Motivated by possible spintronics applications in antiferromagnets, it was recently observed that symmetry admits magnets that combine attractive features of both ferromagnets and antiferromagnets. These systems, dubbed altermagnets, have been the subject of intense study with direct spectroscopic evidence, from ARPES and RIXS, techniques reported in a handful of materials in the last year. Inelastic neutron scattering (INS) is one of the most powerful direct probes of magnetism and has recently been used to witness a splitting of magnon bands in MnTe that is compatible with altermagnetism although the nature and origin of the splitting remain to be fully characterized. However, the full power of neutron scattering for such systems comes from using polarized neutrons to measure the chirality of the magnon bands. Such a measurement provides a direct characterization of altermagnetism directly from the spin wave excitations. In this article, we present results on MnF_2 once thought to be an archetypal antiferromagnet. We present a polarized INS data that demonstrate the material is, in fact, altermagnetic. It had long been realized that the magnon bands in this material should have a weak splitting coming from the long-range dipolar coupling. Our data is the first to visualize this splitting directly. While the dipolar splitting on its own is not altermagnetic, using a domain biased sample, the data reveals a nonzero chirality in the neutron scattering cross section that reverses sign between the two magnon modes. It is this feature that clearly demonstrates altermagnetism in MnF_2. This finding highlights the potential for polarized INS to characterize altermagnets not least through its exquisite sensitivity to fine-structure in the magnon spectrum.

High-resolution neutron spectroscopy on Ce2Hf2O7 reveals a correlated state characterized by distinct dipolar scattering signals-quasielastic and inelastic contributions consistent with 'photon' and 'spinon' excitations in quantum spin ice. These signals coexist with weak octupolar scattering. Fits of thermodynamic data using numerical methods indicate a dominant octupolar exchange, Jx or Jy, with substantial dipolar Jz and minute dipole-octupole Jxz couplings. The Jxz value is corroborated by an independent fit of the neutron scattering amplitude balance between dipolar and octupolar 'photon' contributions, highlighting its importance to understand neutron scattering results in this family. Ce2Hf2O7 enriches the landscape of dipole-octupole pyrochlore physics, and reveals a 'quantum multipolar liquid' where hybrid correlations involve multiple terms in the moment series expansion, opening questions regarding their intertwining and hierarchy in quantum phases.

The recently discovered dipole-octupole pyrochlore magnet Ce_2Hf_2O_7 is a promising three-dimensional quantum spin liquid candidate which shows no signs of ordering at low temperature. The low energy effective pseudospin-1/2 description in a magnetic field is characterized by the XYZ Hamiltonian and a Zeeman term where the dipolar local z-component of the pseudospin couples to the local z-component of the applied magnetic field, while the local x- and y-components of the pseudospin remain decoupled as a consequence of their octupolar character. Using effective Hamiltonian parameters determined in V. Poree et al., arXiv:2305.08261 (2023), remarkable experimental features can be reproduced, as for instance the specific heat and magnetization data as well as the continuum of states seen in neutron scattering. Here we investigate the thermodynamic response to magnetic fields applied along the global [110] direction using specific heat measurements and fits using numerical methods, and solve the corresponding magnetic structure using neutron diffraction. Specific heat data in moderate fields are reproduced well, however, at high fields the agreement is not satisfactory. We especially observe a two-step release of entropy, a finding that demands a review of both theory and experiment. We address it within the framework of three possible scenarios, including an analysis of the crystal field Hamiltonian not restricted to the two-dimensional single-ion doublet subspace. We conclusively rule out two of these scenarios and find qualitative agreement with a simple model of field misalignment with respect to the crystalline direction. We discuss the implications of our findings for [111] applied fields and for future experiments on Ce_2Hf_2O_7 and its sister compounds.

As an instance of geometrical frustration with non-magnetic degrees of freedom, we explore the physics of local spin S≥ 1 moments on the pyrochlore lattice that interact via pure quadrupolar couplings. In the presence of spin-orbit coupling, there are nine allowed couplings between nearest neighbor quadrupoles. We determine the semi-classical phases and survey the phase diagram of the model. One may view the Hamiltonian as being composed of two copies of the well-studied dipolar model with couplings between the copies, and we find that each easy-plane dipolar phase has two quadrupolar counterparts. As geometrical frustration is important over broad swathes of the parameter space, there are many classical quadrupolar liquids and regions with order-by-disorder selection of discrete states. Order-by-disorder with quadrupoles admits cubic terms in the Landau theory whose effects appear in Monte Carlo simulations and flavor wave calculations for fixed spin S. We showcase a number of examples of quadrupolar spin liquids, including one realizing a rank-3 symmetric tensor gauge theory exhibiting 6-fold pinch point singularities. We discuss remarkable differences between the quadrupolar physics of different spin quantum number. We also discuss connections to the non-Kramers rare earth pyrochlore materials.

