Collinear Spin Research Articles

Relation between spin and orbital magnetism in excited states of ferromagnetic materials

We report the first-principles study of the orbital magnetism, the magnetic anisotropy energy, the ratio of the spin, and the orbital moments in nano-sized systems perturbed from their magnetic ground state. We investigate one monolayer thick films of Co, Fe, and FePt. Two types of the perturbation are studied. First, the collinear spin structure is rotated continuously between the easy and hard axes. Second, the non-collinear spin structures are considered varying in both the angles between spin moments and the direction of the net magnetization. In agreement with the experiment we obtain a variety of behaviours. We show that the magnetic anisotropy energy can both increase and decrease with increasing magnetic disorder. The type of behaviour depends on the variation of the electronic structure with increasing angles between atomic moments. We obtain the effect of band narrowing accompanying the spin disorder that correlates with the band narrowing obtained experimentally in a laser irradiated system. In agreement with this experiment we show that the ratio of the spin and orbital moments can both remain unchanged and vary strongly. We analyse the applicability of Bruno's picture, which suggests proportionality between magnetic-anisotropy energy and orbital moment anisotropy for non-collinear spin configurations. We study the non-collinearity of the atomic spin and orbital moments and demonstrate that the response of the orbital moments to the variation of the spin structure can be unexpected and spectacular.

Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions

For the time being isotropic three-body exchange interactions are scarcely explored and mostly used as a tool for constructing various exactly solvable one-dimensional models, although, generally speaking, such competing terms in generic Heisenberg spin systems can be expected to support specific quantum effects and phases. The Heisenberg chain constructed from alternating S=1 and sigma=1/2 site spins defines a realistic prototype model admitting extra three-body exchange terms. Based on numerical density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we demonstrate that the additional isotropic three-body terms stabilize a variety of partially-polarized states as well as two specific non-magnetic states including a critical spin-liquid phase controlled by two Gaussinal conformal theories as well as a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. Most of the established effects are related to some specific features of the three-body interaction such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest-neighbor clustering of the spins. It may be expected that most of the predicted effects of the isotropic three-body interaction persist in higher space dimensions.

Spin-orbital driven ferroelectricity

We study the effect of octahedron rotation on the electric polarization with spin–orbit coupling. Employing local coordinates to represent the tilting of the ligands' octahedra, we evaluate the electric polarization in a chain of transition metal ions with non-polar octahedron rotation. We find the orbital ordering produced by the ligands' rotation and the spin order, together, determine the polarization features, manifesting that non-vanishing polarization appears in collinear spin order and the direction of polarization is no more restricted in the plane of spin rotation in cycloidal ordering.

Electromagnon by chiral spin dynamics in the triangular lattice antiferromagnet

From high field electron spin resonance measurements in illuminating polarized light, we have revealed the existence of electromagnon, i.e., magnon excitation by oscillatory electric fields of light, in the field-induced 1/5-plateau phase of the triangular lattice antiferromagnet ${\mathrm{CuFeO}}_{2}$. We indicate that peculiar magnon modes, which generate uniform fluctuation of the vector spin chirality at wave vector $k=0$, appear in the magnetic ordered phase with a collinear spin structure on triangular lattice. Our experimental results demonstrate that such magnon modes couple with an electric component of light, leading to the emergence of the electromagnon. Moreover, the measurements in circularly polarized light exhibit an anomalous behavior that circular dichroism, which is usually found in magnetic resonance, is absent in the resonance signal of the electromagnon. The microscopic mechanism of the electromagnon in ${\mathrm{CuFeO}}_{2}$ is also discussed.

Polar octahedral rotations, cation displacement and ferroelectricity in multiferroic SmCrO3

Our thorough synchrotron diffraction studies provide a clue on the origin of ferroelectricity in SmCrO3. Careful observation demonstrates that polar order develops in the paramagnetic state. Rietveld refinement of the diffraction data confirms that emergence of polar order is correlated with the structural transformation from centrosymmetric Pbnm to non-centrosymmetric Pna21 space group of the distorted orthorhombic structure. Rotations of polar CrO6 octahedra and Sm displacement are proposed to be correlated with the emergence of polar order, which is extended over a wide temperature range and increases gradually with decreasing temperature. This is consistent with the relaxor behavior as evident from the frequency-dependent dielectric response satisfying the Vogel-Fulcher law. A non-collinear to collinear spin transformation is suggested well below the spin reorientation transition. Appearance of ferroelectricity without any correlation to the antiferromagnetic order in SmCrO3 suggests a new class of ferroelectricity. All-electron full-potential first-principles calculation demonstrates significant Sm-Cr hybridization near the Fermi level, which substantiates the experimental findings.

