Mn $K\alpha$ x-ray fluorescence holography (XFH) measurements were performed on a single crystal of a ${\mathrm{Bi}}_2{\mathrm{Te}}_3{\mathrm{Mn}}_{0.1}$ topological insulator at 100 and 300 K to search for the impurity sites of the Mn atoms in this functional crystal. The three-dimensional atomic images were reconstructed using an $L_1$-regularized linear regression. X-ray absorption fine-structure (XAFS) experiments were also carried out at 30–300 K to obtain additional structural information. The local structural information was obtained from these data, such as the positions of the Mn impurity sites, the Mn-Te interatomic distances, the lattice distortions, and the positional fluctuations around the impurity Mn atoms. The possible Mn impurity sites are twofold, i.e., an interlayer site with an octahedral symmetry and a substitutional site of Te on the layer surface. A distinct temperature dependence is seen in the positional fluctuations of the impurity Mn atoms in the substitutional site. These findings for the impurity sites cannot be easily obtained by diffraction or XAFS experiment in the usual way, but only using a combination of the XFH and XAFS measurements.

We present theoretical studies of the intrinsic spin-orbit torque (SOT) in a single-domain ferromagnetic layer with Rashba spin-orbit coupling (SOC) using the nonequilibrium Green's function formalism for a tight-binding Hamiltonian. We find that, in the case of a small electric field, the intrinsic SOT to first order in SOC has only the field-like torque symmetry and can be interpreted as the longitudinal spin current induced by the charge current and Rashba field. We analyze the results in terms of the material-related parameters of the electronic structure, such as the band filling, bandwidth, exchange splitting, and the Rashba SOC strength. On the basis of these numerical and analytical results, we discuss the magnitude and sign of SOT. Our results suggest that the different sign of SOT in identical ferromagnets with different supporting layers, e.g., Co/Pt and Co/Ta, can be attributed to electrostatic doping of the ferromagnetic layer by the support.

The insulating magnetic material ${\mathrm{Fe}}_3{\mathrm{PO}}_4{\mathrm{O}}_3$ features a noncentrosymmetric lattice composed of ${\mathrm{Fe}}^{3+}$ triangular units. Frustration, due to competing near-neighbor ($J_1$) and next-nearest-neighbor ($J_2$) antiferromagnetic interactions, was recently suggested to be the origin of an antiferromagnetic helical ground state with unusual needlelike nanoscale magnetic domains in ${\mathrm{Fe}}_3{\mathrm{PO}}_4{\mathrm{O}}_3$. Magnetic dilution is shown here to tune the ratio of these magnetic interactions, thus providing deeper insight into this unconventional antiferromagnet. Dilution of the ${\mathrm{Fe}}^{3+}$ lattice in ${\mathrm{Fe}}_3{\mathrm{PO}}_4{\mathrm{O}}_3$ was accomplished by substituting nonmagnetic ${\mathrm{Ga}}^{3+}$ to form the solid solution series ${\text{Fe}}_{3-x}{\text{Ga}}_x{\text{PO}}_4{\text{O}}_3$ with $x=0.012$, 0.06, 0.25, 0.5, 1.0, 1.5. Magnetic susceptibility and neutron powder diffraction data from this series are presented. A continuous decrease of both the helical pitch length and the domain size is observed with increasing dilution up to at least $x=0.25$, while for $x\ge 0.5$, the compounds lack long-range magnetic order entirely. The decrease in the helical pitch length with increasing $x$ can be qualitatively understood by reduction of the ratio of $J_2/J_1$ in the Heisenberg model, consistent with mean-field considerations. Intriguingly, the magnetic correlation length in the $ab$ plane remains nearly equal to the pitch length for each value of $x\le 0.25$, showing that the two quantities are intrinsically connected in this unusual antiferromagnet.

