Frustrated Ferromagnet Research Articles

Strongly Correlated Molecular Magnet with Curie Temperature above 60 K

Summary Two-dimensional crystals with ferromagnetic ordering would lead to unprecedented possibilities for magnetic, magneto-optic, and magnetoelectric applications. However, long-range ferromagnetic ordering in two-dimensional van der Waals materials is strongly diminished by thermal fluctuation, while three-dimensional systems show the stiffness of magnetic ordering temperature to magnetic fields. Here, we report the discovery of intrinsic ferromagnetic ordering temperature of 60 K in an iron/tetracyanoquinodimethane layer via superconducting precursor. In such a molecular ferromagnet, an unprecedented control of ferromagnetic fluctuation temperature by ∼200% improvement is realized through magnetic fields. We demonstrate magnetodielectric coupling with a concomitant transition in magnetic ordering. A small magnetic field of 0.01 T enables an effective route to realize a sizable transition shift in magnetodielectric states. Stimulated by photoirradiation, it manifests a hidden metallic conducting state, declaring a metallic ferromagnet. The molecular ferromagnet and photoirradiation-induced hidden metallic phase present a “holy grail” in the field of molecular conducting magnets.

Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field

A continuum model of frustrated ferromagnets is analyzed in detail in the regime of low applied magnetic field, $H_0<1/4$, where the ground state is a spatially varying conical spiral. By changing variables to a corotating spin field, the model is reformulated as a gauged sigma model in a fixed background gauge, allowing the construction of stable isolated Skyrmions, and stable multi-Skyrmion clusters, which approach the conical ground state at spatial infinity. Owing to the spatial anisotropy induced by the ground state, these Skyrmions exhibit only discrete symmetries, and are of neither N\'eel nor Bloch type. These Skyrmions are continuously connected to the more familar solutions in the high field regime ($H_0>1/4$), acquiring axial symmetry in the limit $H_0\rightarrow 1/4$. The propagation of small amplitude spin waves through the conical ground state is also analyzed and is found to depend strongly on both $H_0$ and propagation direction relative to the ground state. In contrast to spin waves in the high field regime ($H_0>1/4$) there is no spectral gap: waves may propagate with any angular frequency.

Special temperatures in frustrated ferromagnets

The description and detection of unconventional magnetic states, such as spin liquids, is a recurring topic in condensed matter physics. While much of the efforts have traditionally been directed at geometrically frustrated antiferromagnets, recent studies reveal that systems featuring competing antiferromagnetic and ferromagnetic interactions are also promising candidate materials. We find that this competition leads to the notion of special temperatures, analogous to those of gases, at which the competing interactions balance, and the system is quasi-ideal. Although induced by weak perturbing interactions, these special temperatures are surprisingly high and constitute an accessible experimental diagnostic of eventual order or spin-liquid properties. The well characterised Hamiltonian and extended low-temperature susceptibility measurement of the canonical frustrated ferromagnet Dy2Ti2O7 enables us to formulate both a phenomenological and microscopic theory of special temperatures for magnets. Other members of this class of magnets include kapellasite Cu3Zn(OH)6Cl2 and the spinel GeCo2O4.

Electron spin resonance for the detection of long-range spin nematic order

In this paper we propose that electron spin resonance (ESR) measurements enable us to detect the long-range spin nematic order. We show that the frequency of the paramagnetic resonance peak in the ESR spectrum is shifted by the ferroquadrupolar order parameter together with other quantities. The ferroquadrupolar order parameter is extractable from the angular dependence of the frequency shift. In contrast, the antiferroquadrupolar order parameter is usually invisible in the frequency shift. Instead, the long-range antiferroquadrupolar order yields a characteristic resonance peak in the ESR spectrum, which we call a magnon-pair resonance peak. This resonance corresponds to the excitation of the bound magnon pair at the wave vector $\bm k={\bm 0}$. Reflecting the condensation of bound magnon pairs, the field dependence of the magnon-pair resonance frequency shows a singular upturn at the saturation field. Moreover, the intensity of the magnon-pair resonance peak shows a characteristic angular dependence and it vanishes when the magnetic field is parallel to one of the axes that diagonalize the weak anisotropic interactions. We confirm these general properties of the magnon-pair resonance peak in the spin nematic phase by studying an $S=1$ bilinear-biquadratic model on the square lattice in the linear flavor-wave approximation. In addition, we argue applications to the $S=1/2$ frustrated ferromagnets and also the $S=1/2$ orthogonal dimer spin system SrCu$_2$(BO$_3$)$_2$, both of which are candidate materials of spin nematics. Our theory for the antiferroquadrupolar ordered phase is consistent with many features of the magnon-pair resonance peak experimentally observed in the low-magnetization regime of SrCu$_2$(BO$_3$)$_2$.

