An accurate determination of the immiscibility of helium in hydrogen has a direct impact on the understanding of the interior structure and of the evolution of Jovian planets. We extend our previous work on hydrogen-helium mixtures [Morales, Schwegler, Ceperley, Pierleoni, Hamel, and Caspersen, Proc. Natl. Acad. Sci. (USA) 106, 1324 (2009)] to lower pressures and lower temperatures, across the molecular dissociation regime in hydrogen to the low-pressure molecular liquid. Using density-functional-theory-based molecular dynamics together with thermodynamic integration techniques, we calculate the Gibbs free energy of the dense liquid as a function of pressure, temperature, and composition. We address the importance of the nonideal entropy of mixing in the solubility of helium in hydrogen and find that it is critically important in the molecular regime. The resulting demixing temperatures smoothly connect measurements done in diamond anvil cells to the high-temperature and -pressure conditions found in giant planet interiors.

Recent theoretical calculations predict an ideal shear strength over 50 GPa for CrB${}_4$, placing it well above ultrahard ReB${}_2$ in terms of strength and thus suggesting possible superhardness of CrB${}_4$. This result, however, is contradicted by the latest experimental measurements that produced a relatively low Vickers hardness around 23 GPa, which is about the same as the hardness value of ReB${}_2$. To solve this intriguing problem, we have performed a systematic first-principles study that unveils two fundamental constraints that limit the strength of CrB${}_4$: (i) a quantum-mechanical effect involving a transition between two-center and three-center bonding among the boron atoms that reduces the rigidity and directionality of the boron bonding and (ii) a mechanistic effect caused by the pressure beneath the indenter that drives a lateral bond and volume expansion that further stretches and weakens the boron bonds in addition to the shear deformation in the CrB${}_4$ structure under Vickers indentation hardness tests. These effects lead to considerably reduced strength of CrB${}_4$, producing an ideal (i.e., an upper bound) indentation strength of 27 GPa that is consistent with the experimental results. These constraints also explain previous results on the pure shear and indentation strength for ReB${}_2$, WB${}_3$, and MoB${}_3$, limiting their ideal (Vickers) indentation strength below 30 GPa irrespective of the composition and structural details. The present results suggest that transition-metal boron compounds are unlikely to become superhard as previously predicted.

Making use of the energetics and equations of state of defective uranium dioxide that are calculated with first-principles methods, we demonstrate the possibility of constraining the formation energy of point defects by measuring the transition pressures of the corresponding pseudo phase of defects. The mechanically stable range of fluorite structure of UO${}_2$, which dictates the maximum possible pressure of relevant pseudo phase transitions, gives rise to defect formation energies that span a wide band and overlap with the existing experimental estimates. We reveal that the knowledge about pseudo phase boundaries can not only provide important information on energetics that is helpful for reducing the scattering in current estimates, but also be valuable for guiding theoretical assessments, even to validate or disprove a theory. In order to take defect interactions into account and to extrapolate the physical quantities at finite stoichiometry deviations to that near the stoichiometry, we develop a general formalism to describe the thermodynamics of a defective system. We also show that it is possible to include interactions among defects in a simple expression of a point defect model (PDM) by introducing an auxiliary constant mean field. This generalization of the simple PDM leads to great versatility that allows one to study nonlinear effects of stoichiometry deviation on materials' behavior. It is a powerful tool to extract the defect energetics from finite defect concentrations to the dilute limit. Besides these, the full content of the theoretical formalism and some relevant and interesting issues, including reentrant pseudo transition, multiple-defect coexistence, charged defects, and possible consequence of instantaneous defective response in a quantum crystal, are explored and discussed.

Specific heat measurements in zero magnetic field are presented on a homologous series of geometrically frustrated antiferromagnetic Heisenberg garnet systems. Measurements of Gd${}_3$Ga${}_5$O${}_{12}$, grown with isotopically pure Gd, agree well with previous results on samples with naturally abundant Gd, showing no ordering features. In contrast, samples of Gd${}_3$Te${}_2$Li${}_3$O${}_{12}$ and Gd${}_3$Al${}_5$O${}_{12}$ are found to exhibit clear ordering transitions at 243 and 175 mK, respectively. The effects of low level disorder are studied through dilution of Gd${}^{3+}$ with nonmagnetic Y${}^{3+}$ in Gd${}_3$Te${}_2$Li${}_3$O${}_{12}$. A thorough structural characterization, using x-ray diffraction, is performed on all of the samples studied. We discuss possible explanations for such diverse behavior in very similar systems.

