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The three-dimensional charge density wave (CDW) compound ${\mathrm{Lu}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ undergoes a first-order CDW phase transition at around 200 K. An atypical CDW state is found, that is characterized by an incommensurate CDW with $\mathbf{q}=[0.2499(3),0.4843(4),0.2386(2)]$ at 60 K, and a large orthorhombic-to-triclinic lattice distortion with $\ensuremath{\beta}=91.945{(2)}^{\ensuremath{\circ}}$. We present the modulated crystal structure of the incommensurate CDW state. Structural analysis shows that the CDW resides on the zigzag chains of iridium atoms along $\mathbf{c}$. The structural distortions are completely similar between nonmagnetic ${\mathrm{Lu}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ and previously studied isostructural magnetic ${\mathrm{Er}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ with the small differences explained by the different values of the atomic radii of Lu and Er. Such a similarity is unique to ${R}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ $(R=\mathrm{rare}\phantom{\rule{0.28em}{0ex}}\mathrm{earth})$. It differs from, for example, the rare-earth CDW compounds ${R}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ for which ${\mathrm{Lu}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ and ${\mathrm{Er}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ possess entirely different CDW states. We argue that the mechanism of CDW formation, thus, is different for ${R}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ and ${R}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$.

The first-order charge density wave (CDW) phase transition of ${\mathrm{Er}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ is characterized by a crystal structure analysis, and electrical resistivity, magnetic susceptibility and specific heat measurements. The incommensurate CDW is accompanied by a strong lattice distortion, from which it is shown that the CDW resides on zigzag chains of iridium atoms. The CDW transition affects the magnitude of the local magnetic moments on ${\mathrm{Er}}^{3+}$, implying strong coupling between CDW and magnetism. This could account for the observation that magnetic order is suppressed down to at least 0.1 K in the high-quality single crystal presently studied. Any disorder in the crystallinity, as in ceramic material, broadens and suppresses the CDW transition, while magnetic order appears at 2.1 K.

We report a soft x-ray resonant magnetic scattering study of the spin configuration in multiferroic thin films of ${\mathrm{Co}}_{0.975}{\mathrm{Ge}}_{0.025}{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$ (Ge-CCO) and ${\mathrm{CoCr}}_{2}{\mathrm{O}}_{4}$ (CCO) under low and high magnetic fields from 0.2 to 6.5 T. A characterization of Ge-CCO at a low magnetic field was performed, and the results were compared with those of pure CCO. The ferrimagnetic phase transition temperature ${T}_{C}\ensuremath{\approx}95\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and the multiferroic transition temperature ${T}_{S}\ensuremath{\approx}27\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ in Ge-CCO are comparable with those observed in CCO. In Ge-CCO, the ordering wave vector ($qq0$) observed below ${T}_{S}$ is slightly larger compared with that of CCO, and unlike CCO, the diffraction intensity consists of two contributions that show a dissimilar x-ray polarization dependence. In Ge-CCO, the coercive field observed at low temperatures was larger than the one reported for CCO. In both compounds, an unexpected reversal of the spiral helicity, and therefore the electric polarization, was observed on simply magnetic field cooling. In addition, we find a change in the helicity as a function of momentum transfer in the magnetic diffraction peak of Ge-CCO, indicative of the presence of multiple magnetic spirals.

Orthorhombic $\mathrm{HoMn}{\mathrm{O}}_{3}$ is a multiferroic in which Mn antiferromagnetic order induces ferroelectricity. A second transition occurs within the multiferroic phase, in which a strong enhancement of the ferroelectric polarization occurs concomitantly to antiferromagnetic ordering of Ho $4f$ magnetic moments. Using the element selectivity of resonant x-ray diffraction, we study the magnetic order of the Mn $3d$ and Ho $4f$ moments. We explicitly show that the Mn magnetic order is affected by the Ho $4f$ magnetic ordering transition. Based on the azimuthal dependence of the $(0\phantom{\rule{0.16em}{0ex}}q\phantom{\rule{0.16em}{0ex}}0)$ and $(0\phantom{\rule{0.16em}{0ex}}1\ensuremath{-}q\phantom{\rule{0.16em}{0ex}}0)$ magnetic reflections, we suggest that the Ho $4f$ order resembles an $ac$ cycloid. Using nonresonant diffraction, we show that the magnetically induced polar lattice distortion is unaffected by the Ho ordering, suggesting a mechanism through which the Ho order affects ferroelectric polarization without affecting the lattice in the same manner as the Mn order.

