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The Mott insulator $\alpha$-RuCl$_3$ has generated great interest in the community due to its possible field-induced Kitaev quantum spin liquid state. Despite enormous effort spent trying to obtain the form of the low energy Hamiltonian, there is currently no agreed upon set of parameters which is able to explain all of the data. A key piece of missing information lies in the determination of the magnetic form factor of Ru$^{3+}$, particularly for a true quantitative treatment of inelastic neutron scattering data. Here we present the experimentally derived magnetic form factor of Ru$^{3+}$ in the low spin 4$d^5$ state using polarized neutron diffraction within the paramagnetic regime on high quality single crystals of $\alpha$-RuCl$_3$. We observe strong evidence of an anisotropic form factor, expected of the spin-orbit coupled $j_{\textrm{eff}} = \frac{1}{2}$ ground state. We model the static magnetization density in increasing complexity from simple isotropic cases, to a multipolar expansion, and finally \emph{ab initio} calculations of the generalized $j_{\textrm{eff}} = \frac{1}{2}$ ground state. Comparison of both single ion models and inclusion of Cl$^-$ anions support the presence of hybridization of Ru$^{3+}$ with the surrounding Cl$^{-}$ ligands.

Stacking variations in quasi-2D materials can have an important influence on material properties, such as changing the topology of the band structure. Unfortunately, the weakness of van der Waals interactions makes it difficult to compute the stacking dependence of properties, and even in a material as simple as graphite the stacking energetics remain unclear. Mo$_{1-x}$W$_{x}$Te$_{2}$ is a material in which three differently-stacked phases are conveniently accessible by temperature changes: $1T^{\prime}$, $T^*_d$, and the reported Weyl semimetal phase $T_d$. The transitions proceed via layer sliding, and the corresponding interlayer shear mode (ISM) is relevant not just for the stacking energetics, but for understanding the relationship between the Weyl physics and structural changes. However, the interlayer interactions of Mo$_{1-x}$W$_{x}$Te$_{2}$ are not well understood, with wide variation in computed properties. We report inelastic neutron scattering of the ISM in a Mo$_{0.91}$W$_{0.09}$Te$_{2}$ crystal. The ISM energies are generally consistent with the linear chain model (LCM), as expected given the weak interlayer interaction, though there are some discrepancies from predicted intensities. However, the interlayer force constants $K_x$ in the $T^*_d$ and $1T^{\prime}$ phases are substantially weaker than that of $T_d$, at 76(3)% and 83(3)%, respectively. Considering that the relative positioning of atoms in neighboring layers is approximately the same regardless of overall stacking, our results suggest that longer-range influences, such as stacking-induced band structure changes, may be responsible for the substantial change in the interlayer vibrational coupling. These findings should elucidate the stacking energetics of Mo$_{1-x}$W$_{x}$Te$_{2}$ and other van der Waals layered materials., Comment: supplement included

The interplay between strong electron correlation and band topology is at the forefront of condensed matter research. As a direct consequence of correlation, magnetism enriches topological phases and also has promising functional applications. However, the influence of topology on magnetism remains unclear, and the main research effort has been limited to ground state magnetic orders. Here we report a novel order above the magnetic transition temperature in magnetic Weyl semimetal (WSM) CeAlGe. Such order shows a number of anomalies in electrical and thermal transport, and neutron scattering measurements. We attribute this order to the coupling of Weyl fermions and magnetic fluctuations originating from a three-dimensional Seiberg-Witten monopole, which qualitatively agrees well with the observations. Our work reveals a prominent role topology may play in tailoring electron correlation beyond ground state ordering, and offers a new avenue to investigate emergent electronic properties in magnetic topological materials., Comment: Errors found in theoretical section of the paper

We report a comprehensive inelastic neutron scattering study of the hybrid molecule-based multiferroic compound (ND4)2FeCl5D2O in the zero-field incommensurate cycloidal phase and the high-field quasi-collinear phase. The spontaneous electric polarization changes its direction concurrently with the field-induced magnetic transition, from mostly aligned with the crystallographic a-axis to the c-axis. To account for such change of polarization direction, the underlying multiferroic mechanism was proposed to switch from the spin-current model induced via the inverse Dzyalloshinskii-Moriya interaction to the p-d hybridization model. We perform a detailed analysis of the inelastic neutron data of (ND4)2FeCl5D2O using linear spin-wave theory to quantify magnetic interaction strengths and investigate possible impact of different multiferroic mechanisms on the magnetic couplings. Our result reveals that the spin dynamics of both multiferroic phases can be well-described by a Heisenberg Hamiltonian with an easy-plane anisotropy. We do not find notable differences between the optimal model parameters of the two phases. The hierarchy of exchange couplings and the balance among frustrated interactions remain the same between two phases, suggesting that magnetic interactions in (ND4)2FeCl5D2O are much more robust than the electric polarization in response to delicate reorganizations of the electronic degrees of freedom in an applied magnetic field., Comment: 18 pages, 4 main figures, 1 Table

