Spiral Spin Order Research Articles

Magnetic evolution from the superparamagnetism in nanospinel chromites Cd1−xCoxCr2O4 (0 ≤ x ≤ 1.0)

Magnetic properties of the spinel-type Cd1−xCoxCr2O4 (0 ≤ x ≤ 1.0) nanocrystals are systematically studied. Complementary results of the inductively coupled plasma optical emission spectroscopy (ICP-OES) and the dispersive X-ray spectroscopy (EDX) indicate cations redistribution with increased Cr concentration from the nanoparticle core to the surface. Powder X-ray diffraction (XRD) reveals an obtained single spinel phase of average crystallite size of 7–10 nm that is in consistence with TEM particle size. The lattice constant exhibits a general decrease by incorporating the smaller Co atoms, however its behavior violates Vegard’s law. An observed kink anomaly in the lattice constant behavior at x ~ 0.4 is attributed to the cations redistribution and further preferred site occupations. Static magnetization and AC susceptibility measurements reveal competitive magnetic phases in the solid solution nanocrystals. A superparamagnetic state of the noninteracting and single domain CdCr2O4 nanoparticles expands first to higher blocking temperatures at x < 0.4 before it evolves to a core collinear ferrimagnetic (FIM) state with coexisting surface spin-glass freezing. The low-temperature core spiral spin orders survive in the FIM phase. A tentative magnetic phase diagram is presented and discussed in a frame of effects of the type and redistribution of cations as well as emergent uncompensated surface spins on the nearest and next nearest neighbor exchanges in chromite nanospinels.

Enhancement of Curie- and spin-spiral temperatures with doping Fe in multiferroic CoCr2O4 nanoparticles

Abstract Multiferroic, CoCr2O4 bulk material undergoes successive magnetic transitions such as paramagnetic to collinear ferrimagnetic state at Curie temperature (TC) and non-collinear spin-spiral ordering temperature TS followed by a lock-in-transition TL. In this paper, the rich sequence of magnetic transitions in CoCr2O4 nanoparticles after doping with iron ions are investigated by varying the concentration from x = 10 to 40%. With increasing iron concentration from 10 to 40%, while TC increases from 102 to 160 K higher than the TC of pure CoCr2O4, TS increases from 26 to 40 K. Later transition is clearly shown by sharp transition in specific heat measurement. While enhancement in TC is attributed to increase in lattice expansion and the exchange interaction between tetrahedral (A) and octahedral (B) sites, spin-spiral ordering is dictated by B-B interaction. Further, we have examined the magnetic transitions through neutron scattering using polarized neutron beam along three orthogonal directions. We observe that the para to ferrimagnetic transition is found to be continuous and the spiral ordering is diffused in nature irrespective of composition.

Magnetic-field-induced incommensurate to collinear spin order transition in NiBr2

The triangular spin lattice of NiBr2 is a canonical example of the frustrated helimagnet that shows a collinear commensurate antiferromagnetic to an incommensurate spin helix phase transition on cooling. Herein, we have studied a self-flux grown NiBr2 single crystal by neutron diffraction and low temperature magnetization measurements at fields up to 14 T. Experimental findings enable the deduction of the driving force responsible for the spin spiral ordering. The neutron diffraction data reveal satellite peaks representing characteristic features of an incommensurate magnetic state. The satellites develop symmetrically below TN=44.0(1)K, replacing the main magnetic reflections. Interestingly, a field-induced incommensurate to commensurate spin phase transition has been successfully demonstrated, which enforces the spin helix to restore the high temperature compensated antiferromagnetic structure. This reorientation can be described by a spin-flop in the (a–b) basal plane of a triangular spin lattice system. The findings offer a novel way for spin helix control of incommensurate phases, having immense scientific and technological implications in the next-generation data storage devices.

Magnetic phase transition and multiferroic phase separation in Ho1-xGdxMnO3

In the orthorhombic (o) RMnO3 compound, it is known that the magnetic state can change from the A-type antiferromagnetic (A-AFM) through a spiral spin order (SSO) into the E-AFM state with the decrease in the R ionic radius (rR). The magnetic phase transition from the E-AFM state to the A-AFM state is expected, but no experimental realization has been reported. In this study, this process in o-Ho1-xGdxMnO3 (x: 0–0.6) is reported. A substitution of Ho with Gd enables the transition of the multiferroic ground state from the E-AFM order (at x ≤ 0.1) to the SSO (at x > 0.4). Accompanied by the quenched disorder, a multiferroic phase separation state is demonstrated in the intermediate composition range of 0.1 < x < 0.4 near the phase boundary between the E-AFM and SSO. This phase-separated state is believed to enhance the ferroelectric polarization and magnetoelectric coupling. Our results demonstrate the dependences of the multiferroic properties of RMnO3 on rR and confirm that the multiferroic phase separation is an effective approach to enhance the multiferroic properties of RMnO3.

