Ordering in ferromagnets with random anisotropy

Magnetic irreversibility and magnetization processes in Ni5Al3/NiO core/shell nanoparticle system

This work brings out many interesting facets of magnetism in the Ni5Al3/NiO core/shell nanoparticle system. Theweakandstrongmagnetic irreversibility lines (TWI(H)andTSI(H)) reproduce the previously reportedH - Tphase diagram at fieldsH⩽30 Oe, but strong departures occur forH > 30 Oe. Comparison with the theoretically predictedH - Tphase diagram allows us to identifyTWIwithTCG+SG, where the paramagnetic (PM)-chiral glass (CG) and PM-spin glass (SG) phase transitions occursimultaneously, andTSIwithTSG, the temperature at which transition to the replica symmetry breakingSGstate takes place. TheTSI(H)transition line abruptly ends at the point (H≃30 Oe,T≃90K). AsHexceeds 30 Oe, a new transition appears which gets completely suppressed at fieldsH>1 kOewhere the magnetic irreversibility ceases to exist. Nointrinsiclong-range ferromagnetic ordering exists but fields as low as 3 kOe suffice to induce long-range ferromagnetic order. At fixed temperatures, the magnetocrystalline anisotropy fluctuations essentially govern the 'approach-to-saturation' in magnetization for fields in the range 3 - 70 kOe. The present nanocrystalline system behaves as an isotropic system with random easy axis in which the magnetization reversal occurs through the coherent rotation of the magnetizations of weakly-interacting single-domain Ni5Al3particles. Saturation magnetization, likeM(T) atH⩾2 kOe, exhibits an anomalous upturn at temperatures below ≈ 30 K. This upturn is associated with the anomalous softening of spin-wave modes which results in the thermal excitation of a large number of non-equilibrium (finite lifetime) magnons. At sub-Kelvin temperatures, these magnons undergo Bose-Einstein condensation.

Spin cones in random-field XY models

We determine the arrangement of spins in the ground state of the XY model with quenched, random fields, on a fully connected graph. Two types of disordered fields are considered, namely, randomly oriented magnetic fields and randomly oriented crystal fields. Orientations are chosen from a uniformly isotropic distribution, but disorder fluctuations in each realization of a finite system lead to a breaking of rotational symmetry. The result is an interesting pattern of spin orientations found by solving a system of coupled, nonlinear equations within perturbation theory and also by exact numerical continuation. All spins lie within a cone for small enough ratio of field to coupling strength, with an interesting distribution of spin orientations, with peaks at the cone edges. The orientation of the cone depends strongly on the realization of disorder, but the opening angle does not. In the case of random magnetic fields, the cone angle widens as the ratio increases till a critical value at which there is a first-order phase transition and the cone disappears. With random crystal fields, there is no phase transition and the cone angle approaches 180^{∘} for large values of the ratio. At finite low temperatures, Monte Carlo simulations show that the formation of a cone and its subsequent alignment along the equilibrium direction occur on two different timescales.

Observation of spin-glass-like characteristics in ferrimagnetic TbCo through energy-level-selective approach

Rare earth (RE)–transition metal (TM) ferrimagnetic alloys are gaining increasing attention because of their potential use in the field of antiferromagnetic spintronics. The moment from RE sub-lattice primarily originates from the 4f-electrons located far below the Fermi level (E_F), and the moment from TM sub-lattice arises from the 3d-electrons across the E_F. Therefore, the individual magnetic moment configurations at different energy levels must be explored to clarify the microscopic mechanism of antiferromagnetic spin dynamics. Considering these issues, here we investigate the energy-level-selective magnetic moment configuration in ferrimagnetic TbCo alloy. We reveal that magnetic moments at deeper energy levels are more easily altered by the external magnetic field than those near the E_F. More importantly, we find that the magnetic moments at deeper energy levels exhibit a spin-glass-like characteristics such as slow dynamics and magnetic moment freezing whereas those at E_F do not. These unique energy-level-dependent characteristics of RE-TM ferrimagnet may provide a better understanding of ferrimagnet, which could be useful in spintronic applications as well as in spin-glass studies.

