Collinear States Research Articles

Phase transition of square-lattice antiferromagnets at finite temperature

The magnetic properties of the two-dimensional ${J}_{1}\ensuremath{-}{J}_{2}$ model with both exchanges ${J}_{1}$ and ${J}_{2}$ being antiferromagnetic and a single-ion anisotropy at nonzero temperature are investigated. As ${J}_{2}/{J}_{1}<1/2$ ($>1/2$), only the N\'eel (collinear) state exists. When ${J}_{2}/{J}_{1}=1/2$, both the N\'eel and collinear states can exist and have the same N\'eel temperature. The calculated free energies show that there can occur a phase transition between the two states below the N\'eel point when the single-ion anisotropy is strong enough. It is a first-order transition at nonzero temperature. It is possible that the doping in real materials can modify the ratio of ${J}_{2}/{J}_{1}$ to reach $1/2$ so as to implement the phase transition.

Location of the Potts-critical end point in the frustrated Ising model on the square lattice

We report on Monte Carlo simulations for the two-dimensional frustrated $J_1$-$J_2$ Ising model on the square lattice. Recent analysis has shown that for the phase transition from the paramagnetic state to the antiferromagnetic collinear state different phase-transition scenarios apply depending on the value of the frustration $J_2 / J_1$. In particular a region with critical Ashkin-Teller-like behavior, i.e., a second-order phase transition with varying critical exponents, and a noncritical region with first-order indications were verified. However, the exact transition point $[J_2/J_1]_C$ between both scenarios was under debate. In this paper we present Monte Carlo data which strengthens the conclusion of Jin \et [Phys. Rev. Lett. \textbf{108}, 045702 (2012)] that the transition point is at a value of $J_2/J_1 \approx 0.67$ and that double-peak structures in the energy histograms for larger values of $J_2/J_1$ are unstable in a scaling analysis.

Spin reorientation and magnetization reversal in the perovskite oxides, YFe1−xMnxO3 (0≤x≤0.45): A neutron diffraction study

Members of the YFe1−xMnxO3 (0≤x≤0.45) family crystallize in the GdFeO3 type orthorhombic perovskite structure (space group Pnma) where the Fe and Mn ions are disordered at the 4b crystallographic site. Upon substitution of Mn at the Fe-site in the canted antiferromagnetic YFeO3 (TN=640K), a first-order spin-reorientation transition occurs at a temperature, TSR, where the magnetic structure changes from the canted to a collinear state. With increasing Mn-concentration, TSR increases whereas TN decreases. Neutron diffraction studies on the x=0.4 sample reveal that the spin structure changes from Γ4 to Γ1 below TSR. Intriguingly, when x=0.4 and 0.45, a temperature-induced magnetization reversal is observed below a compensation temperature T⁎ (T⁎<TSR<TN). The reversal is explained on the basis of a ferrimagnetic ground state resulting from antiferromagnetic coupling of the canted moments of Fe–O–Fe and Mn–O–Mn with that of Fe–O–Mn ordering.

First-principles study of magnetism in Pd3Fe under pressure

Recent experiments on Pd${}_{3}$Fe intermetallics [M. L. Winterrose et al., Phys. Rev. Lett. 102, 237202 (2009)] have revealed that the system behaves like a classical invar alloy under high pressure. The experimental pressure-volume relation suggests an anomalous volume collapse and a substantial increase in bulk modulus around the pressure where invar behavior is observed. With the help of first-principles density functional theory based calculations, we have explored various magnetic phases (ferromagnetic, fully and partially disordered local moment, spin spiral) in order to understand the effect of pressure on magnetism. Our calculations reveal that the system does not undergo a transition from a ferromagnetic to a spin-disordered state, as was thought to be the possible mechanism to explain the invar behavior of this system. We rather suggest that the anomaly in the system could possibly be due to the transition from a collinear state to noncollinear magnetic states upon the application of pressure.

Spin-wave dynamics for the high-magnetic-field phases of the frustrated CuFeO2antiferromagnet: Predictions for inelastic neutron scattering

We evaluate the spin-wave spectra for the high-field phases of the frustrated triangular lattice antiferromagnet with a focus on the observed high-magnetic-field phases of CuFeO${}_{2}$. After determining the appropriate magnetic ground state using a combination of Monte Carlo simulations and variational methods for a two-dimensional triangular lattice, we evaluate the spin excitation frequencies and intensities using a rotational Holstein-Primakoff expansion for both the collinear and noncollinear states. These predictions should help experimentalists to identify the magnetic ground states of CuFeO${}_{2}$ and other triangular-lattice antiferromagnets using inelastic neutron scattering.