The three-dimensional charge density wave (CDW) compound ${\mathrm{CuV}}_{2}{\mathrm{S}}_{4}$ is known to undergo phase transitions at $\ensuremath{\sim}91$ and $\ensuremath{\sim}50\phantom{\rule{4pt}{0ex}}\mathrm{K}$. Employing single-crystal x-ray diffraction on an annealed crystal, we confirm the formation of an incommensurate CDW at ${T}_{\text{CDW}}\ensuremath{\approx}91\phantom{\rule{4pt}{0ex}}\mathrm{K}$, and we establish the nature of the transition at ${T}_{\text{lock-in}}\ensuremath{\approx}50\phantom{\rule{4pt}{0ex}}\mathrm{K}$ as a lock-in transition toward a threefold superstructure. As-grown crystals develop the same incommensurate CDW as the annealed crystal does, but they fail to go through the lock-in transition. Instead, the length of the modulation wave vector continues to decrease down to low temperatures in as-grown crystals. These findings are corroborated by distinct temperature dependencies of the electrical resistivity, magnetic susceptibility, and specific heat measured on as-grown and annealed crystals. A superspace model for the crystal structure of the incommensurate CDW suggests that the formation of extended vanadium clusters is at the origin of the CDW. In the lock-in phase, short and long V-V distances persist, but clusters now percolate the entire crystal. The lowering toward orthorhombic symmetry appears to be responsible for the precise pattern of short and long V-V distances. However, the orthorhombic lattice distortion is nearly zero for the annealed crystal, while it is visible for the as-grown material, again suggesting the role of lattice defects in the latter.

We employ resonant soft x ray diffraction to individually study the magnetic ordering of the Mn and the Tm sublattices in single crystalline films of orthorhombic (o )TmMnO3. The same magnetic ordering wave vector of (0 q 0) with q ˜ 0.46 is found for both ionic species suggesting that the familiar antiferromagnetic order of the Mn ions induces a magnetic order on the Tm unpaired 4f electrons. Indeed intensity variations of magnetic reflections with temperature corroborate this scenario. Calculated magnetic fields at the Tm sites are used as a model magnetic structure for the Tm which correctly predicts intensity variations at the Tm resonance upon azimuthal rotation of the sample. The model allows ruling out a bc cycloid modulation of the Mn ions as the cause for the incommensurate ordering as found in TbMnO3. The structural distortion which occurs in the ferroelectric phase below TC was followed through nonresonant diffraction of structural reflections forbidden by the high temperature crystal symmetry. The (0 q 0) magnetic reflection appears at the Mn resonance well above TC indicating that this reflection is sensitive also to the intermediate sinusoidal magnetic phase. The model presented suggests that the Tm 4f electrons are polarized well above the ferroelectric transition and are possibly not affected by the transition at TC. The successful description of the induced order observed at the Tm resonance is a promising example for future element selective studies in which “spectator” ions may allow access to previously unobtainable information about other constituent ions. DOI: 10.1103/PhysRevB.91.235144

X-ray magnetic circular dichroism (XMCD) and x-ray magnetic linear dichroism (XMLD) have been used to investigate the Fe magnetic response during the spin-reorientation transition (SRT) in $\mathrm{TmFe}{\mathrm{O}}_{3}$. Comparing the Fe XMLD results with neutron-diffraction and magnetization measurements on the same sample indicates that the SRT has an enhanced temperature range in the near surface region of approximately 82 to 120 K compared to approximately 82 to 92 K in bulk. This view is supported by complementary resonant soft x-ray-diffraction experiments at the Tm ${M}_{5}$ edge. These measurements find an induced magnetic moment on the Tm sites, which is well described by a dipolar mean-field model originating from the Fe moments. Even though such a model can describe the $4f$ response in the experiments, it is insufficient to describe the SRT even when considering a change in the $4f$ anisotropy. Moreover, the results of the Fe XMCD show a different temperature evolution through the SRT, the interpretation of which is hampered by additional spectral shape changes of the XCMD signal.