Magnetic field-induced ferroelectricity in S\u2009=\u20091/2 kagome staircase compound PbCu3TeO7

Ni3V2O8 is an archetypical multiferroic material with a kagome staircase structure of S = 1 (Ni2+) spins whose complex interplay between spin ordering and ferroelectricity has been studied for more than a decade. Here, we report a new kagome staircase compound PbCu3TeO7 with Cu2+ (S = 1/2) spins that exhibits two Néel temperatures at TN1 = 36 K and TN2 = 24 K, and a magnetic field (H)-induced electric polarization (P) below TN2. Pyroelectric and magnetoelectric current measurements in magnetic fields up to 60 T reveal that for H||c of ~ 8.3 T, a spin-flop transition induces a transverse P||a with a magnitude of 15 µC/m2 below TN2. Furthermore, for a parallel configuration with P//H//a, two spin-flop transitions occur, the first at ~ 16 T with P//a of 14 µC/m2, and the second at ~ 38 T, where P disappears. Monte Carlo simulations based on 12 major exchange interactions uncover that a sinusoidal amplitude modulation of the spins occurs along the b-axis below TN1 and an incommensurate, proper screw-type spin order occurs in the ac-plane below TN2. The simulation results show that P//a under H//c stems from a spin-flop transition facilitating an ab-plane-type spiral order, while the two successive spin-flop transitions for H//a result in spiral spin orders in the ab- and bc-planes. Based on the experimental and theoretical results, we establish field-induced magnetic and electric phase diagrams for the two H directions, demonstrating that the distorted kagome staircase structure with competing intra–interlayer interactions and lifted frustration creates a plethora of different noncollinear spin textures of S = 1/2 spins that in turn induce electric polarization.

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

The electrons in the edge channels of two-dimensional topological insulators can be described as a helical Tomonaga-Luttinger liquid. They couple to nuclear spins embedded in the host materials through the hyperfine interaction, and are therefore subject to elastic spin-flip backscattering on the nuclear spins. We investigate the nuclear-spin-induced edge resistance due to such backscattering by performing a renormalization-group analysis. Remarkably, the effect of this backscattering mechanism is stronger in a helical edge than in nonhelical channels, which are believed to be present in the trivial regime of InAs/GaSb quantum wells. In a system with sufficiently long edges, the disordered nuclear spins lead to an edge resistance which grows exponentially upon lowering the temperature. On the other hand, electrons from the edge states mediate an anisotropic Ruderman-Kittel-Kasuya-Yosida nuclear spin-spin interaction, which induces a spiral nuclear spin order below the transition temperature. We discuss the features of the spiral order, as well as its experimental signatures. In the ordered phase, we identify two backscattering mechanisms, due to charge impurities and magnons. The backscattering on charge impurities is allowed by the internally generated magnetic field, and leads to an Anderson-type localization of the edge states. The magnon-mediated backscattering results in a power-law resistance, which is suppressed at zero temperature. Overall, we find that in a sufficiently long edge the nuclear spins, whether ordered or not, suppress the edge conductance to zero as the temperature approaches zero.

Magnetoelectric and Raman spectroscopic studies of monocrystalline MnCr2O4

MnCr2O4 that exhibits spin frustration and complex spiral spin order is of great interest from both fundamental as well as application-oriented perspectives. Unlike CoCr2O4 whose ground state presents the coexistence of commensurate spiral spin order (CSSO) and ferroelectric order, MnCr2O4 shows no multiferroicity. One reason is that the spiral spin order is highly sensitive to the oxygen concentration in MnCr2O4. Here, we have successfully grown high-quality single-crystalline MnCr2O4 by the chemical vapor transport method. We observe a new first-order magnetic transition from the incommensurate spiral spin order (ICSSO) at 19.4 K to the CSSO at 17.4 K. This magnetic transition is verified by magnetization, specific heat, and magnetoelectric measurements, which also confirm that the ground state exhibits the coexistence of the CSSO and magnetoelectricity below 17.4 K. Interestingly, the temperature evolution of Raman spectra between 5.4 and 300 K suggests that the structure remains the same. We also find that the phase-transition temperature of the CSSO decreases as applied magnetic field increases up to 45 kOe.