We have used micromagnetic simulations performed with open and periodic boundary conditions to study the influence of the presence of array boundaries on the spectra and spatial profiles of collective spin-wave excitations in arrays of magnetic nanoelements. The spectra and spatial profiles of collective spin waves excited in isolated arrays of nanoelements and those forming a part of quasi-infinite arrays are qualitatively different even if the same excitation field is used in the simulations. In particular, the use of periodic boundary conditions suppresses the excitation of nonuniform collective modes by uniform excitation fields. However, the use of nonuniform excitation fields in combination with periodic boundary conditions is shown to enable investigation of the structure of magnonic dispersion curves for quasi-infinite arrays (magnonic crystals) in different directions in the reciprocal space and for different magnonic bands. The results obtained in the latter case show a perfect agreement with those obtained with the dynamical matrix method for infinite arrays of nanoelements of the same geometry and magnetic properties.

We have performed ${}^{75}$As nuclear magnetic resonance (NMR) Knight shift measurements on single crystals of NaFe${}_{0.975}$Co${}_{0.025}$As to show that its superconductivity is a spin-paired, singlet state consistent with predictions of the weak-coupling BCS theory. We use a spectator nucleus, ${}^{23}$Na, uncoupled from the superconducting condensate, to determine the diamagnetic magnetization and to correct for its effect on the ${}^{75}$As NMR spectra. The resulting temperature dependence of the spin susceptibility follows the Yosida function as predicted by BCS for an isotropic, single-valued energy gap. Additionally, we have analyzed the ${}^{23}$Na spectra that become significantly broadened by vortices to obtain the superconducting penetration depth as a function of temperature with ${\lambda }_{ab}\left(0\right)=5327\pm 78$ Å.

Rotation of polarization of light on transmission and reflection at materials with time-reversal breaking (Faraday and Kerr effects, respectively) has been studied for over a hundred years. We add to such phenomena by studying the optical properties of magnetochiral states, which are states with loop currents such that there is finite Hall effect at zero applied magnetic field. Qualitatively new features arise in reflection and transmission in such a state. This state is shown to be induced in underdoped cuprates given their observed magnetoelectric loop-current order and certain lattice symmetries. These results explain the observation of Kerr effects with unusual properties and help further confirm the nature of the symmetry breaking in underdoped cuprates.

We theoretically consider the proximity effect in semiconductor-superconductor hybrid nanostructures, which are being extensively studied in the context of the ongoing search for non-Abelian Majorana fermions in solid state systems. Specifically, we consider the dependence on the thickness of the semiconductor in the direction normal to the interface, a physical effect that has been uncritically neglected in prior work on the subject. Quite surprisingly, we find the unanticipated result that increasing the semiconductor thickness leads to a suppression of the induced superconducting gap due to proximity-induced interband coupling. As a result, in the limit of strong semiconductor-superconductor coupling, the proximity-induced gap becomes much smaller than the bulk superconductor gap and depends weakly on the interface transparency.

Magnetic structures in La${}_{1.37}$Sr${}_{1.63}$Mn${}_2$O${}_7$ single crystal under hydrostatic pressures of up to 0.8 GPa are investigated by neutron diffraction measurements to determine the magnetic phase diagram under hydrostatic pressure. The ground state is found to be a ferromagnetic (FM${}_{\mathrm{uniaxial}}$) structure under hydrostatic pressures of up to 0.8 GPa, in which the magnetic moments of Mn ions are parallel to the $c$ axis. Under hydrostatic pressures of $P$ < 0.75 GPa, the FM${}_{\mathrm{uniaxial}}$ structure changes to a canted antiferromagnetic (CAFM) structure at approximately 70 K and the CAFM structure directly changes to a paramagnetic (PM) structure at approximately 120 K. Under hydrostatic pressures of 0.75 GPa ≤ $P$ ≤ 0.8 GPa, the FM${}_{\mathrm{uniaxial}}$ structure changes to a CAFM structure at approximately 70 K, and the CAFM structure changes to a PM structure at approximately 120 K via an antiferromagnetic (AFM${}_{\mathrm{planar}}$) structure at approximately 95 K in which the magnetic moment lies in the $ab$ plane. The relationship between the magnetic structure and the distortion of the MnO${}_6$ octahedra is also discussed.

