Anisotropic Spin Research Articles

Relationship between the Formation of Magnetic Clusters and Hexagonal Phase of Gold Matrix in AuxFe1-x Nanophase Thin Films.

AuxFe1−x nanophase thin films of different compositions and thicknesses were prepared by co-deposition magnetron sputtering. Complex morpho-structural and magnetic investigations of the films were performed by X-ray Diffraction, cross-section Transmission Electron Microscopy, Selected Area Electron Diffraction, Magneto Optical Kerr Effect, Superconducting Quantum Interference Device magnetometry and Conversion Electron Mössbauer Spectroscopy. It was proven that depending on the preparation conditions, different configurations of defect α-Fe magnetic clusters, i.e., randomly distributed or auto-assembled in lamellar or filiform configurations, can be formed in the Au matrix. A close relationship between the Fe clustering process and the type of the crystalline structure of the Au matrix was underlined, with the stabilization of a hexagonal phase at a composition close to 70 at. % of Au and at optimal thickness. Due to different types of inter-cluster magnetic interactions and spin anisotropies, different types of magnetic order from 2D Ising type to 3D Heisenberg type, as well as superparamagnetic behavior of non-interacting Fe clusters of similar average size, were evidenced.

Spectrum of the quantum integrable {D}_2^{(2)} spin chain with generic boundary fields

Exact solution of the quantum integrable {D}_2^{(2)} spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe ansatz equations of the {D}_2^{(2)} model are derived via off-diagonal Bethe ansatz.

Tunable spin–charge conversion in class-I topological Dirac semimetals

We theoretically demonstrate that class-I topological Dirac semimetals (TDSMs) can provide a platform for realizing both electrically and magnetically tunable spin–charge conversion. With time-reversal symmetry, the spin component along the uniaxial rotation axis (z axis) is approximately conserved, which leads to an anisotropic spin Hall effect; the resulting spin Hall current relies on the relative orientation between the external electric field and the z axis. The application of a magnetic field, on the other hand, breaks time-reversal symmetry, driving the TDSM into a Weyl semimetal phase and, consequently, partially converting the spin current to a charge Hall current. Using the Kubo formulas, we numerically evaluate the spin and charge Hall conductivities based on a low-energy TDSM Hamiltonian together with the Zeeman coupling. Besides the conventional tensor element of the spin Hall conductivity σxyz, we find that unconventional components, such as σxyx and σxyy, also exist and vary as the magnetic field is rotated. Likewise, the charge Hall conductivity also exhibits appreciable tunability upon variation of the magnetic field. We show that such tunability—as well as large spin–charge conversion efficiency—arises from the interplay of symmetry and band topology of the TDSMs.

Dome-shaped phase diagram in the spin-1 XY ferromagnet with biquadratic exchange and longitudinal easy-axis crystal field

We investigate the phase diagram of a spin-1 ferromagnetic XY model in the presence of a longitudinal easy-axis crystal field assuming bilinear (J) and biquadratic (I) exchange interactions between nearest neighbors spins and using the two-time Green Functions framework at the level of the Devlin strategy. Employing both analytical estimates and numerical calculations, we find that the structure of the crystal-field-induced phase boundary changes sensibly as the ratio alpha = I/J increases. In particular, when alpha overcomes a characteristic value alpha ^*, two quantum critical points appear which are connected by a dome-shaped critical line. Due to the paradigmatic nature of the anisotropic spin model here considered, we believe that our findings may provide useful insights into the physical origin of recent experimental results found for some innovative materials which exhibit two quantum critical points and dome-shaped phase diagrams induced by non-thermal control parameters driving a non-conventional quantum criticality.Graphic abstract

Preferred Spin Excitations in the Bilayer Iron-Based Superconductor CaK(Fe_{0.96}Ni_{0.04})_{4}As_{4} with Spin-Vortex Crystal Order.

Spin-orbit coupling (SOC) is a key to understand the magnetically driven superconductivity in iron-based superconductors, where both local and itinerant electrons are present and the orbital angular momentum is not completely quenched. Here, we report a neutron scattering study on the bilayer compound CaK(Fe_{0.96}Ni_{0.04})_{4}As_{4} with superconductivity coexisting with a noncollinear spin-vortex crystal magnetic order that preserves the tetragonal symmetry of the Fe-Fe plane. In the superconducting state, two spin resonance modes with odd and even L symmetries due to the bilayer coupling are found similar to the undoped compound CaKFe_{4}As_{4} but at lower energies. Polarization analysis reveals that the odd mode is c-axis polarized, and the low-energy spin anisotropy can persist to the paramagnetic phase at high temperature, which closely resembles other systems with in-plane collinear and c-axis biaxial magnetic orders. These results provide the missing piece of the puzzle on the SOC effect in iron-pnictide superconductors, and also establish a common picture of c-axis preferred magnetic excitations below T_{c} regardless of the details of magnetic pattern or lattice symmetry.

