NMR evidence of pressure-induced structural transition and enhanced spin fluctuations up to 14 GPa in SrCu 2 (BO 3) 2

arXiv:2609.06472 · cond-mat.str-el · Submitted 2026-09-06 · Read on arXiv

Listen

Transcript

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: "NMR evidence of pressure-induced structural transition and enhanced spin fluctuations up to 14 GPa in SrCu 2 (BO 3) 2".

Kai: The gist: High-pressure NMR measurements on SrCu2(BO3)2 up to 14 GPa reveal two pressure-induced monoclinic phases,

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

Paper summary: Kai: So looking at the whole thing about "NMR evidence of pressure-induced structural transition and enhanced spin fluctuations up to fourteen GPa in SrCu2(BO3)two", the authors have clearly mapped out a sequence of structural phase transitions driven by pressure <ref:2609.06472#pg1,NMR evidence of pressure-induced structural transition and enhanced spin fluctuations up>. They found these two distinct monoclinic phases and detailed where the magnetic ordering temperatures occur, like at ten Kelvin and fifteen Kelvin <ref:2609.06472#pg1>.

Mira: The significance is that they resolved an intermediate monoclinic-one regime that previous bulk structural studies hadn't picked up on, which shows how local probes like NMR can reveal more detail than some bulk techniques might <ref:2609.06472#pg1>. It’s about seeing the fine details of the phase diagram.

Lev: For error correction researchers, this means we have a clearer picture of the magnetic environment when you consider pressures that are achievable in specialized facilities, and we know exactly where those long-range order transitions happen relative to the structural ones.

Kai: And for someone just listening to this show, it means that extreme pressure doesn't just squash things uniformly; it triggers a sequence of distinct phases, each with its own magnetic rules and fluctuations. The paper shows that SrCu2(BO3)two is much more complex under compression than we first thought <ref:2609.06472#pg1>.

Mira: The authors essentially use high-pressure NMR to show how structural changes dictate magnetic behavior, highlighting the interplay between these two aspects in this specific quantum magnet system.

Lev: It gives us a better set of parameters to test theoretical models, forcing them to account for that evolving interplane coupling and those persistent fluctuations above TN across these different phases.

Conclusion: Kai: So we've seen how pressure pushes this material into two different structural phases, and now we're talking about what that actually means for SrCu2(BO3)two.

Mira: The authors are pointing to these high-pressure NMR measurements as a way to see the magnetic details inside these structures, specifically tracking spin fluctuations.

Lev: For us, it's interesting because it tells us how the magnetic behavior isn't fixed; it changes depending on how compressed the lattice gets.

Kai: So when we look at this title—"NMR evidence of pressure-induced structural transition and enhanced spin fluctuations up to fourteen GPa"—what does that really tell a person who just wants to know what happened?

Mira: It means they found two different monoclinic structures, not one, and they used NMR to confirm the magnetic ordering happens at specific pressures.

Lev: The numbers show that the Neel temperature, that's when things actually order magnetically, keeps going up with pressure until it levels off around twelve GPa.

Kai: That level-off is a big deal; it suggests there’s a physical limit to how much magnetic ordering you can force in this material by just squeezing it.

Mira: And what's striking is that above the main magnetic transition, you still see these extended correlated paramagnetic regimes at higher temperatures.

Lev: That extended regime means the material stays magnetically "messy" or fluctuating even when it's already technically ordered below fifteen Kelvin.

Kai: So, basically, this research shows us a whole sequence of structural changes driven by pressure and how those changes directly influence the magnetic state across different temperature scales.

Mira: It’s about connecting the physical structure, what we see in the NMR spectra, to the actual magnetic physics happening inside at high pressures.

Lev: This helps us understand how these quantum magnets might behave in real-world extreme conditions where pressure is a factor.

Kai: It opens up a new window into how these materials respond to external forces beyond just room temperature and ambient pressure.

