In contrast to magnetic order formed by electrons' dipolar moments, ordering phenomena associated with higher-order multipoles (quadrupoles, octupoles, etc.) are more difficult to characterize because of the limited choice of experimental probes that can distinguish different multipolar moments. The heavy-fermion compound CeB6 and its La-diluted alloys are among the best-studied realizations of the long-range-ordered multipolar phases, often referred to as "hidden order". Previously the hidden order in phase II was identified as primary antiferroquadrupolar (AFQ) and field-induced octupolar (AFO) order. Here we present a combined experimental and theoretical investigation of collective excitations in the phase II of CeB6. Inelastic neutron scattering (INS) in fields up to 16.5 T reveals a new high-energy mode above 14 T in addition to the low-energy magnetic excitations. The experimental dependence of their energy on the magnitude and angle of the applied magnetic field is compared to the results of a multipolar interaction model. The magnetic excitation spectrum in rotating field is calculated within a localized approach using the pseudo-spin presentation for the Gamma8 states. We show that the rotating-field technique at fixed momentum can complement conventional INS measurements of the dispersion at constant field and holds great promise for identifying the symmetry of multipolar order parameters and the details of inter-multipolar interactions that stabilize hidden-order phases.

We report an experimental and theoretical study of the low-temperature specific heat C and magnetic susceptibility χ of the layered anisotropic triangular-lattice spin-1/2 Heisenberg antiferromagnets Cs_{2}CuCl_{4-x}Br_{x} with x=0, 1, 2, and 4. We find that the ratio J^{'}/J of the exchange couplings ranges from 0.32 to ≈0.78, implying a change (crossover or quantum phase transition) in the materials' magnetic properties from one-dimensional (1D) behavior for J^{'}/J<0.6 to two-dimensional (2D) behavior for J^{'}/J≈0.78. For J^{'}/J<0.6, realized for x=0, 1, and 4, we find a magnetic contribution to the low-temperature specific heat, C_{m}∝T, consistent with spinon excitations in 1D spin-1/2 Heisenberg antiferromagnets. Remarkably, for x=2, where J^{'}/J≈0.78 implies a 2D magnetic character, we also observe C_{m}∝T. This finding, which contrasts the prediction of C_{m}∝T^{2} made by standard spin-wave theories, shows that Fermi-like statistics also plays a significant role for the magnetic excitations in spin-1/2 frustrated 2D antiferromagnets.

We have carried out bulk-sensitive hard x-ray photoelectron spectroscopy measurements on in situ cleaved and ex situ polished SmB6 single crystals. Using the multiplet structure in the Sm 3d core level spectra, we determined reliably that the valence of Sm in bulk SmB6 is close to 2.55 at similar to 5 K. Temperature dependent measurements revealed that the Sm valence gradually increases to 2.64 at 300 K. From a detailed line shape analysis we can clearly observe that not only the J = 0 but also the J = 1 state of the Sm 4f(6) configuration becomes occupied at elevated temperatures. Making use of the polarization dependence, we were able to identify and extract the Sm 4f spectral weight of the bulk material. Finally, we revealed that the oxidized or chemically damaged surface region of the ex situ polished SmB6 single crystal is surprisingly thin, about 1 nm only.

The Heisenberg model on a triangular lattice is a prime example for a geometrically frustrated spin system. However most experimentally accessible compounds have spatially anisotropic exchange interactions. As a function of this anisotropy, ground states with different magnetic properties can be realized. On the other hand, the J(1)-J(2) model on the square lattice is a well-known example for frustration induced by competing exchange. The classical phase diagrams of the two models are related in a broad range of the control parameter phi - tan(-1)(J(2)/J(1)). In both cases three different types of ground states are realized, each model having a ferromagnetic and an antiferromagnetic region in the phase diagram, and a third phase with columnar magnetic order for the square lattice and an in general incommensurate spiral structure for the triangular lattice. Quantum effects lift degeneracies in the non-FM phases and lead to additional nonmagnetic regions in the phase diagrams. The contribution of zero point fluctuations to ground state energy, wave vector, and ordered moment is discussed.

We investigate the frustrated two-dimensional S = 1/2 next nearest neighbor anisotropic Heisenberg antiferromagnet on a square lattice as described by the J(1a,) (b) - J(2) model. We use spin-wave theory and exact diagonalization for finite tiles including a new method for the finite size scaling procedure. We present results obtained from the extension of our numerical method to finite magnetic fields as well as from spin-wave theory. The induced uniform and the staggered moment in the antiferromagnetically ordered phases in the presence of a magnetic field are calculated. They deviate strongly from classical behaviour depending on frustration ratio J(2)/J(1a), (b) and the J(1a),(b) exchange anisotropy. The magnetization becomes strongly nonlinear and is suppressed from the classical value. This is due to enhanced quantum fluctuations already at moderate frustration.

