Strong Easy-axis Anisotropy Research Articles

Current induced magnetization dynamics and magnetization switching in superconducting ferromagnetic hybrid (F|S|F) structures

We investigate the current induced magnetization dynamics and magnetization switching in an unconventional p-wave superconductor sandwiched between two misaligned ferromagnetic layers by numerically solving the Landau-Lifshitz-Gilbert equation modified with current induced Slonczewski's spin torque term. A modified form of the Ginzburg-Landau free energy functional has been used for this purpose. We demonstrated the possibility of current induced magnetization switching in the spin-triplet ferromagnetic superconducting hybrid structures with a strong easy axis anisotropy and the condition for magnetization reversal. The switching time for such arrangement is calculated and is found to be highly dependent on the magnetic configuration along with the biasing current. This study would be useful in designing the practical superconducting-spintronic devices.

Ferromagnetism and glassiness on the surface of topological insulators

We investigate the nature of the ordering among magnetic adatoms, randomly deposited on the surface of topological insulators. Restricting ourselves to dilute impurity and weak coupling (between itinerant fermion and magnetic impurities) limit, we show that for arbitrary amount of chemical doping away from the apex of the surface Dirac cone the magnetic impurities tend to arrange themselves in a spin-density-wave pattern, with the periodicity approximately $\pi/k_F$, where $k_F$ is the Fermi wave vector, when magnetic moment for impurity adatoms is isotropic. However, when magnetic moment possesses strong Ising or easy-axis anisotropy, pursuing both analytical and numerical approaches we show that the ground state is ferromagnetic for low to moderate chemical doping, despite the fragmentation of the system into multiple ferromagnetic islands. For high doping away from the Dirac point as well, the system appears to fragment into many ferromagnetic islands, but the magnetization in these islands is randomly distributed. Such magnetic ordering with net zero magnetization, is referred here as ferromagnetic spin glass, which is separated from the pure ferromagnet state by a first order phase transition. We generalize our analysis for cubic topological insulators (supporting three Dirac cones on a surface) and demonstrate that the nature of magnetic orderings and the transition between them remains qualitatively the same. We also discuss the possible relevance of our analysis to recent experiments.

Bubble and skyrmion crystals in frustrated magnets with easy-axis anisotropy

We clarify the conditions for the emergence of multiple-${\bf Q}$ structures out of lattice and easy-axis spin anisotropy in frustrated magnets. By considering magnets whose exchange interaction has multiple global minima in momentum space, we find that both types of anisotropy stabilize triple-${\bf Q}$ orderings. Moderate anisotropy leads to a magnetic field-induced skyrmion crystal, which evolves into a bubble crystal for increasing spatial or spin anisotropy. The bubble crystal exhibits a quasi-continuous (devil's staircase) temperature dependent ordering wave-vector, characteristic of the competition between frustrated exchange and strong easy-axis anisotropy.

Can Non-Kramers Tm(III) Mononuclear Molecules be Single-Molecule Magnets (SMMs)?

In recent years, plentiful lanthanide-based (Tb(III) , Dy(III) , and Er(III) ) single-molecule magnets (SMMs) were studied, while examples of other lanthanides, for example, Tm(III) are still unknown. Herein, for the first time, we show that by rationally manipulating the coordination sphere, two thulium compounds, 1[(Tp)Tm(COT)] and 2[(Tp*)Tm(COT)] (Tp=hydrotris(1-pyrazolyl)borate; COT=cyclooctatetraenide; Tp*=hydrotris(3,5-dimethyl-1-pyrazolyl)borate), can adopt the structure of non-Kramers SMMs and exhibit their behaviors. Dynamic magnetic studies indicated that both compounds showed slow magnetic relaxation under dc field and a relatively high effective energy barrier (111 K for 1, 46 K for 2). Magnetic diluted 1 a[(Tp)Tm0.05 Y0.95 (COT)] and 2 a[(Tp*)Tm0.05 Y0.95 (COT)] even exhibited magnetic relaxation under zero dc field. Relativistic ab initio calculations combined with single-crystal angular-resolved magnetometry measurements revealed the strong easy axis anisotropy and nearly degenerated ground doublet states. The comparison of 1 and 2 highlights the importance of local symmetry for obtaining Tm SMMs.

