Collinear Spin Order Research Articles

Spin-charge coupling and decoupling in perovskite-type iron oxides (Sr1−xBax)2/3La1/3FeO3

The perovskite-type iron oxide Sr$_{2/3}$La$_{1/3}$FeO$_3$ is known to show characteristic spin-charge ordering (SCO), where sixfold collinear spin ordering and threefold charge ordering are coupled with each other. Here, we report the discovery of a spin-charge decoupling and an antiferromagnetic (AFM) state competing with the SCO phase in perovskites (Sr$_{1-x}$Ba$_x$)$_{2/3}$La$_{1/3}$FeO$_3$. By comprehensive measurements including neutron diffraction, M$\"{o}$ssbauer spectroscopy, and x-ray absorption spectroscopy, we found that the isovalent Ba$^{2+}$ substitution systematically reduces the critical temperature of the SCO phase and additionally yields the spin-charge decoupling in $x$ > 0.75. Whereas the ground state remains in the SCO phase in the whole $x$ region, an unexpected G-type AFM phase with incoherent charge ordering or charge fluctuation appears as the high-temperature phase in the range of $x$ > 0.75. Reflecting the competing nature between them, the G-type AFM phase partially exists as a metastable state in the SCO phase at low temperatures. We discuss the origin of the spin-charge decoupling and the emergence of the G-type AFM phase with charge fluctuation in terms of the bandwidth reduction by the Ba substitution.

Exploration of trivial and nontrivial electronic phases and of collinear and noncollinear magnetic phases in low-spin d5 perovskites

The $4d$ and $5d$ transition metal oxides have become important members of the emerging quantum materials family due to competition between onsite Coulomb repulsion ($U$) and spin-orbit coupling (SOC). Specifically, the systems with $d^5$ electronic configuration in an octahedral environment are found to be capable of posessing invariant semimetallic state and perturbations can lead to diverse magnetic phases. In this work, by formulating a multi-band Hubbard model and performing SOC tunable DFT+$U$ calculations on a prototype SrIrO$_3$ and extending the analysis to other iso-structural and isovalent compounds, we present eight possible electronic and magnetic configurations in the $U$-SOC phase diagram that can be observed in the family of low-spin $d^5$ perovskites. They include the protected Dirac semimetal state, metal and insulator regimes, collinear and noncollinear spin ordering. The latter is explained through connecting hopping interactions to the rotation and tilting of the octahedra as observed in GdFeO$_3$. Presence of several soft phase boundaries makes the family of $d^5$ perovskites an ideal platform to study electronic and magnetic phase transitions under external stimuli.

Microstructural, dielectric, magneto-electric and optical properties of single phase Ca3CoMnO6

Type II intrinsic multiferroics oxide Ca3CoMnO6 (CCMO) having collinear spin ordering and non-zero polarization is a fascinating compound from the view point of fundamental and technological applications. Room temperature properties of Ca2.7Sr0.3CoMn1-xFexO6 ceramics with dilute Fe doping (x) have been investigated. Rietveld refinements of X-ray diffraction data confirmed single rhombohedral phase with R-3c space group for all the samples. Frequency dependent dielectric properties with low loss tangents measured in frequency range of 1 MHz to 1 GHz, showed an increase in the real permittivity upon Fe doping within the entire frequency range; which is attributed to doping induced optimal modification in Co/Mn ratios. Room temperature ME coupling coefficient of the order of 1.7 mV/cm Oe for pure CCMO is achieved and the mechanism is explained through exchange striction model. It suggested that the dilute Fe substitution (or Mn deficiency) break the inter chain interactions to some extent, in otherwise, quasi collinear magnetic chain structure. Kubelka-Munk function was applied to analyse the optical measurements, which revealed an increase in reflectance and refractive indices with doping of Fe into pure CCMO. Consequently, the optical band gaps were found to systematically decrease from 2.25 eV to 1.80 eV upon Fe doping at the Mn-site.

