Helimagnetic Research Articles

High‐Efficiency Alignment of 3D Biotemplated Helices via Rotating Magnetic Field for Terahertz Chiral Metamaterials

AbstractA high‐efficiency strategy is proposed to fabricate helix terahertz metamaterials through the large‐area alignment of 3D microhelices. The Spirulina were used as biotemplates to massively produce 3D magnetic helices by way of nickel electroless deposition. It is noteworthy that the helix angle α, instead of the aspect ratio, determines their magnetizing properties, quite distinct from other magnetic particles. The tight helix (α ˃ ≈55°) can be magnetized along the short axis, and the loose helix (α ˂ ≈55°) along the long axis. Based on this magnetization property, the rotating magnetic field (100 mT, 1 Hz) is introduced to efficiently align the tight helices and control their long axis perpendicular to the rotating plane. This is the first time that the mass alignment of complex 3D microhelices is achieved via a rotating magnetic field, and the programmable alignment of helix‐units, i.e., vertical, horizontal, or hybrid orientation can also be developed. Moreover, the as‐prepared materials with vertical helices exhibit remarkable chirality, and those with horizontal helices show polarization conversion about 20%. These helix metamaterials could be adopted in creating functional photonic devices in THz frequency regime, and the magnetic alignment may open up future possibilities for high‐efficiency fabrication of metamaterials for practical engineering applications.

Twists in ferromagnetic monolayers with trigonal prismatic symmetry

Two-dimensional materials such as graphene or hexagonal boron nitride are indispensable in industry. The recently discovered 2D ferromagnetic materials also promise to be vital for applications. In this work, we develop a phenomenological description of non-centrosymmetric 2D ferromagnets with trigonal prismatic crystal structure. We chose to study this special symmetry group since these materials do break inversion symmetry and therefore, in principle, allow for chiral spin structures such as magnetic helices and skyrmions. However, unlike all non-centrosymmetric magnets known so far, we show that the symmetry of magnetic trigonal prismatic monolayers neither allow for an internal relativistic Dzyaloshinskii-Moriya interaction (DMI) nor a reactive spin-orbit torque. We demonstrate that the DMI only becomes important at the boundaries, where it modifies the boundary conditions of the magnetization and leads to a helical equilibrium state with a helical wavevector that is inherently linked to the internal spin orientation. Furthermore, we find that the helical wavevector can be electrically manipulated via dissipative spin-torque mechanisms. Our results reveal that 2D magnets offer a large potential for unexplored magnetic effects.

Winding Up Quantum Spin Helices: How Avoided Level Crossings Exile Classical Topological Protection.

A magnetic helix can be wound into a classical Heisenberg chain by fixing one end while rotating the other one. We show that in quantum Heisenberg chains of finite length, the magnetization slips back to the trivial state beyond a finite turning angle. Avoided level crossings thus undermine classical topological protection. Yet, for special values of the axial Heisenberg anisotropy, stable spin helices form again, which are nonlocally entangled. Away from these sweet spots, spin helices can be stabilized dynamically or by dissipation. For half-integer spin chains of odd length, a spin slippage state and its Kramers partner define a qubit with a nontrivial Berry connection.