Magnetic ground state of the two isostructual polymeric quantum magnets[Cu(HF2)(pyrazine)2]SbF6and[Co(HF2)(pyrazine)2]SbF6investigated with neutron powder diffraction

The magnetic ground state of two isostructural coordination polymers (i) the quasi two-dimensional S = 1/2 square-lattice antiferromagnet [Cu(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$; and (ii) a new compound [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$, were examined with neutron powder diffraction measurements. We find the ordered moments of the Heisenberg S = 1/2 Cu(II) ions in [Cu(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$ are 0.6(1)$\mu_{B}$, whilst the ordered moments for the Co(II) ions in [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$ are 3.02(6)$\mu_{B}$. For Cu(II), this reduced moment indicates the presence of quantum fluctuations below the ordering temperature. We show from heat capacity and electron spin resonance measurements, that due to the crystal electric field splitting of the S = 3/2 Co(II) ions in [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$, this isostructual polymer also behaves as an effective spin-half magnet at low temperatures. The Co moments in [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$ show strong easy-axis anisotropy, neutron diffraction data which do not support the presence of quantum fluctuations in the ground state and heat capacity data which are consistent with 2D or close to 3D spatial exchange anisotropy.

Rational electrostatic design of easy-axis magnetic anisotropy in a Zn(II) -Dy(III) -Zn(II) single-molecule magnet with a high energy barrier.

Two novel trinuclear complexes [ZnCl(μ-L)Ln(μ-L)ClZn][ZnCl3 (CH3 OH)]⋅3 CH3 OH (Ln(III) =Dy (1) and Er (2)) have been prepared from the compartmental ligand N,N'-dimethyl-N,N'-bis(2-hydroxy-3-formyl-5-bromo-benzyl)ethylenediamine (H2 L). X-ray studies reveal that Ln(III) ions are coordinated by two [ZnCl(L)](-) units through the phenoxo and aldehyde groups, giving rise to a LnO8 coordination sphere with square-antiprism geometry and strong easy-axis anisotropy of the ground state. Ab initio CASSCF+RASSI calculations carried out on 1 confirm that the ground state is an almost pure MJ =±15/2 Kramers doublet with a marked axial anisotropy, the magnetic moment is roughly collinear with the shortest DyO distances. This orientation of the local magnetic moment of the Dy(III) ion in 1 is adopted to reduce the electronic repulsion between the oblate electron shape of the MJ =±15/2 Kramers doublet and the phenoxo-oxygen donor atoms involved in the shortest DyO bonds. CASSCF+RASSI calculations also show that the ground and first excited states of the Dy(III) ion are separated by 129 cm(-1) . As expected for this large energy gap, compound 1 exhibits, in a zero direct-current field, thermally activated slow relaxation of the magnetization with a large Ueff =140 K. The isostructural Zn-Er-Zn species does not present significant SMM behavior as expected for the prolate electron-density distribution of the Er(III) ion leading to an easy-plane anisotropy of the ground doublet state.

Magnetic properties of MnBi based alloys: First-principles calculations for MnBi-Co and MnBi-Co-Fe cases

First-principles calculations of fundamental magnetic properties were performed for ordered MnBi, MnBi-Co, and MnBi-Co-Fe alloys to evaluate maximum energy product (BH)max. Full potential linear-augmented plane wave (FLAPW) and linear-muffin-tin-orbital (LMTO) calculations using density functional theory (DFT) within the local spin density approximation (LSDA) were used and found to give a reasonable description of saturation magnetization (Ms), effective anisotropy constant (Keff), and Curie temperature (Tc) for NiAs-structured MnBi crystal. We found that upon addition of Co, the Ms and Keff increased, while Tc reduced. The magnetic anisotropy changed from weak anisotropy easy plane for MnBi to the strong easy axis anisotropy for MnBi-Co and MnBi-Co-Fe.

Strong single-ion anisotropy and anisotropic interactions of magnetic adatoms induced by topological surface states

The nature of the magnetism brought about by Fe adatoms on the surface of the topological insulator Bi2Se3 was examined in terms of density functional calculations. The Fe adatoms exhibit strong easy-axis magnetic anisotropy in the dilute adsorption limit due to the topological surface states (TSS). The spin exchange J between the Fe adatoms follows a Ruderman-Kittel-Kasuya-Yosida (RKKY) behavior with substantial anisotropy, and the Dzyaloshinskii-Moriya (DM) interaction between them is quite strong with |D/J|~0.3 under the mediation by the TSS, and can be further raised to ~0.6 by an external electric field. The apparent single-ion anisotropy of a Fe adatom is indispensable in determining the spin orientation.

