Specific heat, elastic neutron scattering, and muon spin rotation $\left(\mu \mathrm{SR}\right)$ experiments have been carried out on a well-characterized sample of “stuffed” (Pr-rich) ${\mathrm{Pr}}_{2+x}{\mathrm{Ir}}_{2-x}{\mathrm{O}}_{7-\delta }$. Elastic neutron scattering shows the onset of long-range spin-ice “2-in/2-out” magnetic order at $T_M=0.93$ K, with an ordered moment of $1.7\left(1\right){\mu }_{\mathrm{B}}/\text{Pr}$ ion at low temperatures. Approximate lower bounds on the correlation length and correlation time in the ordered state are 170 Å and 0.7 ns, respectively. $\mu \mathrm{SR}$ experiments yield an upper bound 2.6(7) mT on the local field $B_{\mathrm{loc}}^{4f}$ at the muon site, which is nearly two orders of magnitude smaller than the expected dipolar field for long-range spin-ice ordering of $1.7{\mu }_B$ moments (120–270 mT, depending on muon site). This shortfall is due in part to splitting of the non-Kramers crystal-field ground-state doublets of near-neighbor ${\mathrm{Pr}}^{3+}$ ions by the ${\mu }^{+}$-induced lattice distortion. For this to be the only effect, however, $\sim 160$ Pr moments out to a distance of $\sim 14$ Å must be suppressed. An alternative scenario, which is consistent with the observed reduced nuclear hyperfine Schottky anomaly in the specific heat, invokes slow correlated Pr-moment fluctuations in the ordered state that average $B_{\mathrm{loc}}^{4f}$ on the $\mu \mathrm{SR}$ time scale $(\sim {10}^{-7}\text{s})$, but are static on the time scale of the elastic neutron scattering experiments $(\sim {10}^{-9}\text{s})$. In this picture, the dynamic muon relaxation suggests a ${\mathrm{Pr}}^{3+}4f$ correlation time of a few nanoseconds, which should be observable in a neutron spin echo experiment.

A large and high-quality single crystal $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}$, the optimal superconductor of a reported $(\mathrm{L}{\mathrm{i}}_{1-x}\mathrm{F}{\mathrm{e}}_x)\mathrm{OHF}{\mathrm{e}}_{1-y}\mathrm{Se}$ system, has been successfully synthesized via a hydrothermal ion-exchange technique. The superconducting transition temperature $\left(T_c\right)$ of 42 K is determined by magnetic susceptibility and electric resistivity measurements, and the zero-temperature upper critical magnetic fields are evaluated as 79 and 313 T for the field along the $c$ axis and the $ab$ plane, respectively. The ratio of out-of-plane to in-plane electric resistivity ${\rho }_c/{\rho }_{ab}$ is found to increase with decreasing temperature and to reach a high value of 2500 at 50 K, with an evident kink occurring at a characteristic temperature $T^{*}=120\mathrm{K}$. The negative in-plane Hall coefficient indicates that electron carriers dominate in the charge transport, and the hole contribution is significantly reduced as the temperature is lowered to approach $T^{*}$. From $T^{*}$ down to $T_c$ we observe the linear temperature dependencies of the in-plane electric resistivity and the magnetic susceptibility for the FeSe layers. Our findings thus reveal that the normal state of $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}$ becomes highly two dimensional and anomalous prior to the superconducting transition, providing an insight into the mechanism of high-$T_c$ superconductivity.

The degeneracies in the spinor band structure of bcc Fe are studied from first principles. We find numerous isolated band touchings carrying chiral charges of magnitude one (Weyl points) or two (double-Weyl nodes), as well as nonchiral degeneracy loops (nodal rings). Some degeneracies are located on symmetry lines or planes in the Brillouin zone and others at generic low-symmetry points, realizing all possible scenarios consistent with the magnetic point group. We clarify the general theory relating the chiral band touchings to the Chern numbers of the Fermi sheets enclosing them and use this approach to determine the Chern numbers on the Fermi surface of bcc Fe. Although most Fermi sheets enclose Weyl nodes, in almost all cases the net enclosed charge vanishes for symmetry reasons, resulting in a vanishing Chern number. The exceptions are two inversion-symmetric electron pockets along the symmetry line $\mathrm{\Delta }$ parallel to the magnetization. Each of them surrounds a single Weyl point, leading to Chern numbers of $\pm 1$. These small topological pockets contribute a sizable amount to the nonquantized part of the intrinsic anomalous Hall conductivity, proportional to their reciprocal-space separation. Variation of the Fermi level (or other system parameters) may lead to a touching event between Fermi sheets, accompanied by a transfer of Chern number between them.

