Easy-axis Antiferromagnet Research Articles

Multicritical behavior in frustrated spin systems with non-collinear order

We investigate the phase diagram and, in particular, the nature of the multicritical point in three-dimensional frustrated N-component spin models with non-collinear order in the presence of an external field, for instance easy-axis stacked triangular antiferromagnets in the presence of a magnetic field along the easy axis. For this purpose we study the renormalization-group flow in a Landau–Ginzburg–Wilson ϕ 4 theory with symmetry O ( 2 ) ⊗ [ Z 2 ⊕ O ( N − 1 ) ] that is expected to describe the multicritical behavior. We compute its MS ¯ β functions to five loops. For N ⩾ 4 , their analysis does not support the hypothesis of an effective enlargement of the symmetry at the multicritical point, from O(2) ⊗ [ Z 2 ⊕ O ( N − 1 ) ] to O(2) ⊗ O( N). For the physically interesting case N = 3 , the analysis does not allow us to exclude the corresponding symmetry enlargement controlled by the O(2) ⊗ O(3) fixed point. Moreover, it does not provide evidence for any other stable fixed point. Thus, on the basis of our field-theoretical results, the transition at the multicritical point is expected to be either continuous and controlled by the O(2) ⊗ O(3) fixed point or to be of first order.

Spin-reorientation and multidomain states in the spin-flop region of uniaxial antiferromagnets

Based on an effective phenomenological energy, a strongly pronounced two-scale character is demonstrated for magnetic states of easy-axis antiferromagnets. Near the spin-flop field, magnetic properties are determined by weaker interaction terms than those in the major part of the magnetic phase diagram. Field and angular dependencies of the magnetic susceptibility tensor are calculated for homogeneous and multidomain states. Their peculiarities in the vicinity of the spin-flop can be employed for investigations on magnetic states and material parameters of easy-axis antiferromagnets. Corresponding experiments on the orthorhombic layered antiferromagnet (C2H5NH3)2CuCl4 are presented. The evolution of multidomain states and their phase boundaries are determined in the spin-flop region.

Antiferromagnetic domain walls in lightly doped layered cuprates

Recent ESR data shows rotation of the antiferromagnetic (AF) easy axis in lightly doped layered cuprates upon lowering the temperature. We account for the ESR data and show that it has significant implications on spin and charge ordering according to the following scenario: In the high temperature phase AF domain walls coincide with (110) twin boundaries of an orthorhombic phase. A magnetic field leads to annihilation of neighboring domain walls resulting in antiphase boundaries. The latter are spin carriers, form ferromagnetic lines and may become charged in the doped system. However, hole ordering at low temperatures favors the (100) orientation, inducing a pi/4 rotation in the AF easy axis. The latter phase has twin boundaries and AF domain walls in (100) planes.

Tuning the antiferromagnetic easy axis direction in exchange bias bilayers

The exchange bias effect is measured for a Co/NiO bilayer before and after it has been cooled down from 580 K in 1.5 kOe magnetic field applied at 45° to the initial exchange-bias direction. The angular variation of the hysteresis loop shift for the treated sample showed three distinct minima and maxima, in contrast to that of the as-made sample, which is characteristic for a system with aligned ferromagnetic and antiferromagnetic easy axes. This behavior is qualitatively well explained in the framework of the domain-wall formation model applied for the off-aligned case.

Phonon mechanism of the antiferromagnetic photogalvanic effect

The phonon mechanism of generation of photogalvanic current in centroantisymmetric tetragonal antiferromagnets with magnetic symmetry excluding the occurrence of a toroidal momentum is considered. It is demonstrated that photocurrent can be caused by scattering of charge carriers by phonons with a polarization other than longitudinal. The polarization of the phonons involved in scattering is determined by the long-range part of the electron-phonon interaction induced by polarization of the lattice due to the magnetoelectric effect. Conditions are given for the observation of photogalvanic current in easy-axis antiferromagnets.

