Helical Spin Density Wave Research Articles

Spontaneous Chirality Flipping in an Orthogonal Spin-Charge Ordered Topological Magnet

The asymmetric distribution of chiral objects with opposite chirality is of great fundamental interest ranging from molecular biology to particle physics. In quantum materials, chiral states can build on inversion-symmetry-breaking lattice structures or emerge from spontaneous magnetic ordering induced by competing interactions. Although the handedness of a chiral state can be changed through external fields, a spontaneous chirality flipping has yet to be discovered. We present experimental evidence of chirality flipping via changing temperature in a topological magnet EuAl4, which features orthogonal spin density waves (SDW) and charge density waves (CDW). Using circular dichroism of Bragg peaks in the resonant magnetic x-ray scattering, we find that the chirality of the helical SDW flips through a first-order phase transition with modified SDW wavelength. Intriguingly, we observe that the CDW couples strongly with the SDW and displays a rare commensurate-to-incommensurate transition at the chirality flipping temperature. Combining with first-principles calculations and angle-resolved photoemission spectroscopy, our results support a Fermi surface origin of the helical SDW with intertwined spin, charge, and lattice degrees of freedom in EuAl4. Our results reveal an unprecedented spontaneous chirality flipping and lay the groundwork for a new functional manipulation of chirality through momentum-dependent spin-charge-lattice interactions. Published by the American Physical Society 2024

Tuning the spin of Dirac fermions on the surface of topological insulators in proximity to a helical spin density wave

We investigate the spin tunability of Dirac fermions on the surface of a 3D topological insulator in proximity to a helical spin density wave, acting as an applied one-dimensional periodic potential for spins produced by spiral multiferroic oxide. It is observed that the spin mean values of Dirac fermion undergo oscillations under the influence of such a periodic potential created by the exchange field of magnetization. The tunability of spin is strongly affected by the strength, orientation and period of the exchange field. In particular, the mean values of spin are anisotropic around the Dirac point, depending strongly on the amplitude and spatial period of the periodic potential. We also find that the spin expectation values change significantly by changing the plane of magnetization. Interestingly, the in-plane components of spin mean values perform pronounced oscillations, whereas the out of plane component does not oscillate at all. The oscillations of planar components of spin are originated from the spin-momentum locking on the surface of topological insulator.

The effect of vanadium substitution on the structural and magnetic properties of (Fe[formula omitted]V[formula omitted])[formula omitted]Ga[formula omitted

Fe3Ga4 displays a complex magnetic phase diagram that is sensitive and tunable with both electronic and crystallographic structure changes. In order to explore this tunability, vanadium-doped (Fe1−xVx)3Ga4 has been synthesized and characterized. High-resolution synchrotron X-ray diffraction and Rietveld refinement show that samples up to 20% V-doping remain isostructural to Fe3Ga4 and display a linear increase in unit cell volume as doping is increased. Magnetic measurements reveal a suppression of the antiferromagnetic helical spin-density wave (SDW) with V-doping, revealed by changes in both the low-temperature ferromagnetic–antiferromagnetic (FM–AFM) transition (T1) and high-temperature AFM–FM transition (T2). At 7.5% V-doping, the metamagnetic behavior of the helical AFM SDW phase is no longer observed. These results offer an avenue to effective tuning of the magnetic order in Fe3Ga4 for devices, as well as increased understanding of the magnetism in this system.

Magnetotransport of thin film topological insulators in proximity with helical spin density wave

The magnetoconductivity of an ultrathin film of topological insulator in proximity with helical spin density wave is calculated. Pronounced Weiss oscillations periodic in the inverse magnetic field appear for upper and bottom surfaces. With finite Zeeman coupling and hybridization across the surfaces Weiss oscillations for the top surface are more pronounced than the bottom surface. However in the absence of Zeeman coupling both the surfaces show same magnitude of oscillations.

Phase shift in skyrmion crystals

The magnetic skyrmion crystal is a periodic array of a swirling topological spin texture. Since it is regarded as an interference pattern by multiple helical spin density waves, the texture changes with the relative phase shifts among the constituent waves. Although such a phase degree of freedom is relevant to not only magnetism but also transport properties, its effect has not been elucidated thus far. We here theoretically show that a phase shift in the skyrmion crystals leads to a tetra-axial vortex crystal and a meron-antimeron crystal, both of which show a staggered pattern of the scalar spin chirality and give rise to nonreciprocal transport phenomena without the spin-orbit coupling. We demonstrate that such a phase shift can be driven by exchange interactions between the localized spins, thermal fluctuations, and long-range chirality interactions in spin-charge coupled systems. Our results provide a further diversity of topological spin textures and open a new field of emergent electromagnetism by the phase shift engineering.

