Helical Spin Configuration Research Articles

Weyl metallic state induced by helical magnetic order

In the rapidly expanding field of topological materials there is growing interest in systems whose topological electronic band features can be induced or controlled by magnetism. Magnetic Weyl semimetals, which contain linear band crossings near the Fermi level, are of particular interest owing to their exotic charge and spin transport properties. Up to now, the majority of magnetic Weyl semimetals have been realized in ferro- or ferrimagnetically ordered compounds, but a disadvantage of these materials for practical use is their stray magnetic field which limits the minimum size of devices. Here we show that Weyl nodes can be induced by a helical spin configuration, in which the magnetization is fully compensated. Using a combination of neutron diffraction and resonant elastic x-ray scattering, we find that below TN = 14.5 K the Eu spins in EuCuAs develop a planar helical structure which induces two quadratic Weyl nodes with Chern numbers C = ±2 at the A point in the Brillouin zone.

Exchange coupling at the interface of antiferromagnet and rare-earth bilayers

Helical or non-collinear structures in rare-earth (RE) when topologically stable, can form the basis of realizing all-spin-based technology. Strong coupling at the ferromagnet (FM)-RE interface, reported earlier, originates from the number of irreversible spins owing to the imbalance in the non-collinear configuration within the RE layer. Here, we explore the exchange coupling between an antiferromagnet (AF) and a rare-earth (RE) i.e. within Mn3Ir//Dy bilayers for two different Dy thicknesses. A frustrated inter-domain magnetic interaction at the exchange-coupled interfaces of AF–RE specimen with the thicker Dy layer leads to a coexistence of spin-freezing like ordering around the temperature range where the helical spin configuration is expected to be established. Due to the small number of irreversible spins within the RE, the corresponding interfacial coupling around the temperature range of the helical phase remains weak leading to minimal exchange bias field irrespective of the Dy thickness.

The in-plane spin helicity of coplanar helical spin configurations of frustrated single trimer V3 and Cu3 nanomagnets, inversion (switching) of spin helicity

The in-plane spin helicities of coplanar non-collinear spin configurations of frustrated spin states of the single trimer V3 and Cu3 molecular nanomagnets with the Dzialoshinsky-Moriya (DM) coupling in transverse magnetic fields are considered. Spin operators of the in-plane helicity were proposed. These operators provide the quantum numbers of the in-plane spin helicity, which characterize helicities of all classical coplanar 120° helical spin configurations and distinguish helical configurations of the same vector chirality. The in-plane spin helicity depends on direction and strength of transverse magnetic field. The increase of the field strength leads to the non-linear reduction of magnitude of the spin helicity of spin configurations correlated with their energy, magnetizations and vector chirality. The in-plane spin helicity is inverse proportional to the energy; the decrease of helicity correlates with an increase of magnetization. Spin helicity of distorted DM trimers was considered, distortions result in reduction of magnitude of the spin helicity of deformed coplanar helical spin configurations. The in-plane spin helicity of coplanar helical spin configurations in the ground state demonstrates the field- and deformation- induced inversion (switching) that can be used in applications of the spin helicity in molecular devices.

Detection of in-depth helical spin structures by planar Hall effect

We developed a method to determine the magnetic helicity and to study reversal mechanisms in exchange biased nanostructures using Planar Hall Effect (PHE). As a test case, we use an in-depth helical spin configuration that occurs during magnetization reversal in exchange coupled Ni/FeF2 heterostructures. We show the way to induce and determine the sign of the helicity from PHE measurements on a lithographically patterned cross. The helicity sign can be controlled by the angle between the externally applied magnetic field and a well-defined unidirectional anisotropy axis. Furthermore, the PHE signal reveals complex reversal features due to small deviations of the local unidirectional anisotropy axes from the crystallographic easy axis. The simulations using an incomplete domain wall model are in excellent agreement with the experimental data. These studies show that helical spin formations in nanomagnetic systems can be studied using laboratory-based magnetotransport.