Spin-induced ferroelectricity in a triangular-lattice antiferromagnet studied by magnetoelectric coupling tensors

The spin-induced electric polarization in multiferroics with long-period modulated magnetic structure and some polar crystals is difficult to calculate directly due to the modeling limitation or the lack of a reference paraelectric phase. We propose a general method to investigate spin-induced polarization by combining symmetry arguments and first-principles calculations, and demonstrate it in the triangular-lattice delafossite structure. Two special spin models based on the four-sublattice orthorhombic supercell were used to calculate the polarization induced by spin-current and $p\text{\ensuremath{-}}d$ hybridization mechanisms, respectively. All the polarization components appearing in various spiral spin orders can be explained by the two different spin-current mechanisms through analyzing the symmetry of ${\mathbf{S}}_{a}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{b}$ vectors, where ${\mathbf{S}}_{a}$ and ${\mathbf{S}}_{b}$ represents the neighbor spins. We confirm that the $p\text{\ensuremath{-}}d$ hybridization mechanism only plays a minor role in the origins of polarization in addition to causing the $2q$ lattice modulation, where $q$ is the magnetic modulation wave number.

Resonant x-ray scattering reveals possible disappearance of magnetic order under hydrostatic pressure in the Kitaev candidate γ−Li2IrO3

Honeycomb iridates such as $\gamma$-Li$_2$IrO$_3$ are argued to realize Kitaev spin-anisotropic magnetic exchange, along with Heisenberg and possibly other couplings. While systems with pure Kitaev interactions are candidates to realize a quantum spin liquid ground state, in $\gamma$-Li$_2$IrO$_3$ it has been shown that the balance of magnetic interactions leads to the incommensurate spiral spin order at ambient pressure below 38 K. We study the fragility of this state in single crystals of $\gamma$-Li$_2$IrO$_3$ using resonant x-ray scattering (RXS) under applied hydrostatic pressures of up to 3.0 GPa. RXS is a direct probe of the underlying electronic order, and we observe the abrupt disappearance of the $q$=(0.57, 0, 0) spiral order at a critical pressure $P_c = 1.5\ $GPa with no accompanying change in the symmetry of the lattice. This dramatic disappearance is in stark contrast with recent studies of $\beta$-Li$_2$IrO$_3$ that show continuous suppression of the spiral order in magnetic field; under pressure, a new and possibly nonmagnetic ground state emerges.

Dielectric properties of complex magnetic field induced states in PbCuSO4(OH)2

Spin spirals, which coexist with collinear spin order in linarite PbCuSO4(OH)2, indicate electrical polarisation textures of spin-multipolar phases. We derive experimental evidence by a detailed investigation of the magnetic-field dependent dielectric and electric polarization properties at low temperatures. Linarite exhibits a quasi-one-dimensional frustrated S = ½ spin chain, which forms 3D spin-spiral order in zero magnetic field for T < 2.85 K. Recently, due to the monoclinic lattice of linarite with CuO2 ribbon chains, complex magnetic field induced states were found. These spin-multipolar phases, which compete with spin-density waves at low magnetic fields, exist in close vicinity to the transition from the spin spiral into field induced spin polarized state. Via antisymmetric Dzyaloshinskii-Moriya interaction spin-driven ferroelectricity develops in the spin-spirals state. Via electric polarization measurements this allows to prove the transitions into complex magnetic field induced phases. Thorough analyses of the temperature and magnetic field dependent dielectric properties of a naturally grown single crystalline sample provide a detailed (T,H) phase diagrams for the three different crystallographic directions.

Magnetocrystalline interactions in spinel MnCr2O4 single crystal probed by electron spin resonance

Abstract In this work we present a detailed magnetization, electron spin resonance (ESR) and specific capacity study on spinel MnCr2O4 single crystals in an extended temperature range of 5–300 K. The field-induced effect of the magnetization indicates the strong spin-lattice coupling in MnCr2O4 single crystal. The following results are obtained by the ESR investigation: (i) Below 35 K, since the spiral spin order, a driving force of the multiferroic (MF) effect, becomes obvious, the line shape of ESR shows asymmetric characters and the ferromagnetic resonance (FMR) model of Smit and Beljers formulation is invalid; (ii) The temperature dependence of Gilbert damping parameter α, reflecting the strength of the spin-lattice coupling, shows an abnormal behavior due to the local lattice distortion in MnCr2O4 single crystal. And the distortion is a triggering force for the formation of spiral spin order. Moreover, our research helps to understand the origin of the MF effect in MnCr2O4.

