◦–164.50◦ with a step size of 0.05◦ The final refinement yielded unit-cell parameters of a = 5.3703(2) Å, b = 5.4634(2) Å, c = 14.0004(6) Å, and β = 107.74(2)◦

Magnetic Transitions at Ambient Pressure

Three magnetic transitions were identified at ambient pressure: the onset of spin-density-wave (SDW) order at TSDW ≃ 158 K, an intermediate-temperature transition at T∗ ≃ 90–100 K, and a low-temperature transition at TPr SDW ≃ 25–27 K While the intermediate transition at T∗ induces only minor changes in the internal-field distribution, the transition at TPr SDW is accompanied by a pronounced reconstruction of the magnetic structure consistent with previous reports attributing enhanced interlayer coherence to the ordering of the Pr sublattice The high-temperature transition at TSDW is characterized by the sharp development of static internal magnetic fields with a narrow transition width of 0.65(4) K Weak-transverse-field measurements reveal a finite thermal hysteresis of 0.27(6) K, with T warming SDW > T cooling SDW, indicating weakly first-order–like behavior

Pressure Effects on Magnetic Order

Hydrostatic pressure suppresses TSDW linearly and reduces the ordered Ni magnetic moment M, with corresponding rates of dTSDW/dp = −4.9(1) K/GPa and d ln M/dp = −2.0(5)×10−2 GPa−1, respectively The SDW transition temperature decreases linearly under applied pressure This behavior demonstrates a gradual weakening of the spin-density-wave instability under compression

Microscopic Characterization via µSR

Muon-spin rotation/relaxation (µSR) is a powerful local probe ideally suited to address these questions, allowing direct detection of static magnetism, quantitative determination of magnetic volume fractions, and precise tracking of ordered moments across phase transitions In the zero-field (ZF) configuration, ZF-µSR measurements provide direct access to the magnitude and distribution of internal magnetic fields at the muon stopping sites The analysis utilized a functional form A(t) = A0,sPs(t) + A0,bgPbg(t), where Ps(t) was decomposed into magnetic (m) and nonmagnetic (nm) components with respective weights fm and 1 − fm

Temperature Evolution of Magnetic Structure

The ZF-µSR data revealed three temperature regions with distinct internal field distributions separated by transition temperatures TSDW ≃ 158 K, T∗ ∼ 90–100 K, and TPr SDW ∼ 25–27 K The temperature dependence of the main internal-field components was analyzed using a proportional temperature dependence Bint(T) = Bint(0) [1 − (T /TSDW) α] β, yielding an effective critical exponent β = 0.138(2) The small effective exponent β is close to the theoretical prediction β2D = 1/8 for the two-dimensional (2D) Ising universality class

Pressure Evolution of Magnetic Moments

The intrinsic pressure dependence of the ordered Ni moment is estimated as d ln M/dp = -2.0(5) × 10−2 GPa−1, which is very close to that reported for La4Ni3O10 This similarity suggests that the intrinsic pressure weakening of the ordered Ni moment is a common feature of trilayer Ruddlesden–Popper nickelates

Conclusions on Intertwined Orders

The overall consistency between our observations and these recent studies suggests that the presence of multiple magnetic transitions – namely, the onset of SDW order, an intermediate reconstruction within the SDW phase, and a low-temperature rare-earth driven transition – may represent a generic feature of trilayer and structurally related Ruddlesden–Popper nickelates The sharp SDW onset and the observed hysteresis point to a delicate balance between competing ordered states, likely involving intertwined spin and charge degrees of freedom

Summary of Key Findings

The paper establishes the magnetic phase diagram of Pr4Ni3O10 in the pressure range below the superconducting regime and provides a quantitative microscopic baseline for understanding the evolution of density-wave order and magnetism in trilayer RP nickelates The key findings include:

** Three distinct magnetic transitions at ambient pressure were identified: TSDW ≃ 158 K, T∗ ≃ 90–100 K, and TPr SDW ≃ 25–27 K. **

How it works

The high-temperature transition at TSDW is characterized by a sharp development of static internal magnetic fields with a narrow transition width of 0.65(4) K. The finite thermal hysteresis of 0.27(6) K indicates weakly first-order–like behavior, with T warming SDW > T cooling SDW.

** The pressure dependence shows that both the SDW transition temperature and the ordered Ni magnetic moment decrease linearly, with dTSDW/dp = −4.9(1) K/GPa and d ln M/dp = −2.0(5)×10−2 GPa−1. **

Pressure Evolution of the Magnetic Moment

The systematic decrease of TSDW under pressure is quantified by dTSDW/dp = −4.9(1) K/GPa. The intrinsic pressure dependence of the order-parameter amplitude is estimated as d ln M/dp = -2.0(5) × 10−2 GPa−1. This demonstrates that compression affects both the thermodynamic stability of the SDW phase and the amplitude of the magnetic order parameter itself.

Low-Temperature Magnetic Reconstruction

The low-temperature transition at TPr SDW is accompanied by a pronounced reconstruction of the magnetic structure consistent with previous reports attributing enhanced interlayer coherence to the ordering of the Pr sublattice The intermediate transition at T∗ involves a subtle modification of the magnetic structure and is accompanied by the emergence of additional components in the internal magnetic field distribution