Toroidal Magnetic Moment Research Articles

Magnetodielectric Effect in a Triangular Dysprosium Single-Molecule Toroics.

Single-molecule toroics are molecular magnets with vortex distribution of magnetic moments. The coupling between magnetic and electric properties such as the magnetodielectric effect will provide potential applications for them. Herein, the observation of significant magnetodielectric effect in a triangular Dy3 crystal with toroidal magnetic moment and multiple magnetic relaxations is reported. The analysis of magnetic and electric properties implies that the magnetodielectric effect is closely related to the strong spin-lattice coupling, magnetic interactions of Dy3+ ions, as well as molecular packing models.

Unusual magnetic relaxation in a single-molecule magnet with toroidal magnetic moments

We report the synthesis and characterization of a single-molecule magnet composed of triangular clusters of dysprosium ions. The structural study shows that the symmetry changes from one polar point group (mm2) at room temperature to another polar point group (m) at low temperature. Magnetic studies and theory calculations illustrate that the vortex distribution of magnetic dipoles in the triangular dysprosium clusters forms a toroidal magnetic moment. Interestingly, the analysis of AC magnetic susceptibility reveals the coexistence of three distinct magnetic relaxation processes, corresponding to the Raman, Orbach, and QTM relaxation pathways, respectively. The sum of three modified Debye functions is successfully used to describe the multiple relaxation behavior.

The Proton and Occam’s Razor

Otto Stern’s 1933 measurement of the unexpectedly large proton magnetic moment indicated to most physicists that the proton is not a point particle. At that time, many physicists modeled elementary particles as point particles, and therefore Stern’s discovery initiated the speculation that the proton might be a composite particle. In this work, we show that despite being an elementary particle, the proton is an extended particle. Our work is motivated by the experimental data, which we review in section 1.By applying Occam’s Razor principle, we identify a simple proton structure that explains the origin of its principal parameters. Our model uses only relativistic and electromagnetic concepts, highlighting the primary role of the electromagnetic potentials and of the magnetic flux quantum Φ M = h/e. Unlike prior proton models, our methodology does not violate Maxwell’s equation, Noether’s theorem, or the Pauli exclusion principle.Considering that the proton has an anapole (toroidal) magnetic moment, we propose that the proton is a spherical shaped charge that moves at the speed of light along a path that encloses a toroidal volume. A magnetic flux quantum Φ M = h/e stabilizes the proton’s charge trajectory. The two curvatures of the toroidal and poloidal current loops are determined by the magnetic forces associated with Φ M . We compare our calculations against experimental data.

Visualization of fast ion phase-space flow in plasmas well-below, near and well-above Alfvén eigenmode stability threshold in tokamak

Transport of fast ions along certain local phase space paths, referred to as fast ion phase-space flow, has been systematically measured by an imaging neutral particle analyzer (INPA) in three plasma regimes, which are well-below, near, and well-above the Alfvén eigenmode stability threshold (Du et al 2021 Phys. Rev. Lett. 127 235002). (1) In plasmas well-below the Alfvén eignenmodes (AE) stability threshold, fast ions are well-confined on passing particle orbits without noticeable transport over the phase space. The observed INPA images agree well with the synthetic INPA images, using the fast ion distribution predicted by neoclassical theory. (2) In plasmas near the AE stability threshold, INPA images in the presence of AE activity moderately deviate from those without AE activity. The image difference can be well interpreted by AE-driven, phase-space fast ion flow. Paths of this flow over the velocity space (or streamlines) are reconstructed by the intersection lines of curved Eʹ and µ surfaces, referred to as Eʹ and µ line (where ; E, P ζ and µ are the energy, canonical toroidal momentum and magnetic moment of ions; ω and n are the angular frequency and toroidal mode number of AEs, respectively). Resonant fast ions move radially inward by gaining energy and move radially outward by losing energy and the trajectory well aligns with the Eʹ and µ lines that pass through the mode resonances near the injection energy of neutral beams. (3) In plasmas well-above the AE stability threshold, fast ion phase-space dynamics shows additional features. Fast ions are transported out of the birth positions so promptly along the streamlines that the slowing-down process from the injection energy is not observable, exhibiting strong critical gradient behavior at local phase space. As a result, the increase of electron temperature is very small, in spite of an increase of beam power by . It should be emphasized that the directions of phase-space transport, induced by AEs with different frequencies, structures and mode numbers, do not largely differ.

Ferroelectric Single-Molecule Magnet with Toroidal Magnetic Moments.