Micromagnetic description of twisted spin spirals in the B20 chiral magnet FeGe from first principles

Using the model of classical Heisenberg exchange and Dzyaloshinskii-Moriya (DM) interaction, we show that the ground state of the B20 FeGe chiral magnet is a superposition of twisted helical spin-density waves formed by different sublattices of the crystal. Such twisted spin-density waves propagate in the same direction but with different phases and different directions of the rotation axes. We derive an advanced micromagnetic expression describing the exchange and DM interaction for such magnetic structures. In particular, we show that such magnetic order gives rise to new contributions to the micromagnetic energies of the exchange and DM interactions. By employing first-principles calculations based on density functional theory and using our micromagnetic model we show that the magnitude of the spin-spiral twist in B20 FeGe is of the same order as global spiraling. While the energy difference between the ground state of twisted spirals and the ferromagnetic state is in good agreement with the experimental results, for the spin spirals without a twist it is smaller by a factor of 3. In addition, we verify our results by employing spin-dynamics simulations. This calls for new experiments exploring the ground state properties of B20 chiral magnets.

Numerical Study of Multiple Helical Spin Density Waves and Vortex Spin Structures in Itinerant Electron System

Multiple spin density waves and related vortex-type magnetic structures in the itinerant electron system with inversion symmetry have been investigated on the basis of the Hubbard model and the generalized Hartree-Fock approximation combined with the recursion method. Possible magnetic phase diagram on the fcc lattice is presented in the space of the Coulomb interaction strength and the electron occupation number. It is found that the 2Q multiple helical spin density waves (SDW) with half-skyrmion half-antiskyrmion paired structure, the 3Q multiple helical SDW with 3 dimensional type vortex structure, the 4Q multiple SDW with partially ordered state, and a new type of 12Q multiple SDW showing both the half-skyrmion-type vortex structure and the partially ordered state can be stabilized around the Stoner instability line. The stability of their structures is explained on the basis of their electronic structures.

Multiple Helical Spin Density Waves and Magnetic Skyrmions in Itinerant Electron System

Magnetic structures and their stability of the multiple helical spin density waves (MHSDW) and related magnetic skyrmions in itinerant electron system have been investigated on the basis of both the phenomenological and microscopic theories. It is shown by using the Ginzburg-Landau (GL) theory and the Application Visualization System (AVS) that the magnetic skyrmion structures emerge as a MHSDW and can be stabilized in itinerant electron system on the fcc lattice even if there is no Dzyaloshinskii-Moriya interaction. Moreover, by using the generalized Hartree-Fock theory for the Hubbard model, the antiferromagnetic skyrmion structure found in the GL theory is shown to be stabilized on the fcc lattice in the vicinity of the half-filled electron number.

μSR study of stoichiometric NbFe2

The magnetic ground state of nominally stoichiometric single crystalline NbFe2 is investigated by bulk magnetisation and muon spin relaxation techniques. Magnetic order clearly emerges below the critical temperature TN=10.3K and is dominated by randomly orientated quasi-static moments. The local field distribution observed by muons can be explained by the phenomenological Gaussian-broadened-Gaussian Kubo Toyabe relaxation function. The observed short range order could be used to describe a new magnetic ground state, but a helical spin density wave with an incommensurate amplitude modulation cannot be ruled out. The sensitivity of μSR to the local magnetic field distribution in the vicinity of the quantum critical point (QCP) in NbFe2 is clearly demonstrated via comparison with already published work. This suggests detailed measurements of the muon relaxation as the QCP is approached will reveal further details of the field distribution and fluctuations in Nb1−yFe2+y.

Modulated spin helicity stabilized by incommensurate orbital density waves in a quadruple perovskite manganite

Through a combination of neutron diffraction and Landau theory we describe the spin ordering in the ground state of the quadruple perovskite manganite ${\mathrm{CaMn}}_{7}{\mathrm{O}}_{12}$---a magnetic multiferroic supporting an incommensurate orbital density wave that onsets above the magnetic ordering temperature, ${T}_{\mathrm{N}1}=90$ K. The multi-$\mathbf{k}$ magnetic structure in the ground state was found to be a nearly-constant-moment helix with modulated spin helicity, which oscillates in phase with the orbital occupancies on the ${\mathrm{Mn}}^{3+}$ sites via trilinear magneto-orbital coupling. Our phenomenological model also shows that, above ${T}_{\mathrm{N}2}=48$ K, the primary magnetic order parameter is locked into the orbital wave by an admixture of helical and collinear spin density wave structures. Furthermore, our model naturally explains the lack of a sharp dielectric anomaly at ${T}_{\mathrm{N}1}$ and the unusual temperature dependence of the electrical polarization.