We review a key subset of the experimental studies that have recently focused on cubic pyrochlore magnets whose pseudospin-1 $/$ 2 degrees of freedom have mixed dipolar and octupolar character. We discuss how this comes about and how the character of the pseudospin-1 $/$ 2 can be experimentally determined. The minimal spin Hamiltonian for such magnetic insulators is known to give rise to a rich phase diagram with both disordered U(1) quantum spin ice (QSI) states and all-in–all-out (AIAO) noncollinear ordered states, each with dipolar and octupolar character. We focus primarily on experimental studies on two such single crystal systems, the $\TimesFont{J}$ = 5 $/$ 2 Ce2Zr2O7 and the $\TimesFont{J}$ = 9 $/$ 2 Nd2Zr2O7. We make the case that Ce2Zr2O7 is an excellent QSI ground-state candidate material, close to the border between QSIs with dipolar and octupolar symmetry. Nd2Zr2O7 exhibits an AIAO ordered phase, featuring an order parameter consisting of dipolar and octupolar magnetic moments. It is found to reside close to a QSI phase boundary and features dynamic fragmentation in its excitation spectrum.

We study the stability of the antiferromagnetic all-in--all-out state observed in dipolar-octupolar pyrochlores that have neodymium as the magnetic species. Different types of disorder are considered, either affecting the immediate environment of the Nd$^{3+}$ ion, or substituting it with a non-magnetic ion. Starting from the well studied Nd$_2$Zr$_2$O$_7$ compound, Ti substitution on the Zr site and dilution on the Nd magnetic site with La substitution are investigated. The recently discovered entropy stabilized compound NdMox, which exhibits a high degree of disorder on the non magnetic site is also studied. Using a range of experimental techniques, especially very low-temperature magnetization and neutron scattering, we show that the all-in--all-out state is very robust and withstands substitutional disorder up to large rates. From these measurements, we estimate the Hamiltonian parameters and discuss their evolution in the framework of the phase diagram of dipolar-octupolar pyrochlore magnets.

Two decades of work have shown that the physics of Tb-based pyrochlores is controlled by a subtle equilibrium between quadrupole-quadrupole and dipolar-dipolar magnetic interactions, as exemplified by the ordered spin ice Tb2Sn2O7 and the quantum spin liquid candidate Tb2Ti2O7. The high-entropy approach is thus quite promising, as it offers the possibility of a delicate tuning of chemical disorder. In this work, we investigate the entropy-stabilized pyrochlore compound Tb2(TiZrHfGeSn)2O7. We report the lack of long range magnetic order, yet the observed magnetic diffuse scattering is characteristic of antiferromagnetic first-neighbor correlations. The crystal field excitation spectrum, with broaden levels, visibly reflects the smooth environmental disorder of the Tb environment. The low energy dynamics are characterized by a narrow mode at about 0.4 meV, consistent with specific heat. Remarkably, as illustrated by a model of random isotropic shifts of oxygen atoms around Tb ions, the spectral weight of this mode is a direct consequence of deviations from the D3d symmetry at Tb sites. In the light of these results, quadrupolar interactions are also discussed. Frustrated magnetic systems such as pyrochlores are interesting for the complexity of their competing low-temperature phases. Here, the intrinsic disorder of the entropy-stabilized compound Tb2(TiZrHfGeSn)2O7 is utilized to investigate the elusive ground state of Tb-based pyrochlore magnets.

Electronic spins can form long-range entangled phases of condensed matter named quantum spin liquids. They are expected to form in frustrated magnets that do not exhibit symmetry-breaking order down to zero temperature. Quantum spin ice is a theoretically well-established example described by an emergent quantum electrodynamics, with quasiparticle excitations behaving like photons and fractionally charged matter. However, in frustrated magnets it remains difficult to establish convincing experimental evidence for quantum spin liquid ground states and their fractional excitations. Here we study the time-dependent magnetic response of the candidate quantum spin ice material Ce2Sn2O7. We find a gapped spectrum that features a threshold and peaks that match theories for pair production and propagation of fractional matter excitations strongly coupled to a background quantum electrodynamic field. The multiple peaks in our neutron spectroscopy data are a specific signature of the so-called π-flux phase of quantum spin ice, providing spectroscopic evidence for fractionalization in a three-dimensional quantum spin liquid. Quantum fluctuations in frustrated magnets are expected to produce unconventional emergent behaviour. Neutron spectroscopy measurements now provide evidence for emergent gauge fields in a pyrochlore spin ice.