Magnetic structure map for face-centered tetragonal iron: Appearance of a collinear spin structure

For face-centered cubic (fcc) and tetragonal (fct) iron a large number of magnetic configurations as a function of crystal structural parameters were studied by means of density functional theory. The stability of magnetic structures was defined by the magnetic re-orientation energy $\Delta {E}^i_\text{reor}$ as the difference of the total energy of configuration $i$ and that of the fcc ferromagnetic state. The Cluster Expansion technique was applied to several volumes deriving $\Delta {E}_\text{reor}$ for more than 90.000 collinear spin structures for each volume. A variety of structures with promisingly low $\Delta {E}_\text{reor}$ were tetragonally distorted according to a two-dimensional mesh defined by volume per atom and $c/a$ ratio of the distortion. At each of the points on this mesh $\Delta E_\text{reor}$ of all collinear structure were compared to results for non-collinear spin spirals (SS) which were calculated for a grid of propagation directions. The lowest $\Delta {E}_\text{reor}$ of all investigated spin structures then defined the magnetic structure map spanned by volume per atom and $c/a$ ratio. Three local minima were identified and for each of the minima SS were calculated on a fine grid of propagation vectors. For the volume per atom of 10.6 \AA$^3$ and the distortion range $0.94 \le c/a \le 1.01$ we found a new, surprisingly simple collinear spin structure with four atoms per fct unit cell to be the most stable one. This structure was called AFM/NM because it consists of two atoms with anti-ferromagnetically ordered local moments of $\pm 1.8 \mu_\text{B}$ and of two nonmagnetic atoms with zero local moment. It seems that the newly detected AFM/NM structure explains a variety of puzzling experimental results.

Emergence of spin spiral magnetic order in Mn based inverse Heusler alloys

In this article we demonstrate, by first principles density functional calculations, the emergence of spin-spiral magnetic order in Mn2NiX(X=Al,Ga,In,Sn) inverse Heusler alloys with the application of pressure. This noncollinearity originates from the features in the band structures and the nesting of fermi surfaces of collinear spin bands. The calculated interatomic magnetic exchange parameters suggest that the frustrations in the Mn sublattice with octahedral symmetry are responsible for the stabilization of a noncollinear state. We propose that the pressure induced stabilization of spin-spiral magnetic order is a general feature of magnetic alloys crystallizing in inverse Heusler structures.

Pinned magnetic moments in exchange bias: Role of the antiferromagnetic bulk spin structure

Magneto-optical Kerr effect measurements of epitaxial AFM/FM bilayers and FM/AFM/FM trilayers on ${\mathrm{Cu}}_{3}$Au(001), where ``AFM'' stands for a Ni${}_{25}$Mn${}_{75}$ antiferromagnetic layer, and ``FM'' for ferromagnetic layers that are either Ni or Ni/Co with out-of-plane or in-plane easy axis of magnetization, show that trilayers with collinear magnetization directions of both FM layers exhibit always a much lower exchange bias field ${H}_{\mathrm{eb}}$ at a fixed temperature compared to bilayers of the same Ni${}_{25}$Mn${}_{75}$ thickness. At the same time, the blocking temperature for exchange bias ${T}_{b}$ is strongly reduced. In trilayers with orthogonal easy axes of the two FM layers (in-plane and out-of-plane), in contrast, both ${H}_{\mathrm{eb}}$ and ${T}_{b}$ are nearly identical to that of the corresponding bilayers. Such a behavior can be explained by pinned magnetic moments inside the bulk of the AFM layer that coexist independently for orthogonal spin directions, but have to be equally shared between both interfaces in the case of collinear spin directions. This result thus also confirms a 3Q-like noncollinear spin structure of Ni${}_{25}$Mn${}_{75}$.