Timescale distributions of spin fluctuations in the S=2 kagome antiferromagnet CsMn3F6 ( SeO3)2

We report the static and dynamical properties of a newly discovered $S=2$ kagome antiferromagnet ${\mathrm{CsMn}}_{3}{\mathrm{F}}_{6}{({\mathrm{SeO}}_{3})}_{2}$. By combining dc and ac magnetic susceptibilities, specific heat, electron spin resonance (ESR), and muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$), we identify two characteristic temperatures ${T}^{*}=8$ K and $T=|{\mathrm{\ensuremath{\Theta}}}_{\text{CW}}|=49(1)$ K, thereby three distinct regimes: a paramagnetic, a cooperative paramagnetic, and a quasistatic ordered state. At high temperature ($T>|{\mathrm{\ensuremath{\Theta}}}_{\text{CW}}|$), the ac susceptibility and ESR linewidth show a power-law dependence, reflecting short-range spin-spin correlations of the paramagnetic ${\mathrm{Mn}}^{3+}$ ions. In the cooperative paramagnetic regime (${T}^{*}<T<|{\mathrm{\ensuremath{\Theta}}}_{\text{CW}}|$), the ESR signals evince the development of dichotomic spin correlations, which is interpreted in terms of the distinct timescales of in-plane and out-of-plane spin fluctuations. Remarkably, we observe a broad maximum at the characteristic temperature scale of ${T}_{\text{cl}}=20$ K ($\ensuremath{\approx}|{J}_{\text{cl}}|$) in the specific heat and ESR results, suggesting short-range ordering. At low temperatures below ${T}^{*}$, the $\ensuremath{\mu}\mathrm{SR}$ data suggest the presence of dynamically fluctuating fields with partially frozen moments, consistent with the absence of long-range order evidenced by specific heat and magnetic susceptibility data. A magnetic behavior that depends on the chosen time window points to the presence of multiple timescales and temporally anisotropic spin correlations, as predicted for a classical kagome antiferromagnet.

Magnetic properties and noncollinear spin structure of the tin-rich stannide Ho5Co6Sn18

We have investigated the magnetic, structural, and thermodynamic properties of ${\mathrm{Ho}}_{5}{\mathrm{Co}}_{6}{\mathrm{Sn}}_{18}$ through x-ray and neutron diffraction, magnetization, and specific heat measurements. ${\mathrm{Ho}}_{5}{\mathrm{Co}}_{6}{\mathrm{Sn}}_{18}$ displays a magnetic transition at ${T}_{M}=3.4\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and can be described with the magnetic space group $I{4}_{1}/a{c}^{\ensuremath{'}}{d}^{\ensuremath{'}}$. The two holmium sublattices Ho(1) and Ho(2) exhibit different magnetic behaviors. Ferromagnetic order on the Ho(1) site develops into a net magnetization along the $c$ axis below ${T}_{M}$. In contrast, the ordering of the Ho(2) site is determined by geometric magnetic frustrations. The Ho(2) spins order into the noncollinear, two-in-two-out antiferromagnetic pattern on the $\mathrm{Ho}{(2)}_{4}$ tetrahedron. At 60 mK, the ordered moment of Ho(2) reaches $4.01\phantom{\rule{0.16em}{0ex}}(8)\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$, which is about half of the Ho(1) moment. Upon the application of a magnetic field, ferromagnetic components along the $c$ axis are induced on Ho(2), along with the in-plane antiferromagnetic components, indicating the XY-like spin anisotropy of the Ho(2) spins. A magnetic quasielastic neutron scattering signal is observed above ${T}_{M}$ and significantly weakens with the magnetic ordering.

