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REVIEW 4 major objections 5 minor 189 references

The Gr\"uneisen parameter applied to critical phenomena and experimental investigations of correlated phenomena in molecular conductors

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Cosmic expansion is recast as a caloric effect through the effective Grüneisen parameter, identified with the equation-of-state parameter ω.

arxiv 2411.13743 v1 pith:IZAWPHOQ submitted 2024-11-20 cond-mat.str-el cond-mat.othercond-mat.stat-mech

Lucas Squillante This is my paper · ORCID
classification cond-mat.str-elcond-mat.othercond-mat.stat-mech
keywords Grüneisenparameterequation-of-statedarkenergycaloriceffectsquantumcriticalphenomenaMottinsulatorchargeorderingTMTTFsalts
topics Dark Energy
open problems Dark Energy
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

The thesis tries to establish that the effective Grüneisen parameter $\Gamma_{\mathrm{eff}}$, which in condensed matter measures how pressure changes with internal energy at fixed volume, is the same object as the cosmological equation-of-state parameter $\omega$. If that identification is right, the expansion of the universe becomes a thermodynamic cooling and heating process: radiation and matter eras cool as the universe expands, and the dark-energy era behaves like an inverse caloric effect. The thesis also claims that the sign change of $\Gamma_{\mathrm{eff}}$ between decelerated and accelerated expansion is analogous to crossing a critical point, and that the Einstein field equations already contain $\Gamma_{\mathrm{eff}}$ through the energy-momentum tensor. Alongside that, it applies the various Grüneisen parameters to zero-field quantum criticality, adiabatic magnetization, and caloric-effect maximization, and reports dielectric, Raman, and fluorescence data on (TMTTF)$_2$X molecular conductors.

What carries the argument

The load-bearing object is the effective Grüneisen parameter $\Gamma_{\mathrm{eff}}=\alpha_p v_0 B_T/c_v=v_0(\partial p/\partial U)_v$, which measures the pressure change per internal-energy change at fixed volume. The thesis's central move is to recognize that the cosmological perfect-fluid equation of state $p=\omega\rho$ is formally the Mie-Grüneisen equation $p=\Gamma_{\mathrm{eff}}E/v$ once $\rho=E/v$, so the two dimensionless coefficients coincide. This identification, together with the perfect-fluid adiabatic temperature-evolution law integrated to $T v^{\Gamma_{\mathrm{eff}}}=\mathrm{constant}$, carries the entire cosmological argument; the other Grüneisen parameters (magnetic, electric, polar, elastic) are generated from Maxwell relations and quantify the corresponding caloric effects, connecting the same thermodynamic machinery to quantum criticality, the elastocaloric effect, and materials design.

What would settle it

Measure the late-time cosmic temperature evolution and compare with $T v^{\Gamma_{\mathrm{eff}}}=\mathrm{constant}$: for the claimed dark-energy value $\Gamma_{\mathrm{eff}}=-1$, the relation predicts $T\propto v\propto a^3$ as the universe expands, whereas cosmic microwave background temperature measurements give $T_{\mathrm{CMB}}\propto(1+z)\propto a^{-1}$; a continued decrease of $T_{\mathrm{CMB}}$ at low redshift would falsify the caloric reading.

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Extended reading notes

Core claim

On its own terms, the thesis derives $\Gamma_{\mathrm{eff}}=v_0(\partial p/\partial U)_v$, recalls the perfect-fluid temperature evolution law $\dot{T}/T=(\partial p/\partial\rho)_n\,\dot{n}/n$, and identifies $(\partial p/\partial\rho)_n$ with $\omega$. Since $\rho=E/v$, this gives $\omega=v(\partial p/\partial E)_n$, which is exactly $\Gamma_{\mathrm{eff}}$. Writing $T_{\mu\nu}=(1+\omega)\rho u_\mu u_\nu+\rho\omega g_{\mu\nu}$ then shows that the Einstein equations can be written with $\Gamma_{\mathrm{eff}}$ in place of $\omega$. The thesis integrates the temperature-evolution law to $T v^{\Gamma_{\mathrm{eff}}}=\mathrm{constant}$, interprets the expansion as a barocaloric and inverse-barocaloric effect, and reads the sign change of $\Gamma_{\mathrm{eff}}$ from the matter-dominated to the dark-energy-dominated era as a condensed-matter-like critical-endpoint transition. The accompanying experiments probe possible multiferroic behavior in the Fabre salts: a dielectric constant maximum at the charge-ordering temperature, a magnetic-field suppression of a Raman mode, and a fluorescence background five orders of magnitude larger in the hydrogenated than in the deuterated salt.