The Helical Magnet MnSi: Skyrmions and Magnons

Since the late 1970s, MnSi has played a major role in developing the theory of helical magnets in non-centrosymmetric materials showing the Dzyaloshinsky-Moriya interaction (DMI). With a long helimagnetic pitch of 175 Å as compared to the lattice d-spacing of 4.55 Å, it was ideal for performing neutron studies, especially as large single crystals could be grown. A (B-T)-phase diagram was measured, and in these studies, under the application of a field of about 180 mT perpendicular to the scattering vector Q, a so-called A-phase in the B-T phase diagram was found and first interpreted as a re-orientation of the magnetic helix. After the surprising discovery of the skyrmion lattice in the A-phase in 2009, much interest arose due to the rigidity of the skyrmionic lattice, which is only loosely bound to the crystal lattice, and therefore only relatively small current densities can already induce a motion of this lattice. A very interesting approach to even better understand the complex structures in the phase diagram is to measure and model the spin excitations in MnSi. As the helimagnetic state is characterized by a long pitch of about 175 Å, the associated characteristic excitations form a band structure due to Umklapp scattering and can only be observed at very small Q with energies below 1 meV. Similarly, the excitations of the skyrmion lattice are very soft and low-energetic. We investigated the magnons in MnSi in the whole (B,T)-phase diagram starting in the single-k helimagnetic state by applying a small magnetic field, B = 100 mT. This way, the complexity of the magnon spectrum is significantly reduced, allowing for a detailed comparison of the data with theory, resulting in a full theoretical understanding of the spin system of MnSi in all its different magnetic phases.

Linear magnetic susceptibility of a finite XY chain model with magnetic helices as metastable states

Abstract A finite-size ferromagnetic chain of classical XY spins, where each of the two edge spins is exchange-coupled to a fictitious fully-pinned spin, is investigated in the presence of a weak in-plane perturbation (external magnetic field or uniaxial anisotropy). Within a macrospin approximation, the above chain model can be representative of a soft ferromagnetic film consisting of N parallel atomic layers, sandwiched between two magnetically hard films. In zero field, the model has a ferromagnetic collinear ground state and admits a class of metastable helical states containing an integer number of twists. Analytical expressions are obtained for the linear corrections to the helical magnetic configuration and for the local magnetic susceptibility tensor. The dependence of the integral susceptibility of the chain, χ , on the number of spins in the chain, N, is also calculated. It is found that χ ∝ N 3 for small values of the helix mode ( m ≪ N ), while χ ∝ N 2 for large values of the helix mode ( m ≈ N + 1 4 ).

3D-Spatial encoding with permanent magnets for ultra-low field magnetic resonance imaging

We describe with a theoretical and numerical analysis the use of small permanent magnets moving along prescribed helical paths for 3D spatial encoding and imaging without sample adjustment in ultra-low field magnetic resonance imaging (ULF-MRI). With our developed method the optimal magnet path and orientation for a given encoding magnet number and instrument architecture can be determined. As a proof-of-concept, we studied simple helical magnet paths and lengths for one and two encoding magnets to evaluate the imaging efficiency for a mechanically operated ULF-MRI instrument with permanent magnets. We demonstrate that a single encoding magnet moving around the sample in a single revolution suffices for the generation of a 3D image by back projection.

Precipitating ordered skyrmion lattices from helical spaghetti and granular powders

Magnetic skyrmions have been the focus of intense research due to their potential applications in ultra-high density data and logic technologies, as well as for the unique physics arising from their antisymmetric exchange term and topological protections. In this work we prepare a chiral jammed state in chemically disordered (Fe, Co)Si consisting of a combination of randomly-oriented magnetic helices, labyrinth domains, rotationally disordered skyrmion lattices and/or isolated skyrmions. Using small angle neutron scattering, (SANS) we demonstrate a symmetry-breaking magnetic field sequence which disentangles the jammed state, resulting in an ordered, oriented skyrmion lattice. The same field sequence was performed on a sample of powdered Cu2OSeO3 and again yields an ordered, oriented skyrmion lattice, despite relatively non-interacting nature of the grains. Micromagnetic simulations confirm the promotion of a preferred skyrmion lattice orientation after field treatment, independent of the initial configuration, suggesting this effect may be universally applicable. Energetics extracted from the simulations suggest that approaching a magnetic hard axis causes the moments to diverge away from the magnetic field, increasing the Dzyaloshinskii-Moriya energy, followed subsequently by a lattice re-orientation. The ability to facilitate an emergent ordered magnetic lattice with long-range orientation in a variety of materials despite overwhelming internal disorder enables the study of skyrmions even in imperfect powdered or polycrystalline systems and greatly improves the ability to rapidly screen candidate skyrmion materials.