Magnetic order on a topological insulator surface with warping and proximity-induced superconductivity

We determine the nature of the magnetic order on the surface of a topological insulator (TI) which develops due to hexagonal warping and the resulting Fermi surface (FS) nesting in the presence of a repulsive Hubbard interaction. For this purpose we investigate the spin susceptibility and derive a Landau theory to compare the different accessible phases. For a nearly hexagonal FS and sufficiently strong interaction the magnetic ground state is formed by a skyrmion lattice, i.e., by a superposition of three helical spin density waves which preserves C$_3$ symmetry. The magnetic ground state is topologically nontrivial with a nonzero skyrmion charge, which can be stabilized and controlled by an applied magnetic field. By bringing the TI in proximity to a conventional superconductor one can engineer a C$_3$-symmetric topological superconductor. We explore the modification of the phase diagram as well as the mutual influence between the skyrmion structure and a multipolar distribution of supercurrents, which can provide information about the underlying skyrmion charge.

Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states

We theoretically obtain the phase diagram of localized magnetic impurity spins arranged in a one-dimensional chain on top of a one- or two-dimensional electron gas with Rashba spin-orbit coupling. The interactions between the spins are mediated by the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism through the electron gas. Recent work predicts that such a system may intrinsically support topological superconductivity when a helical spin-density wave is formed in the spins, and superconductivity is induced in the electron gas. We analyze, using both analytical and numerical techniques, the conditions under which such a helical spin state is stable in a realistic situation in the presence of disorder. We show that it becomes unstable towards the formation of (anti) ferromagnetic domains if the disorder in the impurity spin positions $\delta R$ becomes comparable with the Fermi wave length. We also examine the stability of the helical state against Gaussian potential disorder in the electronic system using a diagrammatic approach. Our results suggest that in order to stabilize the helical spin state, and thus the emergent topological superconductivity, a sufficiently strong Rashba spin-orbit coupling, giving rise to Dzyaloshinskii-Moriya interactions, is required.

Anisotropic surface transport in topological insulators in proximity to a helical spin density wave

We study the effects of spatially localized breakdown of time reversal symmetry on the surface of a topological insulator (TI) due to proximity to a helical spin density wave (HSDW). The HSDW acts like an externally applied one-dimensional periodic (magnetic) potential for spins on the surface of the TI, rendering the Dirac cone on the TI surface highly anisotropic. The decrease in group velocity along the direction $\mathrm{x\ifmmode \hat{}\else \^{}\fi{}}$ of the applied spin potential is twice as great as that perpendicular to $\mathrm{x\ifmmode \hat{}\else \^{}\fi{}}$. At the Brillouin zone boundaries, it also gives rise to new semi-Dirac points that have a linear dispersion along $\mathrm{x\ifmmode \hat{}\else \^{}\fi{}}$ but a quadratic dispersion perpendicular to $\mathrm{x\ifmmode \hat{}\else \^{}\fi{}}$. The group velocity of electrons at these new semi-Dirac points is also shown to be highly anisotropic. Experiments using TI systems on multiferroic substrates should realize our predictions. We further discuss the effects of other forms of spin density waves on the surface transport property of TIs.

Emergence of the persistent spin helix in semiconductor quantum wells

According to Noether's theorem, for every symmetry in nature there is a corresponding conservation law. For example, invariance with respect to spatial translation corresponds to conservation of momentum. In another well-known example, invariance with respect to rotation of the electron's spin, or SU(2) symmetry, leads to conservation of spin polarization. For electrons in a solid, this symmetry is ordinarily broken by spin-orbit coupling, allowing spin angular momentum to flow to orbital angular momentum. However, it has recently been predicted that SU(2) can be achieved in a two-dimensional electron gas, despite the presence of spin-orbit coupling. The corresponding conserved quantities include the amplitude and phase of a helical spin density wave termed the 'persistent spin helix'. SU(2) is realized, in principle, when the strengths of two dominant spin-orbit interactions, the Rashba (strength parameterized by alpha) and linear Dresselhaus (beta(1)) interactions, are equal. This symmetry is predicted to be robust against all forms of spin-independent scattering, including electron-electron interactions, but is broken by the cubic Dresselhaus term (beta(3)) and spin-dependent scattering. When these terms are negligible, the distance over which spin information can propagate is predicted to diverge as alpha approaches beta(1). Here we report experimental observation of the emergence of the persistent spin helix in GaAs quantum wells by independently tuning alpha and beta(1). Using transient spin-grating spectroscopy, we find a spin-lifetime enhancement of two orders of magnitude near the symmetry point. Excellent quantitative agreement with theory across a wide range of sample parameters allows us to obtain an absolute measure of all relevant spin-orbit terms, identifying beta(3) as the main SU(2)-violating term in our samples. The tunable suppression of spin relaxation demonstrated in this work is well suited for application to spintronics.

