In the nonlocal spin valve (NLSV) geometry, four-terminal electrical Hanle effect measurements have the potential to provide a particularly simple determination of the lifetime $\left({\tau }_s\right)$ and diffusion length $\left({\lambda }_{\mathrm{N}}\right)$ of spins injected into nonmagnetic (N) materials. Recent papers, however, have demonstrated that traditional models typically used to fit such data provide an inaccurate measurement of ${\tau }_s$ in ferromagnet (FM)/N metal devices with low interface resistance, particularly when the separation of the source and detector contacts is small. In the transparent limit, this shortcoming is due to the back diffusion and subsequent relaxation of spins within the FM contacts, which is not properly accounted for in standard models of the Hanle effect. Here we have used the separation dependence of the spin accumulation signal in NLSVs with multiple FM/N combinations, and interfaces in the diffusive limit, to determine ${\lambda }_{\mathrm{N}}$ in traditional spin valve measurements. We then compare these results to Hanle measurements as analyzed using models that either include or exclude spin sinking. We demonstrate that differences between the spin valve and Hanle measurements of ${\lambda }_{\mathrm{N}}$ can be quantitatively modelled provided that both the FM contact-induced isotropic spin sinking and the full three-dimensional geometry of the devices, which is particularly important at small contact separations, are accounted for. We find, however, that considerable difficulties persist, in particular due to the sensitivity of fitting to the contact interface resistance and the FM contact magnetization rotation, in precisely determining ${\lambda }_{\mathrm{N}}$ with the Hanle technique alone, particularly at small contact separations.

The general concepts of spin wave theory are adapted to the spin torque driven dynamics of a self-polarized system based on two layers coupled via interlayer exchange (conservative coupling) and mutual spin torque (dissipative coupling). An analytical description of the nonlinear dynamics is proposed and validated through numerical simulations. In contrast to the single layer model, the phase equation of the coupled system has a contribution coming from the dissipative part of the LLGS equation. It is shown that this is a major contribution to the frequency mandatory to describe well the most basic features of the dynamics of this coupled system. Using the proposed model a specific feature of coupled dynamics is addressed: the redshift to blueshift transition observed in the frequency current dependence of this kind of exchange coupled systems upon increasing the applied field. It is found that the blueshift regime can only occur in a region of field where the two linear eigenmodes contribute equally to the steady state mode (i.e., high mode hybridization). Finally, a general perturbed Hamiltonian equation for the coupled system is proposed.

Nonreciprocal directional dichroism (NDD) is investigated on a magnetic resonance with both electric and magnetic dipole activities, i.e., electromagnon, for a chiral-lattice helimagnet $\mathrm{B}{\mathrm{a}}_3\mathrm{NbF}{\mathrm{e}}_3\mathrm{S}{\mathrm{i}}_2{\mathrm{O}}_{14}$ by terahertz spectroscopy under the magnetic field. In the Voigt geometry, the electromagnon resonance causes the NDD in the helimagnetic phase in accord with the spin-driven ferroelectric polarization, whose polarity is uniquely selected owing to the structural chirality. In the Faraday geometry, all possible optical effects, including natural optical activity, magnetic optical activity and magnetochiral effect showing NDD, are separately evaluated by terahertz polarimetry technique. The NDD is manifested in the electromagnon resonance in the helimagnetic phase, while a formation of helimagnetic spin structure enhances the natural optical activity inherent to the structural chirality.

The spin superfluid analogy can be extended to include Josephson-like oscillations of the spin current. In a system of two antiferromagnetic insulators (AFMIs) separated by a thin metallic spacer, a threshold spin chemical potential established perpendicular to the direction of the Néel vector field drives terahertz oscillations of the spin current. This spin current also has a nonlinear, time-averaged component which provides a “smoking gun” signature of spin superfluidity. The time-averaged spin current can be detected via the inverse spin Hall effect in a metallic spacer with large spin-orbit coupling. The physics illustrated here with AFMIs also applies to easy-plane ferromagnetic insulators. These findings may provide a new approach for experimental verification of spin superfluidity and realization of a terahertz spin oscillator.