The crystalline and magnetic structures of Ca$_2$Ru$_{1-x}$Fe$_x$O$_4$ (x=0.02, 0.05, 0.08 and 0.12) have been studied using neutron and X-ray diffraction. The Fe-doping reduces the Ru-O bond length in both apical and planar directions. The smaller Ru(Fe)O$_6$ octahedron leads to its reduced distortion. The $Pbca$ space group is maintained in all the Fe-dopings, so is the octahedral flattening. Warming has a similar effect on the lattice to that of the Fe-doping in releasing the distorted octahedra but precipitates an abrupt octahedral elongation near the N$\acute{e}$el temperature. Two competing antiferromagnetic orders, $A$- and $B$-centered phases have been observed. The Fe-doping-relaxed crystal structure prefers the latter to the former. As the doping increases, the $B$-centered phase continuously grows at the cost of the $A$-centered one and eventually replaces it at x=0.12. The absence of the two-dimensional antiferromagnetic critical fluctuations above the magnetic transition temperature and the three-dimensional magnetic correlation below the transition, together with the anomalous lattice response, point to an important role of orbital degree of freedom in driving the magnetic phase competition.

The composition dependence of the structural transition between the monoclinic 1T$^{\prime}$ and orthorhombic T$_{d}$ phases in the Mo$_{1-x}$W$_{x}$Te$_{2}$ Weyl semimetal was investigated by elastic neutron scattering on single crystals up to $x \approx 0.54$. First observed in MoTe$_{2}$, the transition from T$_{d}$ to 1T$^{\prime}$ is accompanied by an intermediate pseudo-orthorhombic phase, T$_{d}^{*}$. Upon doping with W, the T$_{d}^{*}$ phase vanishes by $x \approx 0.34$. Above this concentration, a phase coexistence behavior with both T$_{d}$ and 1T$^{\prime}$ is observed instead. The interlayer in-plane positioning parameter $\delta$, which relates to the 1T$^{\prime}$ $\beta$ angle, decreases with temperature as well as with W substitution, likely due to strong anharmonicity in the interlayer interactions. The temperature width of the phase coexistence remains almost constant up to $x \approx 0.54$, in contrast to the broadening reported under pressure., Comment: supplement in separate file

The electron-phonon interaction (EPI) is instrumental in a wide variety of phenomena in solid-state physics, such as electrical resistivity in metals, carrier mobility, optical transition and polaron effects in semiconductors, lifetime of hot carriers, transition temperature in BCS superconductors, and even spin relaxation in diamond nitrogen-vacancy centers for quantum information processing. However, due to the weak EPI strength, most phenomena have focused on electronic properties rather than on phonon properties. One prominent exception is the Kohn anomaly, where phonon softening can emerge when the phonon wavevector nests the Fermi surface of metals. Here we report a new class of Kohn anomaly in a topological Weyl semimetal (WSM), predicted by field-theoretical calculations, and experimentally observed through inelastic x-ray and neutron scattering on WSM tantalum phosphide (TaP). Compared to the conventional Kohn anomaly, the Fermi surface in a WSM exhibits multiple topological singularities of Weyl nodes, leading to a distinct nesting condition with chiral selection, a power-law divergence, and non-negligible dynamical effects. Our work brings the concept of Kohn anomaly into WSMs and sheds light on elucidating the EPI mechanism in emergent topological materials., Comment: 30 pages, 4 main figures, 11 supplementary figures and 1 theoretical derivation. Feedback most welcome

Thermoelectrics are promising by directly generating electricity from waste heat. However, (sub-)room-temperature thermoelectrics have been a long-standing challenge due to vanishing electronic entropy at low temperatures. Topological materials offer a new avenue for energy harvesting applications. Recent theories predicted that topological semimetals at the quantum limit can lead to a large, non-saturating thermopower and a quantized thermoelectric Hall conductivity approaching a universal value. Here, we experimentally demonstrate the non-saturating thermopower and quantized thermoelectric Hall effect in the topological Weyl semimetal (WSM) tantalum phosphide (TaP). An ultrahigh longitudinal thermopower Sxx= 1.1x10^3 muV/K and giant power factor ~525 muW/cm/K^2 are observed at ~40K, which is largely attributed to the quantized thermoelectric Hall effect. Our work highlights the unique quantized thermoelectric Hall effect realized in a WSM toward low-temperature energy harvesting applications., Comment: 54 pages total, 5 main figures + 22 supplementary figures. To appear in Nature Communications (2020)

