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Time-hidden magnetic order in a multi-orbital Mott insulator

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Pith's one-line read Photo-doping Ca2RuO4 produces a metastable intra-layer ferromagnetic state at 10 microseconds, after antiferromagnetic order has melted and carriers have recombined, with broken glide-plane symmetry.

desk verdict Real metastable FM-like state found at 10 µs, but the 'intermediate timescale' emergence claim rests on a stroboscopic pre-pump snapshot, not on resolved dynamics. read the letter →

arxiv 2507.17146 v1 pith:K6FWQSKS submitted 2025-07-23 cond-mat.str-el cond-mat.mes-hall

Xinwei Li , Iliya Esin , Youngjoon Han , Yincheng Liu , Hengdi Zhao , Honglie Ning , Cora Barrett , Jun-Yi Shan
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Kyle Seyler Gang Cao Gil Refael David Hsieh
This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hall
keywords Ca2RuO4Mottinsulatorphoto-dopingmetastablemagneticordersecond-harmonicgenerationferromagnetismintermediatetimescaleorbitalsplitting
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports that shining near-infrared pulses on the Mott insulator Ca2RuO4 creates a magnetic state that has no counterpart in the equilibrium phase diagram. The state is detected 10 microseconds after excitation, a time window usually skipped between ultrafast and long-lived regimes. At that moment the usual antiferromagnetic order has already melted and the photo-created carriers have already recombined, and the optical signatures point to intra-layer ferromagnetic order with the crystal's glide plane broken. The authors propose a non-thermal route: photo-doping temporarily shrinks the orbital splitting below a critical value, trapping the system in a ferromagnetic valley of its energy landscape. If right, this expands the search for hidden electronic phases to intermediate timescales where states can be transiently trapped.

What carries the argument

The control parameter is the orbital splitting between the dxy orbital and the dyz/xz doublet in the flattened RuO6 octahedra. Photodoping reduces that splitting by lowering the charge gap, and when it drops below a critical value the intra-layer magnetic ground state switches from antiferromagnetic (moments along b) to ferromagnetic (moments along c). The experiments use two bulk-sensitive probes: magnetic-field-induced second-harmonic generation, whose time-reversal-odd tensor records the magnetic point group, and modulation-based differential birefringence, which detects loss of the bc glide plane. The timescale argument is carried by the transient-trapping mechanism proposed for systems with competing orders, in which the system is captured in a local valley while the original potential landscape is restored. The two-site exact-diagonalization model supplies the splitting-dependent energy landscape and the weak azimuthal anisotropy that explains slow domain growth.

What would settle it

Run the same pump-probe experiment at a repetition rate low enough (for example 1 kHz) that the sample fully relaxes between pulses, and look for the ferromagnetic signal 10 microseconds after a single pump pulse; if the signal disappears, the 10 microsecond state is a multi-pulse artifact rather than the single-cycle intermediate-time state.

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Extended reading notes

Core claim

The central claim is that photo-doping Ca2RuO4 at fluences above a threshold melts the intralayer antiferromagnetic order within about 2 ps and then leaves the crystal in a metastable state that, by 10 microseconds, shows second-harmonic and birefringence signatures incompatible with any equilibrium phase: the bc glide plane is broken and the magnetic point group drops from m to 1, consistent with intra-layer ferromagnetic moments pointing along the c-axis. The state appears only after the antiferromagnetic order parameter has collapsed and after photocarriers have recombined, and only below the Neel temperature; it is insulating, and it relaxes back to the antiferromagnetic state within a minute. Exact-diagonalization of a two-site model of the RuO6 network shows that reducing the orbital splitting below a critical value switches the ground state from antiferromagnetic (b-axis) to ferromagnetic (c-axis), and that the ferromagnetic valley has very weak in-plane anisotropy, so small domains can take much longer than electronic relaxation times to grow into a detectable net signal.

Load-bearing premise

The 10 microsecond snapshot is taken while a 100 kHz pulse train is still hitting the sample, and the paper's Section S12 concedes that the crystal does not fully recover between pulses; the whole picture assumes that what is seen at 10 microseconds is the state produced within one excitation cycle rather than an accumulated multi-pulse effect.