Relationship between ferroelectricity and Dzyaloshinskii-Moriya interaction in multiferroics and the effect of bond-bending

We studied the microscopic mechanism of multiferroics, in particular, with the ``spin current'' model [H. Katsura et al., Phys. Rev. Lett. 95, 057205 (2005)]. Starting from a system with helical spin configuration, we solved for the forms of the electron wave functions and analyzed their characteristics. The relation between ferroelectricity and Dzyaloshinskii-Moriya interaction [I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958) and T. Moriya, Phys. Rev. 120, 91 (1960)] is clearly established. There is also a simple relation between the electric polarization and the wave vector of magnetic orders. Finally, we show that the bond-bending existing in transition metal oxides can enhance ferroelectricity.

Creation of Helical Vortices during Magnetization of Aligned Carbon Nanotubes Filled with Fe: Theory and Experiment

We report a novel magnetic phenomenon consisting of the formation of helical spin configurations during the magnetization of densely packed ferromagnetic nanowires encapsulated inside carbon nanotubes. We studied the hysteresis loops when the magnetic fields are applied parallel and perpendicular to the nanotubes axes. We also performed theoretical calculations on aligned nanowire arrays that clearly indicate the creation of helical spin vortices in the hysteresis loops. The latter are caused by the presence of strong dipolar interactions among neighboring wires.

Coexisting ferro- and helimagnetism in Dy/Y superlattices

Neutron diffraction studies on Dy/Y superlattices grown with the c axis at an angle of approximately 35° to the film plane reveal a coexistence of helical antiferromagnetic order and ferromagnetic order. The coexistence of magnetic phases has been determined to arise from the development during growth of surface facets of the Y buffer layer, which was grown on bcc (211) Ta or Nb substrates. One of the superlattice facets produces an isotropic expansion of the Dy basal plane which favors the helical antiferromagnetic spin configuration, while the other facet causes an anisotropic contraction of the Dy basal plane that favors ferromagnetism. The net result of the growth anomaly is the apparent coexistence of the two magnetic states as observed by neutron scans made with the scattering vector oriented parallel to the nominal c crystal axis of the superlattice.

Magnetic properties of SrFe 1- xCo xO 3

Magnetic and neutron diffraction measurements have been made on the cubic perovskite-type SrFe 1- x Co x x O 3. These oxides exhibit a helical spin configuration for 0 ⩽ x ≤ 0.1 and ferromagnetism for 0.2 ≤ x ⩽ 1. The results obtained indicate that Fe 4+ ions are nearly in a high-spin state.

Mössbauer study of the magnetic structure of FeP

The compound FeP shows, at low temperatures and in zero external magnetic field, a helical spin configuration for iron with a propagation vector along the c-axis as deduced from neutron diffraction studies. We have performed 57Fe Mössbauer measurements in the temperature interval between 295 K and 4.2 K and in an external magnetic field on both powder specimen and single crystals of FeP. The results show a nearly temperature independent electric quadrupole interaction strength eQVzz of 1.34 mm/s and a Néel temperature of 115 K. It was, however, impossible to fit the Mössbauer spectra below TN using a simple double spiral model. Instead a bunched spiral model with the spins crowded along the a-axis gave very good fits. The magnetic hyperfine field was furthermore found to be modulated in the ab-plane. The maximum field of +3.6 T was found along the a-direction while the overall field, presumably spread over all other directions, was 0.2 T. The measurements in external magnetic field showed that the grains become partially oriented with the basal plane parallel to the external field.

Applications of the coherent state representation in the theory of magnetism: II. Helical spin configurations

In a previous paper, the coherent state representation of spin wave states was used to derive the low temperature expansion for the free energy of the Heisenberg model of a ferromagnet. In this paper, the same formalism is applied to anisotropic systems which are usually described semiclassically. The coherent state parameters are shown to be ideally suited for describing certain of the resulting helical spin configurations. The coherent state approach emphasizes the analogy of these states to superfluid boson systems. A model spin Hamiltonian appropriate to Erbium is chosen and discussed in this light. In particular, the transition in a transverse magnetic field from the ground state cone configuration to a fan configuration, the stability and possible metastability of these states and the fluctuations about them are investigated. Numerical estimates show at least qualitative agreement with experiment.