Materials that coexist magnetic and electric properties on the molecular scale in single‐molecule magnets (SMMs) with peculiar quantum behaviors have promise in molecular electronics and spintronics. Nevertheless, such molecular materials are limited in potentials because their magnetic signal cannot be transformed into an electrical signal through magnetoresistance or Hall effects for their high insulativity. The discovery of an entirely new material, ferroelectric SMMs (FE SMMs) is reported. This FE SMM also shows single‐molecule magnetic behaviors, toroidal magnetic moments, and room‐temperature ferroelectricity. The toroidal moment is formed by a vortex distribution of magnetic dipoles in triangular Dy3 clusters. The analysis of ac magnetic susceptibility reveals the coexistence of three distinct magnetic relaxation processes at low temperatures. The ferroelectricity is introduced by incorporating polar alcohol molecules in the structure, which is confirmed by the X‐ray diffraction and optical second harmonic generation (SHG) measurements. Moreover, the dielectric measurements reveal a ferroelectric‐to‐ferroelectric phase transition around 150 K due to the symmetry change from Pc to Pna21. The coexistence of toroidal moment and ferroelectricity along with quantum magnetism in the rare‐earth single‐molecule magnets yields a unique class of multiferroics.

Temperature-sensitive spin-wave nonreciprocity induced by interlayer dipolar coupling in ferromagnet/paramagnet and ferromagnet/superconductor hybrid systems

Spin-wave (SW) spectra have theoretically been studied in a thin film of a ferromagnet (FM) on a substrate from a paramagnet (PM) (an FM above the critical temperature) or from superconductor (SC). A spin wave propagating in the FM induces the dynamic magnetization and superconducting current in the underlying PM and SC, respectively, which affect the SW propagation by their magnetic fields. As a result of this interaction, the SW spectrum becomes nonreciprocal to depend on the sign of the SW wave vector q. We show that the nonreciprocal contribution to the SW spectra in FM/PM and FM/SC systems is given by the frequency shift of {\Delta}{\omega}(q)={\omega}(q)-{\omega}(-q)=a(T)({\tau}{\cdot}q) with {\tau}=(n{\times}M) being the toroidal magnetic moment, M the FM magnetization, n the unit vector normal to the FM/PM(SC) interface, and a(T) the temperature-dependent constant of a dipole nature, whose sign depends on the substrate type. As the {\Delta}{\omega}(T) dependence is strong at temperatures T close to the critical temperature Tc for the FM-PM or normal metal-SC transition, one gets a possibility to control the frequency SW nonreciprocity with temperature variation near Tc. The dipolar mechanism we propose for SW frequency nonreciprocity is promising for introducing this property of SW propagation into functional devices.

Strategies to Design Single-Molecule Toroics Using Triangular {Ln3} n Motifs.

In this mini-review, we highlight the research advanced in the field of single-molecule toroics (SMTs) with a specific focus on the triangular Ln3-based SMTs. SMTs are molecules with a toroidal magnetic state and are insensitive to homogeneous magnetic fields but cooperate with charge and spin currents. The rapid growth in the area of SMTs witnessed in recent years is correlated not only to the interest to understand the fundamental physics of these molecules but also to the intriguing potential applications proposed, as the SMTs have several advantages compared to other classes of molecules such as single-molecule magnets (SMMs). The important chemico-structural strategy in SMT chemistry is to choose and design ligand and bridging species that will help to attain toroidal behavior. Considering this primarily, all the Dy3 SMTs reported so far are summarized, showing how utilizing different peripheral ligands influences the toroidal nature beyond the role of the symmetry of the molecule and stronger dipolar interactions. Likewise, linking Dy3 toroidal units through 3d ions with suitable peripheral/bridging ligands enhances the toroidal magnetic moment and leads to fascinating physics of ferrotoroidal/antiferrotoridal behavior. Further, we have also summarized the recently reported non-Dy triangular SMTs.

Numerical study of neutral beam injection prompt loss at KSTAR poloidal limiters

We use a newly developed simulation tool to numerically study fast-ion loading on plasma-facing components (PFCs) at the Korea Superconducting Tokamak Advanced Research facility in the high-poloidal-β plasma operation regime. The new code can calculate neutral beam ionization and follow the guiding center orbit of ionized particles. The results of the simulation indicate that fast ions ionized in the high-field side drift out and strike the PFCs as they rotate poloidally. Momentum projection onto a phase space defined by canonical toroidal angular momentum and magnetic moment leads to a simple criterion to avoid fast-ion loading on poloidal limiters (PLs), which are PFCs that are toroidally localized on the low-field side. Control of fast-ion loss is examined by varying the plasma current and plasma boundary. A larger plasma current and inner shifting of the outer plasma boundary is predicted to substantially reduce fast-ion loading on the PLs. The proposed phase-space criterion is qualitatively consistent with the results of the simulation of fast-ion control.