Combustion synthesis of Co2 + substituted Li0.5Cr0.5Fe2O4 nano-powder: Physical and magnetic interactions

Nanocrystalline ferrite powders of Co2+ substituted Li0.5Cr0.5Fe2O4 were synthesized by sol-gel auto-combustion method. The samples were obtained by annealing at relatively low temperature at 600°C and investigated by XRD, TEM, IR, magnetization, and dielectric and resistivity measurements. Lattice parameter, X-ray density, crystallite size and bulk density are found to increase, whereas specific surface area and porosity size showed the decreasing trend with the Co2+ substitution. Splitting of major absorption bands related to Li+ substituted ferrites was observed in IR spectra. Site occupancy is obtained from XRD and the variation of the cation distribution has been discussed on the basis of site preference of the substituting cations. Substitution of the magnetic Co2+ ions considerably improved the magnetic properties; as reflected by the advancement in the values of saturation magnetization and coercivity. The variation of the magneton number with the Co2+ content is satisfactorily explained on the basis of Néel's collinear spin ordering model. Resistivity plots show the semiconducting nature of the synthesized samples. The observed variation in resistivity is explained by Verwey hopping mechanism. The dielectric constant and dielectric loss tangent were also studied as a function of temperature.

Series of phase transitions and multiferroicity in the quasi-two-dimensional spin-12triangular-lattice antiferromagnetBa3CoNb2O9

We have investigated the magnetic and electric ground states of a quasi-two-dimensional triangular lattice antiferromagnet (TLAF), ${\mathrm{Ba}}_{3}{\mathrm{CoNb}}_{2}{\mathrm{O}}_{9}$, in which the effective spin of Co${}^{2+}$ is 1/2. At zero field, the system undergoes a two-step transition upon cooling at ${T}_{N2}=1.36$ K and ${T}_{N1}=1.10$ K and enters a 120${}^{\ensuremath{\circ}}$ ordered state. By applying magnetic fields, a series of spin states with fractions of the saturation magnetization ${M}_{s}$ are observed. They are spin states with 1/3, 1/2, 2/3 (or $\sqrt{3}/3$) ${M}_{s}$. The ferroelectricity emerges in all spin states, either with collinear or noncollinear spin structure, which makes ${\mathrm{Ba}}_{3}{\mathrm{CoNb}}_{2}{\mathrm{O}}_{9}$ another unique TLAF exhibiting both a series of magnetic phase transitions and multiferroicity. We discuss the role of quantum fluctuations and magnetic anisotropy in contributing more complex phase diagram compared to its sister multiferroic TLAF compound ${\mathrm{Ba}}_{3}$NiNb${}_{2}{\mathrm{O}}_{9}$ [J. Hwang et al., Phys. Rev. Lett. 109, 257205 (2012)].

Tuning of magnetic transition temperatures in nanoparticles of CoCr2O4 multiferroic by B-site mixing

Pure CoCr2−xFexO4 nanoparticles synthesized through conventional coprecipitation technique show particle size distribution in the range of 16–20 and 6–10nm for x=0.1 and 0.2 respectively. Magnetic and specific heat measurements show an enhancement of paramagnetic to collinear ferrimagnetic transition temperature, Tc from 100 to 110K and to a short range non-collinear spiral ordering, Ts from 18 to 36K with increasing x from 0.1 to 0.2 respectively. In addition, a strong disagreement between the paramagnetic moment obtained from the fitting of χ−1=T/C+1/χ0–b/(T−θ) and ferrimagnetic moment measured from the M vs. H loop at 10K corroborates the nonsaturation behavior of magnetization at 50–100kOe field and an order of magnitude higher coercivity (Hc). The enhancement of Tc and Ts with increasing Fe concentration is attributed to an intrinsic change in non-collinear to collinear spin structure and strong JA–B interaction.

Heisenberg-Kitaev model on the hyperhoneycomb lattice

Motivated by recent experiments on $\ensuremath{\beta}$-Li${}_{2}$IrO${}_{3}$, we study the phase diagram of the Heisenberg-Kitaev model on a three-dimensional lattice of tricoordinated Ir${}^{4+}$, dubbed the hyperhoneycomb lattice. The lattice geometry of this material, along with Ir${}^{4+}$ ions carrying ${J}_{\mathrm{eff}}=1/2$ moments, suggests that the Heisenberg-Kitaev model may effectively capture the low-energy spin-physics of the system in the strong-coupling limit. Using a combination of semiclassical analysis, exact solution, and slave-fermion mean-field theory, we find, in addition to the spin liquid, four different magnetically ordered phases depending on the parameter regime. All four magnetic phases---the N\'eel, the polarized ferromagnet, the skew-stripy, and the skew-zig-zag---have collinear spin ordering. The three-dimensional ${Z}_{2}$ spin liquid, which extends over an extended parameter regime around the exactly solvable Kitaev point, has a gapless Majorana mode with a deformed Fermi circle (codimensions, ${d}_{c}=2$). We discuss the effect of the magnetic field and finite temperature on different phases that may be relevant for future experiments.