Load-bearing premise

The load-bearing premise is that the universe, or each of its eras, is a perfect fluid obeying the Mie-Grüneisen equation of state $p = \Gamma_{\mathrm{eff}}E/v$; if that equation of state fails for the cosmological fluid, the equality $\Gamma_{\mathrm{eff}}=\omega$ becomes only a relabeling and the Einstein-equation embedding carries no new content.

Editorial extensions

If this is right

  • If $\Gamma_{\mathrm{eff}}=\omega$ is correct, the two cosmic eras correspond to caloric effects: expansion cools the universe for $\Gamma_{\mathrm{eff}}>0$ and heats it for $\Gamma_{\mathrm{eff}}<0$.
  • The decelerated-to-accelerated transition acquires a thermodynamic signature as a sign change in $\Gamma_{\mathrm{eff}}$, analogous to crossing a critical end point, with a possible symmetry-breaking reading via Noether's theorem.
  • The dark-energy equation-of-state parameter would not be a fixed constant but would inherit the temperature and volume dependence of the thermodynamic coefficients inside $\Gamma_{\mathrm{eff}}$, implying a time-dependent $\Lambda(t)$ or $G(t)$ if the universe continues to cool and expand.
  • Because the Einstein equations can be written with $\Gamma_{\mathrm{eff}}$ inside the energy-momentum tensor, anisotropic cosmic expansion could be studied with the elastic Grüneisen parameter $\Gamma_{\mathrm{ec}}$, giving a condensed-matter route to stress-tensor effects in cosmology.
  • Within condensed matter, the same framework predicts that intrinsic local fields suppress the divergent Grüneisen signature of genuine zero-field quantum phase transitions, and that an adiabatic temperature increase can magnetize a paramagnet without applying an external magnetic field.

Reading between the lines

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

  • If the equality $\Gamma_{\mathrm{eff}}=\omega$ is taken as physical rather than merely formal, it suggests importing condensed-matter measurement strategies—thermal expansion, heat capacity, compressibility—into cosmology, where the analogous quantities would have to be inferred from luminosity-distance or baryon-acoustic-oscillation data; that is a testable program, not something the thesis carri
  • The relation $T v^{\Gamma_{\mathrm{eff}}}=\mathrm{constant}$ gives a clean discriminant for the eras: for $\Gamma_{\mathrm{eff}}=1/3$ it reproduces $T\propto a^{-1}$ for radiation, while for $\Gamma_{\mathrm{eff}}=-1$ it predicts $T\propto a^3$ for the dark-energy era; checking the temperature-redshift history at late times would test the cosmic side of the identification.
  • The experimental finding that deuteration lowers the fluorescence background of the TMTTF salts by five orders of magnitude suggests a materials-design route to cleaner Raman and optical studies of charge ordering and magneto-optical effects in this family.
  • The generalized Grüneisen construction from Maxwell relations is not limited to pressure, magnetic field, electric field, or polarization; the same derivation would generate new caloric coefficients for any adiabatically varied thermodynamic field, such as chemical potential or shear components, which could be tested in other correlated systems.
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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

4 major / 5 minor

Summary. This Ph.D. thesis derives and generalizes the Grüneisen parameter (effective, magnetic, electric, polar, and elastic) from Maxwell relations and applies it to model paramagnets, zero-field quantum phase transitions, caloric effects, and cosmology, where Γeff is identified with the cosmological equation-of-state parameter ω. The experimental part reports dielectric, Raman, and fluorescence measurements on the molecular conductors (TMTTF)2X, including a magnetic-field-induced reduction of a Raman line in deuterated (TMTTF)2PF6 and a large fluorescence contrast between (TMTTF)2AsF6 and deuterated (TMTTF)2PF6.

Significance. The thermodynamic derivations in Chapter 2 are mostly standard and the unified presentation of the various Grüneisen parameters via Maxwell relations is a useful pedagogical contribution. The magneto-optical Raman observation in Sec. 3.3.2, if confirmed, would be of interest to the organic-conductor community. However, the headline cosmological claim (Γeff = ω) is an identity under the assumed Mie-Grüneisen equation of state rather than a testable derivation; the zero-field QPT suppression and the adiabatic magnetization proposal rest on ad hoc model assumptions. The manuscript therefore does not deliver on its most ambitious claims, although several local results are sound and clearly presented.