In a ferrimagnet, there are two magnetic sublattices coupled antiferromagnetically. The dynamics of the two magnetic sublattices isn’t well understood, as the magnetic moments for each reside at different energy levels. Here, Park et al show that the magnetic moments at deeper energy levels show spin-glass like characteristics.

Random anisotropy magnet at finite temperature

We present finite-temperature Monte Carlo studies of a 2D random-anisotropy (RA) magnet on lattices containing one million spins. The correlated spin-glass state predicted by analytical theories is reproduced in simulations, as are the field-cooled and zero-field-cooled magnetization curves observed in experiments. The orientations of lattice spins begin to freeze when the temperature is lowered. The freezing transition is due to the energy barriers generated by the RA rather than due to random interactions in conventional spin-glasses. We describe freezing by introducing the time-dependent spin-glass order parameterqand the spin-melting timeτ_Mdefined viaq=τ_M/tabove freezing, wheretis the time of the experiment represented by the number of Monte Carlo steps.

Exotic magnetic behaviour and evidence of cluster glass and Griffiths like phase in Heusler alloys Fe2-xMnxCrAl (0 ≤ x ≤ 1)

We present a detailed study of structural, magnetic and thermodynamic properties of a series of Heusler alloys Fe_2-xMn_xCrAl (x = 0, 0.25, 0.5, 0.75 and 1). Structural investigation of this series is carried out using high resolution synchrotron X-ray diffraction. Results suggest that with increasing Mn concentration, the L2₁ structure of Fe₂CrAl is destabilized. The DC magnetization results show a decrement in paramagnetic (PM) to ferromagnetic (FM) phase transition temperature (T_C) with increasing Mn concentration. From the systematic analysis of magnetic memory effect, heat capacity, time dependent magnetization, and DC field dependent AC susceptibility studies it is observed that, Fe₂CrAl exhibits cluster glass(CG)-like transition approximately at 3.9 K (T_f2). The alloys, Fe_1.75Mn_0.25CrAl and Fe_1.5Mn_0.5CrAl exhibit double CG-like transitions near T_f1 ~ 22 K, T_f2 ~ 4.2 K and T_f1 ~ 30.4 K, T_f2 ~ 9.5 K respectively, however, in Fe_1.25Mn_0.75CrAl, a single CG-like transition is noted at T_f2 ~ 11.5 K below T_C. Interestingly, FeMnCrAl shows the absence of long ranged magnetic ordering and this alloy undergoes three CG-like transitions at ~22 K (T_f^*), 16.6 K (T_f1) and 11 K (T_f2). At high temperatures, a detailed analysis of temperature response of inverse DC susceptibility clearly reveals the observation of Griffiths phase (GP) above 300 K (T*) in Fe₂CrAl and this phase persists with Mn concentration with a decrement in T*.

Anisotropic Temperature-Dependent Interaction of Ferromagnetic Nanoparticles Embedded Inside CNT

We analyze the magnetization versus magnetic field curves of Fe-based nanoparticles embedded inside CNT. Measurements were performed at different temperatures and orientations of the magnetic field. We demonstrate that, for the parallel field the magnetic anisotropy dominates and the coherent anisotropy is of great importance at low temperatures. At high temperatures, the exchange coupling becomes stronger, but the coherent anisotropy still occurs. For the perpendicular field, the coherence anisotropy is absent, and the dimensionality of the system reduces to 2D. The results are discussed in the framework of the correlation functions of the magnetic anisotropy axes.

Spin glass properties mapped by coercivity in ferromagnet/spin glass bilayers

We report on a study on the spin glass (SG) anisotropy (K _SG) and interfacial exchange coupling (J _IF) dependent coercivity (H _C) at the ferromagnet/SG interface, based on a modified Monte Carlo Metropolis algorithm. It is shown that K _SG and J _IF are interdependent while taking effect on different magnetic degrees of freedom and different time scales, resulting in complicated H _C behaviors. By means of a micromagnetic approximation approach, we analytically explain the H _C behaviors with respect to K _SG and J _IF. The dynamic SG surplus magnetization and the SG spin rotatability at the interface, hard to be detected experimentally, have proven to play crucial roles. This paper elucidates the weak anisotropy dependence of SG magnetic properties, and predicts that the SG features can be tunable at will by precisely controlling the magnetic parameters.