We present quantum oscillations observed in the heavy-fermion compound YbPtBi in magnetic fields far beyond its field-tuned, quantum critical point. Quantum oscillations are observed in magnetic fields as low as 60 kOe at 60 mK and up to temperatures as high as 3 K, which confirms the very high quality of the samples as well as the small effective mass of the conduction carriers far from the quantum critical point. Although the electronic specific heat coefficient of YbPtBi reaches $\sim 7.4\mathrm{J}/\mathrm{mol}{\mathrm{K}}^2$ in zero field, which is one of the highest effective mass values among heavy-fermion systems, it is suppressed quickly by an applied magnetic field. The quantum oscillations were used to extract the quasiparticle effective masses of the order of the bare electron mass, which is consistent with the behavior observed in specific heat measurements. Such small effective masses at high fields can be understood by considering the suppression of Kondo screening.

Using angle-resolved photoemission spectroscopy (ARPES), we revealed the surface electronic structure and superconducting gap of $\left({\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}\right)\mathrm{OH}\mathrm{Fe}\mathrm{Se}$, an intercalated FeSe-derived superconductor without antiferromagnetic phase or Fe-vacancy order in the FeSe layers, and with a superconducting transition temperature $\left(T_c\right)\sim 40$ K. We found that $\left({\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}\right)\mathrm{OH}$ layers dope electrons into FeSe layers. The electronic structure of surface FeSe layers in $\left({\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}\right)\mathrm{OH}\mathrm{Fe}\mathrm{Se}$ resembles that of ${\mathrm{Rb}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2$ except that it only contains half of the carriers due to the polar surface, suggesting similar quasiparticle dynamics between bulk $\left({\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}\right)\mathrm{OH}\mathrm{Fe}\mathrm{Se}$ and ${\mathrm{Rb}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2$. Superconducting gap is clearly observed below $T_c$, with an isotropic distribution around the electron Fermi surface. Compared with $A_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2(A=\text{K},\mathrm{Rb},\mathrm{Cs},\mathrm{Tl}/\text{K})$, the higher $T_c$ in $\left({\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}\right)\mathrm{OH}\mathrm{Fe}\mathrm{Se}$ might be attributed to higher homogeneity of FeSe layers or to some unknown roles played by the $\left({\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}\right)\mathrm{OH}$ layers.

We show that the emergence of the axial anomaly is a universal phenomenon for a generic three-dimensional metal in the presence of parallel electric ($E$) and magnetic ($B$) fields. In contrast to the expectations of the classical theory of magnetotransport, this intrinsically quantum mechanical phenomenon gives rise to the longitudinal magnetoresistance for any three-dimensional metal. However, the emergence of the axial anomaly does not guarantee the existence of negative longitudinal magnetoresistance. We show this through an explicit calculation of the longitudinal magnetoconductivity in the quantum limit using the Boltzmann equation, for both short-range neutral and long-range ionic impurity scattering processes. We demonstrate that the ionic scattering contributes a large positive magnetoconductivity $\propto B^2$ in the quantum limit, which can cause a strong negative magnetoresistance for any three-dimensional or quasi-two-dimensional metal. In contrast, the finite range neutral impurities and zero-range point impurities can lead to both positive and negative longitudinal magnetoresistance depending on the underlying band structure. In the presence of both neutral and ionic impurities, the longitudinal magnetoresistance of a generic metal in the quantum limit initially becomes negative, and ultimately becomes positive after passing through a minimum. We discuss in detail the qualitative agreement between our theory and recent observations of negative longitudinal magnetoresistance in Weyl semimetals TaAs and TaP, Dirac semimetals ${\text{Na}}_3\text{Bi}, {\text{Bi}}_{1-x}{\text{Sb}}_x$, and ${\text{ZrTe}}_5$, and quasi-two-dimensional metals ${\text{PdCoO}}_2$ and $\alpha -{\left(\text{BEDT-TTF}\right)}_2{\text{I}}_3$, which do not possess any bulk three-dimensional Dirac or Weyl quasiparticles.

Muonium, a positive muon and an electron, is often used as an experimentally accessible substitute for hydrogen in materials research. In semiconductors and insulators, a large amount of information on the hydrogen behavior is deduced from this analogy; however, it is seldom demonstrated that this procedure is justified. We show here, via a comparison of the hyperfine interactions, that in ${\mathrm{TiO}}_2$ muonium and hydrogen form the same configuration with the same basic electronic structure. A detailed description of the bonding characteristics of the muon to the ${\mathrm{Ti}}^{3+}$ polaron is presented. The special role of muon motion within the so-called oxygen channel in the rutile structure, which occurs at a lower temperature than for hydrogen, is emphasized.