major comments (4)
  1. [Sec. 2.3.10, Eq. (2.241)] The identification ω = (∂p/∂ρ)_n = v(∂p/∂E)_n = Γeff is definitional: combining p = ωρ with the Mie-Grüneisen EOS p = Γeff E/v and ρ = E/v forces ω = Γeff by construction. No independent physical content is added. Evaluated from the entropy definition (Eq. 2.48), Γeff becomes 0/0 for the pressureless matter era (S = 0) and for vacuum energy (S = 0), so the era values 1/3, 0, and −1 are imported from ΛCDM rather than computed. Correspondingly, Eq. (2.262) is the standard perfect-fluid energy-momentum tensor Tμν = (1+ω)ρuμuν + ρωgμν with ω renamed Γeff, so the claim that the Einstein field equations 'implicitly incorporate Γeff' is a relabeling rather than a new result.
  2. [Sec. 2.3.10, Eq. (2.249)] The temperature law T v^{Γeff} = const is not consistent with the observed CMB temperature T ∝ 1/a. For matter (Γeff→0) it predicts T = const, and for dark energy (Γeff = −1) it predicts T ∝ v, whereas the CMB temperature falls as 1/a through both eras. The text states that T is 'consistently reduced' during the matter-dominated era, which is contrary to what Eq. (2.249) actually gives.
  3. [Sec. 2.3.2, Eqs. (2.77) and (2.130)] The suppression of the Γmag divergence at B→0 is introduced by assuming Br = √(B² + Bloc²) and adding Bloc as an offset, with the angle θ arbitrarily set to 90° in Eq. (2.76). The conclusion that real paramagnets cannot exhibit a genuine zero-field QPT is therefore a consequence of this model assumption, not an empirical finding. The estimate of Bloc for β-YbAlB4 uses only a dipolar formula (Eq. 2.74) and is not validated against the actual magnetic structure, so the claimed suppression of quantum criticality is not robust.
  4. [Sec. 2.3.4, Eq. (2.139)] The adiabatic magnetization proposal postulates that an adiabatic temperature increase raises Bloc by ΔBloc to conserve entropy. For a fixed dipolar configuration, Bloc is set by the lattice and interactions, not a free thermodynamic variable; the entropy of the Brillouin paramagnet depends on μB B/T, so an adiabatic increase of T at fixed B would change the spin populations without generating an internal-field increment. The mechanism is not derived from a microscopic Hamiltonian and is thus an ad hoc input to the model.
minor comments (5)
  1. [Throughout] The name 'Friedman' should be 'Friedmann' (e.g., Eqs. in Sec. 2.2.3 and throughout Sec. 2.3.10).
  2. [Eq. (2.211)] The Barrett formula as written has unmatched parentheses and unclear placement of the −T0 term; please rewrite it cleanly.
  3. [Fig. 2.17] The labels in this figure are corrupted (e.g., 'eff = ω = 1/3', 'eff = ω → 0', and 'eff = ω 1→'); the correct subscripts and arrows should be restored.
  4. [Sec. 3.3.2] The Raman and fluorescence results are based on single samples and, as the text acknowledges, lack reproducibility checks; they should be explicitly framed as preliminary observations rather than definitive experimental findings.
  5. [Sec. 2.3.10, reference [95]] The cosmological section cites 'Grüneisen meets Einstein (submitted)' as Ref. [95], but a published version exists (Results in Physics 57, 107344 (2024)); the published reference should be cited instead.

Circularity Check

3 steps flagged · score 6.0 of 10

The cosmological identification Γeff = ω (Eq. 2.241) is a relabeling: it is built in by the Mie-Grüneisen/perfect-fluid EOS, and Eq. 2.262 restates the standard perfect-fluid energy-momentum tensor with ω renamed Γeff.

  1. self definitional [Sec. 2.3.10, Eq. (2.241)]
    "Considering the EOS of a perfect fluid, the term(∂p/∂ρ)n is recognized asω. Since ρ = E/v, we have: ω = (∂p/∂ρ)n = (∂p/∂[E/v])n = v(∂p/∂E)n. (2.241) The definition ofω in Eq.2.241 is exactly the same as the definition of the effective Grüneisen parameter Γeff, cf.Eq.2.47."

    For the perfect-fluid EOS p=ωρ, the equality ω=(∂p/∂ρ)_n is itself the definition of ω. Rewriting ρ=E/v makes v(∂p/∂E)_n an algebraic identity, and Eq. 2.47 defines Γeff=v0(∂p/∂U)_v. Hence Γeff=ω holds by construction once the Mie-Grüneisen EOS is assumed; it is not derived from the material Grüneisen definition. The era values 1/3, 0, −1 are imported from ΛCDM rather than computed from Eq. 2.48, which gives 0/0 for pressureless matter and for vacuum energy.