Previous measurements of the superfluid density ${\rho }_s$ and specific heat for ${}^4\mathrm{He}$ have identified effects that are manifest at distances much larger than the correlation length ${\xi }_{3\text{D}}$ [Perron et al., Nat. Phys. 6, 499 (2010); Perron and Gasparini, Phys. Rev. Lett. 109, 035302 (2012); Perron et al., Phys. Rev. B 87, 094507 (2013)]. We report here measurements of the superfluid density which are designed to explore this phenomenon further. We determine the superfluid fraction ${\rho }_s/\rho$ from the resonance of 34-nm films of varying widths $4\le W\le 100\mu \text{m}$. The films are formed across a Corbino ring separating two chambers where a thicker 268-nm film is formed. This arrangement is realized using lithography and direct Si-wafer bonding. We identify two effects in the behavior of ${\rho }_s/\rho$: one is hydrodynamic, for which we present an analysis, and the other is a correlation-length effect which manifests as a shift in the transition temperature $T_c$ relative to that of a uniform 34-nm film uninfluenced by proximity effects. We find that one can collapse both ${\rho }_s/\rho$ and the quality factor of the resonance onto universal curves by shifting $T_c$ as $\mathrm{\Delta }{T}_c\sim W^{-\nu }$. This scaling is a surprising result on two counts: it involves a very large length scale $W$ relative to the magnitude of ${\xi }_{3\text{D}}$ and the dependence on $W$ is not what is expected from correlation-length finite-size scaling which would predict $\mathrm{\Delta }{T}_c\sim W^{-1/\nu }$.

Recent nuclear magnetic resonance and specific heat measurements have provided concurring evidence of spontaneously broken rotational symmetry in the superconducting state of the doped topological insulator ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$. This suggests that the pairing symmetry corresponds to a two-dimensional representation of the $D_{3d}$ crystal point group, and that ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ is a nematic superconductor. In this paper, we present a comprehensive study of the upper critical field $H_{c2}$ of nematic superconductors within Ginzburg-Landau (GL) theory. Contrary to typical GL theories which have an emergent U(1) rotational symmetry obscuring the discrete symmetry of the crystal, the theory of two-component superconductors in trigonal $D_{3d}$ crystals reflects the true crystal rotation symmetry. This has direct implications for the upper critical field. First, $H_{c2}$ of trigonal superconductors with $D_{3d}$ symmetry exhibits a sixfold anisotropy in the basal plane. Second, when the degeneracy of the two components is lifted by, e.g., uniaxial strain, $H_{c2}$ exhibits a twofold anisotropy with characteristic angle and temperature dependence. Our thorough study shows that measurement of the upper critical field is a direct method of detecting nematic superconductivity, which is directly applicable to recently-discovered trigonal superconductors ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$, ${\mathrm{Sr}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$, ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$, and ${\mathrm{Tl}}_x{\mathrm{Bi}}_2{\mathrm{Te}}_3$.

Ferroelectric vortex domains are of significant interest due to their rich physics and potential applications. Here, we propose the crystallographic, strain, and electric conditions for spontaneous vortex domains and study the influence of oxygen octahedral tilt on vortex wall orientations. Using 109° domain walls in $\mathrm{BiFe}{\mathrm{O}}_3$ films as an example, it is demonstrated that vortex domains result from bound charge-density waves, i.e., from alternating positive and negative bound charges. The vortex domains lead to a net curl of the polarization vectors that can be switched by an irrotational electric field.