Editorial extensions

If this is right

  • Microsecond time delays become a valid hunting ground: hidden states in driven quantum materials can appear after electronic and phononic relaxation has finished, when domain coarsening or trapping has had time to act.
  • A fluence threshold and a temperature below the Neel point are required: the intra-layer ferromagnetic state appears only once the pump has melted the antiferromagnetic order and only if the system starts from the antiferromagnetic phase, not from the paramagnet.
  • The new state is thermally inaccessible in equilibrium and is insulating, so it is a different object from the pressure- or strain-driven itinerant ferromagnetism previously reported in Ca2RuO4.
  • The observable onset of the hidden order is set by domain growth, not by the initial electronic relaxation, so optical signals can stay zero for nanoseconds and then rise on the microsecond scale.
  • Within one pulse cycle the state forms, persists for an appreciable fraction of the 10 microsecond period, and then the crystal recovers to the antiferromagnetic state within about a minute, defining the metastable lifetime.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's 10 microsecond point is a stroboscopic pre-pump snapshot in a 100 kHz pulse train; the claim that this is the single-pulse intermediate-time state would be directly tested by a low-repetition-rate or single-shot measurement that lets the sample fully relax between pulses.
  • If the splitting-controlled antiferromagnetic-to-ferromagnetic switch is generic, other d4 or multi-orbital Mott insulators with a similar orbital splitting might host analogous time-hidden ferromagnetic states, and epitaxial strain or chemical pressure might stabilize them in equilibrium.
  • Because optical measurements determine symmetries but not atomic positions, a neutron or resonant X-ray scattering experiment timed to the 10 microsecond window would be a cleaner confirmation of the c-axis ferromagnetic moment arrangement.
  • The weak in-plane anisotropy predicted by the two-site model implies the hidden order should appear as small domains first; spatially resolved probes could observe domain growth directly rather than infer it from the integrated signal.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reports time-resolved second-harmonic generation (SHG) and optical birefringence experiments on the multi-orbital Mott insulator Ca2RuO4. After intense photoexcitation above a critical fluence, the authors observe at a nominal 10 μs delay a state in which the bc glide-plane symmetry is broken, as evidenced by rotational-anisotropy SHG patterns that require a surface magnetic point group 1 tensor fit, and by a bulk-sensitive birefringence asymmetry that is zero in equilibrium and grows above a fluence threshold. The magnetic-field-induced SHG data are interpreted as consistent with intra-layer ferromagnetic order with moments along the c-axis, arising after the intra-layer antiferromagnetic order has melted. A two-site exact-diagonalization model shows that reducing the orbital splitting Δ drives a ground-state crossover from intra-layer AFM to intra-layer FM correlations, and a mean-field calculation shows that photodoping reduces Δ. The authors conclude that photo-doping accesses a metastable 'time-hidden' magnetic state on the intermediate microsecond timescale, distinct from all equilibrium phases.

Significance. If the identification holds, this is a striking result: a metastable, glide-symmetry-broken magnetic state in a Mott insulator that appears on a microsecond timescale, populating a previously little-explored time window between ultrafast and quasi-static regimes. The paper's strengths are its internal consistency and cross-validation: the equilibrium AFM phase is fit with the expected magnetic point group m, the metastable phase requires point group 1, the same conclusion is reached by surface-sensitive SHG and bulk-sensitive birefringence, and the domain-reversal measurements support an ordered state rather than a heating artifact. The two-site model is solved by exact diagonalization and inherits parameters from prior work, with only one fitted spring constant in the mean-field analysis. The main weakness is that the temporal claim of emergence in the intermediate window is not directly established by the data, as discussed below; the state is well characterized at 10 μs under repetitive excitation, but its single-pulse evolution from 100 ps to 10 μs is inferred rather than measured.