Linear hexanuclear helical dysprosium single-molecule magnets: the effect of axial substitution on magnetic interactions and relaxation dynamics.

The reaction between the rigid Schiff-base ligand H4L ([3,6-bis(2-hydroxy-3-methoxybenzylidene)hydrazinecarbonyl]-pyridazine) and different dysprosium(iii) salts afforded two new linear hexanuclear helical clusters, [Dy6L3(SCN)6(DMF)8]·4DMF (1), and [Dy6L3(NO3)6(DMF)4(H2O)2]·8DMF (2), which possess a similar Dy6 core with [Dy6L3(PhCOO)6(CH3OH)6]·11CH3OH·H2O (3). Modulation of the axial ligands around DyIII sites causes different coordination geometries and magnetic interactions, resulting in distinct magnetic relaxation behaviors. Compounds 1 and 2 show typical single-molecule magnet (SMM) properties with effective barriers (Ueff) of 15 and 68 K, respectively, which could greatly profit from strong ferromagnetic interactions compared with compound 3. Presence of a hula-hoop-like geometry of the DyIII ions and stronger ferromagnetic interactions results in better SMM performance of compound 2 than that of 1.

Non-collinear magnetism and electronic transport of boron or nitrogen doped zigzag graphene nanoribbon

Zigzag graphene nanoribbon (ZGNR) is important for novel carbon-based spintronic applications. Currently, most of ZGNR spintronic studies focus on the collinear magnetism where the up-spin and down-spin are separated clearly. But in some cases, e.g. doping and adsorption, the magnetization profile can be modulated and thus noncollinear magnetism can occur. In order to shed light on possible noncollinear magnetism in ZGNR, we study non-collinear magnetism and electronic transport of boron or nitrogen-doped zigzag graphene nanoribbon based on noncollinear density functional theory and non-equilibrium Green's function method. For pristine ZGNR, our results show that the ZGNR presents helical magnetization distribution due to noncollinear magnetization in left and right lead. As the ZGNR is doped with boron and nitrogen atoms, the ZGNR shows a characteristic two-zone feature in the magnetization distribution. Near the dopant site, the magnetic moment of carbon atom is small. However, the magnetic moments of carbon atoms in the left (right) region of dopant are close to those of the left (right) lead. Such a feature provides the possibility of constructing domain walls with various widths on the edge of ZGNR. Moreover, the transmission at the Fermi level (<i>E</i> = 0 eV) decreases with the increase of relative angle between magnetizations of left and right lead, indicating that the spin-flip scattering dominates the electronic transport. However, at <i>E</i> = ±0.65 eV, there is a transmission dip with low transmission, which implies that the dopant induces the strong backscattering. To understand the origin of this dip, we calculate the density of states (DOS) and project the DOS onto each atom of doped ZGNR. The projected DOS shows a large and broad peak at <i>E</i> = −0.65 eV for N-doped ZGNR but at <i>E</i> = +0.65 eV for B-doped ZGNR. The consistency between the position of dip in transmission and the position of peak in DOS indicates that the transmission dip mentioned above is attributed to strong backscattering from the dopant-induced bound state. Our theoretical results are expected to be useful for understanding the noncollinear magnetism and spin scattering in the doped ZGNR-based devices. Also, our work provides a considerable insight into the design of ZGNR-based nanoelectronic devices, such as the transistor based on spin transfer torque effect.