Spin-transfer torque in helical spin-density waves

The current driven magnetization dynamics of a helical spin-density wave is investigated. Expressions for calculating the spin-transfer torque of real systems from first-principles density-functional theory are presented. These expressions are used for calculating the spin-transfer torque for the spin spirals of Er and fcc Fe at two different lattice volumes. It is shown that the calculated torque induces a rigid rotation of the order parameter with respect to the spin spiral axis. The torque is found to depend on the wave vector of the spin spiral and the spin polarization of the Fermi surface states. The resulting dynamics of the spin spiral is also discussed.

Current Driven Magnetization Dynamics in Helical Spin Density Waves

A mechanism is proposed for manipulating the magnetic state of a helical spin density wave using a current. It is shown that a current through a bulk metal with a helical spin density wave induces a spin transfer torque, which gives rise to a rotation of the order parameter. The use of spin transfer torque to manipulate the magnetization in bulk systems does not suffer from the obstacles seen for magnetization reversal using interface spin transfer torque in multilayered systems. The effect is demonstrated by a quantitative calculation of the current induced magnetization dynamics of a rare earth metal, Er. Finally, we propose a setup for experimental verification.

Theory of the Helical Spin Crystal: A Candidate for the Partially Ordered State of MnSi

MnSi is an itinerant magnet which at low temperatures develops a helical spin-density wave. Under pressure it undergoes a transition into an unusual partially ordered state whose nature is debated. Here we propose that the helical spin crystal (the magnetic analog of a solid) is a useful starting point to understand partial order in MnSi. We consider different helical spin crystals and determine conditions under which they may be energetically favored. The most promising candidate has bcc structure and is reminiscent of the blue phase of liquid crystals in that it has line nodes of magnetization protected by symmetry. We introduce a Landau theory to study the properties of these states, in particular, the effect of crystal anisotropy, magnetic field, and disorder. These results compare favorably with existing data on MnSi from neutron scattering and magnetic field studies. Future experiments to test this scenario are also proposed.

Static Magnetic Order in MetallicK0.49CoO2

By means of muon-spin spectroscopy, we have found that K0.49CoO2 crystals undergo successive magnetic transitions from a high-T paramagnetic state to a magnetic ordered state below 60 K and then to a second ordered state below 16 K, even though K0.49CoO2 is metallic at least down to 4 K. An isotropic magnetic behavior and wide internal-field distributions suggest the formation of a commensurate helical spin density wave (SDW) state below 16 K, while a linear SDW state is likely to exist above 16 K. It was also found that exhibits a further transition at 150 K presumably due to a change in the spin state of the Co ions. Since the dependence of the internal-field below 60 K was similar to that for Na0.5CoO2, this suggests that magnetic order is more strongly affected by the Co valence than by the interlayer distance or interaction and/or the charge ordering.

Phenomenological theory of helical multiple spin density waves in FCC transition metals

The relative stability among the 1- Q , 2- Q , and 3- Q helical spin density wave (SDW) states in FCC transition metals has been investigated on the basis of the Ginzburg–Landau free energy with the terms up to the fourth order in magnetic moments. The obtained magnetic-phase diagram in the space of the Landau parameters shows up the possibility of the 3- Q helical multiple SDW states, which has been neglected so far without detailed considerations in the band structure calculations of bulk cubic γ-Fe.

Possibility of Helical Interlayer Coupling in the Magnetic Superlattices and Overlayers

We consider interlayer magnetic coupling in a superlattice and/or overlayer in the case when spacer layer has the tendency towards formation of the helical spin density wave. Within phenomenological Landau-Ginzburg approach we show that the mutual interplay of the SDW and interlayer coupling spin polarization can lead to the helical interlayer coupling. When surface anisotropy is accounted for the effective interaction mimics interlayer biquadratic coupling.