ChemInform Abstract: Density Functional Theory Analysis of the Interplay Between Jahn—Teller Instability, Uniaxial Magnetism, Spin Arrangement, Metal—Metal Interaction, and Spin—Orbit Coupling in Ca3CoMO6 (M: Co, Rh, Ir).

In the isostructural oxides Ca(3)CoMO(6) (M = Co, Rh, Ir), the CoMO(6) chains made up of face-sharing CoO(6) trigonal prisms and MO(6) octahedra are separated by Ca atoms. We analyzed the magnetic and electronic properties of these oxides on the basis of density functional theory calculations including on-site repulsion and spin-orbit coupling, and examined the essential one-electron pictures hidden behind results of these calculations. Our analysis reveals an intimate interplay between Jahn-Teller instability, uniaxial magnetism, spin arrangement, metal-metal interaction, and spin-orbit coupling in governing the magnetic and electronic properties of these oxides. These oxides undergo a Jahn-Teller distortion, but their distortions are weak, so that their trigonal-prism Co(n+) (n = 2, 3) ions still give rise to strong easy-axis anisotropy along the chain direction. As for the d-state split pattern of these ions, the electronic and magnetic properties of Ca(3)CoMO(6) (M = Co, Rh, Ir) are consistent with d(0) < (d(2), d(-2)) < (d(1), d(-1)) but not with (d(2), d(-2)) < d(0) < (d(1), d(-1)). The trigonal-prism Co(3+) ion in Ca(3)Co(2)O(6) has the L = 2 configuration (d(0))(1)(d(2), d(-2))(3)(d(1), d(-1))(2) because of the metal-metal interaction between adjacent Co(3+) ions in each Co(2)O(6) chain, which is mediated by their z(2) orbitals, and the spin-orbit coupling of the trigonal-prism Co(3+) ion. The spins in each CoMO(6) chain of Ca(3)CoMO(6) prefer the ferromagnetic arrangement for M = Co and Rh but the antiferromagnetic arrangement for M = Ir. The octahedral M(4+) ion of Ca(3)CoMO(6) has the (1a)(1)(1e)(4) configuration for M = Rh but the (1a)(2)(1e)(3) configuration for M = Ir, which arises from the difference in the spin-orbit coupling of the M(4+) ions and the Co···M metal-metal interactions.

Density Functional Theory Analysis of the Interplay between Jahn−Teller Instability, Uniaxial Magnetism, Spin Arrangement, Metal−Metal Interaction, and Spin−Orbit Coupling in Ca3CoMO6 (M = Co, Rh, Ir)

In the isostructural oxides Ca(3)CoMO(6) (M = Co, Rh, Ir), the CoMO(6) chains made up of face-sharing CoO(6) trigonal prisms and MO(6) octahedra are separated by Ca atoms. We analyzed the magnetic and electronic properties of these oxides on the basis of density functional theory calculations including on-site repulsion and spin-orbit coupling, and examined the essential one-electron pictures hidden behind results of these calculations. Our analysis reveals an intimate interplay between Jahn-Teller instability, uniaxial magnetism, spin arrangement, metal-metal interaction, and spin-orbit coupling in governing the magnetic and electronic properties of these oxides. These oxides undergo a Jahn-Teller distortion, but their distortions are weak, so that their trigonal-prism Co(n+) (n = 2, 3) ions still give rise to strong easy-axis anisotropy along the chain direction. As for the d-state split pattern of these ions, the electronic and magnetic properties of Ca(3)CoMO(6) (M = Co, Rh, Ir) are consistent with d(0) < (d(2), d(-2)) < (d(1), d(-1)) but not with (d(2), d(-2)) < d(0) < (d(1), d(-1)). The trigonal-prism Co(3+) ion in Ca(3)Co(2)O(6) has the L = 2 configuration (d(0))(1)(d(2), d(-2))(3)(d(1), d(-1))(2) because of the metal-metal interaction between adjacent Co(3+) ions in each Co(2)O(6) chain, which is mediated by their z(2) orbitals, and the spin-orbit coupling of the trigonal-prism Co(3+) ion. The spins in each CoMO(6) chain of Ca(3)CoMO(6) prefer the ferromagnetic arrangement for M = Co and Rh but the antiferromagnetic arrangement for M = Ir. The octahedral M(4+) ion of Ca(3)CoMO(6) has the (1a)(1)(1e)(4) configuration for M = Rh but the (1a)(2)(1e)(3) configuration for M = Ir, which arises from the difference in the spin-orbit coupling of the M(4+) ions and the Co···M metal-metal interactions.