The low energy crystalline electric field (CEF) excitations of f electrons can play a twofold role in heavy fermion and unconventional superconductors. They may act as a glue for the formation of Cooper pairs and simultaneously as a probe to investigate the symmetry of the order parameter. The former has been found in the skutterudite heavy fermion compound PrOs4Sb12, where a singlet–triplet CEF excitation Δ contributes to the pair formation and enhances T c with respect to L aOs4Sb12. In substituted P r(Os1−x Ru x )4Sb12, a continuous increase of Δ leads to a crossing with the local Pr rattling phonon mode and vibronic mode formation caused by magnetoelastic interaction. Furthermore, the T c enhancement turns into a reduction. It is proposed that this signifies a crossover from mainly pair-forming aspherical Coulomb to pair-breaking dipolar exchange scattering with increasing Ru content. In the Ce-based Fe pnictides CEF transitions show anomalous temperature dependence of the line width due to a pronounced feedback effect, which gives direct evidence for the unconventional 3d superconductivity.

Zero and longitudinal field muon spin rotation (muSR) experiments were performed on the superconductors PrPt4Ge12 and LaPt4Ge12. In PrPt4Ge12 below Tc a spontaneous magnetization with a temperature variation resembling that of the superfluid density appears. This observation implies time-reversal symmetry (TRS) breaking in PrPt4Ge12 below Tc = 7.9 K. This remarkably high Tc for an anomalous superconductor and the weak and gradual change of Tc and of the related specific heat anomaly upon La substitution in La_(1-x)Pr_xPt_4Ge_(12) suggests that the TRS breaking is due to orbital degrees of freedom of the Cooper pairs.

The feedback resonance in inelastic neutron scattering (INS) is observed in CeCu2Si2 and CeCoIn5. Below Tc the gap opening may lead to a dispersive spin exciton with an energy ωr/2Δ0<1. Observation of this collective mode at magnetic wave vector Q requires Δ(k+Q)=-Δ(k) which allows to conclude a dx2-y2 gap symmetry for both Ce compounds. A different kind of feedback was observed in the Ce-based ferropnictides. The transition between crystalline electric field (CEF) split Ce-4f states has anomalous shift and linewidth which is explained as an effect of coupling to resonant 3d spin excitations below Tc giving evidence for a s± state.

The superconducting feedback resonance in inelastic neutron scattering (INS) has now been found in numerous unconventional superconductors of the cuprate, ferropnictide, and heavy fermion classes. The collective spin excitation appears below T c at an energy less than the quasiparticle threshold with momentum Q provided the gap changes sign under translation by Q . The resonance has been found in the heavy fermion (HF) superconductors CeCu 2 Si 2 , CeCoIn 5 , and UPd 2 Al 3 , and recently in Fe-pnictide Ba 1− x K x Fe 2 As 2 , BaFe 2− x Co x As 2 , BaFe 2− x Ni x As 2 , and FeSe 1− x Te x compounds and may be a more general phenomenon. Of particular interest is the interaction of the 3d spin exciton with the 4f crystalline electric field (CEF) excitations in rare earth based unconventional superconductors like CeFeAsO 1− x F x pnictide and Nd 2− x Ce x CuO 4 cuprate where a coupling between 3d spin resonance and 4f CEF excitations leads to intriguing interaction effects observed experimentally by INS.

Frustrated magnets in high magnetic field have a long history of offering beautiful surprises to the patient investigator. Here we present the results of extensive classical Monte Carlo simulations of a variety of models of two dimensional magnets in magnetic field, together with complementary spin wave analysis. Striking results include (i) a massively enhanced magnetocaloric effect in antiferromagnets bordering on ferromagnetic order, (ii) a route to an $m=1/3$ magnetization plateau on a square lattice, and (iii) a cascade of phase transitions in a simple model of AgNiO$_2$.

The effect of frustration in various localized and itinerant vanadium oxide compounds is discussed within next nearest neighbors Heisenberg and spin fluctuation models, respectively. In the localized moment case the S = 1/2 J(1) - J(2)-model on a square lattice. exhibits a rich phase diagram with magnetic as well as exotic bidden order phases due to the interplay of frustration and quantum fluctuations. Their signatures in the high field magnetization and in magnetocaloric quantities are surveyed. The possible quantum phase transitions are discussed and applied to layered vanadium oxides of the type AA'VO(PO4)(2) where A, A' = Pb, Zn, Sr, Ba, Cd. In itinerant electron systems magnetic frustration may emerge as a result of electron correlations on a geometrically frustrated lattice. This mechanism causes enhanced spin fluctuations in a large region of momentum space and therefore can lead to a heavy fermion state at low temperatures as in the 3d spinel compound LiV2O4. The evidence from neutron scattering and NMR experiments is discussed within self-consistent renormalization theory based on local density approximation band structure calculations.