Dynamical Susceptibility in a Simple Helical Spin System

Magnetic behavior of the system with a helical spin structure is studied. Hubbard's Hamiltonian is transformed using new operators which indicate that the spin quantization axis at each lattice site is canted with an order of the helical spin configuration. The dynamical transverse susceptibility is studied by means of the double-time two-particle Green function. The equation of motion of this Green function is truncated by RPA decoupling principle. In the ferromagnetic limit, the result is reduced to the well-known one derived by Izuyama, Kim and Kubo. Collective excitation spectra of this system are obtained from χ-1-+(q, Q, ω) = 0 both in the narrow-band (large-gap parameter) approximation and in the wide-band (small gap parameter) approximation. In the itinerant antiferromagnetism, the result is reduced to the sound-like dispersion relation “\hbarω∝qA(Q)” in general. In the ferromagnetic limit (Q →0), the well-known spin wave spectrum “\hbarω∝q2·B(Q)” is also obtained.

Mixed crystals between binary sulphides or selenides with spinel structure

The miscibility between two binary sulphides (selenides) with spinel structure is investigated by means of X-ray diffraction data and measurements of the magnetic properties. In all cases studied (Table 2) a large miscibility is found except for MeCr 2Se 4-CuCr 2Se 4 (Me = Zn, Cd, Hg), Co 3S 4-CuCr 2S 4 and Co 3S 4-CoRh 2S 4. The electrical conduction in Me 1− x Cu x Cr 2Se 4 [(Me = Zn, Cd, Hg) and some magnetic quantities of CoRh 2− x Cr xS 4 and Zn 1− x Cd xCr 2Se 4 are measured. The replacement of a small amount of Me by Cu in MeCr 2Se 4 causes a considerable lowering of the resistivity, which is attributed to the presence of monovalent copper. In CoRh 2− x Cr x S 4 the change from ferrimagnetic CoCr 2S 4 to antiferromagnetic CoRh 2S 4 takes place via Néel's coupling scheme for x #62; 1.65 and Yafet-Kittels' triangular configuration for x < 1.65. In CoRh 1.75Cr 0.25S 4 a transition from the ferrimagnetic to the paramagnetic state occurs via an antiferromagnetic state. In Zn 1− x Cd xCr 2Se 4 the change from a helical spin configuration in ZnCr 2Se 4 to ferromagnetic CdCr 2Se 4 is discussed on the basis of positive CrSeCr and negative CrSeSeCr interactions, use being made of our own measurements and data given in the literature.

On the antiferromagnetism of ZnCr 2Se 4

ZnCr 2Se 4 has a helical spin configuration at low temperatures; the asymptotic Curie temperature is positive (115°K). These properties are explained by the presence of positive CrSeCr and negative CrSeSeCr interactions, which are calculated using Weiss-field approximation. The magnetization is measured as a function of the field at 4.2°K and it is shown that the initial susceptibility agrees with the interactions evaluated.

The magnetoelastic behaviour of antiferromagnets having helical spin configurations

The magnetoelastic behaviour of antiferromagnetic substances possessing a helical spin system has been investigated. It is shown that all magnetoelastic phenomena arise from two distinct effects, termed the anisotropy and exchange magnetostrictions. Equations governing the magnetostriction of single and polycrystals as a function of external field strength have been obtained. The behaviour of a helical spin system in the presence of an axial tension leads to a stress dependence of the ferromagnetic-antiferromagnetic transition temperature. It also leads to the ΔE effect. Recent measurements of the crystal distortion and magnetostriction in dysprosium crystals are analysed and it is shown that at low temperatures both measurements yield the same information. An estimate of the twofold and sixfold magnetostriction constants in the basal plane of dysprosium has been evaluated at 20 °K. The experimental magnetostriction-field data for dysprosium at 144 °K are in good agreement with the predicted behaviour, and the characteristic feature of the magnetostriction of a helical spin system, namely the appearance of a strain along the c axis when a field is applied wholly within the basal plane, is correctly anticipated. The behaviour of holmium is similar, but is complicated by the large hexagonal anisotropy.