major comments (3)
  1. [Fig. 4e and Section S12] The central 'intermediate time window' claim is not directly established by the data. The 10 μs data (e.g., Fig. 2d(iii)) are acquired with the probe pulse arriving slightly before the pump in a 100 kHz train, and Section S12 concedes that for F > Fc the sample does not fully recover between pulses and that the metastable state is already present before the pump arrives. The measurement therefore reports a steady-state, multi-pulse condition rather than the state reached about 10 μs after a single excitation pulse; the signal could accumulate over many cycles. No data are shown between 100 ps and 10 μs, so the slow domain-coalescence evolution in Fig. 4e is inferred, not measured. The abstract's claim that the state 'emerges' in the previously unexplored intermediate window should either be supported by single-pulse or variable-repetition-rate experiments, or be rephrased to describe a metastable state sustained under repetitive excitation.
  2. [Fig. 4e and Section S9] The trapping mechanism is invoked but not demonstrated for Ca2RuO4. The two-site exact-diagonalization calculation establishes that the FM state is a local minimum for Δ below Δc, and the Section S2 mean-field calculation shows that photodoping reduces Δ, but neither calculation simulates the relaxation dynamics or the population of the FM valley after the potential is restored. The statement in Fig. 4e that the system is trapped 'possibly through the transient trapping mechanism proposed by Sun and Millis [22]' is an untested assumption, and the word 'trajectory' in the abstract is stronger than what the calculations show. The authors should either perform a time-dependent simulation of the relaxation or explicitly label this step as a hypothesis.
  3. [Sections S6, S7, and title] The magnetic nature of the new state is inferred from symmetry fits rather than measured by a direct magnetic probe. The BFISH data are fit by a magnetic point group 1 tensor and the birefringence asymmetry shows glide-plane breaking, but no direct measurement of a c-axis ordered moment is presented; the absence of Kerr rotation in Section S7 is attributed to antiparallel stacking of FM planes. The abstract and main text are appropriately cautious in saying the observations are 'consistent with' intra-layer FM order, but the title 'Time-hidden magnetic order' goes beyond the directly measured quantities. A direct probe (e.g., time-resolved resonant x-ray scattering or a local magnetic probe) or a softening of the title and framing is needed.
minor comments (4)
  1. [First paragraph and references] The citation of '[2, 12]' for the steep increase in Δ below TOO and for the 'previous neutron and x-ray diffraction measurements' is incorrect: reference [12] is Dean et al. on Sr2IrO4, not a Ca2RuO4 orbital-order study. Please replace with the appropriate Ca2RuO4 structural references.
  2. [Fig. 4c context, reference [17]] The statement that the AFM-to-FM crossover as Δ is reduced is 'consistent with prior work [17]' appears to cite the wrong reference: [17] is a Keldysh control paper by Li et al., whereas the relevant prior two-site model is Meetei et al. (reference [8] in the main text or [16] in the Supplemental Information). Please correct this citation.
  3. [Section S8 and main text] The notation for the glide-symmetry-breaking order parameter is inconsistent: the main text uses ηFM (Fig. 2f) while Section S8 introduces ηM. Please unify the notation.
  4. [Methods, time-resolved SHG] The phrase '10 μs snapshot was obtained by having the probe pulse arrive slightly before the pump which, in a repetitive measurement, is equivalent to setting the time delay to the laser pulsing period' should explicitly note that this only samples the pre-pump steady state if the system has reached a periodic steady state; the associated assumption is acknowledged in S12 but should also be flagged in the main text.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the glide-symmetry-broken magnetic state is identified by direct symmetry fits to measured SHG and birefringence data, and the model Hamiltonian calculation is an interpretive overlay rather than the source of the empirical claim.