A family of compounds built by a single molecular species, $M$(${\mathrm{tmdt})}_2$, with a metal ion, $M$, and organic ligands, tmdt, affords diverse electronic phases due to $M$-dependent interplays between $d$ electrons in $M$, and $\pi$ electrons in tmdt. We investigated the spin state in $\mathrm{Pd}{\left(\mathrm{tmdt}\right)}_2$, a $\pi$-electron system without a $d$-electron contribution, through ${}^1\mathrm{H}$ nuclear magnetic resonance (NMR) and muon-spin resonance experiments. The temperature profiles of the NMR linewidth, relaxation rate, and asymmetry parameter in muon decay show an inhomogeneous antiferromagnetic order with moments distributed around $\sim 0.1{\mu }_{\mathrm{B}}$ that onsets at above 100 K. This result provides an example of the antiferromagnetic order in a pure $\pi$-electron system in $M$(${\mathrm{tmdt})}_2$, and it demonstrates that correlation among the $\pi$ electrons is so strong as to give the Néel temperature over 100 K. The small and inhomogeneous moments are understandable as the crucial disorder effect in correlated electrons situated near the Mott transition.

Because of the potential application of $\mathrm{Co}{\left(\mathrm{OH}\right)}_2$ in a magnetic cooling system as a result of its superior magnetocaloric effect many people have investigated magnetic properties of $\mathrm{Co}{\left(\mathrm{OH}\right)}_2$. Unfortunately, most of the works have been carried out on the $\beta \text{−}\mathrm{Co}{\left(\mathrm{OH}\right)}_2$ phase due to the fact that the $\alpha \text{−}\mathrm{Co}{\left(\mathrm{OH}\right)}_2$ phase is very unstable and continuously transformed into the stable $\beta \text{−}\mathrm{Co}{\left(\mathrm{OH}\right)}_2$ phase. However, in the present work, using a $\mathrm{Mo}{\mathrm{S}}_2$ sheet as a two-dimensional template, we have been able to synthesize a stable $\alpha \text{−}\mathrm{Co}{\left(\mathrm{OH}\right)}_2$ phase in addition to a $\beta \text{−}\mathrm{Co}{\left(\mathrm{OH}\right)}_2$ phase by varying the layer thickness. It is seen that for thinner samples the $\beta$ phase, while for thicker samples $\alpha$ phase, is grown on the $\mathrm{Mo}{\mathrm{S}}_2$ surface. Magnetic measurements are carried out for the samples over the temperature range from 2 to 300 K and it is seen that for the $\beta$ phase, ferromagnetic ordering with fairly large coercivity (1271 Oe) at 2 K is obtained instead of the usual antiferromagnetism. The most interesting result is the observation of ferromagnetic ordering with a transition temperature (Curie temperature) more than 100 K in the $\alpha \text{−}\mathrm{Co}{\left(\mathrm{OH}\right)}_2$ phase. Complete saturation in the hysteresis curve under application of very low field having coercivity of $\sim 162\mathrm{Oe}$ at 2 K and 60 Oe at 50 K is obtained. A thin stable $\alpha \text{−}\mathrm{Co}{\left(\mathrm{OH}\right)}_2$ phase grown on $\mathrm{Mo}{\mathrm{S}}_2$ surface with very soft ferromagnetic ordering will be very useful as the core material in electromagnets.

The anisotropic magnetoresistance (AMR) near the Verwey temperature $\left(T_{\mathrm{V}}\right)$ is investigated in charge ordered ${\mathrm{Fe}}_3{\mathrm{O}}_4$ epitaxial films. When the temperature continuously decreases below $T_{\mathrm{V}}$, the symmetry of AMR in ${\mathrm{Fe}}_3{\mathrm{O}}_4$(100) film evolves from twofold to fourfold at a magnetic field of 50 kOe, where the magnetic field is parallel to the film surface, whereas AMR in ${\mathrm{Fe}}_3{\mathrm{O}}_4$(111) film maintains twofold symmetry. By analyzing AMR below $T_{\mathrm{V}}$, it is found that the Verwey transition contains two steps, including a fast charge ordering process and a continuous formation process of trimeron, which is comfirmed by the temperature-dependent Raman spectra. Just below $T_{\mathrm{V}}$, the twofold AMR in ${\mathrm{Fe}}_3{\mathrm{O}}_4$(100) film originates from uniaxial magnetic anisotropy. The fourfold AMR at a lower temperature can be ascribed to the in-plane trimerons. By comparing the AMR in the films with two orientations, it is found that the trimeron shows a smaller resistivity in a parallel magnetic field. The field-dependent AMR results show that the trimeron-sensitive field has a minimum threshold of about 2 kOe.