Fe57 Mössbauer spectroscopy study of cycloidal spin arrangements and magnetic transitions in BiFe1−xCoxO3

We report results of a $^{57}\mathrm{Fe}$ M\"ossbauer study focused on Co-substituted $\mathrm{BiF}{\mathrm{e}}_{1\ensuremath{-}x}\mathrm{C}{\mathrm{o}}_{x}{\mathrm{O}}_{3}$ ($x=0.05$). The experimental spectra were analyzed assuming the space-modulated cycloidal magnetic structure with high values of the anharmonicity parameter $m=0.47\ensuremath{-}0.92$ (at 4.7 K). The $m$ parameter increases with increasing temperature to reach its maximum value ($m\ensuremath{\approx}1$) for $x=0.10$, 0.15 corresponding to the transition to a collinear antiferromagnetic structure of easy-plane type (${\ensuremath{\mu}}_{\mathrm{Fe}}\ensuremath{\perp}{c}_{h}$). Such an unusual trend of the anharmonicity parameter $m$(T) increasing with temperature was well reproduced by the molecular field model in which the low-spin to intermediate-spin transition of $\mathrm{C}{\mathrm{o}}^{3+}$ is assumed. At low cobalt content, $\mathrm{BiF}{\mathrm{e}}_{0.95}\mathrm{C}{\mathrm{o}}_{0.05}{\mathrm{O}}_{3}$, the cycloidal structure is retained but with a very high degree of anharmonicity, corresponding to the nearly collinear spin order.

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

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

Ising-XY Transition in Three-dimensional Frustrated Antiferromagnets with Collinear Spin Ordering

Using Monte Carlo simulations, we study the critical behavior of two models of frustrated XY antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state. We consider a classic antiferromagnet on a body-centered cubic lattice with an additional antiferromagnetic exchange interaction between next-nearest spins, and a ferromagnet with an extra antiferromagnetic intralayer exchange. In both models, a single first-order transition on the discrete and continuous order parameters is found. Observed critical pseudo-exponents are in agreement with exponents of XY magnets with a planar spin ordering like a stacked-triangular antiferromagnet and helimagnets belonging to the same symmetry class.

Critical and multicritical behavior in the Ising–Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang–Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.

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

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

Rapid preparation and magnetodielectric properties of trirutile Cr2WO6

Dense pellets of &amp;gt; 99% purity trirutile Cr2WO6 were prepared in one step from starting oxides using spark plasma sintering, leading to simultaneous reaction and consolidation in 3 min at 1473 K. The reducing environment during processing may be partly responsible for the rapid reaction time in these oxides, with partial reduction of Cr3+ and the associated oxygen vacancies allowing rapid diffusion of cations. The low-temperature physical properties of Cr2WO6 were examined, and a new transition at T = 5.9 K was observed as an anomaly in the temperature-dependent dielectric permittivity and a corresponding anomaly in the specific heat. A strong enhancement of the magnetocapacitance is observed below this transition temperature at T = 5.9 K and may be associated with a change from collinear spin order to more complex spin order.

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.

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.

Spin dynamics in the multiferroic materials (invited)

We report high resolution inelastic neutron scattering measurements and spin dynamics calculations in two multiferroic materials: the geometrically frustrated triangular lattice CuFeO2 and mineral Hübnerite MnWO4. In un-doped CuFeO2 a low-T collinear spin structure is stabilized by long range magnetic interactions. When doped with a few percent of gallium, the spin order evolves into a complex noncollinear configuration and the system becomes multiferroic. Similarly, the ground state collinear spin order in pure MnWO4 results from delicate balance between competing magnetic interactions up to 11th nearest neighbors and can be tuned by substitution of Mn ions with magnetic or nonmagnetic impurities. The comprehensive investigation of spin dynamics in both systems help to understand the fundamental physical process and the interactions leading to the close interplay of magnetism and ferroelectricity in this type of materials.

Mossbauer, Raman and X-ray diffraction studies of superparamagnetic NiFe 2O 4 nanoparticles prepared by sol–gel auto-combustion method

Superparamagnetic nickel ferrite single phase nanoparticles with the average crystallite size of ∼9 nm have been synthesized at a low temperature (220 °C) by the sol–gel auto-combustion method. In the present study the as prepared powder was further calcined at different temperatures for 4 h, resulting in nanoparticles of larger size. The nanoparticles exhibited superparamagnetic behavior and changes in cation distribution as revealed by the Mossbauer, Raman and X-ray diffraction studies. The Mossbauer spectra collected at 5 K and under 5 T applied magnetic field showed mixed spinel structure and canted spin order for the nanoparticles, whereas there is collinear spin order with inverse spinel structure for larger particles. The vibrational spectra of the nanoparticles showed a redshift and broadening in the Raman line shape due to confinement effects.

