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Hydrogen and related materials at high density: Physics, chemistry and planetary implications

Recent studies of low-Z molecular materials including hydrogen to multimegabar pressures (less than 300 GPa) have uncovered a range of phenomena relevant to understanding the nature of the interiors of the outer planets and their satellites. Synchrotron x ray diffraction measurements (to 42 GPa) have been used to determine the crystal structure of the solid (hexagonal-close packed) and equation of state. Sound velocities in fluid and solid hydrogen (to 24 GPa) have been inverted to obtain elastic constants and aggregate bulk and shear moduli. In addition, an improved intermolecular potential has been determined which fits both static and shock-wave data. Use of the new potential for the molecular envelope of Jupiter suggests the need for major revisions of existing Jovian models or a reanalysis of reported free oscillations for the planet. Studies at higher pressures (greater than 100 GPa) reveal a sequence of pressure-induced symmetry-breaking transitions in molecular hydrogen, giving rise to three high-pressure phases (1, 2, and 3). Phase 1 is the rotationally disordered hcp phase which persists from low pressure to well above 100 GPa at high temperature (e.g., 300 K). Phase 2 is a low-temperature, high-pressure phase (transition at 100 GPa and 77 K in H2) with spectral features indicative of partial rotational ordering and crystallographic distortion. The transition to Phase 3 at 150 GPa is accompanied by a weakening of the molecular bond, gradual changes in orientational ordering, strong enhancement of the infrared intramolecular vibrational absorption, and strong intermolecular interactions similar to those of ambient-pressure network solids. Studies of the phase diagram reveal a triple point near 130 K and 160 GPa. Higher pressure measurements of vibrational spectra place a lower bound of approximately 250 GPa on the predicted transition pressure for dissociation of molecular hydrogen to form a monatomic metal.

Hemley, R. J.↗

Pressure-induced order–disorder transitions in β-In 2 S 3 : an experimental and theoretical study of structural and vibrational properties

We report this joint experimental and theoretical study of the structural and vibrational properties of β-In 2 S 3 upon compression shows that this tetragonal defect spinel undergoes two reversible pressure-induced order–disorder transitions up to 20 GPa. We propose that the first high-pressure phase above 5.0 GPa has the cubic defect spinel structure of α-In 2 S 3 and the second high-pressure phase ($\phi$-In 2 S 3 ) above 10.5 GPa has a defect α-NaFeO 2 -type (R$\bar{3}$) structure. This phase, related to the NaCl structure, has not been previously observed in spinels under compression and is related to both the tetradymite structure of topological insulators and to the defect LiTiO 2 phase observed at high pressure in other thiospinels. Structural characterization of the three phases shows that α-In 2 S 3 is softer than β-In 2 S 3 while $\phi$-In 2 S 3 is harder than β-In 2 S 3 . Vibrational characterization of the three phases is also provided, and their Raman-active modes are tentatively assigned. Our work shows that the metastable α phase of In 2 S 3 can be accessed not only by high temperature or varying composition, but also by high pressure. On top of that, the pressure-induced β–α–$\phi$ sequence of phase transitions evidences that β-In 2 S 3 , a B III 2 X V 3 compound with an intriguing structure typical of A II B III 2 X VI 4 compounds (intermediate between thiospinels and ordered-vacancy compounds) undergoes: (i) a first phase transition at ambient pressure to a disordered spinel-type structure (α-In 2 S 3 ), isostructural with those found at high pressure and high temperature in other B III 2 X V 3 compounds; and (ii) a second phase transition to the defect α-NaFeO 2 -type structure ($\phi$-In 2 S 3 ), a distorted NaCl-type structure that is related to the defect NaCl phase found at high pressure in A II B III 2 X VI 4 ordered-vacancy compounds and to the defect LiTiO 2 -type phase found at high pressure in A II B III 2 X VI 4 thiospinels. This result shows that In 2 S 3 (with its intrinsic vacancies) has a similar pressure behaviour to thiospinels and ordered-vacancy compounds of the A II B III 2 X VI 4 family, making β-In 2 S 3 the union link between such families of compounds and showing that group-13 thiospinels have more in common with ordered-vacancy compounds than with oxospinels and thiospinels with transition metals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Raman Fingerprints of Phase Transitions and Ferroic Couplings in van der Waals Multiferroic CuCrP 2 S 6