We investigate the influence of the barrier thickness of ${\mathrm{Co}}_{40}{\mathrm{Fe}}_{40}{\mathrm{B}}_{20}$-based magnetic tunnel junctions (MTJs) on the laser-induced tunnel magneto-Seebeck (TMS) effect. Varying the barrier thickness from 1 to 3 nm, we find a distinct maximum in the TMS effect for a 2.6-nm barrier thickness. This maximum is measured independently for two barrier materials, namely, ${\mathrm{MgAl}}_2{\mathrm{O}}_4$ (MAO) and MgO. Additionally, samples with a MAO barrier exhibit a high thermovoltage of more than $350\mu \mathrm{V}$ in comparison to $90\mu \mathrm{V}$ for the MTJs with a MgO barrier when heated with the maximum laser power of 150 mW. Our results allow for the fabrication of improved stacks when dealing with temperature differences across MTJs for future applications in spin caloritronics, the emerging research field that combines spintronics and thermoelectrics.

The antiferromagnetic compound $\mathrm{Ba}\left(\mathrm{TiO}\right){\mathrm{Cu}}_4{\left({\mathrm{PO}}_4\right)}_4$ contains square cupola of corner-sharing ${\mathrm{CuO}}_4$ plaquettes, which were proposed to form effective quadrupolar order. To identify the magnetic structure, we have performed spherical neutron polarimetry measurements. Based on symmetry analysis and careful measurements, we conclude that the orientation of the ${\mathrm{Cu}}^{2+}$ spins form a noncollinear in-out structure with spins approximately perpendicular to the ${\mathrm{CuO}}_4$ motif. Strong Dzyaloshinskii-Moriya interaction naturally lends itself to explain this phenomenon. The identification of the ground-state magnetic structure should serve well for future theoretical and experimental studies into this and closely related compounds.

The anomalous Hall effect (AHE) and the Gilbert damping (GD) are studied theoretically for the partially ordered $L{1}_0$-Fe(Pd,Pt) alloys. The varying alloy order and the spin-orbit coupling, which are due to the change in the Pd/Pt composition, allow for a chemical tuning of both phenomena which play an important role in the spintronic applications. The impact of the antisite disorder on the residual resistivity, AHE, and GD is studied from first principles using recently developed methods employing the Kubo-Bastin approach and the nonlocal torque operator method. The most interesting result is a different behavior of samples with low and high chemical orders. Good agreement between calculated and measured concentration trends is obtained for all quantities studied, while the absolute GD values are underestimated.

We consider the direct three-qubit parity measurement scheme with two measurement resonators, using circuit quantum electrodynamics to analyze its functioning for several different types of superconducting qubits. We find that for the most common, transmon-like qubit, the presence of additional qubit-state-dependent coupling terms of the two resonators hinders the possibility of performing the direct parity measurement. We show how this problem can be solved by employing the tunable coupling qubit (TCQ) in a particular designed configuration. In this case, we effectively engineer the original model Hamiltonian by canceling the harmful terms. We further develop an analysis of the measurement in terms of information gains and provide some estimates of the typical parameters for optimal operation with TCQs.

We study the quasi-two-dimensional quantum O(2) model, a quantum generalization of the Lawrence-Doniach model, within the nonperturbative renormalization-group approach and propose a generic phase diagram for layered three-dimensional systems with an O(2)-symmetric order parameter. Below the transition temperature we identify a wide region of the phase diagram where the renormalization-group flow is quasi-two-dimensional for length scales smaller than a Josephson length $l_J$, leading to signatures of Kosterlitz-Thouless physics in the temperature dependence of physical observables. In particular the order parameter varies as a power law of the interplane coupling with an exponent which depends on the anomalous dimension (itself related to the stiffness) of the strictly two-dimensional low-temperature Kosterlitz-Thouless phase.