  2. renaming known result [Sec. 2.3.10, Eq. (2.262)]
    "Using the EOS of a perfect fluid,Tµν can be expressed as a function ofω as Tµν = (1 +ω)ρuµuν +ρωgµν [91]. Hence, Einstein field equations can be rewritten in terms ofΓeff so that: Rµν− 1/2gµνR + Λgµν = 8πG[(1 + Γeff )ρuµuν +ρΓeffgµν]. (2.262) It is then evident that Einstein field equations implicitly incorporateΓeff through Tµν."

    The stress-energy tensor written here is the standard perfect-fluid form Tμν=(p+ρ)uμuν+pgμν with p=ωρ substituted, and then ω is relabeled Γeff. No independent property of Γeff enters beyond the ratio p/ρ. The claimed embedding into Einstein field equations therefore restates the perfect-fluid EOS in Grüneisen notation; the later anisotropic/imperfect-fluid discussion would require additional dissipative terms that were explicitly set to zero in the derivation of Eq. 2.240.

1 more flagged steps
  1. self definitional [Sec. 2.3.10, Eqs. (2.240)-(2.249)]
    "Integrating both sides of Eq.2.242 and considering that(∂p/∂ρ)n =ω = Γeff, we have: ... ln (T ) +C1 = Γeff [ln (n) +C2] ... T v Γeff =constant. (2.249)"

    Equation 2.249 is the standard adiabatic perfect-fluid temperature law T n^{-ω}=const, obtained after substituting the definitional identity ω=Γeff. Calling the resulting cooling a barocaloric effect, or the Γeff<0 case an inverse barocaloric effect, does not add testable content. Moreover, with the adopted matter-era value Γeff≈0 the law predicts T≈const, not the asserted temperature reduction during the matter-dominated era, so the interpretation is carried entirely by the imported ΛCDM values of ω.

full rationale

The thesis contains a long and largely self-contained set of thermodynamic derivations: the effective Grüneisen parameter from Eqs. 2.44-2.52, the magnetic Grüneisen parameter for the Brillouin paramagnet, the generalization of Grüneisen parameters from Maxwell relations, and the entropy-based caloric-effect analysis are all derived from standard definitions and are not circular. The zero-field QPT suppression is model-based rather than circular: a finite Bloc is postulated and then Γmag is recomputed with Br=(B^2+Bloc^2)^(1/2), so the non-divergence is a consequence of the assumed model, not a hidden fit. The substantive circularity is confined to Section 2.3.10. There, Eq. 2.241 identifies ω with Γeff using only the perfect-fluid EOS and the identity (∂p/∂ρ)_n=v(∂p/∂E)_n, which is exactly the definition of Γeff from Eq. 2.47 under the Mie-Grüneisen EOS. Every subsequent cosmological claim — the temperature law Eq. 2.249, the entropy-era relations Eqs. 2.251-2.254, the sign-change analogy near Eq. 2.260, and the Einstein-equation embedding Eq. 2.262 — inherits this relabeling rather than adding new physics. Since the central cosmological prediction reduces to construction while the rest of the thesis is independent, the appropriate score is 6, not higher. The self-citations to the authors' own papers (Refs. [95], [103], [49], [55]) are real prior publications but are not the load-bearing mechanism here; the circularity is definitional, not citational.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

No new particles, fields, or dimensions are introduced. The new elements are thermodynamic processes, such as adiabatic magnetization, and an interpretative identification of Γeff with omega, neither of which constitutes an invented entity.