Oblate versus Prolate Electron Density of Lanthanide Ions: A Design Criterion for Engineering Toroidal Moments? A Case Study on {LnIII 6 } (Ln=Tb, Dy, Ho and Er) Wheels.

We report four new complexes based on a {LnIII 6 } wheel structure, three of which possess a net toroidal magnetic moment. The four examples consist of {TbIII 6 } and {HoIII 6 } wheels, which are rare examples of non DyIII based complexes possessing a toroidal magnetic ground state, and a {DyIII 6 } complex which improves its toroidal structure upon lowering the crystallographic symmetry from trigonal (R ) to triclinic (P ). Notably the toroidal moment is lost for the trigonal {ErIII 6 } analogue. This suggests the possibility of utilizing the popular concept of oblate and prolate electron density of the ground state MJ levels of lanthanide ions to engineer toroidal moments.

Recent developments in single-molecule toroics.

Single-molecule toroics (SMTs) are defined as bi-stable molecules with a toroidal magnetic state, which have broad application prospects in quantum computing and information storage, and can also be used as multiferroic materials with a magneto-electric coupling effect. Since the first observation of the SMT behavior of typical Dy3 molecules, great progress has been made in the field of SMTs. In this Perspective, we provide an up-to-date overview of the emerging SMT architectures reported in recent years. Accordingly, thirteen representative examples with toroidal magnetization moments are discussed in order to elucidate the synthetic strategy to design SMT complexes and the factors dictating the arrangement of toroidal magnetic moments, and ultimately enlighten the study of SMTs with enhanced toroidal magnetization.

Slow Magnetic Relaxation and Single-Molecule Toroidal Behaviour in a Family of Heptanuclear {CrIII LnIII6 } (Ln=Tb, Ho, Er) Complexes.

The synthesis, magnetic properties, and theoretical studies of three heterometallic {CrIII LnIII6 } (Ln=Tb, Ho, Er) complexes, each containing a metal topology consisting of two Ln3 triangles connected via a CrIII linker, are reported. The {CrTb6 } and {CrEr6 } analogues display slow relaxation of magnetization in a 3000 Oe static magnetic field. Single-crystal measurements reveal opening up of the hysteresis loop for {CrTb6 } and {CrHo6 } molecules at low temperatures. Ab initio calculations predict toroidal magnetic moments in the two Ln3 triangles, which are found to couple, stabilizing a con-rotating ferrotoroidal ground state in Tb and Ho examples and extend the possibility of observing toroidal behaviour in non DyIII complexes for the first time.

Slow Magnetic Relaxation and Single‐Molecule Toroidal Behaviour in a Family of Heptanuclear {CrIIILnIII6} (Ln=Tb, Ho, Er) Complexes

AbstractThe synthesis, magnetic properties, and theoretical studies of three heterometallic {CrIIILnIII6} (Ln=Tb, Ho, Er) complexes, each containing a metal topology consisting of two Ln3 triangles connected via a CrIII linker, are reported. The {CrTb6} and {CrEr6} analogues display slow relaxation of magnetization in a 3000 Oe static magnetic field. Single‐crystal measurements reveal opening up of the hysteresis loop for {CrTb6} and {CrHo6} molecules at low temperatures. Ab initio calculations predict toroidal magnetic moments in the two Ln3 triangles, which are found to couple, stabilizing a con‐rotating ferrotoroidal ground state in Tb and Ho examples and extend the possibility of observing toroidal behaviour in non DyIII complexes for the first time.

Tetranuclear Lanthanide Complexes Containing a Hydrazone-type Ligand. Dysprosium [2 × 2] Gridlike Single-Molecule Magnet and Toroic.

A multidentate hydrazone-type ligand (Z,Z)-bis(1-(pyridin-2-yl)-1-amino-methylidene)oxalohydrazide (H2L) was utilized in the synthesis of three new isomorphous tetranuclear complexes of the general formula [Ln4(HL)4(H2L)2(NO3)4](NO3)4·4CH3OH (Ln = GdIII, 1, TbIII, 2, DyIII, 3) with the gridlike [2 × 2] topology. The analysis of the static magnetic data revealed weak anti-ferromagnetic interaction among lanthanide(III) atoms, whereas dynamic magnetic data led to the observation of the single-molecule magnet behavior in zero static magnetic field for the Dy4 compound 3 with Ueff = 42.6 K and τ0 = 1.50 × 10-5 s. The theoretical CASSCF calculations supported also the presence of the net toroidal magnetic moment, which classifies compound 3 also as a single-molecule toroic.

