Monopole ordered phases in dipolar and nearest-neighbours Ising pyrochlore: from spin ice to the "all-in--all-out" antiferromagnet

We study Ising pyrochlores by means of Monte Carlo simulations. We cover a set of exchange constants ranging from the frustrated ferromagnetic case (spin-ice) to the fully-ordered "all-in--all-out" antiferromagnet in the dipolar model, reinterpreting the results --as in an ionic system-- in terms of a temperature vs. magnetic charge density phase diagram. In spite of its spin nature and the presence of both double and single non-conserved magnetic charges, the dipolar model gives place to a phase diagram which is quite comparable with those previously obtained for on-lattice systems of electric charges, and on spin ice models with conserved number of single magnetic charges. The contrast between these systems, to which we add results from the nearest-neighbours model, put forward other features of our phase diagram --notably, a monopole fluid with charge order at high monopole densities that persists up to arbitrarily high temperatures-- that can only be explained taking into account construction constraints forced by the underlying spin degrees of freedom.Comment: 9 pages, 10 figure

Monte Carlo study on the detection of classical order by disorder in real antiferromagnetic Ising pyrochlores

We use Monte Carlo simulations to evaluate the feasibility of detecting thermal order by disorder in real antiferromagnetic Ising pyrochlores, frustrated by a magnetic field applied in the [110] direction. Building on an ideal system with only nearest-neighbor exchange interactions and a perfectly oriented field, we consider the effects of dipolar interactions and field misalignment. Our approach is special in that it relies more in the possibility to switch on and off the entropic drive towards order than in the absence of (or immunity to) a particular perturbation. It can then be applied, in principle, to other uncontrolled interactions expected to be naturally present in real magnetic materials. We establish the conditions under which entropic effects can be discerned from an interaction drive towards order, show how to use neutron scattering as a means to unveil this mechanism, and discuss possible materials where to test these ideas.Instituto de Física de Líquidos y Sistemas Biológico

Tuning Ginzburg-Landau theory to quantitatively study thin ferromagnetic materials

Along with experiments, numerical simulations are key to gaining insight into the underlying mechanisms governing domain wall motion in thin ferromagnetic systems. However, a direct comparison between numerical simulation of model systems and experimental results still represents a great challenge. Here, we present a tuned Ginzburg-Landau model to quantitatively study the dynamics of domain walls in quasi two-dimensional ferromagnetic systems with perpendicular magnetic anisotropy. This model incorporates material and experimental parameters and the micromagnetic prescription for thermal fluctuations, allowing us to perform material-specific simulations and at the same time recover universal features. We show that our model quantitatively reproduces previous experimental velocity-field data in the archetypal perpendicular magnetic anisotropy Pt/Co/Pt ultra-thin films in the three dynamical regimes of domain wall motion (creep, depinning and flow). In addition, we present a statistical analysis of the domain wall width parameter, showing that our model can provide detailed nano-scale information while retaining the complex behavior of a statistical disordered model.Comment: 18 pages, 8 figure

Domain-wall roughness in GdFeCo thin films: crossover length scales and roughness exponents

Domain-wall dynamics and spatial fluctuations are closely related to each other and to universal features of disordered systems. Experimentally measured roughness exponents characterizing spatial fluctuations have been reported for magnetic thin films, with values generally different from those predicted by the equilibrium, depinning and thermal reference states. Here, we study the roughness of domain walls in GdFeCo thin films over a large range of magnetic field and temperature. Our analysis is performed in the framework of a model considering length-scale crossovers between the reference states, which is shown to bridge the differences between experimental results and theoretical predictions. We also quantify for the first time the size of the depinning avalanches below the depinning field at finite temperatures.Comment: 10 pages, 6 figures. The first two authors contributed equally to this wor

Field-dependent roughness of moving domain walls in a Pt/Co/Pt magnetic thin film

The creep motion of domain walls driven by external fields in magnetic thin films is described by universal features related to the underlying depinning transition. One key parameter in this description is the roughness exponent characterizing the growth of fluctuations of the domain wall position with its longitudinal length scale. The roughness amplitude, which gives information about the scale of fluctuations, however, has received less attention. Albeit their relevance, experimental reports of the roughness parameters, both exponent and amplitude, are scarce. We report here experimental values of the roughness parameters for different magnetic field intensities in the creep regime at room temperature for a Pt/Co/Pt thin film. The mean value of the roughness exponent is $\zeta = 0.74$, and we show that it can be rationalized as an effective value in terms of the known universal values corresponding to the depinning and thermal cases. In addition, it is shown that the roughness amplitude presents a significant increase with decreasing field. These results contribute to the description of domain wall motion in disordered thin magnetic systems.Comment: 10 pages, 7 figure

Anomalous out-of-equilibrium dynamics in the spin-ice material Dy<SUB>2</SUB>Ti<SUB>2</SUB>O<SUB>7</SUB> under moderate magnetic fields

We study experimentally and numerically the dynamics of the spin ice material Dy2Ti2O7 in the low temperature (T) and moderate magnetic field ( B ) regime (T ∈ [0.1, 1.7]  K, B ∈ [0, 0.3]  T). Our objective is to understand the main physics shaping the out-of-equilibrium magnetisation vs temperature curves in two different regimes. Very far from equilibrium, turning on the magnetic field after having cooled the system in zero field (ZFC) can increase the concentration of magnetic monopoles (localised thermal excitations present in these systems); this accelerates the dynamics. Similarly to electrolytes, this occurs through dissociation of bound monopole pairs. However, for spin ices the polarisation of the vacuum out of which the monopole pairs are created is a key factor shaping the magnetisation curves, with no analog. We observe a threshold field near 0.2 T for this fast dynamics to take place, linked to the maximum magnetic force between the attracting pairs. Surprisingly, within a regime of low temperatures and moderate fields, an extended Ohm's law can be used to describe the ZFC magnetisation curve obtained with the dipolar spin-ice model. However, in real samples the acceleration of the dynamics appears even sharper than in simulations, possibly due to the presence of avalanches. On the other hand, the effect of the field nearer equilibrium can be just the opposite to that at very low temperatures. Single crystals, as noted before for powders, abandon equilibrium at a blocking temperature T B which increases with field. Curiously, this behaviour is present in numerical simulations even within the nearest-neighbours interactions model. Simulations and experiments show that the increasing trend in T B is stronger for B ‖[100]. This suggests that the field plays a part in the dynamical arrest through monopole suppression, which is quite manifest for this field orientation.Instituto de Física de Líquidos y Sistemas Biológico