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Quantum entanglement between the spin, orbital and lattice degrees of freedom in condensed matter systems can emerge due to an interplay between spin-orbit and vibronic interactions. Heavy transition metal ions decorated on a face-centered cubic lattice, for example in $5d^1$ double perovskites, are particularly suited to support these quantum entangled states, but direct evidence has not yet been presented. In this work, we report additional peaks in the low-energy spectra of a $5d^1$ double perovskite, Ba$_2$CaReO$_6$, which cannot be explained by adopting a purely classical description of lattice vibrations. Instead, our theoretical analysis demonstrates that these spectroscopic signatures are characteristic of orbital-lattice entangled states in Ba$_2$CaReO$_6$. Crucially, both theory and experiment demonstrate that these quantum-entangled states persist to low temperatures, despite the onset of multipolar order., Comment: 7 pages, 4 figures

Exotic quantum phases, arising from a complex interplay of charge, spin, lattice and orbital degrees of freedom, are of immense interest to a wide research community. A well-known example of such an entangled behavior is the Jahn-Teller effect, where the lifting of orbital degeneracy proceeds through lattice distortions, often accompanied by ordering of spins and metal-insulator transitions. Static distortions, including cooperative behavior, have been associated with colossal magneto-resistance, multiferroicity, high-$T_\mathrm{C}$ superconductivity and other correlated phenomena. Realizations of the dynamic Jahn-Teller effect, on the other hand, are scarce since the preservation of vibronic symmetries requires subtle tuning of the local environment. Here we demonstrate that a highly-symmetrical 5d$^1$ double perovskite Ba$_2$MgReO$_6$, comprising of a 3D array of isolated ReO$_6$ octahedra, fulfils these requirements, resulting in a unique case of a dynamic Jahn-Teller system with strong spin-orbit coupling. Thermodynamic and resonant inelastic x-ray scattering experiments undoubtedly show that the Jahn-Teller instability leads to a ground-state doublet, invoking a paradigm shift for this family of compounds. The restoration of vibronic degrees of freedom arises from a quantum-mechanical zero-point motion, as revealed by detailed quantum chemistry calculations. The dynamic state of ReO$_6$ octahedra persists down to the lowest temperatures, where a multipolar order sets in, allowing for investigations of the interplay between a dynamic JT effect and strongly correlated electron behavior.

We investigate the magnetic order in single crystalline EuCd$_2$Sb$_2$ thin films using a combined theoretical and experimental approach. Resonant elastic x-ray scattering experiments reveal a sharp magnetic peak at $q = (0, 0, \frac{1}{2})$ below $T_N = 7.2$ K, indicative of interlayer antiferromagnetic ordering. Additionally, we observe a weak diffuse magnetic signal centered at $q = (0, 0, 1)$ that persists above $T_N$, up to $T_C \sim 11$ K. Our Monte-Carlo simulations of a classical spin model approximation of the Eu magnetic sublattice demonstrate that the diffuse signal can arise from ferromagnetic coupling in the top few layers due to surface oxidation. On the other hand, the bulk of the sample exhibits antiferromagnetic coupling between layers. Finally, our fit of the model parameters to the magnetic ordering temperatures, shed light on the exchange couplings that are key in stabilizing the observed composite magnetic order., Comment: 7 pages, 4 figures

Clarifying the underlying mechanisms that govern ordering transitions in condensed matter systems is crucial for comprehending emergent properties and phenomena. While transitions are often classified as electronically driven or lattice-driven, we present a departure from this conventional paradigm in the case of the double perovskite Ba$_2$MgReO$_6$. Leveraging resonant and non-resonant elastic x-ray scattering techniques, we unveil the simultaneous ordering of structural distortions and charge quadrupoles at a critical temperature of $T_\mathrm{q}$$\sim$33 K. Using a variety of complementary first-principles-based computational techniques, we demonstrate that while electronic interactions drive the ordering at $T_\mathrm{q}$, it is ultimately the lattice that dictates the specific ground state that emerges. Our findings highlight the crucial interplay between electronic and lattice degrees of freedom, providing a unified framework to understand and predict unconventional emergent phenomena in quantum materials.