Noncollinear Spin States for Density Functional Calculations of Open-Shell and Multi-Configurational Systems: Dissociation of MnO and NiO and Barrier Heights of O3, BeH2, and H4

When the spins of molecular orbitals are allowed to be aligned with different directions in space rather than being aligned collinearly, the resulting noncollinear spin orbitals add extra flexibility to variational optimization of the orbitals, and solutions obtained with collinear spin orbitals may be unstable with respect to becoming noncollinear in the expanded variational space. The goal of the present work is to explore whether and in what way the molecular orbitals of the Kohn-Sham density functional theory become noncollinear when fully optimized for multi-reference molecules, transition states, and reaction paths. (We note that a noncollinear determinant has intermediate flexibility between a collinear determinant and a linear combination of many collinear determinants with completely independent coefficients. However, the Kohn-Sham method is defined to involve the variational optimization of a single determinant, and a noncollinear determinant represents the limit of complete optimization in the Kohn-Sham scheme.) We compare the results obtained with the noncollinear Kohn-Sham (NKS) scheme to those obtained with the widely used unrestricted Kohn-Sham (UKS) scheme for two types of multi-reference systems. For the dissociation of the MnO and NiO transition metal oxides, we find UKS fails to dissociate to the ground states of neutral atoms, while NKS dissociates to the correct limit and predicts potential energy curves that vary smoothly at intermediate bond lengths. This is due to the instability of UKS solutions at large bond distances. For barrier heights of O3, BeH2, and H4, NKS is shown to stabilize the multi-reference transition states by expanding the variational space. Although the errors vary because they are closely coupled with the capability of the employed exchange-correlation functionals in treating the multi-configurational states, these findings demonstrate that results with collinear spin orbitals should be further scrutinized, and future development of exchange-correlation functionals for multi-reference systems should incorporate the flexibilities of NKS.

Relaxor-like improper ferroelectricity induced by Si · Sj-type collinear spin ordering in a M-type hexaferrite PbFe6Ga6O19

M-type hexaferrites with the magnetoplumbite structure are industrially mass produced uniaxial magnets that possess the simplest crystal structure among various hexaferrites. Herein we present an intriguing phenomenon of relaxor-like ferroelectricity observed in a M-type hexaferrite PbFe6Ga6O19 (PFGO) single crystal. The unique feature of the present discovery is that the improper polarization (∼30nCcm−2 at 5K) with a direction parallel to hexagonal [11¯0] arises from the collinear Si·Sj-type spin exchange coupling. This collinear coupling, in turn, is triggered by selective local spin reversal of the Fe3+ magnetic moment at the octahedral 2a sublattice. The frequency-dependent dielectric data indicated relaxor-like responses of PFGO with the Vogel–Fulcher freezing temperature of ∼17K. This freezing temperature for the polar-cluster reorientation coincided with the onset of a rapid decrease in polarization with temperature.

Variation in the structural and magnetic properties of heterovalent Mn2+–Si4+ substituted MnCrFeO nanoparticles

We have synthesized heterovalent Mn2+–Si4+ substituted MnCrFeO nanoparticles with a nominal composition Mn1+xSixCrFe1−2xO4 (x = 0.0–0.3) via sol–gel auto-combustion method. X-ray diffractometer, transmission electron microscopy, magnetization measurements were used to study the effects of Mn2+–Si4+ heterovalent ions on the structural and magnetic properties of MnCrFeO. As a result, it was found that the Mn2+–Si4+ ions affect the crystalline structures and magnetic properties of MnCrFeO. X-ray diffraction pattern showed that the samples have the single phase cubic spinel structure of which the lattice constant slightly increased upon Mn2+–Si4+ substitution. The mean crystallite size of the samples was in the range of 21–27 nm as deduced from the XRD line broadening. Cation distribution was estimated using XRD data and it shows that Mn2+ and Si4+ ions prefer tetrahedral A-site. Magnetic measurement shows that saturation magnetization and magneton number decreased with Mn2+–Si4+ substitution with the formation of a collinear spin arrangement.