Using resonant soft x-ray techniques we follow the magnetic behavior of a strained epitaxial film of $\mathrm{CoC}{\mathrm{r}}_{2}{\mathrm{O}}_{4}$, a type-II multiferroic. The film is [110] oriented, such that both the ferroelectric and ferromagnetic moments can coexist in-plane. X-ray magnetic circular dichroism (XMCD) is used in scattering and in transmission modes to probe the magnetization of Co and Cr separately. The transmission measurements utilized x-ray excited optical luminescence from the substrate. Resonant soft x-ray diffraction (RXD) was used to study the magnetic order of the low temperature phase. The XMCD signals of Co and Cr appear at the same ordering temperature ${T}_{C}\ensuremath{\approx}90\phantom{\rule{4pt}{0ex}}\mathrm{K}$, and are always opposite in sign. The coercive field of the Co and of Cr moments is the same, and is approximately two orders of magnitude higher than in bulk. Through sum rules analysis an enlarged $\mathrm{C}{\mathrm{o}}^{2+}$ orbital moment (${m}_{L}$) is found, which can explain this hardening. The RXD signal of the (q q 0) reflection appears below ${T}_{S}$, the same ordering temperature as the conical magnetic structure in bulk, indicating that this phase remains multiferroic under strain. To describe the azimuthal dependence of this reflection, a slight modification is required to the spin model proposed by the conventional Lyons-Kaplan-Dwight-Menyuk theory for magnetic spinels.

Chiral multiferroic langasites have attracted attention due to their doubly chiral magnetic ground state within an enantiomorphic crystal. We report on a detailed resonant soft x-ray diffraction study of the multiferroic ${\mathrm{Ba}}_{3}{\mathrm{TaFe}}_{3}{\mathrm{Si}}_{2}{\mathrm{O}}_{14}$ at the Fe ${L}_{2,3}$ and oxygen $K$ edges. Below ${T}_{N}$ ($\ensuremath{\approx}27K$) we observe the satellite reflections $(0,0,\ensuremath{\tau}), (0,0,2\ensuremath{\tau}), (0,0,3\ensuremath{\tau})$, and $(0,0,1\ensuremath{-}3\ensuremath{\tau})$ where $\ensuremath{\tau}\ensuremath{\approx}0.140\ifmmode\pm\else\textpm\fi{}0.001$. The dependence of the scattering intensity on x-ray polarization and azimuthal angle indicate that the odd harmonics are dominated by the out-of-plane ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{c}}$ axis) magnetic dipole while the $(0,0,2\ensuremath{\tau})$ originates from the electron density distortions accompanying magnetic order. We observe dissimilar energy dependencies of the diffraction intensity of the purely magnetic odd-harmonic satellites at the Fe ${L}_{3}$ edge. Utilizing first-principles calculations, we show that this is a consequence of the loss of threefold crystal symmetry in the multiferroic phase.

We report an investigation of the superconducting states of ${\mathrm{Lu}}_{3}{\mathrm{Os}}_{4}{\mathrm{Ge}}_{13}$ and ${\mathrm{Y}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Ge}}_{13}$ single crystals by measurements of the electrical resistivity, ac susceptibility, and London penetration depth. The analysis of the penetration depth and the derived superfluid density indicates the presence of nodeless superconductivity and suggests that there are multiple superconducting gaps in both materials. Furthermore, ac susceptibility measurements of both compounds display the peak effect in the low-temperature region of the $H\text{\ensuremath{-}}T$ phase diagram. This anomalous increase of the critical current with field gives an indication of a change of the arrangement of flux lines in the mixed state, as found in some of the isostructural stannide materials.