Using elastic neutron scattering on single crystals of MoTe$_{2}$ and Mo$_{1-x}$W$_{x}$Te$_{2}$ ($x \lesssim 0.01$), the temperature dependence of the recently discovered T$_{d}^{*}$ phase, present between the low temperature orthorhombic T$_{d}$ phase and high temperature monoclinic 1T$^{\prime}$ phase, is explored. The T$_{d}^{*}$ phase appears only on warming from T$_{d}$ and is observed in the hysteresis region prior to the 1T$^{\prime}$ transition. This phase consists of four layers in its unit cell, and is constructed by an "AABB" sequence of layer stacking operations rather than the "AB" and "AA" sequences of the 1T$^{\prime}$ and T$_{d}$ phases, respectively. Though the T$_{d}^{*}$ phase emerges without disorder on warming from T$_{d}$, on cooling from 1T$^{\prime}$ diffuse scattering is observed that suggests a frustrated tendency toward the "AABB" stacking., Comment: Supplement included as separate file

Using ambient pressure x-ray and high pressure neutron diffraction, we studied the pressure effect on structural and magnetic properties of multiferroic Mn$_{1-x}$Co$_x$WO$_4$ single crystals ($x=0, 0.05, 0.135$ and $0.17$), and compared it with the effects of doping. Both Co doping and pressure stretch the Mn-Mn chain along the $c$~direction. At high doping level ($x=0.135$ and $0.17$), pressure and Co doping drive the system in a similar way and induce a spin-flop transition for the $x=0.135$ compound. In contrast, magnetic ground states at lower doping level ($x=0$ and $0.05$) are robust against pressure but experience a pronounced change upon Co substitution. As Co introduces both chemical pressure and magnetic anisotropy into the frustrated magnetic system, our results suggest the magnetic anisotropy is the main driving force for the Co induced phase transitions at low doping level, and chemical pressure plays a more significant role at higher Co concentrations., Comment: 6 pages, 4 figures, to be published in Physical Rev. B

We use single-crystal neutron diffraction to determine the crystal structure symmetry and the magnetic evolution in the rhodium doped iridates $\rm Sr_2Ir_{1-x}Rh_{x}O_4$ ($0\leq x \leq 0.16$). Throughout this doping range, the crystal structure retains a tetragonal symmetry (space group $I4_1/a$) with two distinct magnetic Ir sites in the unit cell forming staggered $\rm IrO_6$ rotation. Upon Rh doping, the magnetic order is suppressed and the magnetic moment of Ir$^{4+}$ is reduced from 0.21 $\rm \mu_B$/Ir for $x=0$ to 0.18 $\rm \mu_B$/Ir for $x=0.12$. The magnetic structure at $x=0.12$ is different from that of the parent compound while the moments remain in the basal plane., Comment: Accepted for publication in Phys. Rev. B

A flop of electric polarization from $P$$\parallel$$c$ ($P_c$) to $P$$\parallel$$a$ ($P_a$) is observed in MnTiO$_3$ as a spin flop transition is triggered by a $c$-axis magnetic field, $H_{\|c}$=7 T. The critical magnetic field $H_{\|c}$ for $P_a$ is significantly reduced in Mn$_{1-x}$Ni$_x$TiO$_3$ (x=0.33). $P_a$ and $P_c$ have been observed with both $H_{\|c}$ and $H_{\|a}$. Neutron diffraction measurements revealed similar magnetic arrangements for the two compositions where the ordered spins couple antiferromagnetically with their nearest intra- and inter-planar neighbors. In the x=0.33 system, the uniaxial and planar anisotropies of Mn$^{2+}$ and Ni$^{2+}$ compete and give rise to a spin reorientation transition at $T_R$. A magnetic field, $H_{\|c}$, aligns the spins along $c$ for $T_R$$<$$T$$<$$T_N$. The rotation of the collinear spins away from the $c$-axis for $T$$<$$T_R$ alters the magnetic point symmetry and gives rise to a new ME susceptibility tensor form. Such linear ME response provides satisfactory explanation for the behavior of the field-induced electric polarization in both compositions. As the Ni content increases to x=0.5 and 0.68, the ME effect disappears as a new magnetic phase emerges., Comment: 7 pages, 7 figures