Y3Cu9(OH)19Cl8 realizes an original anisotropic kagome model hosting a rich magnetic phase diagram [M. Hering et al, npj Computational Materials 8, 1 (2022)]. We present an improved synthesis of large phase-pure single crystals via an external gradient method. These crystals were investigated in details by susceptibility, specific heat, thermal expansion, neutron scattering and local muSR and NMR techniques. At variance with polycristalline samples, the study of single crystals gives evidence for subtle structural instabilities at 33K and 13K which preserve the global symmetry of the system and thus the magnetic model. At 2.1K the compound shows a magnetic transition to a coplanar (1/3,1/3) long range order as predicted theoretically. However our analysis of the spin wave excitations yields magnetic interactions which locate the compound closer to the phase boundary to a classical jammed spin liquid phase. Enhanced quantum fluctuations at this boundary may be responsible for the strongly reduced ordered moment of the Cu2+, estimated to be 0.075muB from muSR.

By combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising-like quantum antiferromagnet BaCo2V2O8 in a longitudinal magnetic field applied along the Ising anisotropy, which is also the chain direction. The external field closes the excitation gap due to the magnetic anisotropy, inducing a transition from the Neel ordered state to an incommensurate longitudinal spin density wave phase. If the field is increased further, another transition into a transverse antiferromagnetic phase takes place at 9 T due to the competition between longitudinal and transverse correlations. We numerically and experimentally show that the model of XXZ chains connected by a weak interchain interaction well reproduces this transition. We also calculate the dynamical susceptibility and demonstrate that it agrees quantitatively with inelastic neutron scattering measurements. In contrast to the abrupt change of magnetic ordering, the spectra do not change much at the transition at 9 T, and the spin dynamics can be described as a Tomonaga-Luttinger liquid. We also refine the modeling of BaCo2V2O8 by including a four-site periodic term arising from the crystal structure which enables one to account for an anomaly of the magnetic susceptibility appearing at 19.5 T, as well as for the anticrossing observed in the inelastic neutron scattering spectra.

Electronic spins can form long-range entangled phases of condensed matter named quantum spin liquids. Their existence is conceptualized in models of two- or three-dimensional frustrated magnets that evade symmetry-breaking order down to zero temperature. Quantum spin ice (QSI) is a theoretically well-established example described by an emergent quantum electrodynamics, with excitations behaving like photon and matter quasiparticles. The latter are fractionally charged and equivalent to the `spinons' emerging from coherent phases of singlets in one dimension, where clear experimental proofs of fractionalization exist. However, in frustrated magnets it remains difficult to establish consensual evidence for quantum spin liquid ground states and their fractional excitations. Here, we use backscattering neutron spectroscopy to achieve extremely high resolution of the time-dependent magnetic response of the candidate QSI material Ce$_2$Sn$_2$O$_7$. We find a gapped spectrum featuring a threshold and peaks that match theories for pair production and propagation of fractional matter excitations (spinons) strongly coupled to a background gauge field. The observed peaks provide evidence for a QSI through spectroscopic signatures of space-time symmetry fractionalization, while the threshold behavior corroborates the regime of strong light-matter interaction predicted for the emergent universe in a QSI.

In this paper, we focus on the thermal transport properties of antiferromagnetic spin chains cuprates. The chain magnetic excitations, the spinons, partake in heat transport at low temperature, but spinon heat transport decays well below room temperature, possibly because of a coupling with phonons. By means of inelastic neutron scattering, we thoroughly study the lattice dynamics of spin chain compounds Sr2CuO3, Ca2CuO3, along with double spin-chain compounds SrCuO2. We come to the conclusion that there are no obvious anomalies in the phonon dispersions, which suggests a weak spinon-phonon coupling regime.

The design of high-density non-volatile memories is a long-standing dream, limited by conventional storage "0" or "1" bits. An alternative paradigm exists in which regions within candidate materials can be magnetized to intermediate values between the saturation limits. In principle, this paves the way to multivalued bits, vastly increasing storage density. Single-molecule magnets, are good examples offering transitions between intramolecular quantum levels, but require ultra-low temperatures and limited relaxation time between magnetization states. It is showed here that the quasi 2D-Ising compound BaFe2(PO4)(2) overcomes these limitations. The combination of giant magneto-crystalline anisotropy, strong ferromagnetic exchange, and strong intrinsic pinning creates remarkably narrow magnetic domain walls, collectively freezing under T-f & AP;15 K. This results in a transition from a soft to a super-hard magnet (coercive force > 14 T). Any magnetization can then be printed and robustly protected from external fields with an energy barrier >9T at 2 K.