Phase diagram of the ground state of a classical anisotropic frustrated ferromagnet

The phase diagram of the ground state is obtained for the one-dimensional easy-axis model of classical spins coupled by ferromagnetic and antiferromagnetic exchanges between nearest and next-nearest neighbors, respectively. The parameters of the incommensurate magnetic structure with a variable step (soliton lattice) are calculated in the mean field approximation from the condition of the collinearity of spins to the effective exchange fields in the continuous approximation. The ground state of the soliton lattice and interfaces between soliton and collinear (ferromagnetic and “up–up–down–down”) phases are determined by the numerical minimization of the average energy over the initial angular velocity of spins.

Theory of NMR1/T1relaxation in a quantum spin nematic in an applied magnetic field

There is now strong theoretical evidence that a wide range of frustrated magnets should support quantum spin-nematic order in applied magnetic field. Nonetheless, the fact that spin-nematic order does not break time-reversal symmetry makes it very difficult to detect in experiment. In this article, we continue the theme begun in [Phys. Rev. B 88, 184430 (2013)], of exploring how spin-nematic order reveals itself in the spectrum of spin excitations. Building on an earlier analysis of inelastic neutron scattering [Phys. Rev. B 91, 174402 (2015)], we show how the NMR 1/T_1 relaxation rate could be used to identify a spin-nematic state. We emphasise the characteristic, universal features of 1/T_1, using a symmetry-based description of the spin-nematic order parameter and its fluctuations.Turning to the specific case of spin-1/2 frustrated ferromagnets, we show that the signal from competing spin-wave excitations can be suppressed through a judicious choice of nuclear site and field direction. As a worked example, we show how P NMR in the square-lattice frustrated ferromagnet BaCdVO(PO_4)_2 is sensitive to spin-nematic order.

Magnetic Vortex Induced by Nonmagnetic Impurity in Frustrated Magnets.

We study the effect of a nonmagnetic impurity inserted in a two-dimensional frustrated ferromagnet above its saturation magnetic field H_{sat} for arbitrary spin S. We demonstrate that the ground state includes a magnetic vortex that is nucleated around the impurity over a finite range of magnetic field H_{sat}≤H≤H_{sat}^{I}. Upon approaching the quantum critical point at H=H_{sat}, the radius of the magnetic vortex diverges as the magnetic correlation length: ξ∝1/sqrt[H-H_{sat}]. These results are derived both for the lattice and in the continuum limit.

Quantum Lifshitz Field Theory of a Frustrated Ferromagnet.

We propose a universal nonlinear sigma model field theory for one-dimensional frustrated ferromagnets, which applies in the vicinity of a "quantum Lifshitz point," at which the ferromagnetic state develops a spin wave instability. We investigate the phase diagram resulting from perturbations of the exchange and of magnetic field away from the Lifshitz point, and uncover a rich structure with two distinct regimes of different properties, depending upon the value of a marginal, dimensionless, parameter of the theory. In the regime relevant for one-dimensional systems with low spin, we find a metamagnetic transition line to a vector chiral phase. This line terminates in a critical end point, beyond which there is at least one multipolar or "spin nematic" phase. We show that the field theory is asymptotically exactly soluble near the Lifshitz point.

Anomalous Temperature and Field Behaviors of Magnetization in Cubic Lattice Frustrated Ferromagnets

Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions are considered near the frustration point where the coefficient D in the spin-wave spectrum Ek ~ Dk2vanishes. Within the Dyson-Maleev formalism it is found that at low temperatures thermal fluctuations stabilize ferromagnetism by increasing the value of D. For not too strong frustration this leads to an unusual "concave" shape of the temperature dependence of magnetization, which is in agreement with experimental data on the europium chalcogenides. Anomalous temperature behavior of magnetization is confirmed by Monte Carlo simulation. Strong field dependence of magnetization (paraprocess) at finite temperature is found near the frustration point.

Theory of inelastic neutron scattering in a field-induced spin-nematic state

The spin-nematic state has proved elusive, due to the difficulty of observing the order parameter in experiment. In this article we develop a theory of spin excitations in a field-induced spin-nematic state, and use it to show how a spin-nematic order can be indentified using inelastic neutron scattering. We concentrate on 2-dimensional frustrated ferromagnets, for which a two-sublattice, bond-centered spin-nematic state is predicted to exist over a wide range of parameters. First, to clarify the nature of spin-excitations, we introduce a soluble spin-1 model, and use this to derive a continuum field theory, applicable to any two-sublattice spin-nematic state. We then parameterise this field theory, using diagrammatic calculations for a realistic microscopic model of a spin-1/2 frustrated ferromagnet, and show how it can be used to make predictions for inelastic neutron scattering. As an example, we show quantitative predictions for inelastic scattering of neutrons from BaCdVO(PO_4)_2, a promising candidate to realise a spin-nematic state at an achievable h\sim 4T. We show that in this material it is realistic to expect a ghostly Goldstone mode, signalling spin-nematic order, to be visible in experiment.