Large ferroelectric polarization in the new double perovskite NaLaMnWO6 induced by non-polar instabilities

Based on density functional theory calculations and group theoretical analysis, we have studied NaLaMnWO(6) compound which has been recently synthesized [G. King, A. Wills and P. M. Woodward, Phys. Rev. B: Condens. Matter, 2009, 79, 224428] and belongs to the AA'BB'O(6) family of double perovskites. At low temperature, the structure has monoclinic P2(1) symmetry, with layered ordering of the Na and La ions and rocksalt ordering of Mn and W ions. The Mn atoms show an antiferromagnetic collinear spin ordering, and the compound has been reported as a potential multiferroic. By comparing the low symmetry structure with a parent phase of P4/nmm symmetry, two distortion modes are found dominant. They correspond to MnO(6) and WO(6) octahedron tilt modes, often found in many simple perovskites. While in the latter these common tilting instabilities yield non-polar phases, in NaLaMnWO(6) the additional presence of the A-A' cation ordering is sufficient to make these rigid unit modes a source of the ferroelectricity. Through a trilinear coupling with the two unstable tilting modes, a polar distortion is induced, although the system has no intrinsic polar instability. The calculated electric polarization resulting from this polar distortion is as large as ∼16 μC cm(-2). Despite its secondary character, this polarization is coupled with the dominant tilting modes and its switching is bound to produce the switching of one of two tilts, enhancing in this way a possible interaction with the magnetic ordering. The transformation of common non-polar purely steric instabilities into sources of ferroelectricity through a controlled modification of the parent structure, as done here by the cation ordering, is a phenomenon to be further explored.

Switching the ferroelectric polarization in theS=1∕2chain cuprateLiCuVO4by external magnetic fields

We present a detailed study of the complex dielectric constant and the ferroelectric polarization in multiferroic $\mathrm{Li}\mathrm{Cu}\mathrm{V}{\mathrm{O}}_{4}$ as function of temperature and external magnetic field. In zero external magnetic field, a spiral spin order with an $\mathbf{a}\mathbf{b}$ helix and a propagation vector along the crystallographic $\mathbf{b}$ direction is established, which induces ferroelectric order with spontaneous polarization parallel to $\mathbf{a}$. The direction of the helix can be reoriented by an external magnetic field and allows switching of the spontaneous polarization. We find a strong dependence of the absolute value of the polarization for different orientations of the spiral plane. Above $7.5\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, $\mathrm{Li}\mathrm{Cu}\mathrm{V}{\mathrm{O}}_{4}$ reveals collinear spin order and remains paraelectric for all field directions. Thus, this system is ideally suited to check the symmetry relations for spiral magnets as predicted theoretically. The strong coupling of ferroelectric and magnetic order is documented and the complex $(H,T)$ phase diagram is fully explored.

Spin ordering in three-dimensional crystals with strong competing exchange interactions

In this paper we discuss magnetic ordering in three-dimensional crystals in which Heisenberg exchange interactions appear to dominate. Particular emphasis is placed on systems with strong competing exchange interactions, called frustrated spin systems. In the absence of such competition, one finds collinear spin ordering. However, strong competing interactions lead to non-collinear structures, often spirals and many variations thereof. The problem of understanding the origin and physical properties of such spin states within the classical Heisenberg model has been intensively addressed by a large community of researchers over the last 2–3 decades. The study of such problems actually began about five decades ago, and led to a large body of literature that has been overlooked in the publications of the last 2–3 decades (with two very recent exceptions). The early work established important fundamental concepts, including an unconventional theoretical approach, the generalized Luttinger–Tisza method and the idea of forced degeneracy. This resulted in the spin state called a ferrimagnetic spiral (FS), which enabled understanding of puzzling neutron diffraction data, plus NMR and ESR measurements, on the spinels XCr2O4, X = Mn, Co. Additional new aspects of this magnetic ordering have been uncovered in two very recent experimental works, indicating a partial spin-liquid-like behaviour and production of ferroelectricity by the pure spiral component of the FS. This exciting relevance of the early work to these modern results and the general lack of awareness of the early work has provided a source of motivation for this review, which covers that early body of work, both theoretical and experimental, and which also connects to the recent studies. A thorough discussion of the calculations, and comparison with experiments is presented. It will be seen that fundamental puzzles remain for these systems.