We report three distinct regions within the $A$ phase in Fe-doped MnSi, based on the evolution of magnetoresistance and the Hall effect as a function of orientation of applied field. Fe impurities as pinning centers and crystalline anisotropy are found to be non-negligible only at the boundary of the $A$ phase. Electrical transport characteristics unique to the $A$ phase not only remain robust but also indicate a freely rotating skyrmion lattice, decoupled from underlying crystal structure or impurity pinning.

We experimentally demonstrate single-pulse all-optical switching in Pt/Co/Gd stacks using linearly polarized laser pulses. This shows that thermal single-pulse switching is not limited to ferrimagnetic alloys, but is also possible in ferrimagnetic multilayers that are highly suitable for future applications due to easy fabrication and (interface) engineering. Moreover, it is shown that the threshold fluence needed for the optical switch strongly depends on the thickness of the Co layer, with a remarkable low threshold fluence of $\approx 1.2$ mJ/${\mathrm{cm}}^2$ for a Co thickness of 0.8 nm. Lastly, helicity-dependent measurements showed no significant effect of the magnetic circular dichroism in these thin magnetic layers.

In this study, the microscopic origins of the voltage-controlled magnetic anisotropy (VCMA) in $3d$-ferromagnetic metals are revealed. Using in situ x-ray fluorescence spectroscopy that provides a high quantum efficiency, electric-field-induced changes in orbital magnetic moment and magnetic dipole $T_{\mathrm{z}}$ terms in ultrathin Co films are demonstrated. An orbital magnetic moment difference of $0.013{\mu }_{\mathrm{B}}$ was generated in the presence of electric fields of $\pm 0.2\mathrm{V}/\mathrm{nm}$. The VCMA of Co was properly estimated by the induced change in orbital magnetic moment, according to the perturbation theory model. The induced change in the magnetic dipole $T_{\mathrm{z}}$ term only slightly contributed to the VCMA in $3d$-ferromagnetic metals.

The robustness of spin liquids with respect to small perturbations, and the way magnetic frustration can be lifted by slight changes in the balance between competing magnetic interactions, remains a rich and open issue. We address this question through the study of the gadolinium aluminum garnet ${\mathrm{Gd}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$, a related compound to the extensively studied ${\mathrm{Gd}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$. We report on its magnetic properties at very low temperatures. We show that despite a freezing at about 300 mK, no magnetic transition is observed, suggesting the presence of a spin-liquid state down to the lowest temperatures, similarly to ${\mathrm{Gd}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$, in spite of a larger ratio between exchange and dipolar interactions. Finally, the phase diagram as a function of field and temperature is strongly reminiscent of the one reported in ${\mathrm{Gd}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$. This study reveals the robust nature of the spin-liquid phase for Gd ions on the garnet lattice, in stark contrast to Gd ions on the pyrochlore lattice for which a slight perturbation drives the compound into a range of magnetically ordered states.

An allotrope of nitrogen formed solely by N-N single bonds is predicted to exist between 100 and 150 GPa. The crystal structure has the Pccn symmetry and is characterized by a distorted tetrahedral network consisting of fused ${\mathrm{N}}_8, {\mathrm{N}}_{10}$, and ${\mathrm{N}}_{12}$ rings. Stability of this structure is established by phonon and vibrational free energy calculations at 0 K and finite temperatures. The simulated x-ray diffraction pattern of the Pccn phase is compared to the pattern of a recently synthesized nitrogen phase at the same $P-T$ conditions, which suggests that the Pccn phase is likely a minor component of the latter. The Pccn phase is expected to form above the stability field of the cubic gauche (cg) phase. The outstanding metastability of this phase is attributed to the intrinsic stability of the $s{p}^3$ bonding as well as the energetically favorable dihedral angles between N-N single bonds, in either gauche or trans conformation. The prediction of another single-bonded phase of nitrogen after the lab-synthesized cg phase will stimulate research on metastable phases of nitrogen and their applications as high-energy-density materials.