Off-equilibrium study of the fluctuation-dissipation relation in the easy-axis Heisenberg antiferromagnet on thekagomélattice

Violation of the fluctuation-dissipation theorem (FDT) in a frustrated Heisenberg model on the kagom\'e lattice is investigated using Monte Carlo simulations. The model exhibits glassy behavior at low temperatures accompanied by very slow dynamics. Both the spin-spin autocorrelation function and the response to an external magnetic field are studied. Clear evidence of a constant value of the fluctuation-dissipation ratio and long-range memory effects is observed in this model. The breakdown of the FDT in the glassy phase follows the predictions of mean-field theory for spin glasses with one-step replica symmetry breaking.

Anisotropy and Ising-type transition of the S=5/2 two-dimensional Heisenberg antiferromagnet Mn-formate di-Urea

Recently reported measurements of specific heat on the compound Mn-formate di-Urea by Takeda et al. [Phys. Rev. B 63, 024425 (2001)] are considered. As a model to describe the overall thermodynamic behavior of such a compound, the easy-axis two-dimensional Heisenberg antiferromagnet is proposed and studied by means of the pure quantum self-consistent harmonic approximation. In particular, it is shown that when the temperature decreases, the compound exhibits a crossover from two-dimensional (2D) Heisenberg to 2D-Ising behavior, followed by a 2D-Ising-type phase transition, whose location allows one to get a reliable estimate of the easy-axis anisotropy driving the transition itself. Below the critical temperature TN=3.77 K, the specific heat is well described by the two-dimensional easy-axis model down to a temperature T*=1.57 K, where a T3 law sets in, possibly marking a low-temperature crossover of magnetic fluctuations from two to three dimensions.

Low-temperature static and dynamic behavior of the easy-axis Heisenberg antiferromagnet on the Kagome lattice

The antiferromagnetic Heisenberg model with easy-axis exchange anisotropy on the Kagome lattice is studied by means of Monte Carlo simulations. From equilibrium properties, we find that the values of the critical exponents associated with the magnetization at the critical temperature ${T}_{c}$ vary with the magnitude of the anisotropy. On the other hand, the spin-spin autocorrelation functions have a stretched exponential behavior with a power-law divergence of the relaxation time at a glasslike temperature ${T}_{g}\ensuremath{\sim}{T}_{c}.$ From nonequilibrium dynamics at a fixed temperature below ${T}_{g},$ aging effects are found which obey the same scaling laws as in spin glasses and polymers.

Anomalous magnetization process in exchange-biased MnPd/Co bilayers

MnPd/Co bilayers sputtered onto Si (1 0 0) substrates with varied MnPd thickness have been investigated. Structural characterization of the bilayers was carried out with an X-ray diffractometer and their magnetic properties were measured by a vibrating-sample magnetometer. As-deposited bilayers exhibit large but quite usual exchange-biased coupling, i.e. the shift of the hysteresis loop towards the field direction opposite to the cooling-field direction. This exchange bias vanishes if the antiferromagnetic (AFM) layer thickness is below a certain value. However, for annealed bilayers with an MnPd layer thickness below a critical value, large exchange bias and asymmetric double-shifted loops are unexpectedly observed when the measuring field is along the cooling-field direction. These anomalies in the magnetization process can be explained if one postulates that the orientation of the AFM easy axis with respect to the spin direction of the ferromagnetic layer is changed when the thickness of the AFM layer decreases.

Electrical and magnetic properties of the cerium–transition metal intermetallics CeTSb 2 (T: Cu, Au, Ni)

We have succeeded in growing single crystals of the cerium–transition metal intermetallics CeTSb 2 (T: Cu, Au, Ni) with the tetragonal structure via the self-flux method, and measured the electrical resistivity, magnetic susceptibility, magnetization and specific heat. CeCuSb 2 and CeAuSb 2 are antiferromagnets with Néel temperatures of 6.9 and 5.0 K, respectively. CeCuSb 2 is a heavy-fermion antiferromagnet with an electronic specific heat coefficient γ=200 mJ/K 2 mol. CeAuSb 2 also is a similar compound with an antiferromagnetic easy axis along the [0 0 1] direction. CeNiSb 2 is a ferromagnet with a Curie temperature of 6.0 K. The easy axis is oriented along [1 0 0], with a moment of 0.6 μ B/Ce.