We study the response of random-singlet quantum critical points to local perturbations. Despite being insulating, these systems are dramatically affected by a local cut in the system, so that the overlap $G=\left|〈{\mathrm{\Psi }}_B|{\mathrm{\Psi }}_A〉\right|$ of the ground-state wave functions with and without a cut vanishes algebraically in the thermodynamic limit. We analyze this Anderson orthogonality catastrophe in detail using a real-space renormalization group approach. We show that both the typical value of the overlap $G$ and the disorder average of $G^{\alpha }$ with $\alpha >0$ decay as power laws of the system size. In particular, the disorder average of $G^{\alpha }$ shows a “multifractal” behavior, with a nontrivial limit $\alpha \to \infty$ that is dominated by rare events. We also discuss the case of more generic local perturbations and generalize these results to local quantum quenches.

In collinear magnets lacking inversion symmetry, application of electric currents induces torques on the magnetization and conversely magnetization dynamics induces electric currents. The two effects, which both rely on spin-orbit interaction, are reciprocal to each other and denoted direct spin-orbit torque (SOT) and inverse spin-orbit torque (ISOT), respectively. We derive expressions for SOT and ISOT within the Kubo linear-response formalism. We show that expressions suitable for density-functional theory calculations can be derived either starting from a Kohn-Sham Hamiltonian with time-dependent exchange field or by expressing general susceptibilities in terms of the Kohn-Sham susceptibilities. For the case of magnetic bilayer systems we derive the general form of the ISOT current induced under ferromagnetic resonance. Using ab initio calculations within density-functional theory, we investigate SOT and ISOT in Co/Pt(111) magnetic bilayers. We determine the spatial distribution of spin and charge currents as well as torques in order to expose the mechanisms underlying SOT and ISOT and to highlight their reciprocity on the microscopic level. We find that the spin Hall effect is position dependent close to interfaces.

Magnetotransport measurements of Shubnikov–de Haas (SdH) oscillations have been performed on two-dimensional electron gases (2DEGs) confined in CdTe and CdMnTe quantum wells. The quantum oscillations in CdMnTe, where the 2DEG interacts with magnetic Mn ions, can be described by incorporating the electron-Mn exchange interaction into the traditional Lifshitz-Kosevich formalism. The modified spin splitting leads to characteristic beating pattern in the SdH oscillations, the study of which indicates the formation of Mn clusters resulting in direct anti-ferromagnetic Mn-Mn interaction. The Landau-level broadening in this system shows a peculiar decrease with increasing temperature, which could be related to statistical fluctuations of the Mn concentration.

The topological magnetoelectric effect in a three-dimensional topological insulator is a novel phenomenon, where an electric field induces a magnetic field in the same direction, with a universal coefficient of proportionality quantized in units of $e^2/2h$. Here, we propose that the topological magnetoelectric effect can be realized in the zero-plateau quantum anomalous Hall state of magnetic topological insulators or a ferromagnet-topological insulator heterostructure. The finite-size effect is also studied numerically, where the magnetoelectric coefficient is shown to converge to a quantized value when the thickness of the topological insulator film increases. We further propose a device setup to eliminate nontopological contributions from the side surface.

We present inelastic neutron-scattering experiments on the $S=1/2$ frustrated gapped quantum magnet piperazinium hexachlorodicuprate (PHCC) under applied hydrostatic pressure. These results show that at 9 kbar the magnetic triplet excitations in the system are gapless, contrary to what was previously reported. Our results are in agreement with recent muon-spin relaxation experiments which found magnetic order above a quantum-critical point at 4.3 kbar. We show that the changes in the excitation spectrum can be primarily attributed to the change in a single exchange pathway.

We propose that the topological magnetoelectric (ME) effect, a hallmark of topological insulators (TIs), can be realized in thin films of TIs in the $\nu =0$ quantum Hall state under magnetic field or by doping two magnetic ions with opposite signs of exchange coupling. These setups have the advantage compared to previously proposed setups that a uniform configuration of magnetic field or magnetization is sufficient for the realization of the topological ME effect. To verify our proposal, we numerically calculate ME response of TI thin films in the cylinder geometry and that of effective 2D models of surface Dirac fermions. The ME response is shown to converge to the quantized value corresponding to the axion angle $\theta =\pm \pi$ in the limit of the large top and bottom surface area of TI films, where nontopological contributions from the bulk and the side surface are negligible.

Recent progress with the thermally driven spin-state crossover in $\mathrm{LaCo}{\mathrm{O}}_3$ has made it increasingly apparent that the nominally nonmagnetic low-spin ground state of this material actually hosts defect-based magnetism. This is investigated here via a small-angle neutron scattering (SANS) study of $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ crystals. The results provide (i) the surprising finding that the spin-state crossover is clearly reflected in SANS via quasieleastic and inelastic scattering from paramagnetic spin fluctuations and excitations, and (ii) evidence for the formation, likely around oxygen defects, of local entities known as magnetic excitons. The latter generate distinct magnetic scattering below 60 K, providing valuable quantitative information on exciton densities and interactions. Potential relevance to the unexpected ferromagnetism recently discovered in epitaxial $\mathrm{LaCo}{\mathrm{O}}_3$ films is discussed.