full rationale

The central empirical result—a metastable state at 10 microseconds with broken bc glide plane and field response consistent with c-axis intra-layer FM order—is derived from polarization-resolved BFISH and birefringence measurements through symmetry-based tensor fits (main text Figs. 2d(iii), 3b; SI Sections S6, S8). The fits use measured intensities as inputs and independently discriminate surface magnetic point group m (bc glide preserved) from point group 1 (glide broken); the birefringence asymmetry Delta-I-perp provides a separate bulk-sensitive check. None of these quantities is generated by the two-site exact-diagonalization model or fitted to its output. The model calculation (Fig. 4c) predicts an AFM-to-FM transition as Delta is reduced, using parameters from prior work (Refs. 7, 16, 17) and a lattice spring constant K calibrated to the equilibrium Delta = 0.72 eV (SI S2); the photoinduced Delta reduction is then inferred from a measured SHG intensity drop, not from the model. This is a consistency argument, not a circular derivation. Self-citations (Refs. 17, 18) are used for carrier-recombination timescales but are corroborated by external Refs. 11 and 12, and they do not carry the symmetry identification. SI Section S12 openly discloses that above F_c the sample does not fully recover between 100 kHz pulses, so the 10 microsecond snapshot is a pre-pump stroboscopic readout; this is a real temporal-resolution caveat but it is an acknowledged limitation, not a case where a prediction equals its input. No fitted parameter is renamed as a prediction, and no load-bearing uniqueness theorem is imported from the authors' prior work.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central experimental claim does not depend on numerical fitting; the model parameters are inherited from prior literature or set by hand and affect only the theoretical interpretation of the trajectory.

free parameters (3)
  • K (Jahn-Teller spring constant) = 0.0926 eV^-1
    Chosen in S2 so the mean-field model converges to the equilibrium Delta=0.72 eV; it is then used to predict a photodoping-induced reduction to Delta=0.3 eV. This is a model input fitted to equilibrium data, not to the metastable-state data.
  • Two-site model parameters (txy=1.5, tyz=1, txz=0, U=10, JH=2.5, lambda=0.4)
    Set by hand from realistic estimates and prior work in S9; they determine the value of Delta_c and the FM-state anisotropy used to argue slow domain growth. They are not fitted to the new measurements.
  • Photodoping fraction in mean-field simulation = 10% of electrons
    S2 moves 10% of the electron population from valence to conduction states to mimic photodoping; the resulting Delta reduction (0.72 to 0.3 eV) is used as evidence that photo-carriers lower Delta. The fraction is a modeling choice.
assumptions (6)
  • domain assumption Surface electric-dipole SHG dominates the lattice response in Ca2RuO4, with point group mm2 (C2 || b).
    Used in S3 to fit RA-SHG patterns and to derive the surface magnetic point group m for the AFM phase; the fits rule out mmm and other candidate groups.
  • domain assumption The c-type BFISH signal is proportional to surface magnetization M, with Ispin approximately 2Pspin/Platt.
    Derived in S5 under the condition |Pspin| << |Platt|, which holds in the data.
  • domain assumption Photo-doping reduces the crystal-field splitting Delta, coupling the pump to the magnetic transition.
    Supported by the mean-field calculation in S2, which uses a Jahn-Teller spring K fitted to equilibrium Delta=0.72 eV and predicts Delta=0.3 eV under 10% photodoping; the experimental support is an indirect SHG intensity drop (Fig. 1e).
  • domain assumption A two-site exact diagonalization model with parameters from prior work captures the AFM-to-FM transition of Ca2RuO4 as a function of Delta.
    S9; the model reproduces the previously predicted Delta_c and is used to argue that the FM state is energetically accessible but weakly anisotropic.
  • domain assumption The transient trapping mechanism for systems with competing orders (Sun and Millis, Ref. 22) applies to Ca2RuO4.
    Invoked in main text Fig. 4e(iii) to explain why the system relaxes into the FM valley rather than back to AFM; no dynamical simulation is performed.
  • domain assumption The 100 kHz stroboscopic geometry with probe before pump provides a valid 10 microsecond snapshot of the metastable state.
    S8 and S12; the persistent effects are acknowledged and argued not to change the conclusions, but the single-cycle interpretation is not directly verified.

