Anisotropic Exchange Interaction Research Articles

Anisotropic exchange interaction of two hole-spin qubits

AbstractSemiconductor spin qubits offer the potential to employ industrial transistor technology to produce large-scale quantum computers. Silicon hole spin qubits benefit from fast all-electrical qubit control and sweet spots to counteract charge and nuclear spin noise. However, the demonstration of a two-qubit interaction has remained an open challenge. One missing factor is an understanding of the exchange coupling in the presence of a strong spin–orbit interaction. Here we study two hole-spin qubits in a silicon fin field-effect transistor, the workhorse device of today’s semiconductor industry. We demonstrate electrical tunability of the exchange splitting from above 500 MHz to close-to-off and perform a conditional spin-flip in 24 ns. The exchange is anisotropic because of the spin–orbit interaction. Upon tunnelling from one quantum dot to the other, the spin is rotated by almost 180 degrees. The exchange Hamiltonian no longer has the Heisenberg form and can be engineered such that it enables two-qubit controlled rotation gates without a trade-off between speed and fidelity. This ideal behaviour applies over a wide range of magnetic field orientations, rendering the concept robust with respect to variations from qubit to qubit, indicating that it is a suitable approach for realizing a large-scale quantum computer.

Exact Matrix Product States at the Quantum Lifshitz Tricritical Point in a Spin-1/2 Zigzag-Chain Antiferromagnet with Anisotropic Γ Term.

Quantum anisotropic exchange interactions in magnets can induce competitions between phases in a different manner from those typically driven by geometrically frustrated interactions. We study a one-dimensional spin-1/2 zigzag chain with such an interaction, Γ term, in conjunction with the Heisenberg interactions. We find a ground state phase diagram featuring a multicritical point where five phases converge: a uniform ferromagnet, two antiferromagnets, Tomonaga-Luttinger liquid, and a dimer-singlet coexisting with nematic order. This multicritical point is simultaneously quantum tricritical and Lifshitz, and most remarkably, it hosts multidegenerate ground state wave functions with the degeneracy increasing in squares of system size. The exact ground states are obtained in the matrix product form opening wide applications to frustration-free models.

Chirality-selective topological magnon phase transition induced by interplay of anisotropic exchange interactions in honeycomb ferromagnet

A variety of distinct anisotropic exchange interactions commonly exist in one magnetic material due to complex crystal, magnetic and orbital symmetries. Here we investigate the effects of multiple anisotropic exchange interactions on topological magnon in a honeycomb ferromagnet, and find a chirality-selective topological magnon phase transition induced by a complicated interplay of Dzyaloshinsky–Moriya interaction and pseudo-dipolar interaction, accompanied by the bulk gap close and reopen with chiral inversion. Moreover, this novel topological phase transition involves band inversion at high symmetry points K and K′, which can be regarded as a pseudo-orbital reversal, i.e. magnon valley degree of freedom, implying a new manipulation corresponding to a sign change of the magnon thermal Hall conductivity. Indeed, it can be realized in 4d or 5d correlated materials with both spin–orbit coupling and orbital localized states, such as iridates and ruthenates, etc. This novel regulation may have potential applications on magnon devices and topological magnonics.

Effect of In-Plane Magnetic Field on Skyrmions in a Centrosymmetric Triangular-Lattice System with Symmetric Anisotropic Exchange Interaction

We report our numerical results on the stability of the skyrmion crystal phase in an external magnetic field for both in-plane and out-of-plane directions in a centrosymmetric host. We analyze a spin model with the two-spin symmetric anisotropic exchange interaction that arises from relativistic spin–orbit coupling on a triangular lattice. By performing simulated annealing, we construct magnetic phase diagrams when the magnetic field is tilted from the out-of-plane field direction to the in-plane field direction. We find a different stability tendency of the skyrmion crystal phase according to the directions of the in-plane field, which provides a signal of the two-spin symmetric anisotropic exchange interaction for stabilizing the skyrmion crystal phase. Our results indicate that the mechanism of the skyrmion crystal phase triggered by the two-spin symmetric anisotropic exchange interaction can be experimentally tested by applying the in-plane magnetic field.