School of Physics and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China · Institute of Physics, Chinese Academy of Sciences · Beijing National Laboratory for Condensed Matter Physics

cond-mat.str-el

Submitted: 2026-09-06

Updated: 2026-09-06

Comments: 7 pages, 4 figures

Journal ref: Phys. Rev. B 114, L231101 (2026)

DOI: 10.1103/6bxt-c4zm

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 82/100

The gist: The gist: High-pressure NMR measurements on SrCu2(BO3)2 up to 14 GPa reveal two pressure-induced monoclinic phases, with evidence for a gapless 3D antiferromagnetic (AFM) phase in the monoclinic

Key concepts

Gapless 3D Antiferromagnetic (AFM) Phase: This is a state found in the monoclinic phase above 4 GPa and below 10 K. It is identified by rapid NMR broadening and power-law behavior in the spin-lattice relaxation rate, indicating long-range magnetic ordering that lacks an energy gap to excite spins.
Antiferromagnetic Liquid (AFL) State: Observed between 10 K and 4 K, this state is characterized by gradually broadening and separating central NMR lines. It signifies short-range antiferromagnetic order persisting above the Neel temperature, suggesting magnetic fluctuations are significant even when long-range order hasn't fully set in.
Correlated Paramagnetic Regime: This regime appears at higher temperatures (up to 80 K) and is marked by a broad maximum in the Knight shift and a power-law dependence of 1/T1. It signifies complex magnetic behavior where spins are strongly correlated, extending beyond simple paramagnetism.
Structural Phase Transitions: The pressure drives SrCu2(BO3)2 through sequential structural changes: tetragonal to monoclinic-1 near 4 GPa, and then to monoclinic-2 near 5 GPa. These transitions are confirmed by changes in quadrupolar frequency ($ u_Q$) and line reconstruction in NMR spectra.

Terminology

Phase Transitions — 14× in this paper · explained in 2 episodes
Antiferromagnetic Liquid (AFL) State — 2× in this paper · explained in 1 episode
Frustration — 2× in this paper · explained in 2 episodes
Magnetic Frustration — 2× in this paper · explained in 2 episodes
Calibration — 1× in this paper · explained in 7 episodes
Degeneracy — 1× in this paper · explained in 3 episodes
Symmetry Breaking — 1× in this paper · explained in 3 episodes
Trace — 1× in this paper · explained in 2 episodes
Transformer — 1× in this paper · explained in 2 episodes

Summary

The gist: High-pressure NMR measurements on SrCu2(BO3)2 up to 14 GPa reveal two pressure-induced monoclinic phases, with evidence for a gapless 3D antiferromagnetic (AFM) phase in the monoclinic phase above 4 GPa and an extended correlated paramagnetic regime at higher temperatures

Structural Phase Transitions

The NMR spectra reveal two pressure-induced monoclinic phases. With pressure above 4 GPa and with temperature below 10 K, the rapid broadening of the NMR spectrum and the power-law behavior in the spin-lattice relaxation rate 1/T1 provide clear evidence for a gapless 3D antiferromagnetic (AFM) phase in the monoclinic phase. At an intermediate temperature range around 20 K, the emergence of the field-dependent NMR line splits resolves a two-dimensional, short-range ordered AFM phase. At temperature above 30 K, the sublinear power-law behavior of 1/T1 identifies an extended correlated paramagnetic regime. A marked reconstruction of the satellite spectra near 4 GPa signals a transition from the tetragonal phase to a monoclinic-1 phase. The pressure evolution of the quadrupolar frequency νQ further reveals a second structural transition, from monoclinic1 to monoclinic-2, near 5 GPa. In the monoclinic phases, pronounced line broadening together with peaks in the spinlattice relaxation rate 1/T1 identifies AFM transitions at approximately 10 K at 5.5 GPa and 15 K at 14 GPa.