Prompt loss of beam ions in KSTAR plasmas

For a toroidal plasma facility to realize fusion energy, researching the transport of fast ions is important not only due to its close relation to the heating and current drive efficiencies but also to determine the heat load on the plasma-facing components. We present a theoretical analysis and orbit simulation for the origin of lost fast-ions during neutral beam injection (NBI) heating in Korea Superconducting Tokamak Advanced Research (KSTAR) device. We adopted a two-dimensional phase diagram of the toroidal momentum and magnetic moment and describe detectable momentums at the fast-ion loss detector (FILD) position as a quadratic line. This simple method was used to model birth ions deposited by NBI and drawn as points in the momentum phase space. A Lorentz orbit code was used to calculate the fast-ion orbits and present the prompt loss characteristics of the KSTAR NBI. The scrape-off layer deposition of fast ions produces a significant prompt loss, and the model and experimental results closely agreed on the pitch-angle range of the NBI prompt loss. Our approach can provide wall load information from the fast ion loss.

A planar triangular Dy3 + Dy3 single-molecule magnet with a toroidal magnetic moment.

A unique Dy6 complex with a planar Dy3 + Dy3 structure was assembled by delicately modifying the axial ligands. Single-molecule magnet behavior and meanwhile a toroidal magnetic moment in the ground state have been observed.

Large Hexadecametallic {Mn(III) -Ln(III) } Wheels: Synthesis, Structural, Magnetic, and Theoretical Characterization.

The synthesis, gas sorption studies, magnetic properties, and theoretical studies of new molecular wheels of core type {Mn(III) 8 Ln(III) 8 } (Ln=Dy, Ho, Er, Y and Yb), using the ligand mdeaH2 , in the presence of ortho-toluic or benzoic acid are reported. From the seven wheels studied the {Mn8 Dy8 } and {Mn8 Y8 } analogues exhibit SMM behavior as determined from ac susceptibility experiments in a zero static magnetic field. From DFT calculations a S=16 ground state was determined for the {Mn8 Y8 } complex due to weak ferromagnetic Mn(III) -Mn(III) interactions. Ab initio CASSCF+RASSI-SO calculations on the {Mn8 Dy8 } wheel estimated the Mn(III) -Dy(III) exchange interaction as -0.1 cm(-1) . This weak exchange along with unfavorable single-ion anisotropy of Dy(III) /Mn(III) ions, however, led to the observation of SMM behavior with fast magnetic relaxation. The orientation of the g-anisotropy of the Dy(III) ions is found to be perpendicular to the plane of the wheel and this suggests the possibility of toroidal magnetic moments in the cluster. The {Mn8 Ln8 } clusters reported here are the largest heterometallic Mn(III) Ln(III) wheels and the largest {3d-4f} wheels to exhibit SMM behavior reported to date.

Single-Molecule Magnetism, Enhanced Magnetocaloric Effect, and Toroidal Magnetic Moments in a Family of Ln4 Squares.

Three cationic [Ln4 ] squares (Ln=lanthanide) were isolated as single crystals and their structures solved as [Dy4 (μ4 -OH)(HL)(H2 L)3 (H2 O)4 ]Cl2 ⋅(CH3 OH)4 ⋅(H2 O)8 (1), [Tb4 (μ4 -OH)(HL)(H2 L)3 (MeOH)4 ]Cl2 ⋅(CH3 OH)4 ⋅(H2 O)4 (2) and [Gd4 (μ4 -OH)(HL)(H2 L)3 (H2 O)2 (MeOH)2 ]Br2 ⋅(CH3 OH)4 ⋅(H2 O)3 (3). The structures are described as hydroxo-centered squares of lanthanide ions, with each edge of the square bridged by a doubly deprotonated H2 L(2-) ligand. Alternating current magnetic susceptibility measurements show frequency-dependent out-of-phase signals with two different thermally assisted relaxation processes for 1, whereas no maxima in χM " appears above 2.0 K for complex 2. For 1, the estimated effective energy barrier for these two relaxation processes is 29 and 100 K. Detailed ab initio studies reveal that complex 1 possesses a toroidal magnetic moment. The ab initio calculated anisotropies of the metal ions in complex 1 were employed to simulate the magnetic susceptibility by using the Lines model (POLY_ANISO) and this procedure yields J1 =+0.01 and J2 =-0.01 cm(-1) for 1 as the two distinct exchange interactions between the Dy(III) ions. Similar parameters are also obtained for complex 1 (and 2) from specific heat measurements. A very weak antiferromagnetic super-exchange interaction (J1 =-0.043 cm(-1) and g=1.99) is observed between the metal centers in 3. The magnetocaloric effect (MCE) was estimated by using field-dependent magnetization and temperature-dependent heat-capacity measurements. An excellent agreement is found for the -ΔSm values extracted from these two measurements for all three complexes. As expected, 3 shows the largest -ΔSm variation (23 J Kg(-1) K(-1) ) among the three complexes. The negligible magnetic anisotropy of Gd indeed ensures near degeneracy in the (2S+1) ground state microstates, and the weak super-exchange interaction facilitates dense population of low-lying excited states, all of which are likely to contribute to the MCE, making complex 3 an attractive candidate for cryogenic refrigeration.