CuCrP 2 S 6 (CCPS), a type-II multiferroic material, exhibits unique phase transitions involving ferroelectric, antiferroelectric, and antiferromagnetic ordering. Here, in this study, we conduct a comprehensive investigation on the intricate phase transitions and their multiferroic couplings in CCPS across a wide temperature range from 4 to 345 K through Raman spectroscopic measurements down to 5 cm –1 . We first assign the observed Raman modes with the support of theoretical calculations and angle-resolved polarized Raman measurements. We further present clear signatures of phase transitions from the analyses of temperature-dependent Raman spectral parameters. Particularly, two low-frequency soft modes are observed at 36.1 cm –1 and 70.5 cm –1 below 145 K, indicating the antiferroelectric to quasi-antiferroelectric transition. Moreover, phonon mode hardening is observed when the temperature increases from 4 to 65 K, suggesting negative thermal expansion (NTE) and strong magnetoelastic coupling below 65 K. These findings advance the understanding of vdW multiferroic CCPS, paving the way for future design and engineering of multiferroicity in cutting-edge technologies, such as spintronics and quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Critical behavior in a chiral molecular model

Understanding the condensed-phase behavior of chiral molecules is important in biology as well as in a range of technological applications, such as the manufacture of pharmaceuticals. Here, we use molecular dynamics simulations to study a chiral four-site molecular model that exhibits a second-order symmetry-breaking phase transition from a supercritical racemic liquid into subcritical D-rich and L-rich liquids. We determine the infinite-size critical temperature using the fourth-order Binder cumulant, and we show that the finite-size scaling behavior of the order parameter is compatible with the 3D Ising universality class. We also study the spontaneous D-rich to L-rich transition at a slightly subcritical temperature of T = 0.985Tc, and our findings indicate that the free energy barrier for this transformation increases with system size as N2/3, where N is the number of molecules, consistent with a surface-dominated phenomenon. The critical behavior observed herein suggests a mechanism for chirality selection in which a liquid of chiral molecules spontaneously forms a phase enriched in one of the two enantiomers as the temperature is lowered below the critical point. Furthermore, the increasing free energy barrier with system size indicates that fluctuations between the L-rich and D-rich phases are suppressed as the size of the system increases, trapping it in one of the two enantiomerically enriched phases. Such a process could provide the basis for an alternative explanation for the origin of biological homochirality. We also conjecture the possibility of observing nucleation at subcritical temperatures under the action of a suitable chiral external field.

Chemistry↗

Asymmetry of the Ferroelectric Phase Transition in BaTiO 3

Symmetry changes during phase transformations fundamentally determine the behavior of thermodynamic systems, governing phenomena as diverse as water evaporation, fermion condensation, and epidemic spreading. Phase transitions are conventionally divided into two classes, and this classification is typically assumed to remain invariant upon reversing the transition. Here, an asymmetric phase transformation is uncovered in the ferroelectric–paraelectric transition of single-crystal BaTiO 3 , a model system for first-order transitions. Under slow temperature variation (≤0.1 °C min −1 ), thermodynamic, dielectric, and domain-structure measurements reveal that the ferroelectric-to-paraelectric transition exhibits latent heat, phase coexistence, and a discontinuous order parameter, while these signatures are absent upon cooling. Complementary phase-field simulations demonstrate similar behavior, attributing it to distinct elastic strain energy accumulation and release during heating and cooling. These findings reveal a first-order character upon heating but a second-order-like behavior upon cooling, challenging the conventional paradigm of symmetric phase-transition classification and suggesting new possibilities for ferroelectric-based energy storage.

