The Influence of Confinement on Phase Transitions (Part 1)

Anders Rosengren (KTH), B. Hjörvarsson (Uppsala University), O. Eriksson (Uppsala University), S T Bramwell (UCL)
This program will run in two installments: February 15 - March 1, 2010 and December 12 - 17, 2010.

The classical theories on phase transitions are based on the thermodynamic limit. This implies infinitely large or small extension on all the systems that are considered. The success of the resulting scaling laws and the corresponding generalisation is impressive. However, these theories fail to address many of the important aspects, as finiteness in extension is apparent in most physical systems.  

As an example, the physics of magnetic multilayers has caused considerable attention lately, largely due to their technological importance. This interest has implied substantial increase in our knowledge and triggered renewed views on e.g. the range of the magnetic interactions. Interactions over large distances are now integrated in the description of the ordering of such systems.  

In classical Monte Carlo calculations the interactions are most frequently mapped onto nearest neighbours. This has been shown to yield a correct behaviour for infinite systems, thus there has been limited driving force to use more complicated models (and CPU intensive) in this type of studies. However, this approach will not hold for finite systems with long-range interactions. Obtaining better understanding of phase transitions of confined systems is not only timely, it will enhance our understanding of dimensional crossovers, as well as the changes in the critical parameters.  

These effects are not limited to magnetic phase transitions. Any second order transition, with corresponding fluctuations is expected to show strong finite size effects, on ordering temperature as well as the critical exponents. Thus, this question is of highly generic nature and has significance within condensed matter physics, chemistry as well as biology.

