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The recently discovered dipole-octupole pyrochlore magnet Ce$_2$Hf$_2$O$_7$ 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 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$_2$Hf$_2$O$_7$ and its sister compounds., Comment: 16 pages, 13 figures

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., Comment: 19 pages, 20 figures (main text: 12 pages, 13 figures)

We investigate the correlated state of Ce$_2$Hf$_2$O$_7$ using neutron scattering, finding signatures of correlations of both dipolar and octupolar character. A dipolar inelastic signal is also observed, as expected for spinons in a quantum spin ice (QSI). Fits of thermodynamic data using exact diagonalization methods indicate that the largest interaction is an octupolar exchange, with a strength roughly twice as large as other terms. A hierarchy of exchange interactions with dominant octupolar and significant dipolar exchange, still in the octupolar QSI phase, rationalises neutron scattering observations. Our results reveal a `quantum multipolar liquid' where correlations involve multiple terms in moment series expansion, opening questions about their intertwining and possible hierarchy., Comment: 6 pages, 3 figures

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 multiple peaks are a specific signature of the $\pi$-flux phase of QSI, providing spectroscopic evidence for fractionalization in a three-dimensional quantum spin liquid., Comment: 19 pages, 6 figures, fixes in references

By combining inelastic neutron scattering and numerical simulations, we study the quasi-one dimensional Ising-like quantum antiferromagnet BaCo$_{2}$V$_{2}$O$_{8}$ in a longitudinal magnetic field applied along the magnetic anisotropy axis, which is also the chain direction. The external field closes the excitation gap due to the magnetic anisotropy, inducing a transition from the N\'eel 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 BaCo$_{2}$V$_{2}$O$_{8}$ by including a four-site periodic term arising from the crystal structure which enables to account for an anomaly of the magnetic susceptibility appearing at 19 T as well as for the anticrossing observed in the inelastic neutron scattering spectra., Comment: 13 pages, 8 figures

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$_2$Hf$_2$O$_{7}$ 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$_2$Sn$_2$O$_7$ and Ce$_2$Zr$_2$O$_7$.

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., Comment: Article in Swiss Neutron News, after R. Sibille et al. Nature Physics 16, 546-552 (2020). https://sgn.web.psi.ch/sgn/snn.html

Anisotropic multiferroic properties of SrMnGe2O6 pyroxene single crystals were systematically investigated by means of magnetization, heat capacity, pyroelectric current measurement and elastic and inelastic neutron scattering experiments. Single crystal neutron diffraction allows us to unambiguously reveal the presence of two incommensurate magnetic orderings: a non-polar amplitude-modulated collinear sinusoidal magnetic structure emerges at TN1=4.36(2)K followed by a polar elliptical cycloidal spin structure below TN2=4.05(2)K. Pyroelectric current measurements on single crystal confirm the appearance of a spontaneous polarization within the (ac) plane below TN2 associated with the latter magnetic symmetry through extended Dzyaloshinsky-Moriya mechanism. The magnetic phase diagram was calculated considering the three isotropic exchange couplings relevant in this system. The magnetic excitations spectra of SrMnGe2O6 measured by inelastic neutron scattering were successfully modeled using a set of exchange interactions consistent with this phase diagram.

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles$^1$. Theories typically define such states using gauge fields and deconfined quasiparticle excitations that emerge from a simple rule governing the local 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 ice in rare-earth pyrochlores - a state described by a lattice gauge theory of quantum electrodynamics$^{2-4}$. However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and 'hidden' orders$^{5-6}$. Here we show that the correlated ground state of a Ce$^{3+}$-based pyrochlore, Ce$_2$Sn$_2$O$_7$, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with the formation of a fluid-like state of matter, but the intensity distribution is weighted to larger scattering vectors, which indicates that the correlated degrees of freedom have a more complex magnetization density than that typical of magnetic dipoles in a spin liquid. The temperature evolution of the bulk properties in the correlated regime below 1 Kelvin is well reproduced using a model of dipole-octupole doublets on a pyrochlore lattice$^{7-8}$. 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' rule. Our work identifies Ce$_2$Sn$_2$O$_7$ as a unique example of a material where frustrated multipoles form a 'hidden' topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.

Combining inelastic neutron scattering and numerical simulations, we study the quasi-one dimensional Ising anisotropic quantum antiferromagnet \bacovo\ in a longitudinal magnetic field. This material shows a quantum phase transition from a N\'eel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnet chains., Comment: 6 pages, 4 figures; 4 additional pages of supplementary information containing 3 figures