Hershkovitz, Asaf [Technion-Israel Institute of Te↗

Thermodynamic insights into the intricate magnetic phase diagram of EuAl 4

The tetragonal intermetallic compound EuAl 4 hosts an exciting variety of low-temperature phases. In addition to a charge density wave below 140 K, four ordered magnetic phases are observed below 15.4 K. Recently, a skyrmion phase was proposed based on Hall effect measurements under a c-axis magnetic field. Here, we present a detailed investigation of the phase transitions in EuAl 4 under c-axis magnetic field. Our dilatometry, heat-capacity, DC magnetometry, AC magnetic susceptibility, and resonant ultrasound spectroscopy measurements reveal three magnetic phase transitions not previously reported. The first key result is a detailed H ∥ [001] magnetic phase diagram mapping the seven phases we observe. Second, we identify a high-field phase, phase VII, which directly corresponds to the region were skyrmions have been previously suggested. Our results provide guidance for future studies exploring the complex magnetic interactions and spin structures in EuAl 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Characterizing the nonequilibrium response of FeRh thin films using time-domain thermoreflectance

Time-domain thermoreflectance (TDTR) characterization of FeRh throughout its first-order antiferromagnetic (AF) to ferromagnetic (FM) transition shows that the transient reflectance ΔR⁡(t)/R strongly depends on the magnetic order of the sample. Using TDTR, which uses optical pulses to induce small temperature excursions, we have found that Δ⁢R⁡(t)/R of the AF phase exhibits a large negative response, while the response of the FM phase is positive. This magnetic phase sensitivity has allowed us to study the transient response of both the AF and FM phases to the pump-pulse excitation and the mixed phase of the material. These results are significant since the ultrafast properties of antiferromagnetic materials and mixed antiferromagnetic and ferromagnetic materials are difficult to detect using other conventional techniques. We have found that the AF phase exhibits a strong subpicosecond decaying signal not observed in the FM phase. The magnetic phase dependence of the sign of Δ⁢R⁡(t)/R is qualitatively explained using the results of ab initio density functional theory calculations. Using the two-temperature model, we found that the change in the thermalization time across the transition is caused by differences in both the electronic heat capacity and the electron-phonon coupling factor of the AF and FM phases. The electron-phonon coupling constant in the AF phase is also determined using the two-temperature model conducted using the ntmpy code package. For the FM phase, we provide boundaries for the magnitude of the electron-phonon coupling factor for the FM phase. Finally, these results indicate that TDTR can be used to study the transient properties of magnetic materials that are otherwise challenging to probe.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Interplay of flat electronic bands with Holstein phonons

Existing quantum Monte Carlo studies have investigated the properties of fermions on a Lieb (CuO 2 ) lattice interacting with on-site or near-neighbor electron-electron coupling. Attention has focused on the interplay of such interactions with the macroscopic degeneracy of local zero-energy modes, from which Bloch states can be formed to produce a flat band in which energy is independent of momentum. The resulting high density of states, in combination with the Stoner criterion, suggests that there should be pronounced instabilities to ordered phases. Indeed, a theorem by Lieb rigorously establishes the existence of ferrimagnetic order. Here we study the charge density wave phases induced by electron-phonon coupling on the Lieb lattice, as opposed to previous work on electron-electron interactions. Our key result is the demonstration of charge density wave phases at one third and two thirds fillings, characterized by long-range density-density correlations between doubly occupied sites on the minority or majority sublattices, and an accompanying gap. Our team also computes the transition temperature to the ordered phase as a function of the electron-phonon coupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Revisiting superconductivity in the extended one-band Hubbard model: Pairing via spin and charge fluctuations

The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while B 1g (d x 2 –y 2 ) and B 2g (d xy ) pairing dominates in the absence of repulsive longer-range Coulomb interactions V NN , the latter induces pairing in other symmetry channels, including, e.g., A 2g (g-wave), nodal A 1g (extended s-wave), or nodal E u (p-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction, V NN < 0, on the superconducting gap structure. Furthermore, depending on the electronic filling, such an attraction boosts E u (p-wave) spin-triplet or B 1g (d x 2 –y 2 ) spin-singlet ordering.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Block-Type Antiferromagnetism in Single Chain Quasi-One-Dimensional K 3 ⁢Fe 2 ⁢Se 4