free parameters (5)
  • Bloc for Brillouin paramagnet = 0.01 T.
    Estimated from dipole-dipole interaction with μ = μB and r = 5 Å (Eq.2.74); used to suppress the Γmag divergence at B = 0 in Sec.2.3.2.
  • Bloc for beta-YbAlB4 = 0.04 T.
    Estimated with μ ≈ 1.94 μB and r ≈ 3.5 Å; used to compute Γmag suppression in Sec.2.3.2.
  • Angle theta between B and Bloc = 90 degrees.
    Assumed for the cosine rule simplification Br ≈ sqrt(B^2 + Bloc^2) in Sec.2.2.2; supports the zero-field QPT conclusion.
  • Adiabatic magnetization temperatures = T1 = 2 mK and T2 = 2.1 mK.
    Chosen values used to compute ΔBloc ≈ 3.2 mT in Eq.2.141 for the proposed adiabatic-magnetization protocol.
  • Barrett formula parameters = A = 0, m = 8.4e4 K, T1 = 60 K, T0 = -35 K (inset); main-panel fit to kappa-(BEDT-TTF)2Cu2(CN)3.
    Fitted to dielectric data in Sec.2.3.9; the ΓE enhancement near the quantum paraelectric plateau is a property of this fit, not an independent prediction.
assumptions (5)
  • standard math Maxwell relations and standard thermodynamic identities are valid for the systems considered.
    Used throughout Sec.2.2 to derive Γ, Γmag, ΓE, and ΓP.
  • domain assumption Real paramagnets always contain a local field Bloc ≈ 0.01-0.04 T from dipole interactions, and Br ≈ sqrt(B^2 + Bloc^2) with theta ≈ 90 degrees.
    Introduced in Sec.2.2.2 and used in Sec.2.3.2 to conclude that Γmag does not diverge at B = 0.
  • domain assumption The universe is a perfect fluid whose pressure obeys the Mie-Grüneisen equation of state p = Γeff E/v with constant omega per era.
    This is the load-bearing premise of Sec.2.3.10; it makes Γeff = omega true by definition.
  • ad hoc to paper Adiabatic temperature increase rearranges neighboring spins so that Bloc increases by ΔBloc to conserve entropy.
    Core of the adiabatic-magnetization proposal in Sec.2.3.4 and Eq.2.139; no experimental evidence is provided.
  • domain assumption Barrett's formula describes quantum paraelectric dielectric response.
    Used in Sec.2.3.9 to derive ΓE enhancement near the epsilon-prime plateau.

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Pith. "Pith review of The Gr\"uneisen parameter applied to critical phenomena and experimental investigations of correlated phenomena in molecular conductors." pith.science (2026). https://pith.science/paper/IZAWPHOQ

@misc{pith2026241113743,
  author       = {Pith},
  title        = {Pith review of: The Gr\"uneisen parameter applied to critical phenomena and experimental investigations of correlated phenomena in molecular conductors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IZAWPHOQ}},
  note         = {Machine review of arXiv:2411.13743}
}
abstract

In this Ph.D. Thesis, a systematic review is performed on the derivation and generalization of the Gr\"uneisen parameter followed by its unprecedented applications to several distinct scenarios, such as magnetic model systems, zero-field quantum phase transitions, the maximization of caloric effects close to any critical-end point based on entropy arguments, the here-proposed adiabatic magnetization of a paramagnetic salt, as well as for Cosmology in the frame of the universe expansion. Since this Ph.D. Thesis is a symbiosis between theoretical and experimental results, an experimental investigation of correlated phenomena was carried out for molecular conductors of the (TMTTF)$_2$X family, where TMTTF is the base molecule tetramethyltetrathiafulvalene and X a monovalent counter-anion such as PF$_6$, SbF$_6$, or AsF$_6$. Such strongly correlated electron systems are considered suitable ones for the exploration of Mott insulating phase, charge-ordering, spin-Peierls, and superconductivity. In particular, the investigation of a possible multiferroic character in these salts was performed via quasi-static (low-frequency) dielectric constant $\varepsilon'$ measurements as a function of temperature where a maximum in $\varepsilon'$ as a function of temperature was observed at the corresponding charge-ordering temperature for both hydrogenated and 97.5% deuterated (TMTTF)$_2$SbF$_6$ salts. Furthermore, Raman measurements were performed on the 97.5% deuterated (TMTTF)$_2$PF$_6$, showing a possible magneto-optical effect on the $\nu_4(a_g)$ vibrational mode of the TMTTF molecule. Yet, fluorescence measurements demonstrated that the fully-hydrogenated (TMTTF)$_2$AsF$_6$ presents an expressive fluorescence background, which is roughly five orders of magnitude lower than that for the 97.5% deuterated variant of (TMTTF)$_2$PF$_6$.

Figures

Figures reproduced from arXiv: 2411.13743 by the authors.