Anisotropic spin dynamics in semiconductor narrow wires from the interplay between spin-orbit interaction and planar magnetic field

The anisotropic spin dynamics in wires based on a [001]-oriented semiconductor quantum well were investigated to determine the effect of applying an in-plane magnetic field both parallel to and perpendicular to the spin-orbit magnetic field, and the interaction between them. In one-dimensional spin motion where the wire width is less than the spin-precession length, it is known that the global spin precession is essentially determined by the spin-orbit induced precession along the wire direction. In this study, our objective is to investigate the nature of anisotropic spin dynamics in such narrow semiconductor wires along various crystal orientations. We proposed an analytic expression for the anisotropic spin-relaxation rates and the Larmor-precession frequencies for the arbitrary magnetic field orientation based on a theoretical understanding of the spin dynamics in the narrow wire structure. This expression describes the interaction between the spin-orbit field and all orientations of the in-plane magnetic field. We experimentally investigated the spin dynamics for lithographically defined 800-nm-width wires oriented along the $[\overline{1}10]$, [100], and [110] crystal orientations using a [001] GaAs/AlGaAs quantum well. Time-resolved Kerr rotation microscopy measurements indicated that the spin-relaxation time was the longest for the in-plane magnetic field perpendicular to the spin-orbit field, whereas the parallel configuration was found to be the shortest among all the directions. The precession frequency was found to have the opposite symmetry. These relations are well explained by the theoretical considerations developed in this work. Because the Rashba and Dresselhaus spin-orbit fields are mutually orthogonal in the [100] crystal orientation, it is possible to evaluate both spin-orbit coefficients from the precession anisotropy. These findings suggest that it is possible to control the spin state in narrow wires approaching the one-dimensional state and evaluate the spin-orbit coefficient. This has the potential to provide a greater understanding of quantum and topological information in semiconductor one-dimensional wires.

Coherent Spin Dynamics of Localized Electrons in Monolayer MoS2.

Compared with itinerant electrons in monolayer transition-metal dichalcogenides, localized electrons exhibit coherent spin precession in transverse magnetic fields B and usually have longer spin relaxation times. Here, we uncover the intrinsic spin dephasing processes of localized electrons whose mechanism remains unclear. Electron spin coherence dynamics are studied by time-resolved Faraday rotation spectroscopy in monolayer MoS2, where four subensembles of localized electrons are found with different g factor values and inhomogeneous broadening. The spin dephasing rates of all four subensembles include a linearly B-dependent part due to g-factor inhomogeneity and a B-independent part dominated by electron-nuclear hyperfine interaction and/or anisotropic exchange interaction. The hyperfine-induced spin dephasing time is ∼30-40 ns, and the anisotropic exchange-induced spin dephasing time is on the order of subnanoseconds. The findings give insight into the coherent spin dynamics of localized electrons in monolayers and the interaction between the electron spin and its environment.

Insights into the anisotropic spin- S Kitaev chain

Recently there has been a renewed interest in properties of the higher-spin Kitaev models, especially their low-dimensional analogues with additional interactions. These quasi-1D systems exhibit rich phase diagrams with symmetry-protected topological phases, Luttinger liquids, hidden order, and higher-rank magnetism. However, the nature of the pure spin-$S$ Kitaev chains are not yet fully understood. Earlier works found a unique ground state with short-ranged correlations for $S = 1$, and an intriguing double-peak structure in the heat capacity associated with an entropy plateau. To understand the low-energy excitations and thermodynamics for general $S$ we study the anisotropic spin-$S$ Kitaev chain. Starting from the dimerized limit we derive an effective low-energy Hamiltonian at finite anisotropy. For half-integer spins we find a trivial effective model, reflecting a non-local symmetry protecting the degeneracy, while for integer $S$ we find interactions among the flux degrees of freedom that select a unique ground state. The effective model for integer spins is used to predict the low-energy excitations and thermodynamics, and we make a comparison with the semiclassical limit through linear spin wave theory. Finally, we speculate on the nature of the isotropic limit.

Enhanced magnetic anisotropy in two-dimensional [formula omitted] by self-intercalation: A DFT study

Searching for two-dimensional (2D) materials with strong out-of-plane magnetic anisotropy is fatal features to 2D ferromagnets with high Curie temperature. In a recent experimental work (Zhao et al. (2020)), the samples they reported seems to meet the basic requirements for inducing large magnetic anisotropy. Based on density functional theory calculations, a large out-of-plane spin anisotropy, magnetic anisotropic energy (MAE) 97meV per supercell, has been observed in the as-synthesized 2H-TaS2 bilayer. Owing to the self-intercalation of Ta atoms who see a crystal field with low symmetry, orbital motions of 5d electrons in these Ta atoms are restored, leading to large spin–orbital coupling (SOC) and a large out-of-plane spin anisotropy. Based on the calculated energy difference between states with different magnetic orders, a rather high Curie temperature for the Ta intercalated 2H-TaS2 is also estimated at nearly 865K. Our study not only demonstrates the effectiveness of such preparation strategies on enhance the strong magnetic anisotropy and Curie temperature of 2H-TaS2 bilayer, but also deepen our understanding on the magnetic anisotropy induced by intrinsic SOC of 2D materials.