One-dimensional (1D) structures provide a unique platform to study the correlated quantum interactions and phase transitions such as unconventional magnetism and superconducting states. Here, we report that iron chalcogenide K 3 ⁢Fe 2 ⁢Se 4 exhibits an unusual block-type canted antiferromagnetic (AFM) order with a clear single chain quasi-1D structure, which is structurally different from the two-leg ladder BaFe 2 ⁢Se 3 , through both experimental measurements and density matrix renormalization group (DMRG) calculations. The narrow bandgap semiconductor K 3 ⁢Fe 2 ⁢Se 4 has a quasi-1D edge-shared FeSe4 tetrahedra chain structure and orders antiferromagnetically below 110 K. The magnetic moments couple antiferromagnetically along the quasi-1D chain direction of the 𝑏 axis and form an up-down-down-up (↑−↓−↓−↑)–like spin structure with a commensurate propagation vector 𝒌=⁢(0,0,0), where block-type spin ↑−↑ or ↓−↓ coupling are between the longer Fe-Fe bonds of the quasi-1D chain. DMRG results show that block antiferromagnetic state is stable in K 3 ⁢Fe 2 ⁢Se 4 and reveal that the block-ordered arrangement of Fe 2.5+ ions spins arise from the competition between ferromagnetic and AFM interaction in the presence of strong electronic correlation. Our research results not only report the discovery of a clear block-type canted antiferromagnetic structure in a real quasi-1D chain material but also provide a theoretical approach to understand the block-type antiferromagnetism in quasi-1D iron chalcogenides.

antiferromagnetism↗

Structural evolution, electrochemical kinetic properties, and stability of A-site doped perovskite Sr(1-x)Yb(x)CoO(3-δ)

Mixed ionic and electronic conducting (MIEC) perovskite SrCoO(3-δ) is a widely studied (electro)catalyst for the oxygen reduction reaction (ORR) and possesses different crystal structures at different temperatures. These temperature dependent phase transitions significantly impact the ordering of oxygen vacancies and electrochemical kinetic properties as well as the reliability of the related devices. Some of the crystal structures formed, e.g. hexagonal phases, turn out to be almost impermeable to oxygen gas. Therefore, it is important to stabilize the crystal structure of SrCoO(3-δ) that favors the ORR over a wide temperature range. Herein, the partial substitution of the A-site Sr with Yb is systematically studied, including synthesis, characterization and analysis of structural evolution, electrochemical kinetic properties, thermal stability, and stability in a CO2-containing atmosphere. The results indicate that Sr(0.90)Yb(0.10)CoO(3-δ) is able to stabilize the tetragonal crystal structure with less ordered oxygen vacancies, leading to polarization resistances of 0.051, 0.115 and 0.272 U sq.cm at 750, 700 and 650 °C, respectively, on symmetrical cells. Sr(0.90)Yb(0.10)CoO(3-δ) demonstrates a very stable surface oxygen vacancy distribution and electronic structure near oxygen vacancies but dissociation of adsorbed oxygen molecules into atomic oxygen is affected by surface Sr segregation, and polarization resistance degradation is mainly induced by surface Sr segregation. Furthermore, Sr(0.90)Yb(0.10)CoO(3-δ) exhibits excellent thermal stability as well as excellent recovery stability and improved polarization performance after a few pure air/CO2-containing air treatment cycles at 700 °C. However, a hysteresis behavior of polarization performance is observed at 650 °C during gas cycling treatment, which may cause long-term degradation of the Sr(0.90)Yb(0.10)CoO(3-δ) electrode. The different polarization behaviors during gas cycling treatment are induced by different sensitivities of the formed surface strontium carbonate and chemisorbed surface oxo-carbonaceous species to different operating temperatures.