Rotatable anisotropy and coercivity in exchange-bias bilayers

A phenomenological approach for polycrystalline exchange-bias bilayers is proposed which explains the coercivity enhancement as well as its temperature and coupling strength dependences. In the model, it is assumed that uncompensated interfacial antiferromagnetic grains can switch their magnetizations irreversibly, producing a rotatable anisotropy. A preferential distribution of the antiferromagnetic easy axes is also considered. An inhomogeneous ferromagnetic magnetization reversal is allowed, assuming that the ferromagnet is divided into domains, each coupled to a stable antiferromagnetic grain only. The antiferromagnetic anisotropy distribution affects the angular dependence of the coercivity, reducing its value in the vicinity of the exchange-bias direction, also smoothing the loop shift variations, more notably for small ferromagnetic uniaxial anisotropy. The inclusion of the rotatable anisotropy changes the shape of the magnetization curves and their characteristics. The larger the relative contribution of the rotatable anisotropy to the effective uniaxial anisotropy, the closer the loop shift angular variation gets to a pure cosine behavior, and no significant effect on the coercivity for strong coupling is detected. The frequently observed peak in the temperature variation of the coercivity is also explained considering the variation of the rotatable anisotropy, which is directly connected to the temperature dependence of the unstable antiferromagnetic grains' magnetization.

Exchange bias flop inFexZn1−xF2/Cobilayers

We have measured the angular dependence of the exchange bias field ${(H}_{E})$ in polycrystalline Co thin films deposited on antiferromagnetic (AF) ${\mathrm{Fe}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{F}}_{2}$ (110) films. Single crystals and twinned AF samples were studied, the latter possessing small grains (\ensuremath{\sim}7.0 nm) with their in-plane [001] easy axes perpendicular to each other. The twinned samples were field cooled through the AF N\'eel temperature with the field at an angle \ensuremath{\alpha} with respect to the twins' perpendicular bisector in the plane of the sample. The most negative ${H}_{E}$ occurred at an angle \ensuremath{\varphi}=0 for 0\ensuremath{\leqslant}\ensuremath{\alpha}\ensuremath{\leqslant}30\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\sim}40\ifmmode^\circ\else\textdegree\fi{}. An exchange bias flop occurred if \ensuremath{\alpha} was increased further, where \ensuremath{\varphi} abruptly shifted by 90\ifmmode^\circ\else\textdegree\fi{}. This means that two equivalent exchange bias field axes exist in this system. A 1.0-nm pure ${\mathrm{FeF}}_{2}$ layer deposited between the ${\mathrm{Fe}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{F}}_{2}$ and Co layers resulted in a sharper exchange bias flop transition, indicating that the pure interface layer acts as a buffer for the interface interaction. In untwinned ${\mathrm{FeF}}_{2}$ samples, a large ${H}_{E}$ was observed with the sample field cooled along the ${\mathrm{FeF}}_{2}$ easy axis, whereas two loops with the same exchange bias magnitude but of opposite sign were observed when the cooling field was applied 90\ifmmode^\circ\else\textdegree\fi{} to the AF easy axis. Changing the cooling field direction to 91\ifmmode^\circ\else\textdegree\fi{} caused the sample to acquire a significant positive ${H}_{E}$ parallel to the AF easy axis. These experiments demonstrate two important notions: (1) that the interface exchange coupling responsible for ${H}_{E}$ is extremely sensitive to the underlying magnetic anisotropy of the AF; and (2) that the direction of the cooling field does not necessarily determine the direction of ${H}_{E}.$

Thickness and angular dependencies of exchange bias in ferromagnetic/antiferromagnetic bilayers

A generalized Meiklejohn–Bean model in which the exchange coupling includes bilinear (direct exchange) and biquadratic (spin–flop) terms is proposed to study the exchange bias in ferromagnetic (FM)/antiferromagnetic (AFM) bilayers. For the strong antiferromagnetic anisotropy, an explicit formula for the exchange bias is derived and used to discuss the thickness and angular dependencies, and a lot of recent experimental results can thus be illustrated. The results show that both the critical thickness of the antiferromagnetic layer displaying the exchange bias and the saturation value of the exchange bias depend on the exchange coupling constants, the angle between the FM easy axis and AFM easy axis, as well as the orientation of an applied field. The bilinear and biquadratic terms will provide competitive contributions to the exchange bias, while the angular variation of the applied field can tune the exchange bias.