The origin of the effect of colossal magneto-resistance (CMR) remains still unexplained. In this work we revisit the spin dynamics of the pseudo-cubic La1-xSrxMnO3 along the Mn-O-Mn bond direction at four x doping values (x < 0.5) and various temperatures and report a new lattice dynamics study at x0=0.2, representative of the optimal doping for CMR. We propose an interpretation of the spin dynamics in terms of orbital polarons. This picture is supported by the observation of a discrete magnetic energy spectrum Enmag (q) characteristic of the internal excitations of "orbital polarons" defined by Mn3+ neighbors surrounding a Mn4+ center with a hole. Because of its hopping, the hole mixes up dynamically all the possible orbital configurations of its surrounding Mn3+ sites with degenerate energies. The Enmag values indicate a lift of orbital degeneracy by phonon excitations. The number n varies with the spatial dimension D of the polaron and the q-range determines its size. At x=0.125 and x=0.3 the spectrum reveals 2D polarons coupled by exchange and 3D "free" polarons respectively, with sizes l=1.67a < 2a in all bond directions. At x0=0.2, the spin and the lattice dynamics provide evidence for chains of orbital polarons of size l=2a with a periodic distribution over ~ 3a and an interaction energy ~ 3 meV. At T < Tc the charges propagate together with the longitudinal acoustic phonons along the chains enhancing their ferromagnetic character. The phase separation between metallic and ferromagnetic chains in a non-metallic matrix may be crucial for CMR.

Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the strongest cases presented has been for the pyrochlore XY antiferromagnet Er2Ti2O7, with the ground state selection proceeding by order by disorder induced through the effects of quantum fluctuations. This identification assumes the smallness of the effect of virtual crystal field fluctuations that could provide an alternative route to picking the ground state. Here we show that this order by virtual crystal field fluctuations is not only significant, but competitive with the effects of quantum fluctuations. Further, we argue that higher-multipolar interactions that are generically present in rare-earth magnets can dramatically enhance this effect. From a simplified bilinear-biquadratic model of these multipolar interactions, we show how the virtual crystal field fluctuations manifest in Er2Ti2O7 using a combination of strong coupling perturbation theory and the random phase approximation. We find that the experimentally observed psi2 state is indeed selected and the experimentally measured excitation gap can be reproduced when the bilinear and biquadratic couplings are comparable while maintaining agreement with the entire experimental spin-wave excitation spectrum. Finally, we comments on possible tests of this scenario and discuss implications for other order-by-disorder candidates in rare-earth magnets., Comment: 16 pages, 6 figures

The chiral Fe-based langasites represent model systems of triangle-based frustrated magnets with a strong potential for multiferroicity. We report neutron scattering measurements for the multichiral Ba3MFe3Si2O14 (M = Nb, Ta) langasites revealing new important features of the magnetic order of these systems: the bunching of the helical modulation along the c-axis and the in-plane distortion of the 120{\textdegree} Fe-spin arrangement. We discuss these subtle features in terms of the microscopic spin Hamiltonian, and provide the link to the magnetically-induced electric polarization observed in these systems. Thus, our findings put the multiferroicity of this attractive family of materials on solid ground.

The low energy dynamical properties of the multiferroic hexagonal perovskite ErMnO3 have been studied by inelastic neutron scattering as well as terahertz and far infrared spectroscopies on synchrotron source. From these complementary techniques, we have determined the magnon and crystal field spectra and identified a zone center magnon only excitable by the electric field of an electromagnetic wave. Using comparison with the isostructural YMnO3 compound and crystal field calculations, we propose that this dynamical magnetoelectric process is due to the hybridization of a magnon with an electro-active crystal field transition., Comment: 6 pages

The CeT2Al10 family of orthorhombic compounds exhibits a very peculiar evolution from a Kondo-insulator (T: Fe) to an unconventional long-range magnetic order (T: Ru, Os). Inelastic neutron scattering experiments performed on single-crystal CeFe2Al10 reveal that this material develops a spin-gap in its magnetic spectral response below ~ 50 K, with a magnetic excitation dispersing from $E = 10.2 \pm 0.5$ meV at the Y zone-boundary point [q = (0,1,0)] to $\approx 12$ meV at the top of the branch. The excitation shows a pronounced polarization of the magnetic fluctuations along a, the easy anisotropy axis. Its behavior is contrasted with that of the (magnonlike) modes previously reported for CeRu2Al10, which have transverse character and exist only in the antiferromagnetic state. The present observation is ascribed to a "magnetic exciton" mechanism invoked to explain a similar magnetic response previously discovered in YbB12., Comment: 4 figures, 6 pages, submitted to Physical Review Letters

\ersn\, is considered, together with \erti, as a realization of the XY antiferromagnet on the pyrochlore lattice. We present magnetization measurements confirming that \ersn\, does not order down to 100 mK but exhibits a freezing below 200 mK. Our neutron scattering experiments evidence the strong XY character of the \er moment and point out the existence of short range correlations in which the magnetic moments are in peculiar configurations, the Palmer-Chalker states, predicted theoretically for an XY pyrochlore antiferromagnet with dipolar interactions. Our estimation of the \ersn\, parameters confirm the role of the latter interactions on top of relatively weak and isotropic exchange couplings.