Study of the ground state and thermodynamic properties of Cu5-NIPA-like molecular nanomagnets

The thermodynamic properties of a spatially anisotropic spin-1/2 Heisenberg model for a Cu5 pentameric molecule is studied through exact diagonalization. The elementary geometry of the finite lattice is defined on nanomolecules consisting of an hourglass structure of two corner-sharing scalene triangles which are related by inversion symmetry. This microscopic magnetic model is quite suitable to describe the molecular nanomagnetic compound Cu5-NIPA. The ground-state phase diagram, as well as the corresponding total magnetization, are obtained as a function of the anisotropic exchange interactions and the external magnetic field. The thermodynamic behavior of the model at finite temperatures is also studied and the corresponding magnetocaloric effects are analyzed for various values of the Hamiltonian parameters.

Scanning nitrogen-vacancy center magnetometry in large in-plane magnetic fields

Scanning magnetometry with nitrogen-vacancy (NV) centers in diamond has emerged as a powerful microscopy for studying weak stray field patterns with nanometer resolution. Due to the internal crystal anisotropy of the spin defect, however, external bias fields—critical for the study of magnetic materials—must be applied along specific spatial directions. In particular, the most common diamond probes made from {100}-cut diamond only support fields at an angle of θ=55° from the surface normal. In this paper, we report fabrication of scanning diamond probes from {110}-cut diamond where the spin anisotropy axis lies in the scan plane (θ=90°). We show that these probes retain their sensitivity in large in-plane fields and demonstrate scanning magnetometry of the domain pattern of Co–NiO films in applied fields up to 40 mT. Our work extends scanning NV magnetometry to the important class of materials that require large in-plane fields.

Reaching the equilibrium state of the frustrated triangular Ising magnet Ca3Co2O6

Ca3Co2O6 is a frustrated magnet consisting of a triangular arrangement of chains of Ising spins. It shows regular magnetization steps vs magnetic field every 1.2 T that are metastable with very slow dynamics. This has puzzled the community for many years and given rise to numerous potential theories. Here we approach the problem by seeking the elusive magnetic equilibrium state at T = 2 K. To this end, we explore two approaches: (1) bypassing the slow dynamics produced by changing fields by instead field-cooling directly to the target temperature, and (2) quantum annealing in transverse magnetic fields. While we observe no measurable effect of the quantum annealing in fields up to 7 T, which is likely due to the large Ising anisotropy of Co spins in this material, we find that for the field cooling in longitudinal fields we achieve the predicted equilibrium 1/3 magnetization. We perform Monte Carlo simulations of the ground state phase diagram and we also simulate the quantum annealing process and find good agreement between experiment and theory. Thus we present an investigation of the elusive ground state properties of the canonical frustrated triangular system Ca3Co2O6.

Charge and Spin Dynamics and Enantioselectivity in Chiral Molecules.

Charge and spin dynamics are addressed in chiral molecules immediately after their instantaneous coupling to an external metallic reservoir. This work describes how a spin polarization is induced in the chiral structure as a response to the charge dynamics. The dynamics indicate that chiral induced spin selectivity is an excited state phenomenon that in the transient regime can be partly captured using a simplistic single-particle description but in the stationary limit definitively shows that electron correlations, e.g., electron–vibration interactions, crucially contribute to sustain an intrinsic spin anisotropy that can lead to a nonvanishing spin selectivity. The dynamics, moreover, provide insight into enantiomer separation, due to different acquired spin polarizations.

Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition

A novel Bethe ansatz scheme is proposed to investigate the exact physical properties of an integrable anisotropic quantum spin chain with competing interactions among the nearest, next nearest neighbor and chiral three spin couplings, where the boundary condition is the twisted one. The eigenvalue of the transfer matrix is characterized by its zero roots instead of the traditional Bethe roots. Based on the exact solution, the conserved momentum and charge operators of this U(1)-symmetry broken system are obtained. The ground state energy and density of rapidities are calculated. It is found that there exist three kinds of elementary excitations and the corresponding dispersion relations are obtained, which gives a different picture from that with periodic boundary condition.

Carrier doping-induced strong magnetoelastic coupling in 2D lattice.