We demonstrate an approach for directly tracking antiferromagnetic (AFM) spin dynamics by measuring ultrafast changes in a magnon resonance. We test this idea on the multiferroic ${\mathrm{HoMnO}}_3$ by optically photoexciting electrons, after which changes in the spin order are probed with a THz pulse tuned to a magnon resonance. This reveals a photoinduced change in the magnon line shape that builds up over 5–12 picoseconds, which we show to be the spin-lattice thermalization time, indicating that electrons heat the spins via phonons. We compare our results to previous studies of spin-lattice thermalization in ferromagnetic manganites, giving insight into fundamental differences between the two systems. Our work sheds light on the microscopic mechanism governing spin-phonon interactions in AFMs and demonstrates a powerful approach for directly monitoring ultrafast spin dynamics.

Wurtzite aluminium nitride (AlN) is a technologically important wide-band-gap semiconductor with an unusually high thermal conductivity, used in optical applications and as a heatsink substrate. Explaining many of its properties depends on an accurate description of its lattice dynamics, which have thus far only been captured in the quasiharmonic approximation. In this work, we show that anharmonic effects have a considerable impact on its phase stability and transport properties, since they are much stronger in the rocksalt phase. We construct a theoretical pressure-temperature phase diagram of AlN, demonstrating that the rocksalt phase is stabilized by increasing temperature, with respect to the wurtzite phase. We recover the thermal conductivity of the wurtzite phase ($320{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ under ambient conditions) and compute the hitherto unknown thermal conductivity of the rocksalt phase ($81{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$). We also show that the electronic band gap decreases with temperature. These findings provide further evidence that anharmonic effects cannot be ignored in simulations of materials intended for high-temperature applications.

We measured the attenuation of GHz frequency surface acoustic waves (SAWs) on the Si (001) surface using an optical pump-probe technique at temperatures between 300 and 600 K. SAWs are generated and detected by a 700 nm Al grating fabricated by nanoimprint lithography. The grating for SAW generation is separated from the grating for SAW detection by $\approx 150\mu \mathrm{m}$. The amplitude of SAWs is attenuated by coupling to bulk waves created by the Al grating, diffraction due to the finite size of the source, and the intrinsic relaxational Akhiezer damping of elastic waves in Si. Thermal phonon relaxation time and Grüneisen parameters are fitted using temperature-dependent measurement. The $fQ$ product of a hypothetical micromechanical oscillator limited by Akhiezer damping at this frequency is $\sim 3\times {10}^{13}$ Hz.

We study the inelastic light scattering response in two- (2D) and three-dimensional (3D) Kitaev spin-liquid models with Majorana spinon band structures in the symmetry classes BDI and D leading to protected gapless surface modes. We present a detailed calculation of the resonant Raman/Brillouin scattering vertex relevant to iridate and ruthenate compounds whose low-energy physics is believed to be proximate to these spin-liquid phases. In the symmetry class BDI, we find that while the resonant scattering on thin films can detect the gapless boundary modes of spin liquids, the nonresonant processes do not couple to them. For the symmetry class D, however, we find that the coupling between both types of light-scattering processes and the low-energy surface states is strongly suppressed. Additionally, we describe the effect of weak time-reversal symmetry breaking perturbations on the bulk Raman response of these systems.

We study the magnetodynamic modes of a magnetic tunnel junction with perpendicular magnetic easy axis (p-MTJ) in in-plane magnetic fields using device-level ferromagnetic resonance spectroscopy. We compare our experimental results to those of micromagnetic simulations of the entire p-MTJ. Using an iterative approach to determine the material parameters that best fit our experiment, we find excellent agreement between experiments and simulations in both the static magnetoresistance and magnetodynamics in the free and reference layers. From the micromagnetic simulations, we determine the spatial mode profiles, the localization of the modes and, as a consequence, their distribution in the frequency domain due to the inhomogeneous internal field distribution inside the p-MTJ under different applied field regimes. We also conclude that the excitation mechanism is a combination of the microwave voltage modulated perpendicular magnetic anisotropy, the microwave Oersted field, and the spin-transfer torque generated by the microwave current.