The dynamical magnetic correlations in \tbti\, have been investigated using polarized inelastic neutron scattering. Dispersive excitations are observed, emerging from pinch points in reciprocal space and characterized by an anisotropic spectral weight. Anomalies in the crystal field and phonon excitation spectrum at Brillouin zone centers are also reported. These findings suggest that Coulomb phases, although they present a disordered ground state with dipolar correlations, allow the propagation of collective excitations. They also point out a strong spin-lattice coupling, which likely drives effective interactions between the $4f$ quadrupolar moments.

We present a model which accounts for the high field magnetisation at very low temperature in two pyrochlore frustrated systems, Er2Ti2O7 and Tb2Ti2O7. The two compounds present very different ground states: Er2Ti2O7, which has a planar crystal field anisotropy, is an antiferromagnet with T_N=1.2K, whereas Tb2Ti2O7 is expected to have Ising character and shows no magnetic ordering down to 0.05K, being thus labelled a ``spin liquid''. Our model is a mean field self-consistent calculation involving the 4 rare earth sites of a tetrahedron, the building unit of the pyrochlore lattice. It includes the full crystal field hamiltonian, the infinite range dipolar interaction and anisotropic nearest neighbour exchange described by a 3-component tensor. For Er2Ti2O7, we discuss the equivalence of our treatment of the exchange tensor, taken to be diagonal in a frame linked to a rare earth - rare earth bond, with the pseudo-spin hamiltonian recently developped for Kramers doublets in a pyrochlore lattice. In Tb2Ti2O7, an essential ingredient of our model is a symmetry breaking developping at very low temperature. We compare its prediction for the isothermal magnetisation with that of ``the quantum spin ice'' model.

We have studied the low energy spin dynamics between 4.6K and 0.07K in a Tb2Ti2O7 single crystal sample, by means of inelastic neutron scattering experiments. The spectra consist in a dual response, with a static and an inelastic contribution, showing striking Q-dependences. We propose an interpretation involving an anisotropic exchange interaction in combination with a breaking of the threefold symmetry at the rare earth site. Simulations of the Q-dependent scattering in the Random Phase Approximation account well for the inelastic response.

Spin dynamics in the new Kondo insulator compound CeRu2Al10 has been studied using unpolarized and polarized neutron scattering on single crystals. In the unconventional ordered phase forming below T0 = 27.3 K, two excitation branches are observed with significant intensities, the lower one of which has a gap of 4.8 +/- 0.3 meV and a pronounced dispersion up to about 8.5 meV. Comparison with RPA magnon calculations assuming crystal-field and anisotropic exchange couplings captures major aspects of the data, but leaves unexplained discrepancies, pointing to a key role of direction-specific hybridization between 4f and conduction band states in this compound., Comment: 4 figures, 1 table

Geometrical frustration is a central challenge in contemporary condensed matter physics, a crucible favourable to the emergence of novel physics. The pyrochlore magnets, with rare earth magnetic moments localized at the vertices of corner-sharing tetrahedra, play a prominent role in this field, with a rich variety of exotic ground states ranging from the "spin ices" \hoti\ and \dyti\ to the "spin liquid" and "ordered spin ice" ground states in \tbti\ and \tbsn. Inelastic neutron scattering provides valuable information for understanding the nature of these ground states, shedding light on the crystal electric field (CEF) level scheme and on the interactions between magnetic moments. We have performed such measurements with unprecedented neutron flux and energy resolution, in the "ordered spin ice" \tbsn. We argue that a new interaction, which involves the spin lattice coupling through a low temperature distortion of the trigonal crystal field, is necessary to account for the data.

The spin wave excitations emerging from the chiral helically modulated 120$^{\circ}$ magnetic order in a langasite Ba$_3$NbFe$_3$Si$_2$O$_{14}$ enantiopure crystal were investigated by unpolarized and polarized inelastic neutron scattering. A dynamical fingerprint of the chiral ground state is obtained, singularized by (i) spectral weight asymmetries answerable to the structural chirality and (ii) a full chirality of the spin correlations observed over the whole energy spectrum. The intrinsic chiral nature of the spin waves elementary excitations is shown in absence of macroscopic time reversal symmetry breaking.

The temperature evolution of the crystal and magnetic structures of ferroelectric sulfide AgCrS2 have been investigated by means of neutron scattering. AgCrS2 undergoes at TN = 41.6 K a first-order phase transition, from a paramagnetic rhombohedral R3m to an antiferromagnetic monoclinic structure with a polar Cm space group. In addition to being ferroelectric below TN, the low temperature phase of AgCrS2 exhibits an unconventional collinear magnetic structure that can be described as double ferromagnetic stripes coupled antiferromagnetically, with the magnetic moment of Cr+3 oriented along b within the anisotropic triangular plane. The magnetic couplings stabilizing this structure are discussed using inelastic neutron scattering results. Ferroelectricity below TN in AgCrS2 can possibly be explained in terms of atomic displacements at the magneto-elastic induced structural distortion. These results contrast with the behavior of the parent frustrated antiferromagnet and spin-driven ferroelectric AgCrO2.