Description of spin reorientation transition in Au/Co/Au sandwich with Co film thickness within a simple phenomenological model of ferromagnetic film

Simple phenomenological model of ferromagnetic film characterized by equal energies of surface anisotropies at two sides of a film (symmetric film) is considered. The model is used to describe a two-step spin reorientation transition (SRT) in Au/Co/Au sandwich with Co film thickness: the SRT from perpendicular to canted noncollinear (CNC) state at N⊥=6.3 atomic layers and the subsequent SRT from CNC to in-plane state at N∥=10.05 atomic layers. Analytic expressions for the stability criterion of collinear perpendicular and in-plane states of a film are derived with account of discrete location of atomic layers. The dependence of borders that separate regions corresponding to various magnetic states of a film in the (kB,kS)-diagram on film thickness N is established. kS(kB) is surface (bulk) reduced anisotropy constant. The comparison of theory with experiment related to Au/Co/Au sandwich shows that there is a whole region in the (kB,kS)-diagram corresponding to experimentally determined values of threshold film thicknesses N⊥=6.3 and N∥=10.05. The comparison of this region with similar region determined earlier for a bare Co/Au film within the same model of asymmetric film and characterized by N⊥=3.5, N∥=5.5 shows that the intersection of these regions is not empty. Hence, both the SRT in Au/Co/Au sandwich and in bare Co/Au film with Co film thickness can be described within the same model using the same magnitudes of model parameters kS, kB. Based on this result we conclude that the energy of Neel surface anisotropy at free Co surface is negligible compared to the energy of Co–Au interface anisotropy. It is demonstrated that the destabilization of collinear states in symmetric film leads to occurrence of the ground CNC state and two novel metastable CNC states. These three CNC states exhibit different kinds of symmetry. In case of asymmetric film only ground CNC state occurs on destabilization of collinear states of a film.

Bond operator theory for the frustrated anisotropic Heisenberg antiferromagnet on a square lattice

The quantum anisotropic antiferromagnetic Heisenberg model with single ion anisotropy, spin S=1 and up to the next-next-nearest neighbor coupling (the J1–J2–J3 model) on a square lattice, is studied using the bond-operator formalism in a mean field approximation. The quantum phase transitions at zero temperature are obtained. The model features a complex T=0 phase diagram, whose ordering vector is subject to quantum corrections with respect to the classical limit. The phase diagram shows a quantum paramagnetic phase situated among Neél, spiral and collinear states.

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${}_{2}$.

Study of GdCo/Si/Co/Si Multilayers by Polarized Neutron Reflectivity

In order to better understand the interesting magnetic behaviour found in the Rare Earth-transition metal/(spacer)/transition metal multilayers, a multilayer of Co/[Si/Gd0.36Co0.64/Si/Co]4/glass was studied by SQUID magnetic measurements and polarized neutron reflectivity. A model for the magnetic profile of the sample was proposed, which fitted well the polarized neutron reflectivity measurements at different magnetic states: ferrimagnetic/antiparallel state, under an applied field of 55 Oe, canted states (315 and 675 Oe) and saturation state (1700 Oe). It was found that even at the expected collinear states (ferrimagnet and saturation states), the magnetization was not totally collinear and there was a small component of the magnetization perpendicular to the applied field

Modified spin-wave theory with ordering vector optimization: spatially anisotropic triangular lattice and J1J2J3 model with Heisenberg interactions

We study the ground-state phases of the S=1/2 Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice (SATL) and on the square lattice with up to next-next-nearest-neighbor coupling (the J1J2J3 model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that the MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular, collinear magnetic order is promoted at the expense of non-collinear (spiral) order, and several spiral states that are stable at the classical level disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which the MSW theory breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the SATL, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains. This shows that the MSW theory is—despite its apparent simplicity—a versatile tool for finding candidate regions in the case of spin-liquid phases, which are among prime targets for relevant quantum simulations.