The crucial role of Mn spiral spin order in stabilizing the Dy-Mn exchange striction in multiferroic DyMnO3.

DyMnO3 hosts the less addressed duality of multiferroicity, owing to the Dy-Mn exchange striction and inverse Dzyaloshinskii-Moriya interaction between Mn spin pairs. Although the duality in DyMnO3 has been discussed earlier, there remains a question whether the Mn magnetic sublattice is necessarily multiferroic for generating the Dy-Mn exchange striction. In this work, we investigate the multiferroicity of Dy(Mn1-xFex)O3 (0 ≤ x ≤ 0.1) through detailed magnetic and ferroelectric characterization. It is found that Fe-doping continuously suppresses the independent Dy spin order but instead promotes the Dy-Mn(Fe) coupling. This coupling benefits the Dy-Mn(Fe) exchange striction which remarkably enhances the ferroelectric polarization at a low doping level (x ≤ 0.015), beyond which the Mn spiral spin order breaks down leading to collapse of the macroscopic polarization at x ≥ 0.05. This work discloses the crucial role of Mn spiral spin order in stabilizing the Dy-Mn exchange striction and thus highlights the duality of multiferroicity in DyMnO3.

Direct observation of anisotropic magnetic field response of the spin helix in FeGe thin films

Spiral spin orders often produce various fascinating phenomena via interaction with electronic structures. Examples include, but are not limited to, multiferroicity and skyrmion formation. Among them, a deformed spiral spin structure, which can be viewed as a periodic sequence of 2$\ensuremath{\pi}$ spin-rotation kinks, can exhibit the functionality of information transmission owing to its phase coherence. This is the chiral magnetic soliton lattice (CSL). Here, the authors have succeeded in building a spin spiral in a thin film of the chiral magnet FeGe, and revealed its characteristic magnetic responses. Magnetic anisotropy and boundary conditions inherent to the epitaxial thin film secure the alignment of the spiral winding direction along the film normal, even under external magnetic fields. This constraint leads to the anisotropic deformation of the spin spiral with respect to the magnetic field direction. Especially, the CSL, which is realized under an in-plane magnetic field, transforms with field between states with different numbers of kinks. The authors clearly demonstrate the deformation by direct observation of the spiral propagation vector by use of the small-angle neutron scattering technique.

Spiral magnetic order and pressure-induced superconductivity in transition metal compounds

Magnetic and superconducting ground states can compete, cooperate and coexist. MnP provides a compelling and potentially generalizable example of a material where superconductivity and magnetism may be intertwined. Using a synchrotron-based non-resonant X-ray magnetic diffraction technique, we reveal a spiral spin order in MnP and trace its pressure evolution towards superconducting order via measurements in a diamond anvil cell. Judging from the magnetostriction, ordered moments vanish at the quantum phase transition as pressure increases the electron kinetic energy. Spins remain local in the disordered phase, and the promotion of superconductivity is likely to emerge from an enhanced coupling to residual spiral spin fluctuations and their concomitant suppression of phonon-mediated superconductivity. As the pitch of the spiral order varies across the 3d transition metal compounds in the MnP family, the magnetic ground state switches between antiferromagnet and ferromagnet, providing an additional tuning parameter in probing spin-fluctuation-induced superconductivity.

Photocreating supercooled spiral-spin states in a multiferroic manganite

We demonstrate that dynamics of the ab-spiral-spin order in a magnetoelectric multiferroic Eu0.55Y0.45MnO3 can be unambiguously probed through optical second harmonic signals, generated via the spin-induced ferroelectric polarization. In the case of relatively weak photoexcitation,the ferroelectric and the spiral-spin order remains interlocked, both relaxing through spin-lattice relaxation in the non-equilibrium state. When the additional optical pulse illuminating sample is intense enough to induced a local phase transition thermally, the system creates a metastable state of the bc-spiral-spin order (with the electric polarization P//c) via supercooling across the first-order phase transition between ab- and bc-spiral. The supercooled state of bc-spiral spin is formed in the thermodynamical ground state of ab-spiral (P//a), displaying a prolonged lifetime with strong dependence on the magnetic field along the a-axis. The observed photo-switching between the two distinct multiferroic states sheds light on novel photoinduced phenomena in spiral-spin multiferroics.