THE MAGNETIC STRUCTURES OF CRYSTALS WITH MAGNETIC UNIT CELL UN-IDENTICAL WITH ITS CHEMICAL UNIT CELL

In this work a phenomenological method is developed for the determination of spin configurations of magnetic crystals with a magnetic unit cell un-identical with its chemical unit cell. A finite group, formed of those elements of the space group which are distributed within a magnetic unit cell, is introduced. The expansion of the thermo-dynamic potential in terms of sublattice spin densities is constructed according to the principle that it should be invariant when symmetry operations of the above mentioned group are applied on sublattice spin densities separately. Spin configurations of magnetic crystals are then determined from the minimum condition of thermodynamic potential.With the above method, we have discussed the spin configurations of magnetic crystals of four different types. In each case, the results obtained are consistent with those of neutron diffraction experiments. Under certain conditions the existence of helical spin configuration may also be accounted for with the aid of this method.

Thermal Variation of the Pitch of Helical Spin Configurations

Thermal Variation of the Pitch of Helical Spin Configurations

Magnetization Process of a Helical Spin Configuration

The behavior of a helical spin configuration of a hexagonal crystal in an applied field is discussed for the case where the axis of the helix is identical with the hexagonal c axis and the magnetization vector in each layer is parallel to the basal plane. In a small field applied parallel to the basal plane, a slight deformation of the helix occurs resulting in a small increase in over-all magnetization. If the field surpasses a certain critical value, the helix changes abruptly into a state with high resulting magnetization. In this state the spin directions are oscillating about the direction of the applied field, the magnetization being about 85% of the saturation value. In still higher fields, saturation is reached completely. A helical spin configuration has been found in MnAu2 by Herpin,Mériel, and Villain. We have investigated the properties of the hexagonal oxide (Ba,Sr)2Zn2Fe12O22 which is of the Y-type. The Ba-rich composition is ferrimagnetic and has a preferential plane for the magnetization at all temperatures. The Sr-rich composition has no spontaneous magnetization, but a magnetization equal to the one in the Ba case can easily be induced by an applied field. This behavior can be explained by the assumption of a helical spin configuration. As an other example, we show that the magnetic properties of dysprosium as investigated by Behrendt,Legvold, and Spedding can be explained by assuming a helical spin configuration between 85°K and 178°K. The angle between two neighboring layers is equal to zero at 85°K, the ferromagneticCurie temperature, and increases at higher temperatures. The magnetization process mentioned above is modified slightly in dysprosium by the presence of a strong magnetic anisotropy in the plane. In the presence of this anisotropy the transition between the ferromagnetic state and the helical state turns out to be a first-order transition, which explains the observed specific heat.

Spin configuration and magnetization process in dysprosium

It is shown that the properties of dysprosium can be unambiguously explained by assuming a helical spin configuration. A proposal is given for the spin structure from 85 to 178.5 deg K, which is developed to show the transition from the ferromagnetic state to a helical state with a finite angle alpha /sub 0/ for the direction of magnetization, consistent with the observed peak found in specific heat data. In a similar approach to the Herpin calculation for the behavior of a helix in a perpendicular magnetic field, it was found that a relative magnetizntion of approximately 5% is attained in the critical field, H/ sub K/. In fields surpassing H/sub K/, saturation is not reached immediately, the relative magnetization being approximately 85% theoretically. Complete saturation takes place in a field of approximately 9/4 H/sub K/. An estimate is given for the characteristic angle of the helical structure, alpha /sub 0/ = approximately l2 deg , for H/sub K/ = 10/sup 3/ Oe. (B.O.G.)