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Pith. "Pith review of Time-hidden magnetic order in a multi-orbital Mott insulator." pith.science (2026). https://pith.science/paper/K6FWQSKS

@misc{pith2026250717146,
  author       = {Pith},
  title        = {Pith review of: Time-hidden magnetic order in a multi-orbital Mott insulator},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K6FWQSKS}},
  note         = {Machine review of arXiv:2507.17146}
}
abstract

Photo-excited quantum materials can be driven into thermally inaccessible metastable states that exhibit structural, charge, spin, topological and superconducting orders. Metastable states typically emerge on timescales set by the intrinsic electronic and phononic energy scales, ranging from femtoseconds to picoseconds, and can persist for weeks. Therefore, studies have primarily focused on ultrafast or quasi-static limits, leaving the intermediate time window less explored. Here we reveal a metastable state with broken glide-plane symmetry in photo-doped Ca$_2$RuO$_4$ using time-resolved optical second-harmonic generation and birefringence measurements. We find that the metastable state appears long after intralayer antiferromagnetic order has melted and photo-carriers have recombined. Its properties are distinct from all known states in the equilibrium phase diagram and are consistent with intralayer ferromagnetic order. Furthermore, model Hamiltonian calculations reveal that a non-thermal trajectory to this state can be accessed via photo-doping. Our results expand the search space for out-of-equilibrium electronic matter to metastable states emerging at intermediate timescales.

Figures

Figures reproduced from arXiv: 2507.17146 by the authors.