Magnetoelectric memory effect in the Y-type hexaferrite BaSrZnMgFe12O22**Project supported by the National Natural Science Foundation of China (Grant Nos. 11534015 and 51371193).

We report on the magnetic and magnetoelectric properties of the Y-type hexaferrite BaSrZnMgFe12O22, which undergoes transitions from a collinear ferrimagnetic phase to a proper screw phase at 310 K and to a longitudinal conical phase at 45 K. Magnetic and electric measurements revealed that the magnetic structure with spiral spin order can be modified by applying a magnetic field, resulting in magnetically controllable electric polarization.It was observed that BaSrZnMgFe12O22 exhibits an anomalous magnetoelectric memory effect: the ferroelectric state can be partially recovered from the paraelectric phase with collinear spin structure by reducing magnetic field at 20 K. We ascribe this memory effect to the pinning of multiferroic domain walls, where spin chirality and structure are preserved even in the nonpolar collinear spin state.

Partial Geometric Frustration in Inorganic Supramolecular Spin Systems with One-Dimensional Trigonally Aligned Magnetic Chains ∞1(MCl4)2− (M = Fe2+, Co2+)

Exploration of new spin systems with low-dimensional subunits have been of great interest in the past decades due to their interesting physical properties and potential applications in molecular spintronics. Two inorganic supramolecular complexes, (Hg3S2)(FeCl4) and (Hg3S2)(CoCl4), with trigonally aligned 1-D infinite magnetic ∞1(FeCl4)2− or ∞1(CoCl4)2− chains have been prepared by solid-state reactions. They exhibit 3-D long-range spin order with strong field dependence and field induced metamagnetic behavior. The intrachain and interchain magnetic coupling constants were estimated by DFT+U and DFT+U+SOC calculations and the both complexes can be regarded as partially frustrated spin systems. The spin Hamiltonian was constructed, the ground state is proposed to be incommensurate spiral spin order, which differs from the commensurate 120° spin structure ground state of fully frustrated trigonal case by a little canted angle. This study shows that cooperative magnetic ordering induced by geometric frustration can be realized in inorganic supramolecular systems assembled by weak van der Waals’ interactions.

Dzyaloshinskii-Moriya Interaction and Spiral Order in Spin-orbit Coupled Optical Lattices

We show that the recent experimental realization of spin-orbit coupling in ultracold atomic gases can be used to study different types of spin spiral order and resulting multiferroic effects. Spin-orbit coupling in optical lattices can give rise to the Dzyaloshinskii-Moriya (DM) spin interaction which is essential for spin spiral order. By taking into account spin-orbit coupling and an external Zeeman field, we derive an effective spin model in the Mott insulator regime at half filling and demonstrate that the DM interaction in optical lattices can be made extremely strong with realistic experimental parameters. The rich finite temperature phase diagrams of the effective spin models for fermions and bosons are obtained via classical Monte Carlo simulations.

Magnetic-field-induced ferroelectric polarization flop under pressure in TbMnO3

Magnetoelectric properties of multiferroic TbMnO3 with a cycloidal spiral spin order were investigated as functions of applied pressure and magnetic field. We found that a flop of ferroelectric polarization occurs by applying a magnetic field along the a axis under 2-3 GPa below the Néel temperature of Tb moments. A possible origin of the magnetoelectric transition is discussed based on the observed pressure and magnetic-field profiles of the ferroelectric polarization and the dielectric relaxation. This flop would originate from the 90° rotation of the cycloidal spiral plane from the bc plane to the ab plane.

Ferroelectricity in spiral short-range-ordered magnetic state of spinelMnCr2O4: Significance of topological frustration and magnetoelastic coupling

We report the appearance of ferroelectricity below ${T}_{S}=18$ K, at which short-ranged spiral spin orders, suggesting that ${\mathrm{MnCr}}_{2}{\mathrm{O}}_{4}$ is an improper multiferroic material. Linear heat capacity data and zero-field-cooled memory effect verify reentrant spin-glass-like state below ${T}_{S}$. Synchrotron x-ray diffraction studies confirm significant magnetoelastic coupling at long-range ferrimagnetic order (${T}_{N}=42$ K) and at ${T}_{S}$. We argue that the release of topological spin frustration, produced due to pyrochlore structure of Cr sublattice, is manifested through the significant magnetoelastic effect at ${T}_{N}$ and ${T}_{S}$ and holds the key for spiral spin order driven ferroelectricity in ${\mathrm{MnCr}}_{2}{\mathrm{O}}_{4}$.