Figure 2
Figure 2. depicts that, on one hand, when [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 2.1
Figure 2.1. Spin populations N1/NT (up) and N2/NT (down) represented by the red and blue color data, respectively. Note that when T → 0 K, N1/NT → 1 and N2/NT → 0, which means that the ground-state of the Brillouin-type paramagnet is a ferromagnetic phase. In the regime of high temperatures, i.e., T → ∞, both N1/NT and N2/NT go to 0.5, which means that both configurations, namely spin up and down configurations are equally prob… view at source ↗
Figure 2.2
Figure 2.2. Heat capacity at constant magnetic field cB as a function of T for B = 0.5 T (blue line), B = 1 T (red line), and B = 2 T (orange color line). The maximum on cB is associated with the Schottky anomaly for two-level systems [34, 35]. More details in the main text. third law of Thermodynamics, i.e., S → 0 as T → 0 [1]. Hence, to solve this issue, the mutual interactions between neighboring magnetic moments must be con… view at source ↗
Figures from the paper (41 more)
Figure 2.3
Figure 2.3. Figure 2.3: Magnetization M as a function of T and B for the Brillouin-type paramagnet. Note that in the regime of both T and B close to zero, a step-like behaviour of M is observed. Figure extracted from Ref. [47]. paramagnet, namely [47, 8]: Γmag = −  ∂M ∂T  B cB = − 1 T (∂S…
Figure 2.4
Figure 2.4. Figure 2.4: Schematic representation of T versus B for a magnetic-field-induced quantum phase transition. In panel a), the blue bullet represents a quantum critical point at finite B where a quantum phase transition, for instance, from a magnetic ordered to a quantum disordered …
Figure 2.5
Figure 2.5. Figure 2.5: Entropy S versus B at a fixed T = 5 mK for the Brillouin-type paramagnet (upper panel) considering Bloc = 0 T (blue stars) and Bloc = 0.01 T (red circles) and for β-YbAlB4 for Bloc = 0 T (green stars) and Bloc =0.04 T (orange color circles). Figure extracted from Ref…
Figure 2.6
Figure 2.6. Figure 2.6: Magnetic Grüneisen parameter Γmag as a function of B for the Brillouin-type paramagnet (upper panel) considering Bloc = 0 T (blue line) and Bloc = 0.01 T (red line) and for β-YbAlB4 at T = 5 mK for Bloc = 0 T (orange color line) and Bloc = 0.04 T (green line). Note t…
Figure 2.7
Figure 2.7. Figure 2.7: Magnetic Grüneisen parameter Γmag versus T versus B for β-YbAlB4 considering Bloc = 0 T (upper panel) and Bloc = 0.04 T (lower panel). Figure extracted from Ref. [49]. 2.3.3 Grüneisen parameter and the canonical definition of temperature As well-known from textbooks,…
Figure 2.8
Figure 2.8. Figure 2.8: Upper panel: Magnetic entropy S as a function of the average magnetic energy E at a fixed B = 1 (purple line) and 2 T (orange color line). The slope of (∂S/∂E)B indicates positive, infinite, or negative temperatures. The definition of positive and negative temperatur…
Figure 2.9
Figure 2.9. Figure 2.9: Magnetic entropy S as a function of temperature T for the Brillouin-type paramagnet considering Br = Bloc (cyan solid line) and Br = (Bloc + ∆Bloc) (red dashed line). The inset shows a zoom in the low-T regime describing the proposed steps for performing the adiabati…
Figure 2.10
Figure 2.10. Figure 2.10: Schematic representation of both the normal (σx,−x, σy,−y, and σz,−z) and shear (σxy, σxz, σyx, σyz, σzx, and σzy) stress components in a solid. The dashed lines indicate the compression of the solid only in the x direction by the application of a uniaxial compressi…
Figure 2.11
Figure 2.11. Figure 2.11: Schematic representation of the experimental setup for attaining adiabatic magnetization. In panel A, the paramagnetic insulating sample is inserted into an adiabatic chamber inside a coil connected to an ampere meter and it is supported by two lateral pistons. Esse…
Figure 2.12
Figure 2.12. Figure 2.12: Schematic representation of the proposed experimental setup to carry out and detect the elastocaloric-induced adiabatic magnetization due to the mutual interactions. a) The sample is attached with epoxy to a movable plate, which is connected to a piezoelectric devic…
Figure 2.13
Figure 2.13. Figure 2.13: Peak to peak amplitude of the elastocaloric temperature oscillation T EC pp versus temperature T in which the elascoaloric effect was performed for Ba(Fe0.979Co0.021)2As2 [54]. The uniaxial strain in the x direction ε disp xx is also indicated. It is worth mentionin…
Figure 2.14