We report a single-crystal neutron diffraction study of the layered $\rm Sr_2IrO_4$. This work unambiguously determines the magnetic structure of the system and reveals that the spin orientation rigidly tracks the staggered rotation of the $\rm IrO_6$ octahedra in $\rm Sr_2IrO_4$. The long-range antiferromagnetic order has a canted spin configuration with an ordered moment of 0.208(3) $\mu_B$/Ir site within the basal plane; a detailed examination of the spin canting yields 0.202(3) and 0.049(2) $\mu_B$/site for the a axis and the b axis, respectively. It is intriguing that forbidden nuclear reflections of space group $I4_1/acd$ are also observed in a wide temperature range from 4 K to 600 K, which suggests a reduced crystal structure symmetry. This neutron-scattering work provides a direct, well-refined experimental characterization of the magnetic and crystal structures that are crucial to the understanding of the unconventional magnetism exhibited in this unusual magnetic insulator., Comment: the version appeared in PRB

We present a comprehensive single crystal neutron diffraction investigation of the $\rm Mn_{1-x}Co_{x}WO_4$ with $0.02\leq x \leq0.30$. At lower concentration $x \leq 0.05$, the system is quickly driven into the multiferroic phase with spin structure forming an elliptical spiral order similar to the parent compound. The reduction of electric polarization is ascribed to the tilting of the spiral plane. For $x\sim 0.075$, the magnetic structure undergoes a spin flop transition that is characterized by a sudden rotation of the spin helix envelope into the $ac$ plane. This spin structure persists for concentration up to $x=0.15$, where additional competing magnetic orders appear at low temperature. For $0.17 \leq x \leq 0.30$, the system experiences another spin flop transition and recovers the low-$x$ spiral spin configuration. A simple commensurate spin structure with $\vec{q}=(0.5,0,0)$ is found to coexist with the incommensurate spiral order. The complex evolution of magnetic structure in Co doped $\rm MnWO_4$ contrasts sharply with other transition metal ion doped $\rm Mn_{1-x}A_xWO_4$ (A=Zn, Mg, Fe) where the chemical substitutions stabilize only one type of magnetic structure. The rich phase diagram of $\rm Mn_{1-x}Co_{x}WO_4 $ results from the interplay between magnetic frustration and spin anisotropy of the Co ions., Comment: 13 pages, 17 figures, Revised version as that to appear in PRB

We have combined single crystal neutron and x-ray diffractions to investigate the magnetic and crystal structures of the honeycomb lattice $\rm Na_2IrO_3$. The system orders magnetically below $18.1(2)$ K with Ir$^{4+}$ ions forming zigzag spin chains within the layered honeycomb network with ordered moment of $\rm 0.22(1) \mu_B$/Ir site. Such a configuration sharply contrasts the N{\'{e}}el or stripe states proposed in the Kitaev-Heisenberg model. The structure refinement reveals that the Ir atoms form nearly ideal 2D honeycomb lattice while the $\rm IrO_6$ octahedra experience a trigonal distortion that is critical to the ground state. The results of this study provide much-needed experimental insights into the magnetic and crystal structure crucial to the understanding of the exotic magnetic order and possible topological characteristics in the 5$d$-electron based honeycomb lattice., Comment: Revised version as that to appear in PRB

We have carried out a pressure study of the unconventional superconductor FeTe0.6Se0.4 up to 1.5 GPa by neutron scattering, resistivity and magnetic susceptibility measurements. We have extracted the neutron spin resonance energy and the superconducting transition temperature as a function of applied pressure. Both increase with pressure up to a maximum at ~1.3 GPa. This analogous qualitative behavior is evidence for a correlation between these two fundamental parameters of unconventional superconductivity. However, Tc and the resonance energy do not scale linearly and thus a simple relationship between these energies does not exist even in a single sample. The renormalization of the resonance energy relative to the transition temperature is here attributed to an increased hybridization. The present results appear to be consistent with a pressure-induced weakening of the coupling strength associated with the fundamental pairing mechanism., Comment: 5 pages, 4 figures

The spin-wave excitations of the multiferroic $\rm MnWO_4$ have been measured in its low-temperature collinear commensurate phase using high-resolution inelastic neutron scattering. These excitations can be well described by a Heisenberg model with competing long-range exchange interactions and a single-ion anisotropy term. The magnetic interactions are strongly frustrated within the zigzag spin chain along c axis and between chains along the a axis, while the coupling between spin along the b axis is much weaker. The balance of these interactions results in the noncollinear incommensurate spin structure associated with the magnetoelectric effect, and the perturbation of the magnetic interactions leads to the observed rich phase diagrams of the chemically-doped materials. This delicate balance can also be tuned by the application of external electric or magnetic fields to achieve magnetoelectric control of this type of materials., Comment: 4 pages, 4 figures