The development of lighter low-carbon technologies in the aviation sector raises a technological challenge regarding material durability and wall thermal management. This study aims to introduce a new optically accessible test rig to investigate the interaction between a premixed CH4/air turbulent flame and a parietal cooling air film for various blowing ratios. Laser Doppler velocimetry (LDV) is implemented to measure the cooling air and the mainstream inflow conditions. The impact of the blowing ratio on the mean flame topology is conducted with OH* chemiluminescence. Results show that the flame-wall distance increases with the blowing ratio and eventually reach a plateau, while the flame length constantly decreases. OH Planar-laser induced fluorescence (OH-PLIF) and phosphor thermometry (PT) are performed to assess the near-wall flame structure and the cooling effectiveness. The flame seems to be aerodynamically controlled while the cooled-air momentum has a beneficial impact on the wall temperature.

We report the synthesis of powder and single-crystal samples of the cerium pyrohafnate and their characterization using neutron diffraction, thermogravimetry and X-ray absorption spectroscopy. We evaluate the amount of non-magnetic Ce^4+ defects and use this result to interpret the spectrum of crystal-electric field transitions observed using inelastic neutron scattering. The analysis of these single-ion transitions indicates the dipole-octupole nature of the ground state doublet and a significant degree of spin-lattice coupling. The single-ion properties calculated from the crystal-electric field parameters obtained spectroscopically are in good agreement with bulk magnetic susceptibility data down to about 1 K. Below this temperature, the behavior of the magnetic susceptibility indicates a correlated regime without showing any sign of magnetic long-range order or freezing down to 0.08 K. We conclude that Ce_2Hf_2O_7 is another candidate to investigate exotic correlated states of quantum matter such as the octupolar quantum spin ice recently argued to exist in the isostructural compounds Ce_2Sn_2O_7 and Ce_2Zr_2O_7.

We study the dynamics of the quasi-one-dimensional Ising-Heisenberg antiferromagnet BaCo2V2O8 under a transverse magnetic field. Combining inelastic neutron scattering experiments and theoretical analyses by field theories and numerical simulations, we mainly elucidate the structure of the spin excitation spectrum in the high field phase, appearing above the quantum phase transition point mu0Hc 10 T. We find that it is characterized by collective solitonic excitations superimposed on a continuum. These solitons are strongly bound in pairs due to the effective staggered field induced by the nondiagonal g tensor of the compound, and are topologically different from the fractionalized spinons in the weak field region. The dynamical susceptibility numerically calculated with the infinite time-evolving block decimation method shows an excellent agreement with the measured spectra, which enables us to identify the dispersion branches with elementary excitations. The lowest energy dispersion has an incommensurate nature and has a local minimum at an irrational wave number due to the applied transverse field.

Neutron scattering is a powerful tool to study magnetic structures and dynamics, benefiting from a precisely established theoretical framework. The neutron dipole moment interacts with electrons in materials via their magnetic field, which can have spin and orbital origins. Yet in most experimentally studied cases the individual degrees of freedom are well described within the dipole approximation, sometimes accompanied by further terms of a multipolar expansion that usually act as minor corrections to the dipole form factor. Here we report a unique example of neutrons diffracted mainly by magnetic octupoles. This unusual situation arises in a quantum spin ice where the electronic wavefunction becomes essentially octupolar under the effect of correlations. The discovery of such a new type of quantum spin liquid that comes with a specific experimental signature in neutron scattering is remarkable, because these topical states of matter are notoriously difficult to detect.

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Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles1. Theories define such states using gauge fields and deconfined quasiparticle excitations that emerge from a local constraint governing the ground state of a frustrated magnet. For example, the ‘2-in–2-out’ ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice2–4 in rare-earth pyrochlores. However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and ‘hidden’ orders5,6. Here we show that the correlated ground state of a Ce3+-based pyrochlore, Ce2Sn2O7, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with a fluid-like state where degrees of freedom have a more complex magnetization density than that of magnetic dipoles. The nature and strength of the octupole–octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a ‘2-plus–2-minus’ rule7,8. Our work identifies Ce2Sn2O7 as a unique example of frustrated multipoles forming a ‘hidden’ topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations. A detailed neutron-scattering study reveals a quantum spin liquid behaviour in Ce2Sn2O7 originating from its higher-order magnetic multipolar moments acting on the geometrically frustrated pyrochlore lattice.