Combining Raman scattering measurements with mean-field calculations of the Raman response, we show that Kitaev-like magnetic exchange is dominant in the hyperkagome iridate ${\mathrm{Na}}_{4}{\mathrm{Ir}}_{3}{\mathrm{O}}_{8}$. In the measurements we observe a broad Raman band at $\ensuremath{\sim}3500\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ with a bandwidth $\ensuremath{\sim}1700\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. Calculations of the Raman response of the Kitaev-Heisenberg model on the hyperkagome lattice shows that the experimental observations are consistent with the calculated Raman response where the Kitaev exchange interaction (${J}_{K}$) is much larger than the Heisenberg term ${\mathrm{J}}_{1}$ (${J}_{1}/{J}_{K}\ensuremath{\sim}0.1$). A comparison with the theoretical model gives an estimate of the Kitaev exchange interaction parameter.

We theoretically investigate the transport and magnetotransport properties of three-dimensional Weyl semimetals. Using the random phase approximation--Boltzmann transport scattering theory for electrons scattering off randomly distributed charged impurities, together with an effective medium theory to average over the resulting spatially inhomogeneous carrier density, we smoothly connect our results for the minimum conductivity near the Weyl point with known results for the conductivity at high carrier density. In the presence of a nonquantizing magnetic field, we predict that for both high and low carrier densities, Weyl semimetals show a transition from quadratic magnetoresistance (MR) at low magnetic fields to linear MR at high magnetic fields, and that the magnitude of the $\text{MR}\ensuremath{\gtrsim}10$ for realistic parameters. Our results are in quantitative agreement with recent unexpected experimental observations on the mixed-chalcogenide compound TlBiSSe.

We investigated the crystal structure and lattice excitations of the ternary intermetallic stannide Ca3Ir4Sn13 using neutron and x-ray scattering techniques. For T > T* ~ 38 K the x-ray diffraction data can be satisfactorily refined using the space group Pm-3n. Below T* the crystal structure is modulated with a propagation vector of q = (1/2, 1/2, 0). This may arise from a merohedral twinning in which three tetragonal domains overlap to mimic a higher symmetry, or from a doubling of the cubic unit cell. Neutron diffraction and neutron spectroscopy results show that the structural transition at T* is of a second-order, and that it is well described by mean-field theory. Inelastic neutron scattering data point towards a displacive structural transition at T* arising from the softening of a low-energy phonon mode with an energy gap of Delta(120 K) = 1.05 meV. Using density functional theory the soft phonon mode is identified as a 'breathing' mode of the Sn12 icosahedra and is consistent with the thermal ellipsoids of the Sn2 atoms found by single crystal diffraction data.

The physical properties of the single-crystalline samples of ${\mathrm{Lu}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ have been investigated by magnetic susceptibility, resistivity, and heat capacity studies. We observed multiple charge-density-wave (CDW) transitions in all the measurements. A strong thermal hysteresis at these transitions suggests a possible first order CDW ordering. In addition, the first order nature is ascertained by a very narrow and a huge cusp (62 J/mol K) in the zero field specific heat data which also suggests strong electron-phonon interchain coupling.