The anti-symmetric and anisotropic symmetric exchange interactions between electric dipoles in hafnia

The anti-symmetric and anisotropic symmetric exchange interactions between two magnetic dipole moments – responsible for intriguing magnetic textures (e.g., magnetic skyrmions) – have been discovered since last century, while their electric analogues were either hidden for a long time or still not known. It is only recently that the anti-symmetric exchange interactions between electric dipoles was proved to exist (with materials hosting such an interaction being still rare) and the existence of anisotropic symmetric exchange interaction between electric dipoles remains ambiguous. Here, by symmetry analysis and first-principles calculations, we identify hafnia as a candidate material hosting the non-collinear dipole alignments, the analysis of which reveals the anti-symmetric and anisotropic symmetric exchange interactions between electric dipoles in this material. Our findings can hopefully deepen the current knowledge of electromagnetism in condensed matter, and imply the possibility of discovering novel states of matter (e.g., electric skyrmions) in hafnia-related materials.

Control and Transferability of Magnetic Interactions in Supramolecular Structures: Trimers of {Cr7 Ni} Antiferromagnetic Rings.

A synthetic strategy is demonstrated to prepare two distinct trimers of antiferromagnetically coupled {Cr7 Ni} rings, substantially varying the magnetic interactions between the spin centres. The interactions were studied using multi-frequency cw EPR: in a trimer linked via non-covalent H-bonding interactions no measurable interaction between rings was seen, while in a trimer linked via iso-nicotinate groups isotropic and anisotropic exchange interactions of +0.42 and -0.8 GHz, respectively, were observed. The latter are the same as those for a simpler hetero-dimer system, showing how the spin-spin interactions can be built in a predictable and modular manner in these systems.

Magnetic ground state of NdB4: interplay between anisotropic exchange interactions and hidden order on a Shastry–Sutherland lattice

Magnetic ground state of NdB₄: interplay between anisotropic exchange interactions and hidden order on a Shastry–Sutherland lattice

Instabilities of heavy magnons in an anisotropic magnet

The search for new elementary particles is one of the most basic pursuits in physics, spanning from subatomic physics to quantum materials. Magnons are the ubiquitous elementary quasiparticle to describe the excitations of fully-ordered magnetic systems. But other possibilities exist, including fractional and multipolar excitations. Here, we demonstrate that strong quantum interactions exist between three flavors of elementary quasiparticles in the uniaxial spin-one magnet FeI2. Using neutron scattering in an applied magnetic field, we observe spontaneous decay between conventional and heavy magnons and the recombination of these quasiparticles into a super-heavy bound-state. Akin to other contemporary problems in quantum materials, the microscopic origin for unusual physics in FeI2 is the quasi-flat nature of excitation bands and the presence of Kitaev anisotropic magnetic exchange interactions.

Microscopic description of magnetic nonequilibrium phenomena in erbium orthoferrite

A model of nonequilibrium thermodynamics of erbium orthoferrite is presented. The quantum-mechanical effects in arbitrary magnetic fields, related both to the direction of a general quantization axis and an influence of anisotropic exchange interactions on the magnetic structure, spin-reorientation phase transition, spin reversals, and hysteresis, are considered. Based on recent experimental data on temperature-induced spin switching [Phys. Rev. B 105, 094424 (2022)], a possible mechanism for the exchange bias of magnetic hysteresis loops is proposed. The main parameters of the model Hamiltonian are determined, which point out a strongly competitive character of exchange interactions in erbium orthoferrite.

Anisotropic spin model and multiple- Q states in cubic systems

Multiple-$Q$ states manifest themselves in a variety of noncollinear and noncoplanar magnetic structures depending on the magnetic interactions and lattice structures. In particular, cubic-lattice systems can host a plethora of multiple-$Q$ states, such as magnetic skyrmion and hedgehog lattices. We here classify momentum-dependent anisotropic exchange interactions in the cubic-lattice systems based on the magnetic representation analysis. We construct an effective spin model for centrosymmetric cubic space groups, $Pm\bar{3}m$ and $Pm\bar{3}$, and noncentrosymmetric ones, $P\bar{4}3m$, $P432$, and $P23$: The former include the symmetric anisotropic exchange interaction, while the latter additionally include the Dzyaloshinskii-Moriya interaction. We demonstrate that the anisotropic exchange interaction becomes the origin of the multiple-$Q$ states by applying the anisotropic spin model to the case under $Pm\bar{3}$. We show several multiple-$Q$ instabilities in the ground state by performing simulated annealing. Our results will be a reference for not only exploring unknown multiple-$Q$ states but also understanding the origin of the multiple-$Q$ states observed in both noncentrosymmetric and centrosymmetric magnets like EuPtSi and SrFeO$_3$.