We establish the sign of the linear magnetoelectric (ME) coefficient, $\alpha$, in chromia, Cr$_2$O$_3$. Cr$_2$O$_3$ is the prototypical linear ME material, in which an electric (magnetic) field induces a linearly proportional magnetization (polarization), and a single magnetic domain can be selected by annealing in combined magnetic (H) and electric (E) fields. Opposite antiferromagnetic domains have opposite ME responses, and which antiferromagnetic domain corresponds to which sign of response has previously been unclear. We use density functional theory (DFT) to calculate the magnetic response of a single antiferromagnetic domain of Cr$_2$O$_3$ to an applied in-plane electric field at 0 K. We find that the domain with nearest neighbor magnetic moments oriented away from (towards) each other has a negative (positive) in-plane ME coefficient, $\alpha_{\perp}$, at 0 K. We show that this sign is consistent with all other DFT calculations in the literature that specified the domain orientation, independent of the choice of DFT code or functional, the method used to apply the field, and whether the direct (magnetic field) or inverse (electric field) ME response was calculated. Next, we reanalyze our previously published spherical neutron polarimetry data to determine the antiferromagnetic domain produced by annealing in combined E and H fields oriented along the crystallographic symmetry axis at room temperature. We find that the antiferromagnetic domain with nearest-neighbor magnetic moments oriented away from (towards) each other is produced by annealing in (anti-)parallel E and H fields, corresponding to a positive (negative) axial ME coefficient, $\alpha_{\parallel}$, at room temperature. Since $\alpha_{\perp}$ at 0 K and $\alpha_{\parallel}$ at room temperature are known to be of opposite sign, our computational and experimental results are consistent., Comment: 11 pages, 5 figures

Bose-Einstein condensation (BEC) underpins exotic forms of order ranging from superconductivity to superfluid 4 He. In quantum magnetic materials, ordered phases induced by an applied magnetic field can be described as the BEC of magnon excitations. With sufficiently strong magnetic frustration, exemplified by the system SrCu$_2$(BO$_3$)$_2$ , no clear magnon BEC is observed and the complex spectrum of multi-magnon bound states may allow a different type of condensation, but the high fields required to probe this physics have remained a barrier to detailed investigation. Here we exploit the first purpose-built high-field neutron scattering facility to measure the spin excitations of SrCu$_2$(BO$_3$)$_2$ up to 25.9 T and use cylinder matrix-product-states (MPS) calculations to reproduce the experimental spectra with high accuracy. Multiple unconventional features point to a condensation of $S = 2$ bound states into a spin-nematic phase, including the gradients of the one-magnon branches, the presence of many novel composite two- and three-triplon excitations and the persistence of a one-magnon spin gap. This gap reflects a direct analogy with superconductivity, suggesting that the spin-nematic phase in SrCu$_2$(BO$_3$)$_2$ is best understood as a condensate of bosonic Cooper pairs. Our results underline the wealth of unconventional states yet to be found in frustrated quantum magnetic materials under extreme conditions.

In the rapidly expanding field of topological materials there is growing interest in systems whose topological electronic band features can be induced or controlled by magnetism. Magnetic Weyl semimetals, which contain linear band crossings near the Fermi level, are of particular interest owing to their exotic charge and spin transport properties. Up to now, the majority of magnetic Weyl semimetals have been realized in ferro- or ferrimagnetically ordered compounds, but a disadvantage of these materials for practical use is their stray magnetic field which limits the minimum size of devices. Here we show that Weyl nodes can be induced by a helical spin configuration, in which the magnetization is fully compensated. Using a combination of neutron diffraction and resonant elastic x-ray scattering, we find that EuCuAs develops a planar helical structure below $T_\textrm{N}$ = 14.5 K which induces Weyl nodes along the $\Gamma$--A high symmetry line in the Brillouin zone.