$B$-site-disordered perovskite $\mathrm{CaF}{\mathrm{e}}_{0.5}\mathrm{M}{\mathrm{n}}_{0.5}{\mathrm{O}}_3$ with unusually high valence $\mathrm{F}{\mathrm{e}}^{4+}$ was synthesized using a high-pressure technique. $\mathrm{F}{\mathrm{e}}^{4+}$ randomly distributed at half of the $B$ sites shows charge disproportionation to $\mathrm{F}{\mathrm{e}}^{3+}$ and $\mathrm{F}{\mathrm{e}}^{5+}$. The spins of $\mathrm{F}{\mathrm{e}}^{3+},\mathrm{F}{\mathrm{e}}^{5+}$, and $\mathrm{M}{\mathrm{n}}^{4+}$ order below 90 K. Analysis of low-temperature neutron powder-diffraction data revealed a $G$-type antiferromagnetic structure—where all the nearest-neighboring spins of $\mathrm{F}{\mathrm{e}}^{3+},\mathrm{F}{\mathrm{e}}^{5+}$, and $\mathrm{M}{\mathrm{n}}^{4+}$ couple antiparallel—and the small ordered moment of $0.58{\mu }_{\mathrm{B}}$ reveals local charge ordering that gives rise to predominant $\mathrm{F}{\mathrm{e}}^{3+}$-O-$\mathrm{F}{\mathrm{e}}^{5+}$ antiferromagnetic arrangements. Despite the identical chemical compositions of $\mathrm{CaF}{\mathrm{e}}_{0.5}\mathrm{M}{\mathrm{n}}_{0.5}{\mathrm{O}}_3$ and $\mathrm{C}{\mathrm{a}}_2\mathrm{FeMn}{\mathrm{O}}_6$, the magnetic structure of the present $\mathrm{CaF}{\mathrm{e}}_{0.5}\mathrm{M}{\mathrm{n}}_{0.5}{\mathrm{O}}_3$ is very different from the noncollinear one of layered $B$-site-ordered $\mathrm{C}{\mathrm{a}}_2\mathrm{FeMn}{\mathrm{O}}_6$.

Spin-liquid states are often described as the antithesis of magnetic order. Recently, however, it has been proposed that in certain frustrated magnets the magnetic degrees of freedom may “fragment” in such a way as to give rise to a coexistence of spin liquid and ordered phases. Recent neutron-scattering results [S. Petit, E. Lhotel, B. Canals, M. Ciomaga Hatnean, J. Ollivier, H. Muttka, E. Ressouche, A. R. Wildes, M. R. Lees, and G. Balakrishnan, Nat. Phys. 12, 746 (2016)] suggest that this scenario may be realized in the pyrochlore magnet ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$. These observations show the characteristic pinch-point features of a Coulombic spin liquid occurring alongside the Bragg peaks of an “all-in-all-out” ordered state. Here we explain the quantum origins of this apparent magnetic moment fragmentation, within the framework of a quantum model of nearest-neighbor exchange, appropriate to ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$. This model is able to capture both the ground-state order and the pinch points observed at finite energy. The observed fragmentation arises due to the combination of the unusual symmetry properties of the ${\mathrm{Nd}}^{3+}$ ionic wave functions and the structure of equations of motion of the magnetic degrees of freedom. The results of our analysis suggest that ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ is proximate to a $U\left(1\right)$ spin-liquid phase and is a promising candidate for the observation of a Higgs transition in a magnetic system.

We have characterized the strength of the interfacial Dyzaloshinskii-Moriya interaction (DMI) in ultrathin perpendicularly magnetized CoFeB/MgO films, grown on different underlayers of W, TaN, and Hf, using two experimental methods. First, we determined the effective DMI field from measurements of field-driven domain wall motion in the creep regime, where applied in-plane magnetic fields induce an anisotropy in the wall propagation that is correlated with the DMI strength. Second, Brillouin light spectroscopy was employed to quantify the frequency nonreciprocity of spin waves in the CoFeB layers, which yielded an independent measurement of the DMI. By combining these results, we show that DMI estimates from the different techniques yield only qualitative agreement, which suggests that open questions remain about the underlying models used to interpret these results.