Magnetic-field induced melting of long-range magnetic order akin to Kitaev insulators in the metallic compound Tb5Si3

There have been constant efforts to find ‘exotic’ quantum spin-liquid (QSL) materials. Some of the transition metal insulators dominated by the direction-dependent anisotropic exchange interaction (‘Kitaev model’ for honeycomb network of magnetic ions) are considered to be promising cases for the same. In such Kitaev insulators, QSL is achieved from the zero-field antiferromagnetic state by the application of magnetic-field, suppressing other exchange interactions responsible for magnetic order. Here, we show that the features attributable to long-range magnetic ordering of the intermetallic compound, Tb5Si3, (T N = 69 K), containing honey-comb network of Tb ions, are completely suppressed by a critical applied field, H cr, in heat-capacity and magnetization data, mimicking the behavior of Kitaev physics candidates. The neutron diffraction patterns as a function of H reveal that it is an incommensurate magnetic structure that gets suppressed, showing peaks arising from multiple wave vectors beyond H cr. Increasing magnetic entropy as a function of H with a peak in the magnetically ordered state is in support of some kind of magnetic disorder in a narrow field range after H cr. Such a high-field behavior for a metallic heavy rare-earth system to our knowledge has not been reported in the past and therefore is intriguing.

Ab initio description of magnetic and critical properties of spin-glass pyrochlore NaSrMn2F7

In this study, I have investigated the magnetic and critical properties of manganese pyrochlore fluoride NaSrMn2F7, which exhibits a glass transition at Tf = 2.5 (K) due to charge disorder. A DFT + U + SOC framework is used in this paper to derive spin-Hamiltonian terms, including isotropic and anisotropic exchange interactions. An optimized geometry reveals a local distortion of the F–Mn–F angle along the ⟨111⟩ direction (95.48° and 84.51°), which is considered a weak bond disorder (δJ). Despite the complex structure of this material, first principle calculations show that its magnetic properties are only controlled by the nearest neighbor’s Heisenberg exchange interaction, and other interactions do not affect spin arrangements in the ground state. Thus, this material is considered a suitable candidate for studying electron correlation in spin glasses. Using a replica-exchange framework, Monte Carlo simulations indicate that with δJ=0, no phase transition is observed when magnetic susceptibility changes with temperature. The results demonstrate that the presence of local bond disorder serves as a perturbation, and the degeneracy of the energy manifold of the system persists if its effect is not taken into consideration. Based on δJ=0.13(meV) and the derived spin Hamiltonian, 2.6 (K) is obtained as the phase transition temperature.

Optical Orientation of Excitons in a Longitudinal Magnetic Field in Indirect-Band-Gap (In,Al)As/AlAs Quantum Dots with Type-I Band Alignment

Exciton recombination and spin dynamics in (In,Al)As/AlAs quantum dots (QDs) with indirect band gap and type-I band alignment were studied. The negligible (less than 0.2 μeV) value of the anisotropic exchange interaction in these QDs prevents the mixing of the excitonic basis states and makes the formation of spin-polarized bright excitons possible under quasi-resonant, circularly polarized excitation. The recombination and spin dynamics of excitons are controlled by the hyperfine interaction between the electron and nuclear spins. A QD blockade by dark excitons was observed in the magnetic field, that eliminates the impact of nuclear spin fluctuations. A kinetic model which accounts for the population dynamics of the bright and dark exciton states as well as for the spin dynamics was developed to quantitatively describe the experimental data.

Transversal transport of magnons in a modified Lieb lattice

We studied a two-band magnon insulating model whose geometry is that of a modified Lieb lattice in which one of the sites was removed. Anisotropic ferromagnetic exchange interactions exist between the three nearest neighbors, and the anisotropy opens a gap in the magnon energy band structure. A non-vanishing Berry curvature is induced by a Dzyaloshinskii–Moriya interaction (DMI). The topology of the bands is trivial (in the sense of a null Chern number), but the finite Berry curvature induces Hall-like transport effects whose coefficients were calculated. Their dependence on temperature was studied and shows a resemblance with other magnon insulating systems found in the literature. The dependence on exchange couplings, DMI parameter, and external magnetic field was also investigated.

Interplay of Anisotropic Exchange Interactions and Single-Ion Anisotropy in Single-Chain Magnets Built from Ru/Os Cyanidometallates(III) and Mn(III) Complex.