Criticality in quantum triangular antiferromagnets via fermionized vortices

We reexamine two-dimensional frustrated quantum magnetism with the aim of exploring new critical points and critical phases. We study easy-plane triangular antiferromagnets using a dual vortex approach, fermionizing the vortices with a Chern-Simons field. Herein we develop this technique for integer-spin systems which generically exhibit a simple paramagnetic phase as well as magnetically ordered phases with coplanar and collinear spin order. Within the fermionized-vortex approach, we derive a low-energy effective theory containing Dirac fermions with two flavors minimally coupled to a U(1) and a Chern-Simons gauge field. At criticality we argue that the Chern-Simons gauge field can be subsumed into the U(1) gauge field, and up to irrelevant interactions one arrives at quantum electrodynamics in $2+1$ dimensions (QED3). Moreover, we conjecture that critical QED3 with full SU(2) flavor symmetry describes the O(4) multicritical point of the spin model where the paramagnet and two magnetically ordered phases merge. The remarkable implication is that QED3 with flavor SU(2) symmetry is dual to ordinary critical ${\ensuremath{\Phi}}^{4}$ field theory with O(4) symmetry. This leads to a number of unexpected, verifiable predictions for QED3. A connection of our fermionized-vortex approach with the dipole interpretation of the $\ensuremath{\nu}=1∕2$ fractional quantum Hall state is also demonstrated. The approach introduced in this paper will be applied to spin-$1∕2$ systems in a forthcoming publication.

Quantum fluctuations in geometrically frustrated antiferromagnet

Many geometrically frustrated antiferromagnets have thermodynamically degenerate classical ground states. I investigate the effects of quantum fluctuations as a driving force of symmetry breaking, for the Heisenberg model on the pyrochlore lattice at zero temperature. In the semiclassical limit, I find that a collinear spin order minimizes the zero-point energy and is most stabilized among q =0 orders. In the quantum limit, a two-stage symmetry breaking in the spin-singlet sector is predicted, and the system is separate into two intertwining parts. One part shows a triple- q order of dimers, with a large stabilization energy and gapful excitations. The other part shows a uniform order of either dimers or tetramers, with a substantially reduced energy scale and gapless excitations. The presence of multiple energy scales is a manifestation of geometrical frustration.

Temperature dependences of the high-field magnetization of dilute frustrated ferrimagnetic spinels

Results are presented of an investigation of the magnetic properties of dilute frustrated ferrimagnetic spinels Li0.5Fe2.5−xGaxO4 (x=0.8–1.2), which characterize the main parameters of the ferrimagnetic state and provide evidence of local violation of collinear spin ordering and frustrations. In particular, measurements were made of the concentration dependences of the magnetic moment n0(x) and the Curie point T c (x), the magnetization isotherms σ T (H) at T=4.2 K and H⩽10 kOe, and also the low-and high-field magnetization polytherms σ H (T). It was established that for x⩾0.8 in fields exceeding the technical saturation field H s ∼2 kOe, the temperature dependences of the high-field magnetization σ H (T) between 4.2 and 230 K cannot be described by the Bloch T3/2 law whereas this law is satisfied for undiluted Li spinel (x=0). Over the entire temperature range (4.2–230 K) the experimental curves σ H (T) may be approximated by σ H (T)=σ0(1−AT3/2 − BT5/2) for x=0.8–1.0 and σ H (T)=σ0[1−CT3/2exp(μ(H−H0)/kBT)] for x=1.1, 1.2, where μH0∼15 K is the internal field produced by competition between exchange interactions and frustrations.

Temperature dependence of the heat capacity and saturation magnetization of dilute reentrant ferrimagnetic spinels

Using model objects consisting of dilute reentrant spinels Li0.5Fe2.5−xGaxO4 with x=1.0–1.2, this paper describes the temperature dependence of the magnetic contribution to the heat capacity, Cm(T), at H=0 and temperatures exceeding the freezing temperature (Tf∼10 K) and, for T⩾4.2 K, the low-field magnetization σH(T) and the saturation magnetization σS(T), as well as the magnetization isotherms σT(T) in fields of up to 10 kOe. The specific features of the behavior of the overall characteristics of Cm(T) and σS(T) are found for the states of a frustrated ferrimagnetic that occur in the conditions considered here (H=0 and T>Tf or T⩾4.2 K and strong magnetic fields) and are discussed in connection with changes in the magnetic excitation spectrum caused by local breakdowns of collinear spin ordering and frustrations.