We report a polarized Raman study of the Weyl semimetal TaAs. We observe all the optical phonons, with energies and symmetries consistent with our first-principles calculations. We detect additional excitations assigned to multiple-phonon excitations. These excitations are accompanied by broad peaks separated by $140 {\mathrm{cm}}^{-1}$ that are also most likely associated with multiple-phonon excitations. We also noticed a sizable $B_1$ component for the spectral background, for which the origin remains unclear.

Using an adaptation of Schwinger boson mean field theory (SBMFT) for nonuniform systems, we study the nature of low-energy spin excitations on the square and Bethe lattices at their percolation threshold. The optimal SBMFT parameters are interpreted as on-site potentials and pairing amplitudes, which enables an explanation of why emergent local moments develop in this system on dilution [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 97, 117204 (2006); H. J. Changlani et al., Phys. Rev. Lett. 111, 157201 (2013)] and why the corresponding single-particle frequencies are driven to anomalously low values. We discuss how our mean field calculations suggest the strong link between the presence of sublattice imbalance and long-range antiferromagnetic order and why linear spin wave theory is inadequate for capturing this relation. Within the SBMFT framework, we also extract an energy scale for the interaction between emergent moments, which show qualitative agreement with many-body calculations.

Since the very first experiments, superconducting circuits have suffered from strong coupling to environmental noise, destroying quantum coherence and degrading performance. In state-of-the-art experiments, it is found that the relaxation time of superconducting qubits fluctuates as a function of time. We present measurements of such fluctuations in a 3D-transmon circuit and develop a qualitative model based on interactions within a bath of background two-level systems (TLS) which emerge from defects in the device material. In our model, the time-dependent noise density acting on the qubit emerges from its near-resonant coupling to high-frequency TLS which experience energy fluctuations due to their interaction with thermally fluctuating TLS at low frequencies. We support the model by providing experimental evidence of such energy fluctuations observed in a single TLS in a phase qubit circuit.

We have investigated the structural and magnetic phase transitions in ${\mathrm{EuTi}}_{1-x}{\mathrm{Nb}}_x{\mathrm{O}}_3$ $\left(0\le x\le 0.3\right)$ with synchrotron powder x-ray diffraction, resonant ultrasound spectroscopy, and magnetization measurements. Upon Nb doping, the $Pm\overline{3}m\leftrightarrow I4/mcm$ structural transition shifts to higher temperatures and the room temperature lattice parameter increases while the magnitude of the octahedral tilting decreases. In addition, Nb substitution for Ti destabilizes the antiferromagnetic ground state of the parent compound and long-range ferromagnetic order is observed in the samples with $x\ge 0.1$. The structural transition in pure and doped compounds is marked by a dramatic steplike softening of the elastic moduli near $T_S$, which resembles that of ${\mathrm{SrTiO}}_3$ and can be adequately modeled using the Landau free energy model employing the same coupling between strain and octahedral tilting order parameter as previously used to model ${\mathrm{SrTiO}}_3$.

We report quantum oscillation data on the metallic triangular antiferromagnet ${\mathrm{PdCrO}}_2$. We find that, to very high accuracy, the observed frequencies of ${\mathrm{PdCrO}}_2$ can be reproduced by reconstruction of the (nonmagnetic) ${\mathrm{PdCoO}}_2$ Fermi surface into a reduced zone. The reduced zone corresponds to a magnetic cell containing six chromium sites, giving a $\sqrt{3}\times \sqrt{3}$ in-plane reconstruction, and $\times 2$ interplane reconstruction. The interplane ordering represents a reduction in lattice symmetry, possibly to monoclinic, and an associated lattice distortion is expected. In addition, we report a magnetic transition under an applied in-plane field that is probably equivalent to the spin-flop transition reported for ${\mathrm{CuCrO}}_2$, and present data on its field-angle dependence. We also report measurements of the resistivity of ${\mathrm{PdCrO}}_2$ up to 500 K.

We present a microscopic model of interacting fermions where the ground state degeneracy is topologically protected. The model is based on a double-wire setup with local interactions in a particle number conserving setting. A compelling property of this model is the exact solvability for its ground states and low energy excitations. We demonstrate the appearance of topologically protected edge states and derive their braiding properties on a microscopic level. We find the non-Abelian statistics of Ising anyons, which can be interpreted as Majorana-like edge states.