Helical magnetism in Sr-doped CaMn7O12 films

Noncollinear magnetism can play an important role in multiferroic materials but is relatively understudied in oxide heterostructures compared to their bulk counterparts. Using variable temperature magnetometry and neutron diffraction, we demonstrate the presence of helical magnetic ordering in $\mathrm{CaM}{\mathrm{n}}_{7}{\mathrm{O}}_{12}$ and $\mathrm{C}{\mathrm{a}}_{1\ensuremath{-}x}\mathrm{S}{\mathrm{r}}_{x}\mathrm{M}{\mathrm{n}}_{7}{\mathrm{O}}_{12}$ (for $x$ up to 0.51) thin films. Consistent with bulk $\mathrm{C}{\mathrm{a}}_{1\ensuremath{-}x}\mathrm{S}{\mathrm{r}}_{x}\mathrm{M}{\mathrm{n}}_{7}{\mathrm{O}}_{12}$, the net magnetization increases with Sr doping. Neutron diffraction confirms that the helical magnetic structure remains incommensurate at all values of $x$, while the fundamental magnetic wavevector increases upon Sr substitution. This result demonstrates a chemical-based approach for tuning helical magnetism in quadruple perovskite films and enables future studies of strain and interfacial effects on helimagnetism in oxide heterostructures.

Polarization and QPOs from jets in black hole systems

The historical observations of polarized jet emission for Blazars are reviewed and previous models are discussed. Motivated by this, a model for polarization of both steady and transient behavior using a helical magnetic field is presented. The variety of observed correlations and anti-correlations between the electric polarization angle, the degree of polarization and optical flux can be explained by this model. In addition, the phenomena of quasi-periodic oscillations (QPO) behavior seen in jets in X-ray Binaries (XRBs) is also explained by a model based on helical trajectories of emitting blobs and the resulting time scales and harmonics of the QPO are derived. In both the models, the input parameters are the inclination angle, the Lorentz factor of the jet and pitch angle of the magnetic helix.

Chirality selective spin interactions mediated by the moving superconducting condensate

We show that superconducting correlations in the presence of non-zero condensate velocity can mediate the peculiar interaction between localized spins that breaks the global inversion symmetry of magnetic moments. The proposed interaction mechanism is capable of removing fundamental degeneracies between topologically distinct magnetic textures. For the generic system of three magnetic impurities in the current-carrying superconductor we find the energy term proportional to spin chirality. In realistic superconductor/ferromagnetic/superconductor setups we reveal significant energy differences between various magnetic textures with opposite chiralities. We calculate Josephson energies of junctions through left and right-handed magnetic helices as well as through the magnetic skyrmions with opposite topological charges. Relative energy shifts between otherwise degenerate magnetic textures in these setups are regulated by the externally controlled Josephson phase difference. The suggested low-dissipative manipulation with the skyrmion position in a racetrack geometry can be used for the advanced spintronics applications.

Unravelling Incommensurate Magnetism and Its Emergence in Iron-Based Superconductors

We focus on a broad class of tetragonal itinerant systems sharing a tendency towards the spontaneous formation of incommensurate magnetism with ordering wavevectors $\mathbf{Q}_{1,2}=(\pi-\delta,0)/(0,\pi-\delta)$ or $\mathbf{Q}_{1,2}=(\pi,\delta)/(-\delta,\pi)$. Employing a Landau approach, we obtain the generic magnetic phase diagram and identify the leading instabilities near the paramagnetic-magnetic transition. Nine distinct magnetic phases exist that either preserve or violate the assumed $C_4$-symmetry of the paramagnetic phase. These are single- and double-$\mathbf{Q}$ phases consisting of magnetic stripes, helices and whirls, either in an individual or coexisting manner. These nine phases can be experimentally distinguished by polarized neutron scattering, or, for example, by combining measurements of the induced charge order and magnetoelectric coupling. Within two representative five-orbital models, suitable for BaFe$_2$As$_2$ and LaFeAsO, we find that the incommensurate magnetic phases discussed here are accessible in iron-based superconductors. Our investigation unveils a set of potential candidates for the unidentified $C_2$-symmetric magnetic phase that was recently observed in Ba$_{1-x}$Na$_x$Fe$_{2}$As$_{2}$. Among the phases stabilized we find a spin-whirl crystal, which is a textured magnetic $C_4$-symmetric phase. The possible experimental observation of textured magnetic orders in iron-based superconductor, opens new directions for realizing intrinsic topological superconductors.