Phase diagram of a two-dimensional square lattice of magnetic particles with perpendicular anisotropy

The ground state of an array of small single-domain magnetic particles having perpendicular anisotropy and forming a square two-dimensional lattice is studied in the presence of a magnetic field. The stability of some basic states with respect to nonuniform perturbations is analyzed in a linear approximation, and analytical model calculations and numerical simulation are used for an analysis. The entire set of states at various anisotropy constants and magnetic fields is considered when a field is normal to the array plane. Two main classes of states are possible for an infinite system, namely, collinear and noncollinear states. For collinear states, the magnetic moments of all particles are normal to the array plane. At a sufficiently high anisotropy, a wide class of collinear states exists. At low fields, a staggered antiferromagnetic order of magnetic moments takes place. An increase in the magnetic field causes an unsaturated state, and this state transforms into a saturated (ferromagnetic) state with a parallel orientation of the magnetic moments of all particles at a sufficiently high field. At a lower anisotropy, the ground state of the system is represented by noncollinear states, which include a complex four-sublattice structure for the components of the magnetic moments in the array plane and a nonzero projection of the magnetic moments of the particles onto the field direction. A phase diagram is plotted for the states of an array of anisotropic magnetic particles in the anisotropy constant-magnetic field coordinates. For a finite array of particles, sample boundaries are shown to play a significant role, which is particularly important for noncollinear states. As a result of the effect of the boundaries at a moderate field or anisotropy, substantially heterogeneous noncollinear states with a heterogeneity size comparable with the sample size can appear in the system.

Three-dimensional generalization of theJ1-J2Heisenberg model on a square lattice and role of the interlayer couplingJc

A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two-dimensional frustrated Heisenberg ${J}_{1}$-${J}_{2}$ model has been actively discussed recently. However, recent neutron-scattering data have shown that the pnictides have a relatively large spin-wave dispersion in the direction perpendicular to the planes. This indicates that the third dimension is very important. Motivated by this observation we study the ${J}_{1}$-${J}_{2}$-${J}_{c}$ model that is the three-dimensional generalization of the ${J}_{1}$-${J}_{2}$ Heisenberg model for $S=1/2$ and $S=1$. Using self-consistent spin-wave theory we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. We find that the introduction of the interlayer coupling ${J}_{c}$ suppresses the quantum fluctuations and strengthens the long-range ordering. In the ${J}_{1}$-${J}_{2}$-${J}_{c}$ model, we find two qualitatively distinct scenarios for how the collinear phase becomes unstable on increasing ${J}_{1}$. Either the magnetization or one of the spin-wave velocities vanishes. For $S=1/2$ renormalization due to quantum fluctuations is significantly stronger than for $S=1$, in particular close to the quantum phase transition. Our findings for the ${J}_{1}$-${J}_{2}$-${J}_{c}$ model are of general theoretical interest; however, the results show that it is unlikely that the model is relevant to undoped pnictides.

Quantum phases of the planar antiferromagneticJ1−J2−J3Heisenberg model

We present results of a complementary analysis of the frustrated planar J_1-J_2-J_3 spin-1/2 quantum-antiferromagnet. Using dynamical functional renormalization group, high-order coupled cluster calculations, and series expansion based on the flow equation method, we have calculated generalized momentum resolved susceptibilities, the ground state energy, the magnetic order parameter, and the elementary excitation gap. From these we determine a quantum phase diagram which shows a large window of a quantum paramagnetic phase situated between the Neel, spiral and collinear states, which are present already in the classical J_1-J_2-J_3 antiferromagnet. Our findings are consistent with substantial plaquette correlations in the quantum paramagnetic phase. The extent of the quantum paramagnetic region is found to be in satisfying agreement between the three different approaches we have employed.

Phase Diagram of a Geometrically Frustrated Triangular-Lattice Antiferromagnet in a Magnetic Field

The magnetic phase diagram of a geometrically frustrated triangular-lattice antiferromagnet is evaluated as a function of magnetic field and anisotropy using a trial spin state built from harmonics of a fundamental ordering wave vector. A noncollinear incommensurate state, observed to be chiral and ferroelectric in CuFeO2, appears above a collinear state with 4 sublattices (SLs). The apparent absence of multiferroic behavior for predicted chiral, noncollinear 5-SL states poses a challenge to theories of the ferroelectric coupling in CuFeO2.