The thermodynamic properties of ferromagnetic spin chains have been analyzed with a variety of microscopic methods over the years: Bethe ansatz, spin-wave theory, Schwinger-boson mean-field theory, Green functions, and renormalization group methods. Surprisingly, in all these different studies, the manifestation of the spin-wave interaction in the low-temperature series for the thermodynamic quantities, in the presence of a finite magnetic field, has been largely neglected. In the present work, we address this problem by following a different path, based on the systematic effective Lagrangian method. We evaluate the partition function up to two-loop order and derive the low-temperature expansion of the energy density, entropy density, heat capacity, magnetization, and susceptibility in the presence of a weak external magnetic field. Remarkably, the spin-wave interaction only manifests itself beyond two-loop order. In particular, there is no term of order $T^2$ in the low-temperature series of the free energy density. This is the analog of Dyson's statement that there is no term of order $T^4$ in the low-temperature series of the free energy density in the case of three-dimensional ideal ferromagnets. The range of validity of our series is critically examined in view of the nonperturbatively generated energy gap. We also compare our results with the condensed matter literature and point out that there are some misleading statements.

The occurrence of spin-Hall magnetoresistance (SMR) in platinum (Pt) on top of yttrium iron garnet (YIG) has been investigated, for both in-plane and out-of-plane applied magnetic fields and for different Pt thicknesses [3, 4, 8, and 35 nm]. Our experiments show that the SMR signal directly depends on the in-plane and out-of-plane magnetization directions of the YIG. This confirms the theoretical description, where the SMR occurs due to the interplay of the spin-orbit interaction in the Pt and the spin-mixing conductance at the YIG/Pt interface. Additionally, the sensitivity of the SMR and spin pumping signals on the YIG/Pt interface conditions is shown by comparing two different deposition techniques (e-beam evaporation and dc sputtering).

A spin filtering effect has been evidenced in epitaxial MnFe${}_2$O${}_4$ tunnel barriers directly by Meservey-Tedrow experiments. The asymmetry of the Zeeman-split tunneling conductance curves of the superconducting Al spin analyzer in Pt(111)/MnFe${}_2$O${}_4$(111)/γ-Al${}_2$O${}_3$(111)/Al tunnel junctions revealed a positive spin-polarization (up to +9$\%$), proving the potential of manganese ferrite for generation of a spin-polarized current. A negatively polarized spin filtering being expected theoretically, different mechanisms are discussed to explain both sign and amplitude of the measured spin-polarization.

The thermodynamic properties of the pyrochlore Yb${}_2$Ti${}_2$O${}_7$ material are calculated using the numerical linked-cluster calculation method for an effective anisotropic-exchange spin-$\frac{1}{2}$ Hamiltonian with parameters recently determined by fitting the neutron scattering spin-wave data obtained at high magnetic field. Magnetization $M(T,h)$ as a function of temperature $T$ and for different magnetic fields $h$ applied along the three high-symmetry directions [100], [110], and [111] are compared with experimental measurements on the material for temperature $T>1.8$ K. The excellent agreement between experimentally measured and calculated $M(T,h)$ over the entire temperature and magnetic field ranges considered provides strong quantitative validation of the effective Hamiltonian. It also confirms that fitting the high-field neutron spin-wave spectra in the polarized paramagnetic state is an excellent method for determining the microscopic exchange constants of rare-earth insulating magnets that are described by an effective spin-$\frac{1}{2}$ Hamiltonian. Finally, we present results which demonstrate that a recent analysis of the polarized neutron scattering intensity of Yb${}_2$Ti${}_2$O${}_7$ using a random phase approximation method [Chang et al., Nat. Commun. 3, 992 (2012)] does not provide a good description of $M(T,h)$ for $T\lesssim 10$ K, that is, in the entire temperature regime where magnetic correlations become non-negligible. With the compelling evidence that we now have at hand an accurate microscopic Hamiltonian for Yb${}_2$Ti${}_2$O${}_7$, our work exposes a paradox: why does this material fail to develop long-range ferromagnetic order?