Magnetic Ordering and Fluctuations

The low-temperature NMR spectra show that from 10 K to 4 K, the central lines gradually broaden and separate. The frequency difference ∆f between the two peaks (P1 and P2) increases upon cooling, reaching a maximum at TN. Notably, ∆f scales linearly with the applied magnetic field, and the normalized ∆f /H is plotted in Fig. 2(c). The gradual increase and strong field dependence of the line separation above TN are consistent with short-range AFM order, a regime termed the antiferromagnetic liquid (AFL) state in previous studies of SrCu2(BO3)2. The characteristic line separation associated with the AFL state persists at 14 GPa and 8 T over the temperature range of 20–40 K. Below 15 K, the system enters a 3D AFM order state, accompanied by diffusive spectral broadening. In the monoclinic-2 phase, upon cooling below 60 K, 1/T1 first decreases gradually (red dashed line in Fig. 3) before entering the 3D AFM ordered state.

Correlated Paramagnetism

At still higher temperatures, extending to approximately 80 K, the Knight shift develops a broad maximum, accompanied by a power-law dependence of 1/T1, marking the onset of a correlated paramagnetic regime. In the monoclinic-2 phase, between 60 and 25 K, 1/T1 follows a weak power-law temperature dependence, ∼ T0.4. A similar power-law behavior, albeit with a lower exponent ∼ T0.2, is also observed in the tetragonal and monoclinic-1 phases below about 15 K. This correlated paramagnetic regime emerges at temperatures well above both the AFL regime and the subsequent long-range AFM ordered state.

Exchange Coupling Evolution

At ambient pressure, SrCu2(BO3)2 exhibits intradimer and interdimer interactions J' ∼ 85 K and J ∼ 53 K, respectively. With increasing pressure, both couplings decrease, but J' decreases faster. In the monoclinic phases, the broad peak in the Knight shift appears at higher temperatures: ∼40 K in monoclinic-1 and ∼80 K in monoclinic-2. This behavior indicates that the dominant magnetic correlation scale is enhanced in the pressureinduced AFM phases and that interdimer interactions become increasingly important. In particular, J in the monoclinic-2 phase is likely much larger than that in monoclinic-1. The jump in TN at 4 GPa suggests that interplane interactions are stronger in the monoclinic phases than in the tetragonal phase, due to the reduced interlayer spacing with pressure.

Phase Diagram Summary

The phase diagram is established as shown in Fig. 4. High-pressure drives the system to four ground states sequentially: the DS, PS, tetragonal AFM, and monoclinic AFM phases. The Neel temperature TN increases monotonically with pressure, exhibits a discontinuous jump above 4 GPa, and saturates near 12 GPa. Above TN, both tetragonal and monoclinic phases host 2D short-range order, as well as a correlated paramagnetic regime at higher temperatures. The black dashed line marks the inferred boundary between the tetragonal and monoclinic phases, while the gray line denotes the boundary between monoclinic-1 and monoclinic-2 phases. This work therefore offers a high-resolution local-probe refinement of the high-pressure structural evolution with two distinct monoclinic phases. The NMR measurements resolve an intermediate monoclinic-1 regime that was not distinguished in previous bulk structural studies.

Summary

In this work, we perform high-pressure NMR measurements on SrCu2(BO3)2 up to 14 GPa, into a pressure regime that remains largely unexplored for strongly correlated quantum magnets. A phase diagram is established with distinct phases and features from earlier reports on SrCu2(BO3)2. Our results reveal two structural phase transitions from the tetragonal to two monoclinic phases sequentially. The monoclinic phases host only one gapless 3D AFM ground state at low temperatures, whereas an antiferromagnetic liquid phase with short-range ordering is identified to persist above the Neel temperature. At even higher temperatures, a sublinear temperature dependence of the spin-lattice relaxation rate, together with the absence of NMR line split or broadening, reveals an extended correlated paramagnetic regime.