Figure 2.14. Figure 2.14: Schematic representation of a generic phase diagram temperature T versus tuning parameter g, which can be electric field E, magnetic field B, or pressure p, for instance. Above the critical point, there is a supercritical region and its corresponding Widow line. Bel…
Figure 2.15
Figure 2.15. Figure 2.15: Schematic representation of several contributions to the total entropy: a) coexistence region between two arbitrary phases 1 and 2, b) distinct dipolar configurations in a ferroelectric, c) presence of domain walls in a relaxor-like ferroelectric, d) presence of gra…
Figure 2.16
Figure 2.16. Figure 2.16: Main panel: experimental dielectric constant ϵ results as a function of temperature T for the spin-liquid candidate κ-(BEDT-TTF)2Cu2(CN)3 (pink line) under a pressure of p = 1.45 kbar and frequency f = 380 kHz. Data extracted from Ref. [80]. The blue solid line repr…
Figure 2.17
Figure 2.17. Figure 2.17: Schematic representation of the various eras of the universe, namely a) radiation-, b) matter-, and c) DE-dominated eras. The values of ω, namely Γef f , for each particular era is also shown. Figure extracted from Ref. [95]. [96], being already surpassed. Essential…
Figure 3.1
Figure 3.1. Figure 3.1: Evolution of the critical temperature Tc over the years of conventional, possibly unconventional, and unconventional superconductors. Figure adapted from Ref. [135]. observed superconductivity in a mercury (Hg) sample with Tc ∼ 4 K [132], Meissner and Ochsenfeld [133…
Figure 3.1
Figure 3.1. Figure 3.1: In 1986, Bednorz and Müller observed for the first time superconductivity [PITH_FULL_IMAGE:figures/full_fig_p082_3_1.png]
Figure 3.2
Figure 3.2. Figure 3.2: Little proposed model of a superconducting organic molecule, where the molecule A is defined as the “spine” and B are the side chains attached to the spine at points P, P’, and so on. Picture extracted from Ref. [157]. suggests that in such systems a long chain calle…
Figure 3.3
Figure 3.3. Figure 3.3: Left panel: Schematic temperature versus pressure phase diagram for the Fabre￾Bechgaard salts. The position of the different compounds under ambient pressure is indicated above by the black arrows, such difference is directly connected with the counter-anion chemical…
Figure 3.4
Figure 3.4. Figure 3.4: Molecular structure of the (TMTTF)2X [16], where the counter anions X are shown and the dotted lines between two TMTTF molecules represent the dimers. The triclinic unit cell is outlined by the blue lines and a, b, c and c ∗ (dashed horizontal line) represent the cry…
Figure 3.5
Figure 3.5. Figure 3.5: Quasi-static (fixed frequency f = 1 kHz) dielectric constant as a function of temperature measured in the c ∗ -axis for the fully-hydrogenated (PF6-H12) and 97.5% deuterated (PF6-D12) (TMTTF)2PF6 systems (green and pink circles, respectively), pristine (TMTTF)2AsF6 (…
Figure 3.6
Figure 3.6. Figure 3.6: Schematic representation of the symmetric ag modes ν3 and ν4 and the asymmetric b1u mode ν28 of the TMTTF molecule (left panel). Vibrational frequency as a function of charge per TMTTF molecule (right panel) for the vibrational modes ν3(ag) and ν28(b1u) [176]. Beside…
Figure 3.7
Figure 3.7. Figure 3.7: Left panel: resonance frequency ν0 associated with the ν28 vibrational mode as a function of temperature T for the fully-hydrogenated (TMTTF)2X (X = PF6, AsF6, and SbF6) systems, where a splitting of the resonance frequency is shown at Tco for each salt, since below …
Figure 3.8
Figure 3.8. Figure 3.8: Upper panel: circulation system showing the storage tank containing ∼ 0.55 bar of 4He, the isolation valve, zeolite trap, zeolite trap inlet valve, XDS 10 circulation pump, and exit valves 1 and 2. Lower panel: top view of the Teslatron PT cryostat showing the needle…
Figure 3.9
Figure 3.9. Figure 3.9: F-70 Sumitomo compressor showing the supply and returns 4He lines and the water inlet and outlet lines from the chiller to cool down the compressor during its functioning. However, only the installation of the solenoid valve is not enough to fully protect the OVC fro…
Figure 3.10
Figure 3.10. Figure 3.10: Solenoid valve installed between the turbo pump and the OVC pumping port. When a power loss occurs, it becomes de-energized and closes, protecting the OVC from the ventilation of the turbo pump. When power is re-established, it reopens and the pumping of the OVC is …
Figure 3.11