Quantum fluctuations are of central importance in itinerant ferromagnets; when modeled by a homogeneous electron gas with contact interactions, fluctuations deliver a rich phase diagram featuring a first order ferromagnetic transition preempted by a spin spiral and a paired density wave. In this work we develop the formalism to analyze the effects of fluctuations with a realistic screened Coulomb potential. The finite-ranged interaction suppresses the tricritical point temperature of the first order ferromagnetic transition, bringing theory into line with experiment, while retaining the exotic spin spiral and paired density wave. In an ultracold atomic gas a finite-ranged interaction damps the competing molecular instability, permitting the observation of ferromagnetic correlations.

Vortex loops are generated by the inhomogeneous stray field of a magnetic dipole on top of a current-carrying mesoscopic superconductor. Cutting and recombination processes unfold under the applied drive, resulting in periodic voltage oscillations across the sample. We show that a direct and detectable consequence of the cutting and recombination of these vortex loops in the present setup is the onset of vortices at surfaces where they were absent prior to the application of the external current. The nonlinear dynamics of vortex loops is studied within the time-dependent Ginzburg-Landau theory to describe the profound three-dimensional features of their time evolution.

We present a theoretical and numerical study of the optical binding and optical torque between two Rayleigh particles with arbitrary, complex, scalar dielectric permittivity and magnetic permeability. We use a computational approach based on the discrete dipole approximation to derive the optical force and torque experienced by the particles when illuminated by a linearly or circularly polarized plane wave. We show that optical binding between magnetodielectic particles is qualitatively different from the traditional case involving dielectric particles only. In particular, we show that for certain configurations, the system of two magnetodielectric particles will experience a long-range optical torque whose amplitude envelope does not decay with the separation between the particles.

In this paper several nanodevices which realize basic single heavy-hole qubit operations are proposed and supported by time-dependent self-consistent Poisson-Schrödinger calculations using a four band heavy-hole–light-hole model. In particular we propose a set of nanodevices which can act as Pauli $X$, $Y$, $Z$ quantum gates and as a gate that acts similar to a Hadamard gate (i.e., it creates a balanced superposition of basis states but with an additional phase factor) on the heavy-hole spin qubit. We also present the design and simulation of a gated semiconductor nanodevice which can realize an arbitrary sequence of all these proposed single quantum logic gates. The proposed devices exploit the self-focusing effect of the hole wave function which allows for guiding the hole along a given path in the form of a stable solitonlike wave packet. Thanks to the presence of the Dresselhaus spin-orbit coupling, the motion of the hole along a certain direction is equivalent to the application of an effective magnetic field which induces in turn a coherent rotation of the heavy-hole spin. The hole motion and consequently the quantum logic operation is initialized only by weak static voltages applied to the electrodes which cover the nanodevice. The proposed gates allow for an all electric and ultrafast (tens of picoseconds) heavy-hole spin manipulation and give the possibility to implement a scalable architecture of heavy-hole spin qubits for quantum computation applications.

Charges and spins confined in quantum dots and quantum dot molecules are of great interest for new optoelectronic device applications. The strong confinement in quantum dot structures leads to unique interactions among electrons and holes. A detailed understanding of the magnitude and dynamics of these charge-carrier interactions will be essential to the development of future devices. We present experimental evidence of holes trapped in metastable higher-energy states of InAs/AlGaAs/InAs quantum dot molecules. We present a model for the kinetic pathways that lead to this dynamic hole trapping and analyze the consequences of dynamic hole trapping for carrier relaxation and optical emission.