Acknowledgments

This work is supported by the Scientific Research Innovation Capability Support Project for Young Faculty (Grant No. ZYGXQNJSKYCXNLZCXMM26), the National Key Research and Development Program of China (Grant Nos. 2023YFA1406500 and 2025YFA1412100), and the National Natural Science Foundation of China (Grant Nos. 12374156 and 12134020). A portion of this work was carried out at the Synergetic Extreme Condition User Facility (SECUF, https://cstr.cn/31123.02.SECUF.).

References

[1] L. Balents, “Spin liquids in frustrated magnets,” Nature 464, 199–208 (2010)

[2] L. Savary and L. Balents, “Quantum spin liquids: a review,” Rep. Prog. Phys. 80, 016502 (2016)

[3] Y. Zhou, K. Kanoda, and T.-K. Ng, “Quantum spin liquid states,” Rev. Mod. Phys. 89, 025003 (2017)

[4] B. S. Shastry and B. Sutherland, “Exact ground state of a quantum mechanical antiferromagnet,” Physica B+C 108, 1069–1070 (1981)

[5] A. Koga and N. Kawakami, “Quantum phase transitions in the Shastry-Sutherland model for SrCu2(BO3)2,” Phys. Rev. Lett. 84, 4461–4464 (2000)

[6] P. Corboz and F. Mila, “Tensor network study of the ShastrySutherland model in zero magnetic field,” Phys. Rev. B 87, 115144 (2013)

[7] E. Manousakis, “The spin-1/2 heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides,” Rev. Mod. Phys. 63, 1–62 (1991)

[8] J. Lee, Y. You, S. Sachdev, and A. Vishwanath, “Signatures of a deconfined phase transition on the Shastry-Sutherland lattice: Applications to quantum critical SrCu2(BO3)2,” Phys. Rev. X 9, 041037 (2019)

[9] H. Kageyama, K. Onizuka, T.

Improvements for AI systems

Bold header: Enhanced High-Pressure Structural Phase Identification

The improved system can accurately distinguish between monoclinic-1 and monoclinic-2 phases, as these are resolved by monitoring the quadrupole frequency νQ further reveals a second structural transition, from monoclinic1 to monoclinic-2, near 5 GPa.

Bold header: Correlated Paramagnetism Characterization

The system can identify the extended correlated paramagnetic regime by analyzing the spin-lattice relaxation rate's behavior, specifically noting that Above this [T regime], a sublinear ´temperature dependence of the spin-lattice relaxation rate, together with the absence of NMR line split or broadening, reveals an extended correlated paramagnetic regime.

Bold header: Field Dependence on Magnetic Transitions

The AI can model how external fields affect magnetic ordering by recognizing that an applied field of 8 T is unlikely to qualitatively alter the high-temperature phases above 100 K and that the characteristic temperature T∗ and TN extracted from our finite-field NMR data are consistent with those determined from zero-field specific heat measurements.

Abstract

The Shastry-Sutherland compound SrCu 2 (BO 3) 2 has attracted considerable interest as a platform for exploring quantum phases and quantum phase transitions driven by magnetic frustration. The pressure-induced structural and magnetic phase transitions in SrCu 2 (BO 3) 2, however, remain controversial. To address this issue, we performed high-pressure 11 B nuclear magnetic resonance (NMR) measurements on SrCu 2 (BO 3) 2 up to 14 GPa. The NMR spectra reveal two pressure-induced monoclinic phases. With pressure above 4 GPa and with temperature below 10 K, the rapid broadening of the NMR spectrum and the power-law behavior in the spin-lattice relaxation rate 1/T 1 provide clear evidence for a gapless 3D antiferromagnetic (AFM) phase in the monoclinic phase. At an intermediate temperature range around 20 K, the emergence of the field-dependent NMR line splits resolves a two-dimensional, short-range ordered AFM phase; at temperature above 30 K, the sublinear power-law behavior of 1/T 1 identifies an extended correlated paramagnetic regime.