Using the small angle neutron scattering (SANS) technique we investigated the vortex lattice (VL) in the mixed state of the stannide superconductor Yb$_{3}$Rh$_{4}$Sn$_{13}$. We find a single domain VL of slightly distorted hexagonal geometry for field strengths between 350 and 18500 G and temperatures between T = 0.05 and T = 6.5 K. We observe a clear in-plane rotation of the VL for different magnetic field directions relative to the crystallographic axes. We also find that the hexagonal symmetry of the VL is energetically favorable in Yb$_{3}$Rh$_{4}$Sn$_{13}$ for external fields oriented along axes of different symmetries: twofold [110], threefold [111] and fourfold [100]. The observed behavior is different from other conventional and unconventional superconductors. The superconducting state is characterized by an isotropic gapped order parameter with an amplitude of $\Delta(0)$ = 1.57 $\pm$ 0.05 meV. At the lowest temperatures the field dependence of the magnetic form factor in our material reveals a London penetration depth of $\lambda_{L}$ = 2508 $\pm$ 17 $\AA$ and a Ginzburg coherence length of $\xi$ = 100 $\pm$ 1.3 $\AA$, i.e., it is a strongly type-II superconductor, $\kappa$ = $\lambda_{L}/\xi$ = 25.

We report the magnetic structure of the local moment magnetism in high-quality single crystals of the intermetallic compound Er 5 Ir 4 Si 10 , which shows two charge-density-wave (CDW) transitions (T CDW (1) =155 K and T CDW (2) =55 K). Bulk measurements demonstrate that the system has an effective Curie-Weiss magnetic moment of 9.7μ B and undergoes long-range antiferromagnetic (AFM) ordering at 2.8 K. The neutron-diffraction data establish the AFM structure of the Er 3+ with unequal moments at different Er sites aligned along the c axis where also the CDW transitions occur.

The magnetic field dependence of the critical current is studied in single-crystal samples of the weak pinning type-II superconductor $2H\ensuremath{-}{\mathrm{NbSe}}_{2}$ in the high-temperature and the low-field region of the $(H,T)$ space. The experimental results demonstrate various pinning regimes: a collective pinned quasiordered solid in the intermediate-field range that is destabilized in favor of disordered vortex phases in both high fields near ${H}_{c2}$ and at low fields near ${H}_{c1}.$ The temperature evolution of the pinning behavior demonstrates how the amorphous limit (where the correlation volume is nearly field independent) is approached around the so-called nose region of the reentrant peak-effect boundary. In the high-field regime the rapid approach to the amorphous limit naturally yields a peak effect, i.e., a peak in the critical current. In the low-field regime the crossover to the individual pinning regime gives rise to a ``plateau effect.'' We show that with increasing effective pinning the peak effect shifts away from ${H}_{c2}$ and resembles a ``fishtail'' anomaly.

The peak effect (PE) has been observed in a twinned crystal of YBa 2 Cu 3 O 7-δ for H||c in the low-field range, close to the zero-field superconducting transition temperature [T c (0)]. A sharp depinning transition succeeds the peak temperature T p of the PE. The PE phenomenon broadens and its internal structure smoothens out as the field is increased or decreased beyond the interval between 250 and 1000 Oe. Moreover, the PE could not be observed above 10 kOe and below 20 Oe. The locus of the Tp(H) values is indicative of the occurrence of a reentrant characteristic with a noselike feature located at T p (H)/T c (0)≈0.99 and H≈100 Oe (where the flux line lattice constant a 0 ≈penetration depth λ). The upper part of the PE curve (0.5 L ≈0.25. The vortex phase diagram near T c (0) determined from the characteristic features of the PE in YBa 2 Cu 3 O 7-δ (H||c) bears close resemblance to that in the 2H-NbSe 2 system, in which a reentrant PE had been distinctly observed earlier.

We study effective actions for order parameter fluctuations at low temperature in layered d-wave superconductors such as the cuprates. The order parameter lives on the bonds of a square lattice and has two amplitude and two phase modes associated with it. The low frequency spectral weights for amplitude and relative phase fluctuations is determined and found to be subdominant to quasiparticle contributions. The Goldstone phase mode and its coupling to density fluctuations in charged systems is treated in a gauge-invariant manner. The Gaussian phase action is used to study both the $c$-axis Josephson plasmon and the more conventional in-plane plasmon in the cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum XY model, which incorporates important cutoff effects overlooked in previous studies. A variational analysis of this effective model shows that in the cuprates, quantum effects of phase fluctuations are important in reducing the zero temperature superfluid stiffness, but thermal effects are small for $T << T_c$., Some numerical estimates corrected and figures changed. to appear in PRB, Sept.1 (2000)