In this program we will EXPLORE THE INFLUENCE OF CONFINEMENT ON PHASE TRANSITIONS. This exploration will address both the static as well as the dynamic aspects, as these are intimately linked.
  • Anatoly Belonoshko
  • Anders Bergman
  • Anders Rosengren
  • Andrea Taroni
  • Annica Black-Schaffer
  • Björgvin Hjörvarsson
  • Chunmei Li
  • eddy ardonne
  • Edwin Langmann
  • Elena Vedmedenko
  • Erna Krisztina Delczeg
  • Hannes Jonsson
  • Ivan Shelykh
  • Johan Hellsvik
  • Lars Nordström
  • Martina Ahlberg
  • masoud karimipour
  • Mats Horsdal
  • Mats Wallin
  • Olle Eriksson
  • Paata Kakashvili
  • Patrik Henelius
  • Per Håkan Lundow
  • Peter Holdsworth
  • Robin Stinchcombe
  • Simon Banks
  • Song LU
  • Steve Bramwell
  • Thomas Hase
  • Unnar Arnalds
    • 10:30 AM
      Welcome and Coffee
    • 1
      Introduction and Setting the Stage
      Give a thorough description of the experimental results concerning dimensionally confined magnetic systems.
      Speaker: Prof. Björgvin Hjörvarsson (Uppsala University)
    • 12:00 PM
    • 2
      Critical Temperatures of Finite Samples at Finite Observation Times
      The correlation function is an essential ingredient of any theory of phase transitions, covering electronic systems, liquids or magnets, since it provides direct information on critical properties of a system. With the Ornstein-Zernike law its general analytical form is known for infinite systems at infinite observation times, above the critical temperature. However, important experimental developments involve ever smaller length- and time-scales connected with size- and time-dependent phases like thermally assisted switching of magnetization. For such nano-sized systems, there is up to now no clear understanding of crossover phenomena like the crossover from a paramagnetic state at high temperatures via a superparamagnetic regime to ferro- or antiferromagnetic order at low T, and how they manifest themselves in the correlation function. This is related to the problem that a Curie (or Neel) temperature cannot be defined unambiguously. These problems hamper a reliable interpretation of experimental results. In this talk I will present a particularly simple general expression for the correlation function, covering all sample sizes L, all observation times, and the entire temperature range from zero to infinity. Our numerical and analytical calculations demonstrate that the Curie temperature does not simply decrease with decreasing sample size but rather splits in finite samples for finite observation times. This new result obtained for open boundaries does not violate scaling invariance and recovers all known laws for periodic boundary conditions, infinite observation times and high temperatures as limiting cases. The proposed form for the correlation function allows for a novel and effective procedure to determine above mentioned splitting and critical temperatures which goes beyond the famous Binder cumulants method as it permits an accurate determination of the Curie temperature of infinite and finite objects, as well as the blocking temperature, from a single calculation of a finite object without tedious finite-size scaling.
      Speaker: Dr Elena Vedmedenko (University of Hamburg)
    • 3:00 PM
      Discussion Session
    • 6:00 PM
    • 3
      Magnon Softening in a ferromagnetic monolayer
      We study the Fe/W(110) monolayer system through a combination of first principles calculations and atomistic spin dynamics simulations. We focus on the dispersion of the spin waves parallel to the [001] direction. Our results compare favorably with the experimental data of Prokop et al. [Phys. Rev. Lett. 102, 177206], and correctly capture a drastic softening of the magnon spectrum, with respect to bulk bcc Fe. The suggested shortcoming of the itinerant electron model, in particular that given by density functional theory, is refuted. We also demonstrate that finite temperature effects are significant, and that atomistic spin dynamics simulations represent a powerful tool with which to include these.
      Speaker: Dr Anders Bergman (Uppsala University)
    • 11:00 AM
      Discussion Session
    • 12:00 PM
    • 4
      Confinement and Ordering
      Speaker: Prof. Peter Holdsworth (Ecole Normale Supérieure de Lyon)
    • 2:00 PM
      Discussion Session
    • 5
      Structure modifications in ultra thin films of transition metal oxides
      The talk reviews recent studies on the geometric structure of oxide films in the ultra thin film limit and their implications on their magnetic (multiferroic) properties. In a first example the structural phase transition in pure and Cobalt-doped ZnO-film is discussed. Depending on film thickness a transition from the bulk Wurtzite (WZ)- type structure to the hexagonal-Boron-nitride (h-BN) phase is observed. Cobalt doping leads to a phase segregation in which WZ-type CoO-nanoclusters are coherently embedded into the h-BN host ZnO matrix. The structure model involving locally confined antiferromagnetic CoO-clusters supports recent experimental results on the magnetic properties of diluted magnetic semiconductors. The effect of confinement is also decisive for the multiferroic (ferromagnetic/ferroelectric) properties of the BaTiO3/Fe(001) interface, which is addressed in the second part of the talk. The structure analysis in combination with first principles calculations reveals the onset of an interface dipole at a critical film thickness of two unit cells of BaTiO3. Its influence on the magnetoelectric properties is discussed.
      Speaker: Dr Holger Meyerheim (Max-Planck-Institut für Mikrostrukturphysik, Halle, Germany)
    • 12:00 PM
    • 1:00 PM
      Discussion session
    • 6
      Phase Transitions and Critical Phenomena
      Speaker: Prof. Steve Bramwell (University College London)
    • 7
      Quantum critical points via gravity
      Speaker: Lárus Thorlacius (Nordita)
    • 8
      The effect of geometric constraints on the spin glass transition in binary pyrochlores
      Recent neutron scattering experiments [1] have sharpened the picture of an algebraic spin liquid phase in CsNiCrF6, originally proposed by Zinkin et al. [2]. Anderson famously predicted that systems such as this, with equal numbers of two magnetic species populating a pyrochlore lattice, should favour configurations with two of each type of ion present on every tetrahedron [3]. With this in mind, we have studied a simple model of a system comprised of equal numbers of two species of Heisenberg spins, A and B, distributed randomly across a pyrochlore lattice, but subject to the ice-rules like constraint that each tetrahedron has two A and two B type spins. We have characterized the ground state magnetic behaviour for all possible combinations of the three exchange interactions governing the system. This reveals a large region of exchange parameter space for which the system is in a spin liquid like state consisting of a soup of single species, non-interacting, antiferromagnetic loops. This configuration is robust even in the presence of four ferromagnetic bonds per tetrahedron. We demonstrate that the highly constrained form of quenched disorder imposed on the ion placement removes the possibility of a spin glass transition from this cooperative paramagnetic regime. We go on to discuss how the underlying structural configuration leads to algebraic magnetic correlations, manifested in the familiar bow-tie structure factor. This model is also susceptible to strong finite size influences. A system with finite size will be unable to develop the correct loop distribution to produce the bow-tie structure factor. We are currently investigating how such effects manifest themselves and the implications for more controllable arrays such as can be achieved with, for example, artificial spin ice. [1] T. Fennel et al., unpublished. [2] M. P. Zinkin et al., Phys. Rev. B 56, 11786 (1997) [3] P. W. Anderson, Phys. Rev. 102, 1008 (1956)