Topological Order Generated by a Random Field in a 2D Exchange Model

We study a 2D exchange model with a weak static random field on lattices containing over 10^{8} spins. Ferromagnetic correlations persist on the Imry-Ma scale inversely proportional to the random-field strength and decay exponentially at greater distances. We find that the average energy of the correlated area is close to the ground-state energy of a Skyrmion, while the topological charge of the area is close to ±1. The correlation function of the topological charge density changes sign at a distance determined by the ferromagnetic correlation length, while its Fourier transform exhibits a maximum. These findings suggest that static randomness transforms a 2D ferromagnetic state into a Skyrmion-anti-Skyrmion glass.

Non-collinear ferromagnetic short range order in MgO decked multi-layered graphene

A careful magnetic study of MgO decked multi-layered graphene (MDMLG), synthesized by a combustion process that does not involve the use of graphite (which can be a source of magnetic impurities) was conducted and an elaborate analysis of high-precision magnetization data permits us to completely rule out the presence of a long-range ferromagnetic (FM) ordering at temperatures T ≥ 2.5 K. Instead, a non-collinear FM short-range order persists up to temperatures as high as 300 K and a concomitant paramagnetic component is present at all the temperatures. The observed exponential temperature variations of the 'field-cooled' and 'zero-field-cooled' magnetizations, remanent magnetization, saturation magnetization, coercive field, exchange field and random anisotropy field are shown to basically reflect the exponential growth of the correlation length for the spins at the zigzag edges of graphene as the temperature falls below the temperature, T_x ≅ 10 K where a crossover from extremely weak to moderately weak magnetic anisotropy occurs. In sharp contrast, a paramagnetic response is induced by the defects in nanometer-sized MgO crystallites in MDMLG.

Evidence of superspin-glass behavior in Zn0.5Ni0.5Fe2O4 nanoparticles

We have used dc-magnetization and ac-susceptibility to investigate the superspin dynamics in 9 nm average size Zn(0.5)Ni(0.5)Fe(2)O(4) magnetic particles at temperatures (T) between 3 and 300 K. Dc-magnetization M versus T data collected in a H = 50 Oe magnetic field using a field-cooled-zero-field-cooled protocol indicate that the onset of irreversibility occurs in the vicinity of 190 K. This is confirmed by M versus H|(T) hysteresis loops, as well as by frequency- and temperature-resolved ac-susceptibility data. We demonstrate that this magnetic event is not due to the blocking of individual superspins, but can be unequivocally ascribed to their collective freezing in a spin-glass-like fashion. Indeed, the relative variation (per frequency decade) of the in-phase susceptibility peak temperature is ∼0.032, critical dynamics analysis of this peak shift yields an exponent zν = 10.0 and a zero-field freezing temperature T(g) = 190 K, and, in a magnetic field, Tg(H) is excellently described by the de Almeida-Thouless line δT(g) = 1 - T(g)(H)/T(g) ∝ H(2/3). In addition, out-of-phase susceptibility versus temperature datasets collected at different frequencies collapse on a universal dynamic scaling curve. Finally, memory imprinting during a stop-and-wait magnetization protocol confirms the collective freezing nature of the state below 190 K.

Mixtures composed of liquid crystals and carbon nanotubes

The phenomenological model to describe the liquid crystal-carbon nanotubes mixture presented in a previous paper [P. van der Schoot, V. Popa-Nita, and S. Kralj, J. Phys. Chem. B 112, 4512 (2008)] has been extended to include the isotropic carbon nanotubes-nematic thermotropic liquid crystal interaction. It is assumed that the carbon nanotubes in the isotropic phase act as an external random field on liquid crystal component. The influence of the randomly orientational disorder on the phase diagram of the mixture and orientational order parameters profiles of both components is theoretically analyzed for different values of temperature, volume fraction of carbon nanotubes, nematic carbon nanotubes-nematic liquid crystal coupling strength and the random field strength.