Net Toroidal Magnetic Moment in the Ground State of a {Dy6}-Triethanolamine Ring

A toroidal magnetic moment in the absence of conventional total magnetic moment is observed in a {Dy(6)} ring. The reason for the net toroidal arrangement of the local magnetic moments is the high symmetry of the complex in combination with strong intra-molecular dipolar interactions between Dy ions. The description of single-ion and inter-ion anisotropic magnetic interactions is achieved here for the first time fully ab initio, i.e., without use of phenomenological parameters.

The First {Dy4} Single-Molecule Magnet with a Toroidal Magnetic Moment in the Ground State

A toroidal magnetic moment in the absence of a conventional total magnetic moment was first observed in a novel tetranuclear dysprosium cluster with nonmagnetic ground state. The toroidal state is quite robust with respect to variations of the exchange parameters.

Electric polarization, toroidal moment, spin canting, and chirality induced by Dzialoshinsky–Moriya interactions in aV3cluster analog of multiferroics

The electric polarization and toroidal moments in the spin-frustrated ${\mathrm{V}}_{3}$ single-molecular magnet (${\mathrm{V}}_{3}$) with the out-of-plane $({D}_{z})$ and in-plane $({D}_{x},{D}_{y})$ Dzialoshinsky--Moriya (DM) interaction are studied. It is shown that the spin-current mechanism of polarization proposed by Katsura, Nagaosa, and Balatsky (KNB) [Phys. Rev. Lett. 95, 057205 (2005)] is the driving force of the polarization ${P}_{z}$ induced by the ${D}_{x}$ coupling and directed perpendicular to the ${\mathrm{V}}_{3}$ plane, ${P}_{z}||Z$, in the field $\mathbf{B}||Z.$ The KNB mechanism leads to polarization ${P}_{z}^{}$ which increases nonlinearly with increasing field, reaches a maximum at the avoided level-crossing field ${B}_{\mathrm{A}1}$ and then gradually decreases in ${\mathrm{V}}_{3}^{\mathrm{R}}$ with the ground state of the right vector chirality. Spin dynamics (field-dependent spin canting) in the ground state of this system has the form of the opening of the $({\mathbf{S}}_{1},{\mathbf{S}}_{2},{\mathbf{S}}_{3})$ umbrella by the increasing field up to the maximum canting angle $\ensuremath{\alpha}=\ensuremath{\pi}/4$ and, then, closing it in high fields. In the excited state of the avoided level-crossing structure, the spin dynamics is opposite. ${\mathrm{V}}_{3}^{\mathrm{L}}$ with the ground state of the left chirality demonstrates polarization ${P}_{z}^{}$ in the spin-collinear state and a lack of polarization in the spin-frustrated state. The ${D}_{y}$ coupling results in the field-dependent toroidal magnetic moment ${T}_{z}$. The ${D}_{x},{D}_{y}$ coupling leads to the in-plane $\ensuremath{\phi}$ canting of the spins and coexistence of ${P}_{z}^{}$ and ${T}_{z}$. The coupling between the right vector chirality ${\ensuremath{\kappa}}_{\mathrm{R}}$ and magnetic field ${B}_{z}$ is nonlinear, the negative vector chirality ${\ensuremath{\kappa}}_{\mathrm{L}}$ changes the sign at the level crossing. The polarization ${P}_{z}$ and toroidal moment ${T}_{z}$ are proportional to the radial and tangential in-plane spin fluctuations, respectively, and depend nonlinearly on the value ${\ensuremath{\kappa}}_{\mathrm{R}}$ of the vector chirality, while magnetic moment ${\ensuremath{\mu}}_{z}$ is linear proportional to ${\ensuremath{\kappa}}_{\mathrm{R}}.$ The DM ${\mathrm{V}}_{3}^{}$ nanomagnets are the cluster analogs of multiferroics.