We report neutron scattering measurements on YbMnSb$_2$ which shed new light on the nature of the magnetic moments and their interaction with Dirac fermions. Using half-polarized neutron diffraction we measured the field-induced magnetization distribution in the paramagnetic phase and found that the magnetic moments are well localised on the Mn atoms. Using triple-axis neutron scattering we measured the magnon spectrum throughout the Brillouin zone in the antiferromagnetically ordered phase, and we determined the dominant exchange interactions from linear spin-wave theory. The analysis shows that the interlayer exchange is five times larger than in several related compounds containing Bi instead of Sb. We argue that the coupling between the Mn local magnetic moments and the topological band states is more important in YbMnSb$_2$ than in the Bi compounds., Comment: 8 pages, 8 figures. Submitted to Physical Review B

We address magnetic neutron scattering in the presence of local non-centrosymmetric asymmetries of the magnetization density. Such inversion-symmetry breaking, combined with the absence of time-reversal symmetry, can be described in terms of magnetoelectric multipoles which form the second term after the magnetic dipole in the multipole expansion of the magnetization density. We provide a pedagogical review of the theoretical formalism of magnetic neutron diffraction in terms of the multipole expansion of the scattering cross-section. In particular, we show how to compute the contribution of magnetoelectric multipoles to the scattering amplitude starting from ab initio calculations. We also provide general guidelines on how to experimentally detect long-ranged order of magnetoelectric multipoles using either unpolarized or polarized neutron scattering. As a case study, we search for the presence of magnetoelectric multipoles in CuO by comparing theoretical first-principle predictions with experimental spherical neutron polarimetry measurements., Comment: 17 pages, 8 figures

Recent discovery of topologically non-trivial behavior in Co3Sn2S2 stimulated a notable interest in this itinerant ferromagnet (Tc = 174 K). The exact magnetic state remains ambiguous, with several reports indicating the existence of a second transition in the range 125 -- 130 K, with antiferromagnetic and glassy phases proposed to coexist with the ferromagnetic phase. Using detailed angle-dependent DC and AC magnetization measurements on large, high-quality single crystals we reveal a highly anisotropic behavior of both static and dynamic response of Co3Sn2S2. It is established that many observations related to sharp magnetization changes when B || c are influenced by the demagnetization factor of a sample. On the other hand, a genuine transition has been found at Tp = 128 K, with the magnetic response being strictly perpendicular to the c-axis and several orders of magnitude smaller than for B || c. Calculations using density-functional theory indicate that the ground state magnetic structure consist of magnetic moments canted away from the c-axis by a small angle (~ 1.5deg). We argue that the second transition originates from a small additional canting of moments within the kagome plane, with two equivalent orientations for each spin., Comment: accepted as a Letter in PRB

Control of magnetization and electric polarization is attractive in relation to tailoring materials for data storage and devices such as sensors or antennae. In magnetoelectric materials, these degrees of freedom are closely coupled, allowing polarization to be controlled by a magnetic field, and magnetization by an electric field, but the magnitude of the effect remains a challenge in the case of single-phase magnetoelectrics for application. We demonstrate that the magnetoelectric properties of the mixed-anisotropy antiferromagnet LiNi$_{1-x}$Fe$_x$PO$_4$ are profoundly affected by replacing a fraction of the Ni$^{2+}$ ions with Fe$^{2+}$ on the transition metal site. This introduces random site-dependent single-ion anisotropy energies and causes a lowering of the magnetic symmetry of the system. In turn, magnetoelectric couplings that are symmetry-forbidden in the parent compounds, LiNiPO$_4$ and LiFePO$_4$, are unlocked and the dominant coupling is enhanced by two orders of magnitude. Our results demonstrate the potential of mixed-anisotropy magnets for tuning magnetoelectric properties.

We examine the role of charge, structural, and spin degrees of freedom in the previously poorly understood phase transition in the 5$d^1$ transition-metal double perovskite Cs$_2$TaCl$_6$, using a combination of computational and experimental techniques. Our heat capacity measurements of single-crystalline Cs$_2$TaCl$_6$, reveal a clear anomaly at the transition temperature, $T_\mathrm{Q}$, which was not previously observed in polycrystalline samples. Density functional calculations indicate the emergence of local charge quadrupoles in the cubic phase, mediated by the paramagnetic spins or local structural distortions which then develop into long-range ordered charge quadrupoles in the tetragonal phase. Our resonant elastic x-ray scattering on Cs$_2$TaCl$_6$, single crystals lend support to our calculations. Our work provides new insight into the phase transition in Cs$_2$TaCl$_6$, at $T_\mathrm{Q}$, and demonstrates the utility of this combination of techniques in understanding the complex physics of hidden orders in paramagnetic spin-orbit-entangled compounds.