Two novel 1D heterobimetallic compounds {[MnIII(SB2+)MIII(CN)6]·4H2O}n (SB2+ = N,N'-ethylenebis(5-trimethylammoniomethylsalicylideneiminate) based on orbitally degenerate cyanidometallates [OsIII(CN)6]3- (1) and [RuIII(CN)6]3- (2) and MnIII Schiff base complex were synthesized and characterized structurally and magnetically. Their crystal structures consist of electrically neutral, well-isolated chains composed of alternating [MIII(CN)6]3- anions and square planar [MnIII(SB2+)]3+ cations bridged by cyanide groups. These -ion magnetic anisotropy of MnIII centers. These results indicate that the presence of compounds exhibit single-chain magnet (SCM) behavior with the energy barriers of Δτ1/kB = 73 K, Δτ2/kB = 41.5 K (1) and Δτ1/kB = 51 K, Δτ2 = 27 K (2). Blocking temperatures of TB = 2.8, 2.1 K and magnetic hysteresis with coercive fields (at 1.8 K) of 8000, 1600 Oe were found for 1 and 2, respectively. Theoretical analysis of the magnetic data reveals that their single-chain magnet behavior is a product of a complicated interplay of extremely anisotropic triaxial exchange interactions in MIII(4d/5d)-CN-MnIII fragments: -JxSMxSMnx-JySMySMny-JzSMzSMnz, with opposite sign of exchange parameters Jx = -22, Jy = +28, Jz = -26 cm-1 and Jx = -18, Jy = +20, Jz = -18 cm-1 in 1 and 2, respectively) and single orbitally degenerate [OsIII(CN)6]3- and [RuIII(CN)6]3- spin units with unquenched orbital angular momentum in the chain compounds 1 and 2 leads to a peculiar regime of slow magnetic relaxation, which is beyond the scope of the conventional Glaubers's 1D Ising model and anisotropic Heisenberg model.

Pentagonal-bipyramidal 4d and 5d complexes with unquenched orbital angular momentum as a unique platform for advanced single-molecule magnets: current state and perspectives.

This article overviews the current state and prospects of the concept of advanced single-molecule magnets (SMMs) based on low-spin (S = 1/2) pentagonal-bipyramidal (PBP) 4d3 and 5d3 complexes with unquenched orbital angular momentum. This approach is based on the unique property of PBP 4d3 and 5d3 complexes to cause highly anisotropic spin coupling of perfect uniaxial symmetry, -JzSziSzj - Jxy(SxiSxj + SyiSyj), regardless of the local geometric symmetry. The M(4d/5d)-M(3d) exchange-coupled pairs in the apical positions of the PBP complexes produce Ising-type exchange interactions (|Jz| > |Jxy|), which serve as a powerful source of uniaxial magnetic anisotropy of a SMM cluster. In polynuclear heterometallic 4d/5d-3d complexes embodying PBP 4d/5d units and high-spin 3d ions, anisotropic Ising-type exchange interactions produce a double-well potential with high energy barriers Ueff, which is controlled by the anisotropic exchange parameters Jz, Jxy. Theoretical analysis shows that the barrier is proportional to the difference |Jz - Jxy| and to the number n of the apical 4d/5d-3d pairs in a SMM cluster, Ueff ∝ |Jz - Jxy|n, which provides an opportunity to scale up the barrier Ueff and blocking temperature TB up to the record values. A novel family of 4d/5d complexes with forced PBP coordination provided by structurally rigid planar pentadentate Schiff-base ligands in the equatorial plane is discussed as a better alternative to the cyanometallates. The possibility of a significant increase in the anisotropic exchange parameters Jz, Jxy in PBP complexes with monoatomic apical μ-bridging ligands is examined. The basic principles of molecular engineering the highest barrier through anisotropic exchange interactions of PBP 4d/5d complexes are formulated. The theoretical and experimental results taken together indicate that the concept of high-performance SMMs based on 4d/5d PBP complexes with unquenched orbital angular momentum is an attractive alternative to the currently dominant lanthanide-based SMM strategy.