Spin configurations of the four-sublattice model on rectangular lattice

The spin configurations of the four-sublattice model with seven exchange interaction parameters (four of them are taken as direct-exchange interactions, the other three as super-exchange interactions) on a two-dimensional rectangular lattice have been investigated using a matrix method. For the four sublattices, using the two sets of the exchange parameters, we obtain collinear and non-collinear spin configurations for the given propagation vectors in the ground and the first excited states. When k=0, spin configuration is collinear ferromagnetic mode in the ground state and collinear antiferromagnetic mode in the first excited state. When k=[0.5, 0.5], spin configurations are non-collinear, that is, canted structures.

Exchange interactions and frustrated magnetism in single-side hydrogenated and fluorinated graphene

Magnetism in single-side hydrogenated (C${}_{2}$H) and fluorinated (C${}_{2}$F) graphene is analyzed in terms of the Heisenberg model with parameters determined from first principles. We predict a frustrated ground state for both systems, which means the instability of collinear spin structures and sheds light on the absence of a conventional magnetic ordering in defective graphene demonstrated in recent experiments. Moreover, our findings suggest a highly correlated magnetic behavior at low temperatures offering the possibility of a spin-liquid state.

Ferroelectric ground state and polarization-switching path of orthorhombic YMnO3with coexistingE-type and cycloidal spin phases

Orthorhombic YMO${}_{3}$ ($o$-YMO) is currently being intensively investigated since a single-crystalline thin film of $o$-YMO recently showed a pronounced degree of magnetoelectric coupling. According to first-principles calculations, the ferroelectric ground state is represented by two degenerate $E$-type collinear spin configurations with the computed polarization $P$ of \ensuremath{\sim}1.4 \ensuremath{\mu}C/cm${}^{2}$. The $bc$-cycloidal spin phase is identified as the spin configuration that corresponds to the transition state in the $+P\ensuremath{\leftrightarrow}\ensuremath{-}P$ polarization switching. The remarkable coexistence of the $E$-type and cycloidal spin phases below \ensuremath{\sim}40 K is attributed to a small value of the Kohn-Sham energy difference between these two phases, 2.2 meV per formula unit. A modulated spin structure, which is characterized by the tilting of the Mn-spin vectors to the $a$-axis direction of Pbnm setting, is proposed to account for the observed strong magnetic-field-dependent polarization in $o$-YMO.

Collinear and noncollinear spin ground state of wurtzite CoO

Collinear and noncollinear spin structures of wurtzite phase CoO often appearing in nanosized samples are investigated using first-principles density functional theory calculations. We examined the total energy of several different spin configurations, electronic structure, and the effective magnetic coupling strengths. It is shown that the AF3-type antiferromagnetic ordering is energetically most stable among possible collinear configurations. Further, we found that a spiral spin order can be stabilized by including the relativistic spin-orbit coupling and the noncollinearity of spin direction. Our result suggests that a noncollinear spin ground state can be observed in the transition-metal-oxide nanostructures, which adds an interesting aspect to the nanomagnetism study.

Computer Aided X-Ray Diffraction Intensity Analysis for Spinels: Hands-On Computing Experience

The mineral having chemical compositional formula MgAl2O4 is called “spinel”. The ferrites crystallize in spinel structure are known as spinel-ferrites or ferro-spinels. The spinel structure has a fcc cage of oxygen ions and the metallic cations are distributed among tetrahedral (A) and octahedral (B) interstitial voids (sites). The X-ray diffraction (XRD) intensity of each Bragg plane is sensitive to the distribution of cations in the interstitial voids of the spinel lattice. This leads to the method of determination of distribution of cations in the spinel oxides through XRD intensity analysis. The computer program for XRD intensity analysis has been developed in C language and also tested for the real experimental situation by synthesizing the spinel ferrite materials Mg0.6Zn0.4AlxFe2xO4 and characterized them by X-ray diffractometry. The compositions of Mg0.6Zn0.4AlxFe2-xO4(x = 0.0 to 0.6) ferrites have been prepared by ceramic method and powder X-ray diffraction patterns were recorded. Thus, the authenticity of the program is checked by comparing the theoretically calculated data using computer simulation with the experimental ones. Further, the deduced cation distributions were used to fit the magnetization data using Localized canting of spins approach to explain the “recovery” of collinear spin structure due to Al substitution in Mg-Zn ferrites which is the case if A-site magnetic dilution and non-collinear spin structure. Since the distribution of cations in the spinel ferrites plays a very important role with regard to their electrical and magnetic properties, it is essential to determine the cation distribution in spinel lattice. Keywords—Spinel ferrites, Localized canting of spins, X-ray diffraction, Programming in Borland C.