Proximity effect in a superconductor/exchange-spring-magnet hybrid system

We investigate the proximity effect in a superconductor/ferromagnet S/F hybrid system with a noncollinear magnetic configuration. A new structure of an S/exchange-spring ES magnet is fabricated, where an ES magnet is employed as an F layer since the magnetization configuration is varied from a collinear state to a noncollinear state by a rotating external magnetic field in a well controllable way. We found that the resistance decreases and the superconducting transition temperature increases, as noncollinearity is introduced starting from a collinear state. We interpret that our experimental observation is due to the contribution of the oddtriplet superconducting condensate that survived in a noncollinear magnetization configuration in the ES magnet.

Size-Dependent Spin Structures in Iron Nanoparticles

Using photoemission electron microscopy, we study the magnetization orientation in single 5-25 nm iron particles coupled to a ferromagnetic cobalt support. We find a noncollinear alignment between the particle and substrate magnetization above a particle size of approximately 6 nm and a parallel alignment for smaller sizes. Numerical calculations reveal a transition from an exchange-dominated to an anisotropy-dominated regime on increasing the particle height: the smaller particles are in a single-domain collinear state while larger particles exhibit a spin-spiral magnetic structure determined by the magnetic anisotropy energy.

Orbital order and partial electronic delocalization in a triangular magnetic metalAg2MnO2

Magnetic and electrical properties of ${\text{Ag}}_{2}{\text{MnO}}_{2}$ were examined by elastic and inelastic neutron-scattering measurements and by density-functional calculations. The spins of the triangular antiferromagnet metal ${\text{Ag}}_{2}{\text{MnO}}_{2}$ are found to freeze into a gapless short-range collinear state below 50 K because of a ferro-orbital ordering and spin-orbit coupling of the high-spin ${\text{Mn}}^{3+}$ ions. The decrease in the spin-spin correlation lengths of ${\text{Ag}}_{2}{\text{MnO}}_{2}$ in the order, ${\ensuremath{\xi}}_{b}⪢{\ensuremath{\xi}}_{a}⪢{\ensuremath{\xi}}_{c}$, is explained by the spin-exchange interactions calculated for the ferro-orbital ordered state. The electronic states around the Fermi level have significant contributions from the spin-polarized $\text{Mn}\text{ }3d$ and $\text{O}\text{ }2p$ states, which makes electron-electron scattering dominate over electron-phonon scattering at low temperatures leading to the $\ensuremath{\rho}\ensuremath{\propto}{T}^{2}$ behavior below 50 K.

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.

Structurally driven magnetic state transition of biatomic Fe chains on Ir(001)

Using first-principles calculations, we demonstrate that the magnetic exchange interaction and the magnetocrystalline anisotropy of biatomic Fe chains grown in the trenches of the $(5\ifmmode\times\else\texttimes\fi{}1)$ reconstructed Ir(001) surface depend sensitively on the atomic arrangement of the Fe atoms. Two structural configurations have been considered which are suggested from recent experiments. They differ by the local symmetry and the spacing between the two strands of the biatomic Fe chain. Since both configurations are very close in total energy they may coexist in experiment. We have investigated collinear ferro- and antiferromagnetic solutions as well as a collinear state with two moments in one direction and one in the opposite direction ($\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\uparrow}$-state). For the structure with a small interchain spacing, there is a strong exchange interaction between the strands and the ferromagnetic state is energetically favorable. In the structure with larger spacing, the two strands are magnetically nearly decoupled and exhibit antiferromagnetic order along the chain. In both cases, due to hybridization with the Ir substrate the exchange interaction along the chain axis is relatively small compared to free-standing biatomic iron chains. The easy magnetization axis of the Fe chains also switches with the structural configuration and is out-of-plane for the ferromagnetic chains with small spacing and along the chain axis for the antiferromagnetic chains with large spacing between the two strands. Calculated scanning tunneling microscopy images and spectra suggest the possibility to experimentally distinguish between the two structural and magnetic configurations.

Vortex states in soft magnets in two and three dimensions

The magnetization curves of arrays of near-spherical soft ferromagnetic particles are compared with those of quasi-two-dimensional dots with similar radius prepared by a rapid e-beam lithographic technique. Curves for the three-dimensional particles are anhysteretic and fit a M( H)/ M s=tanh( cμ 0 H) law, whereas the two-dimensional arrays show irreversible segments in the first and third quadrants where the planar vortex state transforms to a collinear state by discontinuous rotation of magnetization about an axis perpendicular to the vortex axis. The additional symmetry of the spherical particle allows this rotation to occur continuously, without energy barriers due to the demagnetizing field.