Fractionalization in an easy-axis Kagome antiferromagnet

We study an antiferromagnetic spin-1/2 model with up to third nearest-neighbor couplings on the Kagome lattice in the easy-axis limit, and show that its low-energy dynamics are governed by a four site XY ring exchange Hamiltonian. Simple ``vortex pairing'' arguments suggest that the model sustains a novel fractionalized phase, which we confirm by exactly solving a modification of the Hamiltonian including a further four-site interaction. In this limit, the system is a featureless ``spin liquid'', with gaps to all excitations, in particular: deconfined S^z=1/2 bosonic ``spinons'' and Ising vortices or ``visons''. We use an Ising duality transformation to express vison correlators as non-local strings in terms of the spin operators, and calculate the string correlators using the ground state wavefunction of the modified Hamiltonian. Remarkably, this wavefunction is exactly given by a kind of Gutzwiller projection of an XY ferromagnet. Finally, we show that the deconfined spin liquid state persists over a finite range as the additional four-spin interaction is reduced, and study the effect of this reduction on the dynamics of spinons and visons.

Magnetic torque of λ-(BETS) 2FeCl 4

Magnetic torque of λ-(BETS) 2 FeCl 4 is measured up to 15 T and down to 0.4 K. Clear first-order spin flop transition between the antiferromagnetic (AF) and the canted antiferromagnetic (CAF) phases is observed in the magnetic field of about 1.2 T and below 9.5 K. The AF easy axis is found to be in the direction tilted by about 30° from the c-axis to the b-axis, which is different from the previous reports on the easy axis (the c-axis). At the step-like transition with hysteresis around H = 10 T between CAF and the field induced ferromagnetic (F) (paramagnetic) phases, the direction of the magnetic easy axis changes. The two transitions on the H - T phase diagram are considered on the basis of the coupled two spin system; Fe 3+ (S = 5/2) and (BETS) 2 (S = 1/2).

Spin-wave interaction and renormalization of magnetic anisotropy in 2D antiferromagnets.

The renormalization of the magnetic anisotropy is investigated in 2D easy-axis antiferromagnets using 1/S expansion. It was shown that in the spin-wave gap Delta appears as the 1/S2 infrared divergent correction which becomes large at T>Delta and demands analysis of the full 1/S expansion. Qualitative consequences of this gap renormalization are discussed in relation to the AFR and neutron scattering experiments.

Coupling mechanisms in exchange biased films (invited)

We use an atomistic Heisenberg model in conjunction with the classical Landau Lifshitz equation for the spin motion to study coupling mechanisms between ferromagnetic (FM) and antiferromagnetic (AFM) films. Calculations for CoO/FM illustrate that there are two coupling mechanisms at work, the spin–flop coupling and an AFM–FM coupling through uncompensated defects. While the latter accounts for exchange bias and related phenomena, the former gives rise to a large coercivity and perpendicular alignment between FM spins and AFM easy axis. A combination of the two mechanisms explains apparent discrepancies between reversible and irreversible measurements of the AFM–FM coupling.

Vortex states in antiferromagnetic crystals

It is shown that axially symmetric two-dimensional nonuniform states can exist in easy-axis and cubic antiferromagnets lacking inversion symmetry, in the form of two-dimensional spatially modulated structures (magnetic vortex lattices) and isolated two-dimensional structures (vortices). The structure and equilibrium dimensions of the lattices and vortices have been determined by numerical solution of differential equations.

Criteria for the existence of generalized surface spin waves

A criterion for the existence of generalized surface spin waves is proposed on the basis of an analysis of the dipole-exchange surface spin dynamics of a tangentially magnetized, semibounded, easy-axis antiferromagnet.

Generalized surface nuclear spin wave induced by external magnetic field

The two-sublattice model of an easy-axis antiferromagnet is used to show that an additional rhombic anisotropy induced by an external magnetic field can lead to the formation of a generalized nuclear spin wave near the surface of the magnet. The criterion for the existence of a generalized surface spin wave is formulated.