Real-time dynamics in a one-dimensional transverse Ising model coupled with the time-dependent oscillating field is analyzed by using the infinite time-evolving block decimation algorithm and Floquet theory. In particular, the transient dynamics induced by the pulse field and their connections to the dynamics by a continuous-wave field are focused on. During the pulse-field irradiation, the order parameter shows a characteristic oscillation, in which the frequency shifts from the pulse-field frequency. This is considered as a kind of the Rabi oscillation, but the frequency strongly depends on the intersite Ising interaction. After turning off the pulse field, the oscillation remains with a frequency $\mathrm{\Omega }$ and a damping constant $\gamma$. In the case of low fluence, both $\mathrm{\Omega }$ and $\gamma$ are scaled by the pulse amplitude over a wide range of the parameter values of the model. In the case of high fluence, $\mathrm{\Omega }$ and $\gamma$ are arranged by a product of the pulse amplitude and the pulse width, which governs the population of the excited state when the pulse field is turned off. Experimental feasibility of the present results is briefly discussed.

In various multiorbital systems, the emergence of the orbital fluctuations and their role on the pairing mechanism attract increasing attention. To achieve deep understanding on these issues, we perform a functional renormalization group (fRG) study for the two-orbital Hubbard model. The vertex corrections for the electron-boson coupling $(U$-VC), which are dropped in the Migdal-Eliashberg gap equation, are obtained by solving the RG equation. We reveal that the dressed electron-boson coupling for the charge channel ${\widehat{U}}_{\mathrm{eff}}^c$ becomes much larger than the bare Coulomb interaction ${\widehat{U}}^0$ due to the $U$-VC in the presence of moderate spin fluctuations. For this reason, the attractive pairing interaction due to the charge or orbital fluctuations is enlarged by the factor ${({\widehat{U}}_{\mathrm{eff}}^c/{\widehat{U}}^0)}^2\gg 1$. In contrast, the spin fluctuation pairing interaction is suppressed by the spin-channel $U$-VC, because of the relation ${\widehat{U}}_{\mathrm{eff}}^s\ll {\widehat{U}}^0$. The present study demonstrates that the orbital or charge fluctuation pairing mechanism can be realized in various multiorbital systems thanks to the $U$-VC, such as in Fe-based superconductors.

Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs substantially. It is straightforward to compute an MPP of a grand-canonical ensemble, also when symmetries are exploited. This paper provides and demonstrates methods for the efficient computation of MPPs of canonical ensembles under utilization of symmetries. Furthermore, we present a scheme for the evaluation of global quantum number distributions using matrix product density operators (MPDOs). We provide exact matrix product representations for canonical infinite-temperature states, and discuss how they can be constructed alternatively by applying matrix product operators to vacuum-type states or by using entangler Hamiltonians. A demonstration of the techniques for Heisenberg spin-$1/2$ chains explains why the difference in the energy densities of canonical and grand-canonical ensembles decays as $1/L$.

We analyze in detail the effect of nontrivial band topology on the area-law behavior of the entanglement entropy in Kitaev's honeycomb model. By mapping the translationally invariant 2D spin model onto 1D fermionic subsystems, we identify those subsystems responsible for universal entanglement contributions in the gapped phases and those responsible for critical entanglement scaling in the gapless phases. For the gapped phases, we analytically show how the topological edge states contribute to the entanglement entropy and provide a universal lower bound for it. For the gapless semimetallic phases and topological phase transitions, the identification of the critical subsystems shows that they fall always into the Ising or the XY universality classes. As our study concerns the fermionic degrees of freedom in the honeycomb model, qualitatively similar results are expected to apply also to generic topological insulators and superconductors.