Figure 3.11. Figure 3.11: Electrical circuit drawn by us to prevent that the solenoid valve opens when power comes back on and the moisture from the ventilation of the turbo pump enters into the OVC. The circuit is composed by a diode, a push button, and a relay. In the case of power being i…
Figure 3.12
Figure 3.12. Figure 3.12: Typical behaviour of the temperature versus time for the magnet (gray), PT2 (red), and sample space (blue). Note that it takes about 28 h for all temperatures to reach equilibrium but the cool down is not finished. The last step (not shown) is to adjust the needle v…
Figure 3.13
Figure 3.13. Figure 3.13: Interior of the zeolite trap and the microporous aluminosilicate minerals are show in the inset. At the top of the zeolite trap, it is shown a heater that is used in its cleaning process. According to Oxford Instruments’ manual regarding the operation of the Teslatr…
Figure 3.14
Figure 3.14. Figure 3.14: Needle valve pressure as a function of time. Note that the pressure is exponentially decreased when the exit valve 2 is opened following a mathematical relation p(t) = p0 exp (−t/τ ), where p0 is the pressure right before the exit valve 2 (see [PITH_FULL_IMAGE:figu…
Figure 3.15
Figure 3.15. Figure 3.15: Top panel: dielectric constant ε ′ measurements as a function of temperature T for the hydrogenated (blue circles) and deuterated (red circles) variant of the (TMTTF)2SbF6 systems for a fixed frequency f = 1 kHz and electric field E = 500 mV/cm. Their corresponding …
Figure 3.16
Figure 3.16. Figure 3.16: Samples attached to the sample holder. From top to bottom the samples are: deuterated variant of (TMTTF)2PF6, hydrogenated variant of (TMTTF)2PF6, (TMTTF)2SbF6, and (TMTTF)2AsF6. The area of the samples were about 2 mm2 and their thickness of about 1 mm. The motivat…
Figure 3.17
Figure 3.17. Figure 3.17: Raman intensity versus intensity at λ = 532 nm without external magnetic field (B = 0 T) for the deuterated variant of (TMTTF)2PF6 at T = 200, 87, 30, and 4 K [PITH_FULL_IMAGE:figures/full_fig_p104_3_17.png]
Figure 3.18
Figure 3.18. Figure 3.18: Raman intensity versus intensity at λ = 532 nm under B = 3 T for the deuterated variant of (TMTTF)2PF6 at T = 200, 87, 30, and 4 K [PITH_FULL_IMAGE:figures/full_fig_p104_3_18.png]
Figure 3.19
Figure 3.19. Figure 3.19: Raman intensity versus intensity at λ = 532 nm under B = 6 T for the deuterated variant of (TMTTF)2PF6 at T = 200, 87, 30, and 4 K. Raman intensity peak at 1476 cm−1 was decreased by about 27 % from 0 to 6 T, which in turn can be interpreted as a magneto-optical eff…
Figure 3.20
Figure 3.20. Figure 3.20: Main panel: Raman intensity as a function of Raman shift for the deuterated variant of the (TMTTF)2PF6 system under B = 0 T (black line), B = 3 T (red line), and B = 6 T (blue line). Inset: zoomed region around the Raman shift 1476 cm−1 to indicate that the increase…
Figure 3.21
Figure 3.21. Figure 3.21: Intensity versus Raman shift for monolayer MoS2 at T = 300 K showing that the intensity of the Raman shift ≈ 405 cm−1 is reduced under B⃗ = 9 T. The vibrational patterns of the corresponding Raman modes are also illustrated. Figure extracted from Ref. [180] [PITH_F…
Figure 3.22
Figure 3.22. Figure 3.22: Fluorescence intensity versus wavelength at T = 190 K and λ = 532 nm for (TMTTF)2AsF6 (red circles) and the deuterated variant of (TMTTF)2PF6 (green circles). writing of this Thesis, such an effect was not reported for the TMTTF-based salts yet. Another key result w…
Figure 6.1
Figure 6.1. Figure 6.1: Schematic representation of the analogy between the precession of the angular momentum vector L⃗ of a peon around the ⃗z axis due to the gravitational field g and the precession of the magnetic moment vector ⃗µ of a spinning nucleus around the ⃗z axis due to an appli…
Figure 6.2
Figure 6.2. Figure 6.2: Schematic representation of the total angular momentum vector J⃗ that makes an angle ϕ in the ⃗z direction. The modulus of |J⃗| = ℏ p J(J + 1) [183] and its projection in the ⃗z axis is mjℏ, where mj is the magnetic quantum number. same direction. Upon considering th…
Figure 6.3
Figure 6.3. Figure 6.3: a) All the individual parts of the SMB connector together with its datasheet. b) The golden tip of the SMB connector is already soldered in the coaxial cable. Special thanks to Leandro Xavier who performed such a delicate repair. 6.5 Joint reports During the period o…

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.