Incommensurate Spiral Phase Research Articles

Incommensurate spiral magnetic order on anisotropic triangular lattice: Dynamical mean-field study in a spin-rotating frame

We study the ground-state magnetism of the half-filled Hubbard model on the anisotropic triangular lattice, where two out of three bonds have hopping $t$ and the third one has $t^\prime$ in a unit triangle. Working in a spin-rotating frame and using the density matrix renormalization group method as an impurity solver, we provide a proper description of incommensurate magnetizations at zero temperature in the framework of the dynamical mean-field theory (DMFT). It is shown that the incommensurate spiral magnetic order for $t^\prime/t\gtrsim 0.7$ survives the dynamical fluctuations of itinerant electrons in the Hubbard interaction range from the strong-coupling (localized-spin) limit down to the insulator-to-metal transition. We also find that the magnetic moment reduction from the localized-spin limit is pronounced in the vicinity of the transition between the commensurate N\'eel and incommensurate spiral phases at $t^\prime/t\sim 0.7$. When the anisotropy parameter $t^\prime/t$ increases from the N\'eel-to-spiral transition, the magnitude of the magnetic moment immediately reaches a maximum and then rapidly decreases in the range of larger $t^\prime/t$ including the isotropic triangular lattice point $t^\prime/t=1$. This work gives a solid foundation for further extension of the study including nonlocal correlation effects neglected at the standard DMFT level.

Spiral versus modulated collinear phases in the quantum axial next-nearest-neighbor Heisenberg model

Motivated by the discovery of spiral and modulated collinear phases in several magnetic materials, we investigate the magnetic properties of Heisenberg spin S=1/2 antiferromagnets in 2 and 3 dimensions, with frustration arising from 2nd-neighbor couplings in one axial direction (the ANNNH model). Our results clearly demonstrate the presence of an incommensurate spiral phase at T=0 in 2 dimensions, extending to finite temperatures in 3 dimensions. The crossover between N\'eel and spiral order occurs at a value of the frustration parameter considerably above the classical value 0.25, a sign of substantial quantum fluctuations. We also investigate a possible modulated collinear phase with a wavelength of 4 lattice spacings, and find that it has substantially higher energy and hence is not realized in the model.

Intertwined nematic orders in a frustrated ferromagnet

We investigate the quantum phases of the frustrated spin-$\frac{1}{2}$ $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice with ferromagnetic $J_1$ and antiferromagnetic $J_2$ and $J_3$ interactions. Using the pseudo-fermion functional renormalization group technique, we find an intermediate paramagnetic phase located between classically ordered ferromagnetic, stripy antiferromagnetic, and incommensurate spiral phases. We observe that quantum fluctuations lead to significant shifts of the spiral pitch angles compared to the classical limit. By computing the response of the system with respect to various spin rotation and lattice symmetry-breaking perturbations, we identify a complex interplay between different nematic spin states in the paramagnetic phase. While retaining time-reversal invariance, these phases either break spin-rotation symmetry, lattice-rotation symmetry, or a combination of both. We therefore propose the $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice as a paradigmatic example where different intimately connected types of nematic orders emerge in the same model.

Resummation of fluctuations near ferromagnetic quantum critical points

We present a detailed analysis of the nonanalytic structure of the free energy for the itinerant ferromagnet near the quantum critical point in two and three dimensions. We analyze a model of electrons with an isotropic dispersion interacting through a contact repulsion. A fermionic version of the quantum order-by-disorder mechanism allows us to calculate the free energy as a functional of the dispersion in the presence of homogeneous and spiraling magnetic order. We resum the leading divergent contributions to derive an algebraic expression for the nonanalytic contribution to free energy from quantum fluctuations. Using a recursion which relates subleading divergences to the leading term, we calculate the full $T=0$ contribution in $d=3$. We propose an interpolating functional form, which allows us to track phase transition lines at temperatures far below the tricritical point and down to $T=0$. In $d=2$, quantum fluctuations are stronger, and nonanalyticities are more severe. Using a similar resummation approach, we find that despite the different nonanalytic structures, the phase diagrams in two and three dimensions are remarkably similar, exhibiting an incommensurate spiral phase near the avoided quantum critical point.