Loop algorithm for classical Heisenberg models with spin-ice type degeneracy

In many frustrated Ising models, a single-spin flip dynamics is frozen out at low temperatures compared to the dominant interaction energy scale because of the discrete "multiple valley" structure of degenerate ground-state manifold. This makes it difficult to study low-temperature physics of these frustrated systems by using Monte Carlo simulation with the standard single-spin flip algorithm. A typical example is the so-called spin ice model, frustrated ferromagnets on the pyrochlore lattice. The difficulty can be avoided by a global-flip algorithm, the loop algorithm, that enables to sample over the entire discrete manifold and to investigate low-temperature properties. We extend the loop algorithm to Heisenberg spin systems with strong easy-axis anisotropy in which the ground-state manifold is continuous but still retains the spin-ice type degeneracy. We examine different ways of loop flips and compare their efficiency. The extended loop algorithm is applied to the following two models, a Heisenberg antiferromagnet with easy-axis anisotropy along the z axis, and a Heisenberg spin ice model with the local <111> easy-axis anisotropy. For both models, we demonstrate high efficiency of our loop algorithm by revealing the low-temperature properties which were hard to access by the standard single-spin flip algorithm. For the former model, we examine the possibility of order-from-disorder and critically check its absence. For the latter model, we elucidate a gas-liquid-solid transition, namely, crossover or phase transition among paramagnet, spin-ice liquid, and ferromagnetically-ordered ice-rule state.

Triangular and Kagome Antiferromagnets with a Strong Easy-Axis Anisotropy

We consider S>3/2 kagome and triangular lattice magnets with strong easy-axis single-ion anisotropy D and antiferromagnetic exchange J. When D>>J, the low energy states selected by the anisotropy map onto configurations of the corresponding classical Ising antiferromagnet. Subleading O(J;{3}S/D;{2}) multispin interaction arising from the transverse quantum dynamics makes the low-temperature behavior very different from the well-known classical case: The kagome magnet goes into a semiclassical spin-liquid state with distinctive and unusual short-range correlations below a crossover temperature T;{*} approximately 0.08J;{3}S/D;{2}, while the triangular magnet undergoes a first-order transition at T_{c} approximately 0.1J;{3}S/D;{2} to an orientationally ordered collinear state that gives rise to a novel zero-magnetization plateau for small magnetic fields along the easy axis. Possible experimental implications are also discussed.

Instability of the collinear phase in a two-dimensional ferromagnet in a strong in-planemagnetic field

It is well-known that in a thin ferromagnetic film with a net magnetization perpendicularto the film the collinear arrangement of spins is unstable in an in-plane fieldH smaller than itssaturation value Hc. The existence of a stripe phase was proposed with elongated domainsof alternating direction of the magnetization component perpendicularto the film. We consider in the present paper the strong-field regimeH<Hc and discuss the minimal microscopic model describing this phenomenon, a two-dimensionalHeisenberg ferromagnet with strong easy-axis anisotropy and dipolar forces. Thenoncollinear (stripe) phase is discussed using the technique of Bose–Einsteincondensation of magnons. Some previously unknown results are observed concerningthe stripe phase. Evolution of the spin arrangement in the noncollinear phase isestablished upon field rotation within the plane. We find a rapid decrease of theperiod of the stripe structure as the field decreases. We demonstrate that spincomponents perpendicular to the film form a sinusoid in the noncollinear phase atH≈Hc that transforms to a step-like profile with decreasing field so that the domain wall densitydecreases from unity to a value much smaller than unity. The spin-wave spectrum in thenoncollinear phase is discussed.