      Speaker: Dr Simon Banks (University College London)
    • 9
      Phase transitions with disorder
      Disordered systems often display new emergent phases and phase transition, for example, spin glasses and similar states in quantum fluids with disorder. Other examples where confinement effects play an important role are given by porous matter. Experiments on such systems often indicate strong finite size effects that need to be understood. We use an approach involving Monte Carlo simulation and scaling analysis to address  these issues. I will describe some of our recent studies.
      Speaker: Prof. Mats Wallin (Theoretical Physics KTH)
    • 12:00 PM
    • 1:00 PM
      Discussion session
    • 10
      Dipolar Systems
      Due to the long range and angular dependence of the dipolar interaction sample shape plays a crucial role in determining the ordered state of magnetic materials where long-range interactions are important. This should also apply to magnetic mulitlayer systems and I propose studying the effects of the often neglected dipolar interaction in these novel materials.
      Speaker: Prof. Patrik Henelius (KTH Royal Institute of Technology)
    • 11
      Methods in simulations
    • 12
      Hunting for monopoles in spin ice
      Speaker: Prof. Peter Holdsworth (Ecole Normale Supérieure de Lyon)
    • 13
    • 12:00 PM
    • 14
      Magnetricity in Spin Ice
      Speaker: Prof. Steve Bramwell (University College London)
    • 15
    • 16
      Future Perspectives
    • 6:00 PM
    • 17
      A family of critical models in d-dimensions
      It is well known that the order parameter for the 2dXY model is zero in the thermodynamic limit, yet it remains measurable even for macroscopic systems. Thus our ability to observe the KT transition via changes in the magnetization is a result of the "confinement" of the system to finite size. We have been working on a family of related models in one and three-dimensions generalizable to d-dimensions) which exhibit behaviour closely analogous to the 2dXY model. We will consider the possibility that confinement in these models may lead to KT type, or possibly other novel, phase transitions.
      Speaker: Dr Simon Banks (University College London)
    • 18
      The p,q-binomial distribution applied to the finite-size Ising model
      Speaker: Dr Per Håkan Lundow (KTH Royal Institute of Technology)
    • 3:15 PM
    • 6:00 PM
    • 19
      Simulation of long time scale evolution in solids
      Speaker: Prof. Hannes Jonsson (University of Iceland)
    • 11:15 AM
      Discussion Session
    • 20
      Magnetic X-ray scattering (part I)
      Speaker: Dr Tom Hase (University of Warwick)
    • 2:15 PM
      Discussion session
    • 21
      Phase Transitions and Dimensionality
      Speaker: Prof. Robin Stinchcombe (University of Oxford)
    • 12:15 PM
    • 22
      First principles theory of magnetism and magnetisation dynamics
      In the talk I will review some recent results on first principles theory of magnetism and magnetic materials. In particular, results of giant magnetic anisotropies will be described, and I will put some emphasis on technological aspects of this property. I will also describe recent developments in theory of spin-dynamics and how this reproduces observations on thin-film magnetism, diluted magnetic semiconductors as well as spin-glasses
      Speaker: Prof. Olle Eriksson (Uppsala University)
    • 23
      The role of higher multipoles in magnetically ordered systems
      In most magnetic phase transitions the focus is on the lowest multipole, the dipole which is directly related to the magnetic moment. We will in this work argue that in some cases higher order multipoles are driving the transition and the dipole is a secondary effect. The concept of spherical tensors or multipoles of an open atomic shell is first reviewed and discussed.Some of these multipoles play an important rule in e.g. x-ray circular dichroism measurements, where with the use of the famous sum rules by Carra et al. the spin and orbital magnetic moments can be deduced. Then we will describe how such multipoles can be calculated in general in both the ground state as well as excited states in terms of density functional methods including a local correlation term, as in e.g. the so-called LDA+U or LDA+DMFT methods. It will be demonstrated how these multipoles can contribute significantly to the exchange and correlation energies of transition metal systems.  Especially, we will discuss in some depth materials where these multipoles act as the main order parameter, sometimes referred to as an "hidden order". Especially, results for two cases will be presented the magnetic/superconducting iron-pnictide LaOFeAs and the heavy fermion compound URu2Si2.
      Speaker: Dr Lars Nordström (Uppsala University)
    • 3:15 PM
      Discussion Session
    • 24
      Infulence of the range of interaction in thin magnetic structures
      The properties of ultrathin magnetic structures are influenced by many length scales that reflect both generic physics and chemical detail. A striking example is the experimentally determined shift of the critical temperature as a function of film thickness. While all systems experience a pronounced suppression in Tc with decreasing film thickness, the magnitude of this shift cannot be reconciled with established theoretical results. In particular, the ratio between the monolayer and bulk limits for the nearest neighbour Ising model is roughly 1/2, whereas experimentally, ratios of the order of 0.1 are commonly measured. By means of detailed Monte Carlo simulations, we resolve this discrepancy by investigating a model with long-range interactions. The model also captures other features of real ultrathin magnets, such as an almost linear temperature dependence for the surface magnetization. Our results demonstrate that the behavior of ultrathin magnetic structures arises from a competition of length scales dictated by their slab-like geometry, the presence of surface boundaries, and crucially, the range of the interactions present.
      Speaker: Andrea Taroni (Uppsala University)
    • 11:15 AM
      Discussion Session
    • 12:15 PM
    • 25
      Software Development
      Open forum
    • 26
      Magnetic scattering from structured surfaces
      Speaker: Dr Tom Hase (University of Warwick)
    • 27
      Discussions and Future Perspectives
      Speaker: Prof. Björgvin Hjörvarsson (Uppsala University)
    • 12:15 PM