The realization of intertwined ferroelasticity and ferromagnetism in two-dimensional (2D) lattices is of great interest for broad nanoscale applications but still remains a remarkable challenge. Here, we propose an alternative approach to realize the strongly coupled ferromagnetism and ferroelasticity by carrier doping. We demonstrate that prototypical 2D β-PbO is dynamically, thermally and mechanically stable. Under hole doping, 2D β-PbO possesses ferromagnetism and ferroelasticity simultaneously. Moreover, the robustness of ferromagnetic and ferroelastic orders is doping tunable. In particular, 2D β-PbO features an in-plane easy magnetization axis that is coupled with the lattice direction, enabling the ferroelastic manipulation of the spin direction. Furthermore, the efficient ferroelastic control of the anisotropic optical property and spin splitting in 2D β-PbO are also clarified. Our study highlights a new direction for 2D magnetoelastic research and enables the possibility for multifunctional devices.

Unravelling the robustness of magnetic anisotropy of a nickelocene molecule in different environments: a first-principles-based study.

Recent scanning tunneling spectroscopy with single metallocene molecule-functionalized tips have proved to be a powerful tool to probe and control individual spins and spin-spin exchange interactions due to the robustness of the magnetic properties of the metallocene molecule in different surroundings. However, accurate prediction of such robustness at a first-principles-based level by the conventional density functional theory (DFT) has remained challenging. In this paper, we have performed a detailed investigation of the evolution of electronic and magnetic properties of a nickelocene molecule (NiCp2) in different environments, i.e., free-standing, adsorbed on Cu(100) and as a functionalized tip apex. Using an embedding method, which combines DFT and the complete active space self-consistent field (CASSCF) method recently developed, we demonstrate that the nickelocene molecule almost preserves its spin and magnetic anisotropy upon adsorption on Cu(100), and also in the position of the tip apex. In particular, the cyclic π* orbital of the Cp rings could hybridize with the singly occupied dπ orbitals of the Ni center of the molecule, protecting these orbitals from external states. Hence the molecular spin maintains S = 1, the same as in the free-standing case, and its magnetic anisotropy is also robust with energies of 3.56, 3.34, and 3.51 meV in free-standing, adsorbed on Cu(100), and functionalized tip apex states, respectively, in good agreement with previous theoretical and experimental results. This work thus provides a first-principles-based understanding of the relevant experiments. Such agreement between theoretical simulations and experimental measurements highlights the potential usefulness of the method for investigating the local electronic and spin states of organometallic molecule-surface composite systems.

Probing Magnetic Anisotropy in Kagome Antiferromagnetic Mn$_3$Ge with Torque Magnetometry

We investigate the magnetic symmetry of the topological antiferromagnetic material Mn$_3$Ge by using torque measurements. Below the Neel temperature, detailed angle-dependent torque measurements were performed on Mn$_3$Ge single crystals in directions parallel and perpendicular to the Kagome basal plane. The out-of plane torque data exhibit $\pm\sin\theta$ and $\sin2\theta$ behaviors, of which the former results from the spontaneous ferromagnetism within the basal plane and the latter from the in- and out-of-plane susceptibility anisotropy. The reversible component of the in-plane torque exhibits $\sin6\varphi$ behavior, revealing the six-fold symmetry of the in-plane magnetic free energy. Moreover, we find that the free energy minima are pinned to the direction of spontaneous ferromagnetism, which correspond to the maxima of the irreversible component of the in-plane torque. We provide an effective spin model to describe the in-plane magnetic anisotropy. Our results demonstrate that the ground state of Mn$_3$Ge is described by the coexistence of a strong six-fold antichiral order and a weak ferromagnetic order induced by second-order spin anisotropy.

Open quantum dynamics theory for a complex subenvironment system with a quantum thermostat: Application to a spin heat bath.

Complex environments, such as molecular matrices and biological material, play a fundamental role in many important dynamic processes in condensed phases. Because it is extremely difficult to conduct full quantum dynamics simulations on such environments due to their many degrees of freedom, here, we treat in detail the environment only around the main system of interest (the subenvironment), while the other degrees of freedom needed to maintain the equilibrium temperature are described by a simple harmonic bath, which we call a quantum thermostat. The noise generated by the subenvironment is spatially non-local and non-Gaussian and cannot be characterized by the fluctuation-dissipation theorem. We describe this model by simulating the dynamics of a two-level system (TLS) that interacts with a subenvironment consisting of a one-dimensional XXZ spin chain. The hierarchical Schrödinger equations of motion are employed to describe the quantum thermostat, allowing for time-irreversible simulations of the dynamics at arbitrary temperature. To see the effects of a quantum phase transition of the subenvironment, we investigate the decoherence and relaxation processes of the TLS at zero and finite temperatures for various values of the spin anisotropy. We observed the decoherence of the TLS at finite temperature even when the anisotropy of the XXZ model is enormous. We also found that the population-relaxation dynamics of the TLS changed in a complex manner with the change in the anisotropy and the ferromagnetic or antiferromagnetic orders of spins.