Spin dynamics of the frustrated easy-axis triangular antiferromagnet2H-AgNiO2explored by inelastic neutron scattering

We report inelastic neutron-scattering measurements of the spin dynamics in the layered hexagonal magnet $2H{\text{-AgNiO}}_{2}$, which has stacked triangular layers of antiferromagnetically coupled ${\text{Ni}}^{2+}$ spins $(S=1)$ ordered in a collinear alternating stripe pattern. We observe a broad band of magnetic excitations above a small gap of 1.8 meV and extending up to 7.5 meV, indicating strongly dispersive excitations. The measured dispersions of the boundaries of the powder-averaged spectrum can be quantitatively explained by a linear spin-wave dispersion for triangular layers with antiferromagnetic nearest- and weak next-nearest-neighbor couplings, a strong easy-axis anisotropy, and additional weak interlayer couplings. The resulting dispersion relation has global minima not at magnetic Bragg wave vectors but at symmetry-related soft points and we attribute this anomalous feature to the strong competition between the easy-axis anisotropy and the frustrated antiferromagnetic couplings. We have also calculated the quantum corrections to the dispersion relation to order $1/S$ in spin-wave theory by extending the work of Chubukov and Jolicoeur [Phys. Rev. B 46, 11137 (1992)] and find that the presence of easy-axis anisotropy significantly reduces the quantum renormalizations predicted for the isotropic model.

Spin-Reorientation Transition of Field-Induced Magnetic Ordering Phases in the Anisotropic Haldane System

A possible spin-reorientation transition in field-induced magnetic ordering phases of the S=1 Haldane system with large easy-plane anisotropy is proposed, using an effective Lagrangian formalism as well as the density matrix renormalization group method. Such a spin-reorientation transition is predicted in the case where the applied magnetic field is inclined from the easy axis of the anisotropy. We point out that this transition has a close connection with a variation of the order parameter even at zero temperature, although it is different from a quantum analog of the so-called spin-flop transition proposed for the system having a strong easy axis anisotropy. In connection with a novel phase observed recently in the Haldane system at high fields, we discuss possible implications for the field-induced magnetic ordering.

Change of easy magnetization direction in TmMn 6Sn 6− xGa x (0.00 < x < 1.22) studied in high magnetic fields

Single crystals of TmMn 6Sn 6− x Ga x compounds (0 ≤ x ≤ 1.22) obtained in a tin flux have been studied by thermomagnetic and high-field magnetization measurements. A collinear-antiferro to heli-magnetic transition at 324 K has been observed in TmMn 6Sn 6. Spin-reorientation transitions at low temperature are found in the compounds with x = 0.66 and 1.22. The magnetization curves in high fields at 4.2 K are interpreted to result from the competition between the Tm–Mn exchange interaction and the magnetocrystalline anisotropy of the Tm and Mn sublattices. A strong easy-plane anisotropy is favored for the Ga-poor compounds and a strong easy-axis anisotropy for the Ga-rich compounds while the compounds of intermediate Ga content (0.51 ≤ x ≤ 0.66) display rather weak magnetocrystalline anisotropy.

Pyrochlore photons: TheU(1)spin liquid in aS=12three-dimensional frustrated magnet

We study the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice in the limit of strong easy-axis exchange anisotropy. We find, using only standard techniques of degenerate perturbation theory, that the model has a U(1) gauge symmetry generated by certain local rotations about the z-axis in spin space. Upon addition of an extra local interaction in this and a related model with spins on a three-dimensional network of corner-sharing octahedra, we can write down the exact ground state wavefunction with no further approximations. Using the properties of the soluble point we show that these models enter the U(1) spin liquid phase, a novel fractionalized spin liquid with an emergent U(1) gauge structure. This phase supports gapped S^z = 1/2 spinons carrying the U(1) ``electric'' gauge charge, a gapped topological point defect or ``magnetic'' monopole, and a gapless ``photon,'' which in spin language is a gapless, linearly dispersing S^z = 0 collective mode. There are power-law spin correlations with a nontrivial angular dependence, as well as novel U(1) topological order. This state is stable to ALL zero-temperature perturbations and exists over a finite extent of the phase diagram. Using a convenient lattice version of electric-magnetic duality, we develop the effective description of the U(1) spin liquid and the adjacent soluble point in terms of Gaussian quantum electrodynamics and calculate a few of the universal properties. The resulting picture is confirmed by our numerical analysis of the soluble point wavefunction. Finally, we briefly discuss the prospects for understanding this physics in a wider range of models and for making contact with experiments.

AFMR in a quasi-1D noncollinear antiferromagnet CsMnI3

The antiferromagnetic resonance (AFMR) spectrum of a quasi-one-dimensional hexagonal antiferromagnet with strong easy-axis anisotropy, CsMnI3, is studied. A phenomenological theory based on the exchange symmetry of this system is developed and the results are compared with scattering experiments.