Emergentc-axis magnetic helix in manganite-nickelate superlattices

The nature of the magnetic order in (La2/3Sr1/3MnO3)9/(LaNiO3)3 superlattices is investigated using x-ray resonant magnetic reflectometry. We observe a new c-axis magnetic helix state in the (LaNiO3)3 layers that had never been reported in nickelates, and which mediates the ~130deg magnetic coupling between the ferromagnetic (La2/3Sr1/3MnO3)9 layers, illustrating the power of x-rays for discovering the magnetic state of complex oxide interfaces. Resonant inelastic x-ray scattering and x-ray absorption spectroscopy show that Ni-O ligand hole states from bulk LaNiO3 are mostly filled due to interfacial electron transfer from Mn, driving the Ni orbitals closer to an atomic-like 3d8 configuration. We discuss the constraints imposed by this electronic configuration to the microscopic origin of the observed magnetic structure. The presence of a magnetic helix in (La2/3Sr1/3MnO3)9/(LaNiO3)3 is crucial for modeling the potential spintronic functionality of this system and may be important for designing emergent magnetism in novel devices in general.

Topological Defects in Helical Magnets

Helical magnets which violated space inversion symmetry have rather peculiar topological defects. In isotropic helical magnets with exchange and Dzyaloshinskii-Moriya interactions there are only three types of linear defects: $\pm\pi$ and $2\pi$-disclinations. Weak crystal anysotropy suppresses linear defects on large scale. Instead planar defects appear: domain walls that separate domains with different preferential directions of helical wave vectors. The appearance of such domain walls in the bulk helical magnets and some of their properties were predicted in the work \cite{Li 2012}. In a recent work by an international team of experimenters and theorists \cite{Schoenherr 2018} the existence of new types of domain walls on crystal faces of helical magnet FeGe was discovered. They have many features predicted by theory \cite{Li 2012}, but display also unexpected properties, one of them is the possibility of arbitrary angle between helical wave vectors. Depending on this angle the domain walls observed in \cite{Schoenherr 2018} can be divided in two classes: smooth and zig-zag. This article contains a mini-review of the existing theory and experiment. It also contains new results that explain why in a system with continuos orientation of helical wave vectors domain walls are possible. We discuss why and at what conditions smooth and zig-zag domain walls appear, analyze spin textures associated with helical domain walls and find the dependence of their width on angle between helical wave vectors.

Induced energy gap in finite-sized superconductor/ferromagnet hybrids

We theoretically study self-consistent proximity effects in finite-sized systems consisting of ferromagnet ($\rm F$) layers coupled to an $s$-wave superconductor ($\rm S$). We consider both $\rm SF_1F_2$ and $\rm SH$ nanostructures, where the $\rm F_1 F_2$ bilayers are uniformly magnetized, and the ferromagnetic $\rm H$ layer possesses a helical magnetization profile. We find that when the $\rm F_1 F_2$ layers are weakly ferromagnetic, a hard gap can emerge when the relative magnetization directions are rotated from parallel to antiparallel. Moreover, the gap is most prominent when the thicknesses of $\rm F_1$ and $\rm F_2$ satisfy $\rm d_{F1}\leq d_{F2}$, respectively. For the $\rm SH$ configuration, increasing the spatial rotation period of the exchange field can enhance the induced hard gap. Our investigations reveal that the origin of these findings can be correlated with the propagation of quasiparticles with wavevectors directed along the interface. To further clarify the source of the induced energy gap, we also examine the spatial and energy resolved density of states, as well as the spin-singlet, and spin-triplet superconducting correlations, using experimentally accessible parameter values. Our findings can be beneficial for designing magnetic hybrid structures where a tunable superconducting hard gap is needed.