Spin-wave dynamics in the KCeS2 delafossite: A theoretical description of powder inelastic neutron-scattering data

Layered rare-earth delafossites $ARX_2$ with $R$ = Yb(III) or Ce(III) have received a lot of interest as potential hosts for a quantum spin-liquid ground state. Some systems of this family that show no long-range order down to the lowest measured temperatures, such as NaYbO$_2$, NaYbS$_2$, and NaYbSe$_2$, are presumed to be in a quantum spin-liquid state. However, other isostructural compounds are known to order antiferromagnetically at subkelvin temperatures. Among them, KCeS$_2$ exhibits stripe-$yz$ magnetic order in the triangular-lattice planes that sets in below 400 mK. Here we investigate the spin-wave spectrum of this ordered phase with powder inelastic neutron scattering and describe it using a model Hamiltonian obtained from first-principles calculations based on the complete $|J,m_J\rangle$ multiplet description of the Ce sites with an anisotropic nearest-neighbor exchange interaction. Combing the current understanding of the exchange interaction in the systems with the effects of texturing in the powder, we have been able to model the inelastic neutron scattering spectrum with high fidelity.

Application of the Heptacyanidorhenate(IV) as a Metalloligand in the Design of Molecular Magnets

This review is devoted to an analysis of currently known heterometallic molecular magnets based on an orbitally degenerate 5d metalloligand, [ReIV(CN)7]3−. Heptacyanidometallates with a pentagonal bipyramidal structure of the coordination site and degenerate ground spin state are the source of anisotropic magnetic exchange interactions upon the formation of cyanide-bonded assemblies involving the paramagnetic complexes of the first transition series. Therefore, the development of methods for chemical design using such molecular magnetic modules is extremely important. If for the 4d congener, isoelectronic [MoIII(CN)7]3−, a family of approximately 40 heterometallic compounds, was obtained, whereas for heptacyanorhenate(IV), no more than 20 are known. However, as a result of recent studies, heterobimetallic magnetic assemblies of all dimensionalities have been synthesized, from 0D to 1D, demonstrating slow magnetization relaxation, to 2D networks and 3D frameworks possessing large magnetic hysteresis. The most anisotropic is a 2D network, PPN[{MnIII(acacen)}2ReIV(CN)7]·Solv, with a critical temperature of 20 K and magnetic hysteresis with a record coercivity for cyanide-bridged molecular materials.

Effective spin model in momentum space: Toward a systematic understanding of multiple-Qinstability by momentum-resolved anisotropic exchange interactions

Multiple-$Q$ magnetic states, such as a skyrmion crystal, become a source of unusual transport phenomena and dynamics. Recent theoretical and experimental studies clarify that such multiple-$Q$ states ubiquitously appear under different crystal structures in metals and insulators. Toward a systematic understanding of the formation of the multiple-$Q$ states in various crystal systems, in this theoretical study, we present a low-energy effective spin model with anisotropic exchange interactions in momentum space. We summarize specific six symmetry rules for nonzero symmetric and antisymmetric anisotropic exchange interactions in momentum space, which are regarded as an extension of Moriya's rule. According to the rules, we construct the effective spin model for tetragonal, hexagonal, and trigonal magnets with crystal- and momentum-dependent anisotropic exchange interactions based on magnetic representation analysis. Furthermore, we describe the origin of the effective anisotropic exchange interactions in itinerant magnets by perturbatively analyzing a multi-band periodic Anderson model with the spin-orbit coupling. We apply the effective spin model to an itinerant magnet in a $P6/mmm$ crystal and find various multiple-$Q$ states with a spin scalar chirality in the ground state. Our results provide a foundation of constructing effective phenomenological spin models for any crystal systems hosting the multiple-$Q$ states, which will stimulate further exploration of exotic multiple-$Q$ states in materials with the spin-orbit coupling.

Dynamical Scaling as a Signature of Multiple Phase Competition in Yb_{2}Ti_{2}O_{7}.

Yb_{2}Ti_{2}O_{7} is a celebrated example of a pyrochlore magnet with highly frustrated, anisotropic exchange interactions. To date, attention has largely focused on its unusual, static properties, many of which can be understood as coming from the competition between different types of magnetic order. Here we use inelastic neutron scattering with exceptionally high energy resolution to explore the dynamical properties of Yb_{2}Ti_{2}O_{7}. We find that spin correlations exhibit dynamical scaling, analogous to behavior found near to a quantum critical point. We show that the observed scaling collapse can be explained within a phenomenological theory of multiple-phase competition, and confirm that a scaling collapse is also seen in semiclassical simulations of a microscopic model of Yb_{2}Ti_{2}O_{7}. These results suggest that dynamical scaling may be general to systems with competing ground states.