Magnetic phase transitions in the NdFe3(BO3)4 multiferroic

Low-temperature studies of the behavior of the sound velocity and attenuation of acoustic modes have been performed on a single crystal NdFe3(BO3)4 Transitions of the magnetic subsystem to the antiferromagnetically ordered state at TN ≈ 30.6 K have been revealed in the temperature behavior of the elastic characteristics. The features in the temperature behavior of elastic characteristics of the neodymium ferroborate and its behavior in the external magnetic field, applied in the basic plane of the crystal, permit us to suppose that the transition to an incommensurate spiral phase is realized in the system. This phase transition behaves as the first order one. H–T phase diagrams for the cases H ∥ a and H ∥ b have been constructed. The phenomenological theory, which explains observed features, has been developed.

Persistent multiferroicity without magnetoelectric effects in CuO

Multiferroicity and magnetoelectric effects in CuO have been investigated by measurements of magnetization, dielectric constant, and electric polarization with and without magnetic fields. Dielectric anomalies which indicate ferroelectric transitions were observed at two magnetic transition temperatures. Ferroelectric polarization was well detected in the incommensurate spiral phase. However, both dielectric constant and polarization have little changes in a 7 T magnetic field. Our study suggests that although with a high multiferroic temperature, the spiral spin structure in CuO is very stable and the induced ferroelectricity sustains even in a high magnetic field, which results in little magnetoelectric effects.

Chemical doping-induced flop of ferroelectric polarization in multiferroicMn0.9Co0.1WO4

We studied the multiferroic properties of the incommensurate spiral phase of ${\text{Mn}}_{1\ensuremath{-}x}{\text{Co}}_{x}{\text{WO}}_{4}$ using single-crystal neutron-diffraction and ferroelectric measurements. Whereas the rotational plane of the spin spiral is parallel to the $b$ axis for $x\ensuremath{\le}0.05$, it flops by $90\ifmmode^\circ\else\textdegree\fi{}$ for $x=0.10$. As a result, the direction of the ferroelectric polarization also flops from the $b$ to the $a$ axis. These results show that the orientation of the ferroelectric polarization in ${\text{MnWO}}_{4}$ can be controlled via chemical doping.

Spiral order induced by distortion in a frustrated square-lattice antiferromagnet

In a strongly frustrated square-lattice antiferromagnet with diagonal coupling J', for J/(2J') < 1, an incommensurate spiral state with propagation vector Q = (\pi +/- \delta, \pi +/- \delta) near (\pi,\pi) competes closely with the Neel collinear antiferromagnetic ground state. For classical Heisenberg spins the energy of the spiral state can be lowered as it adapts to the distortion of the crystal lattice. As a result, a weak superstructural modulation such as exist in doped cuprates might stabilize an incommensurate spiral phase for some range of the parameter J/(2J') close to 1.

Heisenberg magnet with modulated exchange

A modification of the ground state of the classical-spin Heisenberg Hamiltonian in the presence of a weak superstructural distortion of an otherwise Bravais lattice is examined. It is shown that a slight modulation of the crystal lattice with wave vector ${\mathbf{Q}}_{c}$ results in a corresponding modulation of the exchange interaction which, in the leading order, is parametrized by no more than two constants per bond, and perturbs the spin Hamiltonian by adding the ``umklapp'' terms $\ensuremath{\sim}{S}_{\mathbf{q}}^{\ensuremath{\alpha}}{S}_{\mathbf{q}\ifmmode\pm\else\textpm\fi{}{\mathbf{Q}}_{c}}^{\ensuremath{\alpha}}.$ As a result, for a general spin-spiral ground state of the nonperturbed exchange Hamiltonian, an incommensurate shift of the propagation vector Q and additional new magnetic Bragg peaks, at $\mathbf{Q}\ifmmode\pm\else\textpm\fi{}n{\mathbf{Q}}_{c},$ $n=1,2,\dots{},$ appear, and its energy is lowered as it adapts to the exchange modulation. Consequently, the lattice distortion may open a region of stability of the incommensurate spiral phase which otherwise does not win the competition with the collinear N\'eel state. Such is the case for the frustrated square-lattice antiferromagnet. In addition, the umklapp terms provide a commensuration mechanism, which may lock the spin structure to the lattice modulation vector ${\mathbf{Q}}_{c},$ if there is sufficient easy-axis anisotropy, or a magnetic field in an easy plane.