Exceptional points (EPs) were recently predicted to modify the spontaneous emission rate or Purcell factor of narrow-band emitters embedded in resonant cavities. We demonstrate that EPs can have an even greater impact on nonlinear optical processes like frequency conversion by deriving a general formula quantifying radiative emission from a subwavelength emitter in the vicinity of a triply resonant ${\chi }^{\left(2\right)}$ cavity that supports an EP near the emission frequency and a bright mode at the second harmonic. We show that the resulting frequency up-conversion process can be enhanced by up to two orders of magnitude compared to nondegenerate scenarios and that, in contrast to the recently predicted spontaneous-emission enhancements, nonlinear EP enhancements can persist even when considering spatial distributions of broadband emitters, provided that the cavity satisfies special nonlinear selection rules. This is demonstrated via a two-dimensional proof-of-concept PhC designed to partially fulfill the various criteria needed to approach the derived bounds on the maximum achievable up-conversion efficiencies. Our predictions suggest an indirect but practically relevant route to experimentally observe the impact of EPs on spontaneous emission, with implications to quantum information science.

A comprehensive study of the influence of classical anisotropy fields on the magnetic properties of Heisenberg antiferromagnets within unified molecular field theory versus temperature $T$, magnetic field $H$, and anisotropy field parameter $h_{\mathrm{A}1}$ is presented for systems comprised of identical crystallographically-equivalent local moments. The anisotropy field for collinear $z$-axis antiferromagnetic (AFM) ordering is constructed so that it is aligned in the direction of each ordered and/or field-induced thermal-average moment with a magnitude proportional to the moment, whereas that for XY anisotropy is defined to be in the direction of the projection of the moment onto the $xy$ plane, again with a magnitude proportional to the moment. Properties studied include the zero-field Néel temperature $T_{\mathrm{N}}$, ordered moment, heat capacity, and anisotropic magnetic susceptibility of the AFM phase versus $T$ with moments aligned either along the $z$ axis or in the $xy$ plane. Also determined are the high-field magnetization perpendicular to the axis or plane of collinear or planar noncollinear AFM ordering, the high-field magnetization along the $z$ axis of a collinear $z$-axis AFM, spin-flop (SF), and paramagnetic (PM) phases, and the free energies of these phases versus $T,H$, and $h_{\mathrm{A}1}$. Phase diagrams at $T=0$ in the $H_z\text{−}{h}_{\mathrm{A}1}$ plane and at $T>0$ in the $H_z\text{−}T$ plane are constructed for spins $S=1/2$. For $h_{\mathrm{A}1}=0$, the SF phase is stable at low field and the PM phase at high field with no AFM phase present. As $h_{\mathrm{A}1}$ increases, the phase diagram contains the AFM, SF, and PM phases. Further increases in $h_{\mathrm{A}1}$ lead to the disappearance of the SF phase and the appearance of a tricritical point on the AFM-PM transition curve. Applications of the theory to extract $h_{\mathrm{A}1}$ from experimental low-field magnetic susceptibility data and high-field magnetization versus field isotherms for single crystals of AFMs are discussed.

We present a three-dimensional cubic lattice spin model, anisotropic in the $\widehat{z}$ direction, that exhibits fractonlike order. This order can be thought of as the result of interplay between two-dimensional ${\mathbb{Z}}_2$ topological order and spontaneous symmetry breaking along the $\widehat{z}$ direction. Fracton order is a novel type of topological order characterized by the presence of immobile pointlike excitations, named fractons, residing at the corners of an operator with two-dimensional support. As other recent fracton models, ours exhibits a subextensive ground-state degeneracy: On an $L_x\times L_y\times L_z$ three-torus, it has a $2^{2L_z}$ topological degeneracy and an additional symmetry-breaking nontopological degeneracy equal to $2^{L_x{L}_y-2}$. The fractons can be combined into composite excitations that move either in a straight line along the $\widehat{z}$ direction or freely in the $xy$ plane at a given height $z$. While our model draws inspiration from the toric code, we demonstrate that it cannot be adiabatically connected to a layered toric code construction. Additionally, we investigate the effects of imposing open boundary conditions on our system. We find zero energy modes on the surfaces perpendicular to either the $\widehat{x}$ or $\widehat{y}$ directions and their absence on the surfaces normal to $\widehat{z}$. This result can be explained using the properties of the two kinds of composite two-fracton mobile excitations.