Random fields, topology, and the Imry-Ma argument

We consider an n-component fixed-length order parameter interacting with a weak random field in d=1, 2, 3 dimensions. Relaxation from the initially ordered state and spin-spin correlation functions are studied on lattices containing hundreds of millions of sites. At n ≤ d the presence of topological defects leads to strong metastability and glassy behavior, with the final state depending on the initial condition. At n=d+1, when topological structures are nonsingular, the system possesses a weak metastability. At n>d+1, when topological objects are absent, the final, lowest-energy state is independent of the initial condition. It is characterized by the exponential decay of correlations that agrees quantitatively with the theory based upon the Imry-Ma argument.

Computational studies of history dependence in nematic liquid crystals in random environments

Glassy liquid crystalline systems are expected to show significant history-dependent effects. Two model glassy systems are the RAN and SSS (sprinkled silica spin) lattice models. The RAN model is a Lebwohl-Lasher lattice model with locally coupled nematic spins, together with uncorrelated random anisotropy fields at each site, while the SSS model has a finite concentration of impurity spins frozen in random directions. Here Brownian simulation is used to study the effect of different sample histories in the low temperature regime in a three-dimensional (d = 3) model intermediate between SSS and RAN, in which a finite concentration p < p(c) (p(c) the percolation threshold) of frozen spins interacts with neighboring nematic spins with coupling W. Simulations were performed at temperature T ∼ T(NI)/2 (T(NI) the bulk nematic-isotropic transition temperature) for temperature-quenched and field-quenched histories (TQH and FQH, respectively), as well as for temperature-annealed histories (AH). The first two of these limits represent extreme histories encountered in typical experimental studies. Using long-time averages for equilibrated systems, we calculate orientational order parameters and two-point correlation functions. Finite-size scaling was used to determine the range of the orientational ordering, as a function of coupling strength W,p and sample history. Sample history plays a significant role; for given concentration p, as disorder strength W is increased, TQH systems sustain quasi-long-range order (QLRO) and short-range order (SRO). The data are also consistent with a long-range order (LRO) phase at very low disorder strength. By contrast, for FQH and p ≤ 0.1, only LRO and QLRO occur within the range of parameters investigated. The crossover between regimes depends on history, but in general, the FQH phase is more ordered than the AH phase, which is more ordered than the TQH phase. However, at temperatures close to the isotropic-nematic phase transition of pure samples we observe SRO for p = 0.1 even for FQH. We detect also in the QLRO phase a domain-type structural pattern, consistent with ideas introduced by Giamarchi and Doussal [Phys. Rev. B 52, 1242 (1995)] on superconducting flux lattices. In the weak-disorder limit the orientational correlation length obeys the Larkin-Imry-Ma scaling ξ ∼ D(-2/(4-d)).

Exchange bias in iron oxide nanoclusters

Iron oxide nanoclusters have been prepared by the gas-phase aggregation technique to form thin film structures with very high exchange bias values (up to 3000 Oe at low temperatures). Composition has been analysed by x-ray absorption and Mössbauer spectroscopies in order to elucidate the actual origin of the observed magnetic behaviour. The formation of a metal-oxide core-shell arrangement to explain the observed exchange bias has to be discarded since results show no metallic iron content and the main presence of α-Fe(2)O(3). The observed weak ferromagnetism and exchange bias are in agreement with the obtained size of α-Fe(2)O(3) nanoparticles: weak ferromagnetism because of the well-known spin canting in this antiferromagnetic structure and exchange bias because of the interaction between different spin sublattice configurations promoted by the modification of iron coordination in α-Fe(2)O(3) nanoparticles. Moreover, the preparation method is proposed for tuning both magnetization and exchange bias values by modification of the preparation conditions of α-Fe(2)O(3) nanoparticles, which open new possibilities in the design of new materials with required properties.

Instanton glass generated by noise in a Josephson-junction array

We compute the correlation function of a superconducting order parameter in a continuous model of a two-dimensional Josephson-junction array in the presence of a weak Gaussian noise. When the Josephson coupling is large compared to the charging energy, the correlations in the Euclidian space decay exponentially at low temperatures regardless of the strength of the noise. We interpret such a state as a collective Cooper-pair insulator and argue that it resembles properties of disordered superconducting films.