The magnetic, dielectric and structural properties of type-I multiferroic KNiPO$_4$ have been investigated by neutron powder diffraction, magnetization, dielectric and high temperature synchrotron-XRD measurements. Below the N\'{e}el transition of $T_\mathrm{N}$ = 25 K, KNiPO$_4$ displays a weakly non-collinear antiferromagnetic (AFM) structure with the orientation of the Ni$^{2+}$ magnetic moments mainly along $a$ axis. The compound crystallizes in the polar orthorhombic $Pna2_1$ space group at room temperature. A second-order structural phase transition corresponding to the onset ferroelectricity is observed at around $T_\mathrm{C}\sim$ 594(3)$^\circ$C, above which the crystal structure of KNiPO$_4$ adopts the centrosymmetric $Pnma$ space group. The compound also displays another structural phase transition at $T_\mathrm{0}\sim$ 469 -- 488$^\circ$C, with a first-order character, which is attributed to the rearrangement of oxygen ligands, resulting in a change in the nickel ion co-ordination from four to five.

Co$_3$Sn$_2$S$_2$ has recently been predicted to be a Weyl semimetal in which magnetic order is key to its behavior as a topological material. Here we report unpolarized neutron diffraction and spherical neutron polarimetry measurements, supported by magnetization and transport data, which probe the magnetic order in Co$_3$Sn$_2$S$_2$ below $T_\textrm{C} = 177$ K. The results are fully consistent with ferromagnetic order in which the spins on the Co atoms point along the crystal $c$ axis, although we cannot rule out some canting of the spins. We find no evidence for a type of long-ranged $(\textbf{k}=\textbf{0})$ in-plane 120$^\circ$ antiferromagnetic order which had previously been considered as a secondary phase present at temperatures between $\sim$90 K and $T_\textrm{C}$. A discontinuous change in bulk properties and neutron polarization observed at $T = 125$ K when samples are cooled in a field and measured on warming is found to be due to a sudden reduction in ferromagnetic domain size. Our results lend support to the theoretical predictions that Co$_3$Sn$_2$S$_2$ is a magnetic Weyl semimetal.

The antiferromagnetic (AFM) semimetal YbMnSb$_2$ has recently been identified as a candidate topological material, driven by time-reversal symmetry breaking. Depending on the ordered arrangement of Mn spins below the N\'{e}el temperature, $T_\mathrm{N}$ = 345 K, the electronic bands near the Fermi energy can ether have a Dirac node, a Weyl node or a nodal line. We have investigated the ground state magnetic structure of YbMnSb$_2$ using unpolarized and polarized single crystal neutron diffraction. We find that the Mn moments lie along the $c$ axis of the $P4/nmm$ space group and are arranged in a C-type AFM structure, which implies the existence of gapped Dirac nodes near the Fermi level. The results highlight how different magnetic structures can critically affect the topological nature of fermions in semimetals.

We have investigated the magnetic correlations in the candidate Weyl semimetals EuCd$_2Pn_2$, ($Pn$=As, Sb) by resonant elastic X-ray scattering (REXS) at the Eu$^{2+}$ $M_5$ edge. The temperature and field dependence of the diffuse scattering of EuCd$_2$As$_2$ provide direct evidence that the Eu moments exhibit slow ferromagnetic correlations well above the N\'{e}el temperature. By contrast, the diffuse scattering in the paramagnetic phase of isostructural EuCd$_2$Sb$_2$ is at least an order of magnitude weaker. The FM correlations present in the paramagnetic phase of EuCd$_2$As$_2$ could create short-lived Weyl nodes.

We investigated the magnetic structure and dynamics of YbMnBi$_2$, with elastic and inelastic neutron scattering, to shed light on the topological nature of the charge carriers in the antiferromagnetic phase. We confirm C-type antiferromagnetic ordering of the Mn spins below $T_{\rm N} = 290$ K, and determine that the spins point along the $c$-axis to within about $3^\circ$. The observed magnon spectrum can be described very well by the same effective spin Hamiltonian as was used previously to model the magnon spectrum of CaMnBi$_2$. Our results show conclusively that the creation of Weyl nodes in YbMnBi$_2$ by the time-reversal-symmetry breaking mechanism can be excluded in the bulk.