The peak effect (PE) region in a single crystal of ${\mathrm{Ca}}_{3}{\mathrm{Rh}}_{4}{\mathrm{Sn}}_{13}$ is shown to comprise two discontinuous first-order-like transitions located near its onset and peak positions, in accordance with a stepwise fracturing of the flux-line lattice. Magnetization response to thermal cycling across the onset position produces an open hysteresis loop, consistent with the notion of the fracturing. A thermomagnetic history dependence study shows that the critical current density ${J}_{c}(H,T)$ is path dependent over a large part of the $(H,T)$ parameter space. This path dependence ceases above the peak position of the peak effect, suggesting a complete amorphization of the flux-line lattice at ${(T}_{p}{,H}_{p})$ line. A plausible vortex phase diagram has been constructed for ${\mathrm{Ca}}_{3}{\mathrm{Rh}}_{4}{\mathrm{Sn}}_{13}$ in which phases like an elastic solid, a plastic solid, and pinned and unpinned amorphous states have been identified.

We report on the observation of novel features in the minor hysteresis loops in a clean crystal of $2\mathrm{H}\ensuremath{-}{\mathrm{NbSe}}_{2},$ which displays a peak effect. The observed behavior can be explained in terms of a supercooling of the disordered vortex phase while cooling the superconductor in a field. Also, the extent of spatial order in a flux-line lattice formed in ascending fields is different from (and larger than) that in the descending fields below the peak position of the peak effect; this is attributed to a different degree of reorganization of the vortex state induced by changes in the field in the two cases.

We present a phenomenological model to describe features in the hysteretic magnetic response of weak pinning superconductors across the peak effect region. It accounts for the experimentally observed history dependent behavior of critical current density and the metastability of the vortex state prior to and across the peak effect region of superconducting systems such as NbSe2 , CeRu2 , and YBa2Cu3O7. Moreover, this model reduces to Bean’s critical state model as a limiting case. The hysteretic magnetic response of a type-II superconductor provides a measure of pinning of the vortex state. It is traditionally described by Bean’s critical state model 1 ~CSM! in commonly encountered situations where the pinning property is uniquely determined by the magnetic field value at a fixed temperature. But it fails to even qualitatively account for the recent experimental observations in weak pinning samples of systems such as NbSe2 , CeRu2 , YBa2Cu3O7 , Ca3Rh4Sn13 , etc., 2‐5 that exhibit a pronounced peak effect ~PE!. In this paper we propose a model that accounts for all the features of the hysteretic magnetic response described below.

We study muon-spin rotation (mu SR) spectra in the mixed phase of highly anisotropic layered superconductors, specifically Bi2+xSr2-xCaCu2O8+delta (BSCCO), by modeling the fluid and solid phases of pancake Vortices using liquid-state and density functional methods. The role of thermal fluctuations in causing motional narrowing of mu SR line shapes is quantified in terms of a first-principles theory of the flux-lattice melting transition. The effects of random point pinning are investigated using a replica treatment of liquid-state correlations and a replicated density functional theory. Our results indicate that motional narrowing in the pure system, although substantial, cannot account for the remarkably small linewidths obtained experimentally at relatively high fields and low temperatures. We find that satisfactory agreement with the mu SR data for BSCCO in this regime can be obtained through the ansatz that this ''phase'' is characterized by frozen short-range positional correlations reflecting the structure of the liquid just above the melting transition. This proposal is consistent with recent suggestions of a ''pinned liquid'' or ''glassy'' state of pancake Vortices in the presence of pinning disorder. Our results for the high-temperature liquid phase indicate that measurable linewidths may be obtained in this phase as a consequence of density inhomogeneities induced by the pinning disorder. The results presented here comprise a unified, first-principles theoretical treatment of mu SR spectra in highly anisotropic layered superconductors in terms of a controlled set of approximations. [S0163-1829(99)08033-9].