Incommensurate Spiral State Research Articles

Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

Motivated by the magnetic properties of the spin-chain compounds LiCuSbO$_4$$\equiv$LiSbCuO$_4$ and Rb$_2$Cu$_2$Mo$_3$O$_{12}$, we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM)($J_1, J_1^\prime<0$) and next-nearest-neighbor antiferromagnetic ($J_2>0$) couplings. Using the density-matrix renormalization group technique and spin-wave theory we find a first-order transition between a fully-polarized FM and an incommensurate spiral state at $2\alpha=\beta/(1+\beta)$, where $\alpha$ is the frustration ratio $J_2/|J_1|$ and $\beta$ the degree of dimerization $J_1^\prime/J_1$.In the singlet spiral state the spin-gap is vanishingly small in the vicinity of the FM transition, corresponding to a situation of LiCuSbO$_4$. For larger $\alpha$, corresponding to Rb$_2$Cu$_2$Mo$_3$O$_{12}$, and smaller $\beta$ there is a crossover from this frustration induced incommensurate state to an Affleck-Lieb-Kennedy-Tasaki-type valence bond solid state with substantial spin-gaps.

Incommensurate Spiral Order from Double-Exchange Interactions

The double-exchange model describing interactions of itinerant electrons with localized spins is usually used to explain ferromagnetism in metals. We show that for a variety of crystal lattices of different dimensionalities and for a wide range of model parameters, the ferromagnetic state is unstable against a noncollinear spiral magnetic order. We revisit the phase diagram of the double-exchange model on a triangular lattice and show in a large part of the diagram the incommensurate spiral state has a lower energy than the previously discussed commensurate states. These results indicate that double-exchange systems are inherently frustrated and can host unconventional spin orders.

Spin fluctuations and frustrated magnetism in multiferroicFeVO4

We report $^{51}$V nuclear magnetic resonance (NMR) studies on single crystals of the multiferroic material FeVO$_4$. The high-temperature Knight shift shows Curie-Weiss behavior, $^{51}K = a/(T + \theta)$, with a large Weiss constant $\theta \approx$ 116 K. However, the $^{51}$V spectrum shows no ordering near these temperatures, splitting instead into two peaks below 65 K, which suggests only short-ranged magnetic order on the NMR time scale. Two magnetic transitions are identified from peaks in the spin-lattice relaxation rate, $1/^{51}T_1$, at temperatures $T_{N1} \approx$ 19 K and $T_{N2} \approx$ 13 K, which are lower than the estimates obtained from polycrystalline samples. In the low-temperature incommensurate spiral state, the maximum ordered moment is estimated as 1.95${\mu}_B$/Fe, or 1/3 of the local moment. Strong low-energy spin fluctuations are also indicated by the unconventional power-law temperature dependence $1/^{51}T_1 \propto T^2$. The large Weiss constant, short-range magnetic correlations far above $T_{N1}$, small ordered moment, significant low-energy spin fluctuations, and incommensurate ordered phases all provide explicit evidence for strong magnetic frustration in FeVO$_4$.

ESR of coupled spin-1/2 chains in copper pyrazine dinitrate: unveiling geometrical frustration

The spin dynamics of copper pyrazine dinitrate (Cu(C4H4N2)(NO3)2), a model spin-1/2 Heisenberg antiferromagnetic (AF) chain system, was investigated by means of electron spin resonance (ESR). Using the high-field ESR we evidenced the inequivalence of Cu sites belonging to adjacent spin chains in the ac planes of this compound. It was revealed that the dominating interchain interaction is of zig-zag-type. This interaction gives rise to geometrical frustration strongly affecting the character of AF ordering. Combining our experimental findings with the results of a quasiclassical approach we predict that at low temperatures the system orders in an incommensurate spiral state.

Quantum spin fluctuations for a distorted incommensurate spiral

Quantum spin fluctuations are investigated for the distorted incommensurate spiral state of a geometrically frustrated triangular-lattice antiferromagnet. With increasing easy axis anisotropy, the average reduction of the spin amplitude by quantum fluctuations is suppressed but the spiral also becomes more distorted. Quantum fluctuations enhance both the wave vector of the distorted spiral and the critical anisotropy above which it undergoes a first-order transition into a collinear state. An experimental technique is proposed to isolate the effects of quantum fluctuations from the classical distortion of the spiral. This analysis is applied to the elliptical spiral state of doped CuFeO${}_{2}$.

Theory of spin-phonon coupling in multiferroic manganese perovskitesRMnO3

Magnetoelectric phase diagrams of the rare-earth (R) Mn perovskites RMnO3 are theoretically studied by focusing on crucial roles of the symmetric magnetostriction or the Peierls-type spin-phonon coupling through extending our previous work [M. Mochizuki et al., Phys. Rev. Lett. 105, 037205 (2010)]. We first construct a microscopic classical Heisenberg model for RMnO3 including the frustrated spin exchanges, single-ion anisotropy, and Dzyaloshinskii-Moriya interaction. We also incorporate the lattice degree of freedom coupled to the Mn spins via the Peierls-type magnetostriction. By analyzing this model using the replica-exchange Monte-Carlo technique, we reproduce the entire phase diagram of RMnO3 in the plane of temperature and magnitude of the orthorhombic lattice distortion. Surprisingly it is found that in the ab-plane spiral spin phase, the (S.S)-type magnetostriction plays an important role for the ferroelectric order with polarization P//a whose contribution is comparable to or larger than the contribution from the (SxS)-type magnetostriction, whereas in the bc-plane spiral phase, the ferroelectric order with P//c is purely of (SxS) origin. This explains much larger P in the ab-plane spiral phase than the bc-plane spiral phase as observed experimentally, and gives a clue how to enhance the magnetoelectric coupling in the spin-spiral-based multiferroics. We also predict a noncollinear deformation of the E-type spin structure resulting in the finite (SxS) contribution to the ferroelectric order with P//a, and a wide coexisting regime of the commensurate E and incommensurate spiral states, which resolve several experimental puzzles.

Roles of Bond Alternation in Magnetic Phase Diagram of RMnO3

In order to investigate nature of the antiferromagnetic structures in perovskite RMnO3, we study a Heisenberg J1-J2 model with bond alternation using analytical and numerical approaches. The magnetic phase diagram which includes incommensurate spiral states and commensurate collinear states is reproduced. We discuss that the magnetic structure with up-up-down-down spin configuration (E-type structure) and the ferroelectricity emerge cooperatively to stabilize this phase. Magnetoelastic couplings are crucial to understand the magnetic and electric phase diagram of RMnO3.

Quasi‐one‐dimensional S = 1/2 magnet Pb[Cu(SO 4 )(OH) 2 ]: frustration due to competing in‐chain exchange

Zero-field susceptibility and specific heat of Pb[Cu(SO4)(OH)2] (linarite) single crystal were measured. In order to verify that linarite is a quasi-one-dimensional system with competing nearest-neighbour and next-nearest-neighbour in-chain exchange interaction (J1 ≈ –30 K, J2 ≈ 15 K), theoretical results based on electronic structure calculations within the LDA and a phenomenological modelling using the finite-temperature transfer-matrix method are taken into account. The possibility of various ground states is discussed in terms of the screened onsite repulsion Us: commensurate Neel or spin-Peierls phases versus incommensurate spiral states with acute or obtuse pitch angles. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

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.