electrochemical kinetic↗

Coupled Dynamical Phase Transitions in Driven Disk Packings

Under the influence of oscillatory shear, a monolayer of frictional granular disks exhibits two dynamical phase transitions: a transition from an initially disordered state to an ordered crystalline state and a dynamic active-absorbing phase transition. Although there is no reason a priori for these to be at the same critical point, they are. Also, the transitions may also be characterized by the disk trajectories, which are nontrivial loops breaking time-reversal invariance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Europium c -axis ferromagnetism in Eu ( Co 1 - x Ni x ) 2 - y As 2 : A single-crystal neutron diffraction study

Here we report neutron diffraction results for the body-centered-tetragonal series Eu⁢(Co 1-x ⁢Ni x ) 2-y As 2 , x=0.10, 0.20, 0.42, and 0.82, y≤0.10, that detail changes to the magnetic ordering with nominal hole doping. We report the antiferromagnetic (AFM) propagation vectors, magnetic transition temperatures, and the ordered magnetic moments. We find a nonmonotonic change of the AFM propagation vector with x, with a minimum occurring at the tetragonal to collapsed-tetragonal phase crossover. For x=0.10 and 0.82 we find c-axis helix ordering of the Eu magnetic moments (spins) similar to x=0 and 1, with the spins oriented within the ab-plane. For x=0.20 and 0.42 we find higher-temperature c-axis ferromagnetic (FM) order and lower-temperature c-axis cone order. Using the extinction conditions for the space group, we discovered that the Eu spins are ordered in the higher-temperature c-axis FM phase for intermediate values of x, contrary to a previous report suggesting only Co/Ni spin ordering. Although we cannot directly confirm that the Co/Ni spins are also ordered, we suggest that c-axis itinerant-FM ordering of the Co/Ni spins could provide a molecular field that drives FM ordering of the Eu spins, which in turn provides the anisotropy for the lower-temperature c-axis cone order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Phase Diagram of the Easy-Axis Triangular-Lattice 𝐽 1 −𝐽 2 Model

Our work studies the largely unexplored phase diagram of the S = 1/2 easy-axis triangular-lattice J 1 -J 2 model, motivated by recent interest in rare-earth and transition-metal compounds that exhibit strong quantum fluctuations and broad spin excitation continua—hallmarks of spin-liquid behavior. Combining density-matrix renormalization group simulations with analytical insights, we present a comprehensive study of the model that describes these materials. Our results provide compelling evidence for a robust spin-liquid phase stabilized between the exotic supersolid Y phase and the collinear stripe phase, remarkably persistent even in the presence of symmetry-breaking anisotropy. Additionally, we analyze the supersolid Y phase, offering a quantitative characterization of its order parameters and clarifying the surprising absence of a ferromagnetic moment; both features relevant to recent experiments on Ising-like triangular-lattice magnets. Altogether, our work provides the necessary framework and important theoretical guidance to the ongoing searches of the spin liquid and other exotic states in the rare-earth and transition-metal triangular-lattice compounds, as well as for advancing the understanding of anisotropic-exchange magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Gravitational Wave Signal for Quark Matter with Realistic Phase Transition

The cores of neutron stars (NSs) near the maximum mass can realize a transitional change to quark matter (QM). Gravitational waves from binary NS mergers are expected to convey information about the equation of state (EOS) sensitive to the QM transition. Here, in this work, we present the first results of gravitational wave simulation with the realistic EOS that is consistent with ab initio approaches of χ⁢EFT and pQCD and is assumed to go through smooth crossover. We compare them to results obtained with another EOS with a first-order hadron-quark phase transition. Our results suggest that early collapse to a black hole in the post-merger stage after NS merger robustly signifies softening of the EOS associated with the QM onset in the crossover scenario. The nature of the hadron-quark phase transition can be further constrained by the condition that electromagnetic counterparts should be energized by the material left outside the remnant black hole.