Figure 1
Figure 1. Accessing the metastable magnetic state via photo-doping in Ca2RuO4. a, Proposed trajectory (dashed arrows) in the potential energy landscape (∆ vs. OP) from the intra-layer AFM to hidden intra-layer FM state launched by impulsive photo-doping. The moment configura￾tions (small canting angles not depicted) in both states are il￾lustrated, with the bc glide plane marked. The red paraboloid shows the potential energy … view at source ↗
Figure 2
Figure 2. Evidence for a metastable intra-layer ferromagnetic state from SHG. a, Applied B-field directions to study c-type SHG response. b, I 2ω spin(φ) for B ∥ a (red curves) and B ∥ b (blue curves) at various T in Pin–Sout geometry. Curves are vertically offset for clarity. The definition of ηAFM is marked. c, ηAFM versus T. Black line is a guide to the eye. d, Time evolution of I 2ω spin(φ) for distinct polarization combi… view at source ↗
Figure 3
Figure 3. Broken glide-plane symmetry in the metastable state probed by birefringence polarimetry. a, Experimental configuration. Glide-symmetry-breaking is captured by subtracting the cross-polarized reflection intensity at two opposite scattering plane angles about the principal axes of Ca2RuO4. The yellow curve shows I ⊥(φ) calculated for an orthorhombic crystal ([10] Section S7). b, F dependence of ∆I ⊥ (measured at φ = ±… view at source ↗
Figures from the paper (18 more)
Figure 4
Figure 4. Figure 4: Microscopic mechanism of the light-induced metastable state. a, Two-site model of Ca2RuO4 with d 4 filling. The lowest energy spin configurations (red and blue arrows) facilitating virtual hopping between sites (curved dashed arrow) are shown for ∆ > ∆c (top panel) and…
Figure 5
Figure 5. Figure 5: a, Calculated orbital-resolved band structure and density of states of Ca2RuO4 by mean-field theory. b, Proposed mechanism of ∆-tuning by photodoping. c, Band structure that is consistent with a nonequilibrium charge distribution. Details of the model and model paramet…
Figure 6
Figure 6. Figure 6: a-d, Polarization resolved lattice-induced RA-SHG patterns at 80 K in equilibrium. Black solid lines: model fit assuming the mm2 point group. e, Time-resolved SHG intensity of Pin–Pout channel pumped with F = 4 mJ/cm2 , ndh = 3.8 × 10−2 /Ru at 120 K. Black line: fit by…
Figure 7
Figure 7. Figure 7: Fits to BFISH data in the intra-layer AFM phase in equilibrium. a, Sin–Sout, b, Pin–Sout, c, Sin–Pout, d, Pin–Pout. Top (lower) row panels all correspond to the B ∥ a (B ∥ b) configuration. Red circles: experimental data. Blue lines: model calculation. AFM phase shows …
Figure 8
Figure 8. Figure 8: Fits to BFISH data in the metastable magnetic phase. a, Sin–Sout, b, Pin–Sout, c, Sin–Pout, d, Pin–Pout. Top (lower) row panels all correspond to the B ∥ a (B ∥ b) configuration. Red circles: experimental data. Blue lines: model calculation. To explain the I 2ω spin(φ)…
Figure 9
Figure 9. Figure 9: The intra-layer AFM domains under consideration to be averaged out to give the BFISH signal. The rectangles represent [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: Lattice and spin configurations, and associated magnetic point groups and symmetry operators for Ca [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]
Figure 11
Figure 11. Figure 11: Temperature-dependent Kerr rotation (F > Fc pumping, with a vertical field of 0.15 T) and Kerr ellipticity (F < Fc pumping, no vertical field). Rotation and ellipticity signals are nomalized by the same constant and therefore their magnitudes can be compared. of I ⊥(φ…
Figure 12
Figure 12. Figure 12: I ⊥(φ) signal (normalized) within the cross-polarized Sin–Pout channel for a crystal with orthorhombic (blue dashed) and monoclinic (red solid) symmetry. The breaking of the σbc glide plane in the metastable magnetic phase, in addition to exhibiting clear signatures i…
Figure 13
Figure 13. Figure 13: Metastable magnetic order parameter ηM mapped versus temperature and ndh at a pump-probe time delay of 2 ps. ηM = 1 occurs at high fluence and at 10 µs (main text Fig. 2f). In a stroboscopic measurement, we have a photodiode reading I ⊥(φ0), and by modulating the pump…
Figure 14
Figure 14. Figure 14: a, dI⊥(φ0, t) transient (normalized by ηM) at 78 K. b, dI⊥(φ0, t) transient (normalized by ηM) at 250 K. c, dI⊥(−φ0, t) transient (normalized by ηM) at 78 K. d, dI⊥(−φ0, t) transient (normalized by ηM) at 250 K. Red to purple: a series of fluences with ndh=0.15 - 2.69…
Figure 15
Figure 15. Figure 15: a, dI⊥(φ0) (normalized by ηM) versus temperature at 50 ps. b, Same as a but plotting dI⊥(−φ0). c, ηM (calculated from dI⊥(φ0) − dI⊥(−φ0)) versus temperature. Red to purple: a series of fluences with ndh=0.09 - 2.69×10−2 /Ru. Curves are offset. Dashed black lines are p…
Figure 16
Figure 16. Figure 16: Two-site degenerate two-orbital, quarter-filled Hubbard model. a, the ferro-orbital ferromagnetic con￾figuration. b, the ferro-orbital antiferromagnetic configuration. c, the antiferro-orbital ferromagnetic configuration. d, the antiferro-orbital antiferromagnetic con…
Figure 17
Figure 17. Figure 17: Isotropic limit of the intra-layer FM state revealed by the two-site model. a, Lowest eigenstates and corresponding eigen-energies. b, M · B mapped with a weak B field scanned throughout the entire solid angle. Induced M is isotropic and always directed along B. (1) ∆…
Figure 18
Figure 18. Figure 18: a, Fluence dependent differential reflectivity transients at 78 K. Red to purple: a series of fluences with ndh=0.15 - 2.69×10−2 /Ru. The highest fluence is much larger than the critical fluence of the metastable phase transition. b, Differential reflectivity transien…
Figure 19
Figure 19. Figure 19: Optical conductivity spectra of Ca2RuO4 in the un-pumped equilibrium state at 80 K and the 1 eV pumped non￾equilibrium state at a time delay of 0.5 ps (F = 4 mJ/cm2 , ndh = 3.8 × 10−2 /Ru) [PITH_FULL_IMAGE:figures/full_fig_p027_19.png]
Figure 20
Figure 20. Figure 20: a, Laser spot sampling different locations of the crystal. b, Pin–Pout I 2ω spin patterns collected at spot 1 and 2 (in a) in the light-induced metastable state (at high fluence and low temperature); data from spot 1 is reported in the main text. The opposite phase of…
Figure 21
Figure 21. Figure 21: I 2ω (φ) plots for Sin–Pout geometry before (orange) and 0.1 ps after (red) impulsive photo-doping at 80 K. Fluence: ndh = 0.6 × 10−2 /Ru [PITH_FULL_IMAGE:figures/full_fig_p029_21.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.