Photoinduced magnetism and random magnetic anisotropy in organic-based magnetic semiconductor V(TCNE){x} films, for x approximately 2

The V(TCNE){x}, x approximately 2 is an organic-based amorphous ferrimagnet, whose magnetic behavior is significantly affected in the low field regime by the random magnetic anisotropy. It was determined that this material has thermally reversible persistent change in both magnetization and conductivity driven by the optical excitation. Here, we report results of a ferrimagnetic resonance study of the photoinduced magnetism in V(TCNE){x} film. Upon optical excitation (lambda approximately 457.9 nm), the ferrimagnetic resonance spectra display substantial changes in their linewidths and line shifts, which reflect a substantial increase in the random magnetic anistropy. The results reflect the role of magnetic anisotropy in disordered magnets and suggest a novel mechanism of photoinduced magnetism in V(TCNE){x} induced by the increased structural disorder in the system.

Nematic-isotropic transition with quenched disorder

Nematic elastomers do not show the discontinuous, first-order, phase transition that the Landau-De Gennes mean field theory predicts for a quadrupolar ordering in three dimensions. We attribute this behavior to the presence of network crosslinks, which act as sources of quenched orientational disorder. We show that the addition of weak random anisotropy results in a singular renormalization of the Landau-De Gennes expression, adding an energy term proportional to the inverse quartic power of order parameter Q. This reduces the first-order discontinuity in Q. For sufficiently high disorder strength the jump disappears altogether and the phase transition becomes continuous, in some ways resembling the supercritical transitions in external field.

Random anisotropy nematic model: nematic-non-nematic mixture

The influence of a random-anisotropy- (RA-) type disorder on the phase separation of the nematogen-non-nematogen mixture is studied. A combination of the phenomenological Landau-de Gennes and Flory-Huggins theories is used. We assume that the non-nematogen component (i.e., impurity) enforces the RA disorder to the enclosing thermotropic liquid-crystal (LC) phase. The Imry-Ma argument is used according to which the lower-temperature phase exhibits a domain-type pattern. The disorder strength is measured in terms of the dimensionless parameter Lambda. We consider the case in which the LC molecules and impurities mix in the isotropic phase for Lambda=0. The impurities enforce a finite degree of orientational ordering even in the high-temperature paranematic phase. In the low-temperature phase they give rise to a domain-type structure, resulting in the distorted nematic (speronematic) phase. We show that the onset of orientational ordering increases the phase separation tendency. The RA field, however, opposes this tendency. With increasing value of Lambda the difference between the paranematic and speronematic ordering decreases. Consequently the structure of the phase-separated pattern can be much more complex in comparison to the Lambda=0 case.

Reentrant spin-glass transition in a dilute magnet

We perform a large-scale Monte Carlo simulation of a dilute classical Heisenberg model with ferromagnetic nearest neighbor and antiferromagnetic next-nearest neighbor interactions. We found that the model reproduces a reentrant spin-glass transition. That is, as the temperature is decreased, the magnetization increases rapidly below a certain temperature, reaches a maximum value, and then disappears at some lower temperature. The low temperature phase was suggested to be a spin-glass phase that is characterized by ferromagnetic clusters.

Magnetic correlations in nanostructured ferromagnets

Small-angle neutron scattering experiments on nanostructured Fe, Co, and Ni reveal grain-size dependent magnetic correlations across grain boundaries. In Fe, a minimum of the correlation length is observed for grain sizes of the order of the bulk domain-wall width where the coercive field has a maximum. The results are explained within a generalization of the random-anisotropy model that takes into account domain-wall formation within grains and reduced interface coupling.

Quasi-long-range order in nematics confined in random porous media

We study the effect of random porous matrices on the ordering in nematic liquid crystals. The randomness destroys orientational long-range order and drives the liquid crystal into a glass state. We predict two glass phases, one of which possesses quasi-long-range order. In this state the correlation length is infinite and the correlation function of the order parameter obeys a power dependence on the distance. The small-angle light-scattering amplitude diverges but slower than in the bulk nematic. In the uniaxially strained porous matrices two new phases emerge. One type of strain induces an anisotropic quasi-long-range-ordered state while the other stabilizes nematic long-range order.