Magnetic properties of perovskite Ca1−xSrxFeO3

We synthesized Ca1−xSrxFeO3 containing tetravalent iron Fe4+ with high valence by low temperature heat treatment along with ozone oxidization. We investigated the magnetic properties of perovskite Ca1−xSrxFeO3. The charge disproportionation transition temperature (TCD) of Ca1−xSrxFeO3 was observed from x = 0.0 to 0.6 in the magnetic susceptibility measurements. The decrease in TCD occurs is attributed to deformation of the crystal structure. The metamagnetic transitions with hysteresis were observed in the magnetization curves of all the compositions. The metamagnetic behavior is due to helical magnetism, which means that there are intermediate stable states before magnetization is saturated. In the Sr-rich region with x = 0.8 and 1.0, the saturation magnetization shows forced ferromagnetic order with a value of ∼3.2 μB at high magnetic field, H ∼ 60 T.

Magnetic coupling in Mn3O4-coated γ-MnOOH nanowires

Mn3O4-coated γ-MnOOH nanowires were synthesized by using the hydrothermal method. X-ray diffraction and transmission electron microscopy studies reveal that the nanowires have a core (γ-MnOOH)–shell (Mn3O4) structure. The magnetic transition temperature of Mn3O4 is slightly lower than the previously reported value because of the increased thermal disturbance for nanomaterials and the influence of the helical magnetism of γ-MnOOH. The hysteresis loop at 50 K keeps the same shape as was measured below the Néel temperature of Mn3O4 because of the short-range order of γ-MnOOH above the transition temperature. The short-range ordering is responsible for the deviation of the hysteresis loop at 300 K from the linear behavior of a normal paramagnetic phase. The magnetic coupling behavior between Mn3O4 and γ-MnOOH also induces an exchange bias effect in the system. The hysteresis loop shifts to the positive direction with increasing measurement temperature. A lower barrier energy is requested for the reversal of magnetic moments on the interface to generate the exchange bias behavior because of the asymmetric magnetic natures of Mn3O4 and γ-MnOOH, which should possess shorter responsive time compared with the traditional antiferromagnetic-ferromagnetic coupling induced exchange bias systems.

Evolution of Magnetic Double Helix and Quantum Criticality near a Dome of Superconductivity in CrAs

At ambient pressure CrAs undergoes a first-order transition into a double-helical magnetic state at TN = 265 K, which is accompanied by a structural transition. The recent discovery of pressure-induced superconductivity in CrAs makes it important to clarify the nature of quantum phase transitions out of its coupled structural/helimagnetic order. Here we show, via neutron diffraction on the single-crystal CrAs under hydrostatic pressure (P), that the combined order is suppressed at Pc ~ 10 kbar, near which bulk superconductivity develops with a maximal transition temperature Tc ~ 2 K. We further show that the coupled order is also completely suppressed by phosphorus doping in CrAs1-xPx at a critical xc ~ 0.05, above which inelastic neutron scattering evidenced persistent antiferromagnetic correlations, providing a possible link between magnetism and superconductivity. In line with the presence of antiferromagnetic fluctuations near Pc (xc), the A coefficient of the quadratic temperature dependence of resistivity exhibits a dramatic enhancement as P (x) approaches Pc (xc), around which Res(T) has a non-Fermi-liquid form. Accordingly, the electronic specific-heat coefficient of CrAs1-xPx peaks out around xc. These properties provide clear evidences for quantum criticality, which we interpret as originating from a nearly second-order helimagnetic quantum phase transition that is concomitant with a first-order structural transition. Our findings in CrAs highlight the distinct characteristics of quantum criticality in bad metals, thereby bringing out new insights into the physics of unconventional superconductivity such as occurring in the high-Tc iron pnictides.

Time-resolved velocity of a domain wall in a magnetic microwire

The dynamic process of nucleation, propagation, and braking of a single domain wall (DW) has been systematically determined in a Fe-based magnetostrictive microwire under an applied axial magnetic field. While in previous reports the Sixtus-Tonks experiments have provided partial information on the process (i.e., the average velocity), in the present study we report on the instantaneous processes involved in the propagation of the DW, as well as the transient process during the DW depinning. The experimental measurements were carried out using the spontaneous Matteucci effect induced during DW propagation due to the small helical magnetization component created during the fabrication process.