79 ASTRONOMY AND ASTROPHYSICS↗

Parametric tuning of quantum phase transitions in ultracold reactions

Advances in atomic physics have led to the possibility of a coherent transformation between ultracold atoms and molecules including between completely bosonic condensates. Such transformations are enabled by the magneto-association of atoms at a Feshbach resonance which results in a passage through a quantum critical point. In this study, we show that the presence of generic interaction between the constituent atoms and molecules can fundamentally alter the nature of the critical point, change the yield of the reaction and the order of the consequent phase transition. We find that the correlations introduced by this interaction induce nontrivial many-body physics such as coherent oscillations between atoms and molecules, and a selective formation of squeezed molecular quantum states and quantum cat states. We provide analytical and numerical descriptions of these effects, along with scaling laws for the reaction yield in non-adiabatic regimes.

36 MATERIALS SCIENCE↗

Thermally reconfigurable monoclinic nematic colloidal fluids

Fundamental relationships are believed to exist between the symmetries of building blocks and the condensed matter phases that they form. For example, constituent molecular and colloidal rods and disks impart their uniaxial symmetry onto nematic liquid crystals, such as those used in displays. Low-symmetry organizations could form in mixtures of rods and disks, but entropy tends to phase-separate them at the molecular and colloidal scales, whereas strong elasticity-mediated interactions drive the formation of chains and crystals in nematic colloids. To have a structure with few or no symmetry operations apart from trivial ones has so far been demonstrated to be a property of solids alone, but not of their fully fluid condensed matter counterparts, even though such symmetries have been considered theoretically and observed in magnetic colloids. In this work, we show that dispersing highly anisotropic charged colloidal disks in a nematic host composed of molecular rods provides a platform for observing many low-symmetry phases. Depending on the temperature, concentration and surface charge of the disks, we find nematic, smectic and columnar organizations with symmetries ranging from uniaxial to orthorhombic and monoclinic. With increasing temperature, we observe unusual transitions from less- to more-ordered states and re-entrant phases. Most importantly, we demonstrate the presence of reconfigurable monoclinic colloidal nematic order, as well as the possibility of thermal and magnetic control of low-symmetry self-assembly. Our experimental findings are supported by theoretical modelling of the colloidal interactions between disks in the nematic host and may provide a route towards realizing many low-symmetry condensed matter phases in systems with building blocks of dissimilar shapes and sizes, as well as their technological applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effect of Ni substitution on the fragile magnetic system La 5 Co 2 Ge 3

La 5⁢ Co 2 ⁢Ge 3 is an itinerant ferromagnet with a Curie temperature T C of ~3.8K and a remarkably small saturated moment of 0.1µ B /Co. Here we present the growth and characterization of single crystals of the La 5 ⁢(Co 1–x⁢ Ni x ) 2 Ge 3 series for 0.00 ≤ x ≤ 0.186. Here we measured powder x-ray diffraction, composition as well as anisotropic temperature-dependent resistivity, temperature and field-dependent magnetization along with heat capacity on these single crystals. We also measured muon-spin rotation/relaxation (μ⁢SR) for some Ni substitutions (x = 0.027,0.036,0.074) to study the evolution of internal field with Ni substitution. Using the measured data we infer a low temperature, transition temperature-composition phase diagram for La 5 ⁢(Co 1–x ⁢Ni x ) 2 Ge 3 . We find that T C is suppressed for low dopings, x ≤ 0.014; whereas for 0.036 ≤ x ≤ 0.186, the samples are antiferromagnetic with a Néel temperature T N that goes through a weak and shallow maximum (T N ~ 3.4K for x~0.07) and then gradually decreases to 2.4 K by x = 0.186. For intermediate Ni substitutions, 0.016 ≤ x ≤ 0.027, two transition temperatures are inferred with T N >T C . Whereas the T–x phase diagram for La 5 ⁢(Co 1–x ⁢Ni x ) 2 Ge 3 and the T–p phase diagram determined for the parent La 5 ⁢Co 2 ⁢Ge 3 under hydrostatic pressure are grossly similar, changing from a low-doping or low-pressure ferromagnetic (FM) ground state to a high-doped or high-pressure antiferromagnetic (AFM) state, perturbation by Ni substitution enabled us to identify an intermediate doping regime where both FM and AFM transitions occur.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