Spin-wave spectrum of a two-dimensional itinerant electron system: Analytic results for the incommensurate spiral phase in the strong-coupling limit

We study the zero-temperature spin fluctuations of a two-dimensional itinerant-electron system with an incommensurate magnetic ground state described by a single-band Hubbard Hamiltonian. We introduce the (broken-symmetry) magnetic phase at the mean-field (Hartree-Fock) level through a \emph{spiral spin configuration} with characteristic wave vector $\gmathbf{Q}$ different in general from the antiferromagnetic wave vector $\gmathbf{Q_{AF}}$, and consider spin fluctuations over and above it within the electronic random-phase (RPA) approximation. We obtain a \emph{closed} system of equations for the generalized wave vector and frequency dependent susceptibilities, which are equivalent to the ones reported recently by Brenig. We obtain, in addition, analytic results for the spin-wave dispersion relation in the strong-coupling limit of the Hubbard Hamiltonian and find that at finite doping the spin-wave dispersion relation has a \emph{hybrid form} between that associated with the (localized) Heisenberg model and that associated with the (long-range) RKKY exchange interaction. We also find an instability of the spin-wave spectrum in a finite region about the center of the Brillouin zone, which signals a physical instability toward a different spin- or, possibly, charge-ordered phase, as, for example, the stripe structures observed in the high-Tc materials. We expect, however, on physical grounds that for wave vectors external to this region the spin-wave spectrum that we have determined should survive consideration of more sophisticated mean-field solutions.

Spin-wave analysis to the spatially anisotropic Heisenberg antiferromagnet on a triangular lattice

We study the phase diagram at T=0 of the antiferromagnetic Heisenberg model on the triangular lattice with spatially-anisotropic interactions. For values of the anisotropy very close to J_alpha/J_beta=0.50, conventional spin wave theory predicts that quantum fluctuations melt the classical structures, for S=1/2. For the regime J_beta<J_alpha, it is shown that the incommensurate spiral phases survive until J_beta/J_alpha=0.27, leaving a wide region where the ground state is disordered. The existence of such nonmagnetic states suggests the possibility of spin liquid behavior for intermediate values of the anisotropy.

Spiral phases in easy plane J1-J2-J3 triangular antiferromagnets

We present the phase diagram of the S = 12 Heisenberg antiferromagnet on triangular lattices with second and third nearest-neighbor couplings (J1-J2-J3 model). In addition to the classical three-sublattice and collinear states, the spin-wave analysis predicts three novel incommensurate spiral phases. For sufficiently small site spins S there exist regions on the phase diagram where the classical spiral states are completely destroyed by quantum fluctuations.

Linear spin waves in a frustrated Heisenberg model

A Heisenberg model, which has the property that its classical ground state shows a continuous transition from the N\'eel to an incommensurate spiral state, is investigated. It is shown that even for arbitrarily large spin these states are not stable with respect to quantum spin fluctuations in a finite region of the parameter space. Outside this region the order of the classical ground state is not de- stroyed. Thus, the results of linear spin-wave theory suggest the existence of a quantum-spin-liquid state between the N\'eel and an ordered incommensurate spiral phase.

The magnetic structure of holmium. I

The magnetic structure of the incommensurate spiral phase of holmium has been studied using elastic neutron scattering for temperatures between 30 and 18K, the temperature region just above the transition to a ferromagnetic cone phase with a wavevector of 1/6 c*. The results show that the structure consists of commensurate regions separated by spin discommensurations or spin slips. In the commensurate regions, pairs of spins (one on each sublattice) deviate by about 10 degrees from each of the easy directions within the plane, and there is evidence for a c axis antiferromagnetic component which changes domain type from one commensurate region to another. The spin slips, which occur on alternate sublattices, have one plane of spins aligned with the planar easy directions, and are found to disturb the commensurate regions for about three planes on either side of each spin slip.

New high-pressure spiral phase of EuAs3.

At about $P=17$ kbar Eu${\mathrm{As}}_{3}$ undergoes a pressure-induced phase transition from a commensurate phase with magnetic moments parallel to \ifmmode\pm\else\textpm\fi{} [010] to an incommensurate spiral phase with magnetic moments modulated in the (010) plane. At $P=4$ kbar, the ambient pressure commensurate and incommensurate phases are still stable. However, the soliton-lattice behavior of temperature variation of the modulation vector of the incommensurate phase at $P=1$ bar crosses over to a linear behavior at $P=4$ kbar.