We have studied the two-dimensional anisotropic Kondo necklace model with antiferromagnetic (AF) Kondo coupling J(perpendicular to) and exchange coupling between "itinerant" spins J on the square lattice. The bond operator formalism is used to transform the spin model to a hard-core bosonic gas. We have used the Green's function approach to obtain the temperature dependence of spin excitation spectrum (triplet gap). We have also found the temperature dependence of the specific heat and the local spin-correlation function between localized and itinerant spins for various Kondo couplings J(perpendicular to)/J and anisotropies in both coupling strengths. Furthermore we studied the temperature dependence of the structure factor for localized spins which is determined by effective interactions via itinerant spins. For low temperature and close to the quantum critical point we have obtained an analytical formula for temperature dependence of the energy gap and specific heat. Finally we compared our results with those of previous mean-field treatments.

The static spin susceptibility ναβ(q) of spin components Sα and Sβ is examined in the non-centrosymmetric system with the antisymmetric spin-orbit coupling (so-called Rashba coupling), where Sα is α-component of spin. Unlike in centrosymmetric case, off-diagonal spin susceptibilities do not vanish due to the Rashba coupling. The anomalous spin susceptibilities show significant momentum dependences like νxx (q) — νyy (q) ∼ qx2 – qy2 and νxy (q)+ νyx (q) ∼ qxqy Increasing the on-site Coulomb interaction, not only usual spin susceptibility but also anomalous spin susceptibilies are enhanced, especially, around the magnetic instability. As the direct prove to observe the anomalous spin susceptibility, a polarized neutron scattering experiment is proposed.

We discuss the two-dimensional S = 1/2 J(1)-J(2) frustrated Heisenberg model on a square lattice. This model provides a good description of two classes of quasi-two-dimensional vanadates, namely the Li2VOXO4 (X - Si, Ge) and AA'VO(PO4)(2) (A,A' - Pb, Zn, Sr, Ba, Cd) compounds. We use the finite-temperature Lanczos method and spin wave analysis to study the high-field properties of this model in the whole J(1)-J(2) plane.Of particular interest is the saturation field of the low-temperature magnetization. Together with the estimates for the average effective exchange constant J(c) = root J(1)(2) + J(2)(2) from the zero-field heat capacity and Theta(CW) = (J(1) + J(2))/k(B) from the uniform magnetic susceptibility, the saturation field determines the position of a particular compound in the phase diagram uniquely.We give a summary of the results for the experimentally known compounds and show that our numerical findings agree very well with the experimental data for the magnetic susceptibility and the field dependence of the magnetization of the new compound BaCdVO(PO4)(2). This compound is close to the quantum-critical point of the spin-nematic and collinear antiferromagnetic phase of the J(1)-J(2) model as witnessed by a pronounced nonlinear magnetization curve.

We analyze the influence of unconventional superconductivity on crystalline electric-field (CEF) excitations of rare-earth ions in layered superconductors. We show that resonant magnetic excitations of the conduction electrons that have been observed in these systems below ${T}_{c}$ may result in the formation of the bound state in the $4f$-electron susceptibility at energies well below the CEF excitation energy. Our results are in agreement with the observed increase of the linewidth of CEF excitations below ${T}_{c}$ in superconducting ferropnictides and support the ${s}^{\ifmmode\pm\else\textpm\fi{}}$ Cooper-pairing state in these compounds.

The field-angle dependent specific heat and thermal conductivity in the vortex phase of UPd2Al3 is studied using the Doppler shift approximation for the low energy quasiparticle excitations. We first give a concise presentation of the calculation procedure of magnetothermal properties with vortex and FS averages performed numerically. The comparison of calculated field-angle oscillations and the experimental results obtained previously leads to a strong reduction of the possible SC candidate states in UPd2Al3. The possible SC gap functions have node lines in hexagonal symmetry planes containing either the zone center or the AF zone boundary along c. Node lines in non-symmetry planes can be excluded. We also calculate the field and temperature dependence of field-angular oscillation amplitudes. We show that the observed nonmonotonic field dependence and sign reversal of the oscillation amplitude is due to small deviations from unitary scattering.