Inverse transition in the dipolar frustrated Ising ferromagnet: The role of domain walls

We present a theoretical study aimed to elucidate the origin of the inverse symmetry breaking transition observed in ultrathin magnetic films with perpendicular anisotropy. We study the behavior of the dipolar frustrated Ising model in a mean field approximation as well as two other models with simple domain walls. By a numerical analysis we show that the internal degrees of freedom of the domain walls are decisive for the presence of the inverse symmetry breaking transition. In particular, we show that in a sharp domain wall model the inverse transition is absent. At high temperatures the additional degrees of freedom of the extended domain walls increase the entropy of the system leading to a reduction of the free energy of the stripe phase. Upon lowering the temperature the domain walls become narrow and with the corresponding degrees of freedom effectively frozen, which eventually induces an inverse transition to the competing homogeneous phase. We also show that, for growing external field at constant temperature, the stripe width grows strongly when approaching the critical field line and diverges at the transition. These results indicate that the inverse transition is a continuous phase transition and that the domain wall profiles as well as the temperature has little effect on the critical behavior of the period of the domain as function of the applied field.

Nematic phase and phase separation near saturation field in frustrated ferromagnets

We study the effects of quantum fluctuations in magnetic properties of quantum frustrated ferromagnets in a magnetic field. It is shown that a non-classical phase or a phase separation appears due to quantum fluctuations below the saturation field in a parameter range close to the classical zero-field phase boundary between ferromagnetic and antiferromagnetic phases, for the case that the classical antiferromagnetic state is not an eigenstate of the quantum model. As an example to which this argument is applicable, we study the S=1/2 J1-J2 Heisenberg model with ferromagnetic J1 (J1<0) on the bcc lattice using a dilute Bose gas approach. For -1.50097 < J1/J2 < -1.389, magnons form f-wave two-magnon bound states, leading to a spin nematic phase, and for -1.389 < J1/J2 < -0.48 a canted coplanar antiferromagnetic phase appears accompanied with a phase separation below the saturation field.

Inverse transition in a two-dimensional dipolar frustrated ferromagnet

We show that the mean-field phase diagram of the dipolar frustrated ferromagnet in an external field presents an inverse transition in the field-temperature plane. The presence of this type of transition has recently been observed experimentally in ultrathin films of Fe/Cu(001). We study a coarse-grained model Hamiltonian in two dimensions. The model supports stripe and bubble equilibrium phases, as well as the uniform phase. At variance with common expectations, already in a single-mode approximation, the model shows a sequence of uniform-bubbles-stripes-uniform phase transitions upon lowering the temperature at a fixed external field. Going beyond the single-mode approximation leads to the shrinking of the bubbles phase, which is restricted to a small region near the zero-field critical temperature. Monte Carlo simulations results with a Heisenberg model are consistent with the mean-field results.

Spin reorientation transition and phase diagram in an He+ ion irradiated ultrathin Pt/Co(0.5 nm)/Pt film

A rich thermal magnetic phase diagram has been determined by magneto-optical Kerr magnetometry and microscopy in a He+ ion irradiated ultrathin Pt/Co(0.5 nm)/Pt film. The components of the net magnetization and the evolution and disappearance of the ribbonlike magnetic domain pattern have been studied in the perpendicular to in-plane spin reorientation transition temperature region. As observed in a dipolar frustrated ferromagnet, the ribbon pattern blurs progressively with increasing the temperature as due to efficient spatial fluctuations. We emphasize the limitation of present theories for interpreting such a type of dynamic transition.

SU(2)slave-boson formulation of spin nematic states inS=12frustrated ferromagnets

An SU(2) slave boson formulation of bond-type spin nematic orders is developed in frustrated ferromagnets, where the spin nematic states are described as the resonating spin-triplet valence bond (RVB) states. The d-vectors of spin-triplet pairing ansatzes play the role of the directors in the bond-type spin quadrupolar states. The low-energy excitations around such spin-triplet RVB ansatzes generally comprise the (potentially massless) gauge bosons, massless Goldstone bosons, and spinon individual excitations. Extending the projective symmetry group argument to the spin-triplet ansatzes, we show how to identify the number of massless gauge bosons efficiently. Applying this formulation, we next (i) enumerate possible mean field solutions for the S=1/2 ferromagnetic J1-J2 Heisenberg model on the square lattice, with ferromagnetic nearest neighbor J1 and competing antiferromagnetic next-nearest neighbor J2, and (ii) argue their stability against small gauge fluctuations. As a result, two stable spin-triplet RVB ansatzes are found in the intermediate coupling regime around J1:J2 \simeq 1:0.4. One is the Z_2 Balian-Werthamer (BW) state stabilized by the Higgs mechanism and the other is the SU(2) chiral p-wave (Anderson-Brinkman-Morel) state stabilized by the Chern-Simon mechanism. The former Z_2 BW state in fact shows the same bond-type spin quadrupolar order as found in the previous exact diagonalization study [N. Shannon et al., Phys. Rev. Lett. 96, 027213 (2006)].

Stripe width and nonlocal domain walls in the two-dimensional dipolar frustrated Ising ferromagnet

We describe a novel type of magnetic domain wall which, in contrast to Bloch or Neel walls, is non-localized and, in a certain temperature range, non-monotonic. The wall appears as the mean-field solution of the two-dimensional ferromagnetic Ising model frustrated by the long-ranged dipolar interaction. We provide experimental evidence of this wall delocalization in the stripe-domain phase of perpendicularly magnetized ultrathin magnetic films. In agreement with experimental results, we find that the stripe width decreases with increasing temperature and approaches a finite value at the Curie-temperature following a power law. The same kind of wall and a similar temperature dependence of the stripe width is expected in the mean-field approximation of the two-dimensional Coulomb frustrated Ising ferromagnet.

Observation of Stripe Mobility in a Dipolar Frustrated Ferromagnet

We have discovered two novel aspects of the stripe-domain to paramagnetic transition in perpendicularly magnetized Fe films on Cu(100). First, the width of the stripes carrying oppositely oriented spins decreases, close to the transition temperature, with a power law. Second, in a small temperature interval close to the transition temperature, the stripes--which form stationary patterns at low temperatures--become mobile. Various theoretical works have predicted stripe mobility in similar frustrated systems but no direct proof of this phenomenon has been reported so far.

Nematic Order in Square Lattice Frustrated Ferromagnets

We present a new scenario for the breakdown of ferromagnetic order in a two-dimensional quantum magnet with competing ferromagnetic and antiferromagnetic interactions. In this, dynamical effects lead to the formation of two-magnon bound states, which undergo Bose-Einstein condensation, giving rise to bond-centered nematic order. This scenario is explored in some detail for an extended Heisenberg model on a square lattice. In particular, we present numerical evidence confirming the existence of a state with d-wave nematic correlations but no long-range magnetic order, lying between the saturated ferromagnetic and collinear antiferromagnetic phases of the ferromagnetic model J1-J2. We argue by continuity of spectra that this phase is also present in a model with 4-spin cyclic exchange.

Magnetic and magneto-transport properties of rapidly solidified Cu80−Fe20Ni alloys

Abstract Three metastable materials of compositions Cu 80− x Fe 20 Ni x ( x =0, 5, 20 at.%) have been obtained by rapid solidification. Magnetization and magnetoresistance measurements have been performed at different temperatures on as cast samples of all alloys and on annealed samples of the alloy with x =20. A measurable magnetoresistance is observed only for the latter material, a frustrated ferromagnet with short magnetic coherence length. This effect is related to the action of the magnetic field destroying the locally canted arrangement of magnetic spins in the ordered phase.

Influence of the single-ion anisotropy field and the Dzyaloshinsky–Moriya term on bulk spin fluctuations dynamics. Application to the frustrated weak ferromagnet FeF 3

We have theoretically investigated the influence of the anisotropy field and the Dzyaloshinsky–Moriya type coupling on the bulk magnetic excitations in a noncolinear frustrated structure. Application to the cubic frustrated weak ferromagnet FeF 3 is presented. Using a Green function formalism and matching technique procedure, the dispersion curves of the bulk magnons are obtained within a single framework by matching the evanescent and travelling solutions, respectively, of the secular equation, satisfying surface boundary conditions. The calculation concerns, in particular, the spin fluctuation dynamics in the bulk of an antiferromagnetic lattice, the spin order being in the direction normal to the surface boundary. The competing nearest J 1 AB and next nearest neighbours exchange interactions ( J 2 AA(BB)) are considered. The theoretical approach determines the evanescent spin fluctuation field in the two-dimensional plane parallel to the surface. It is shown that the propagating and evanescent spin-waves from a surface are strongly dependent on the values of ratio ε= J 1 AB/ J 2 AA(BB). The presence of anisotropy field and antisymmetric exchange term induces an energy gap on the bulk spin-wave continuum which involves a new ground state of spin quantum.