1 Unusual magnetic ordering due to random impurities and frustration Tim Saunders Supervisor: John Chalker

2 Talk Outline What is a ground state? Frustrated Systems - they occur all the time… Geometry and Frustration – making life simple(ish) Impurities – they’re not always bad! Computer Simulations – faster than real life Summary Summary

3 Ground States Physical systems try to minimise their energy Physical systems try to minimise their energy This is dependent upon many factors including temperature, pressure, density etc. This is dependent upon many factors including temperature, pressure, density etc. Excited State Unique Ground State Excited State Non-Unique Ground State

4 What is Frustration? Protein Folding - BiologyIce - Chemistry Macroscopically Degenerate Ground States

5 Geometric frustration is simpler – systems with only one interaction can be frustrated Geometric frustration is simpler – systems with only one interaction can be frustrated Triangular lattices are the simplest lattice on which frustration can occur Triangular lattices are the simplest lattice on which frustration can occur Geometry and Frustration ?

6 Present in all ‘real’ materials Present in all ‘real’ materials Typically impurities destroy order but sometimes they introduce new behaviour Typically impurities destroy order but sometimes they introduce new behaviour Impurities – they’re not always bad! Kondo Effect Temperature (K) Resistance High Temperature Superconductors Pure system is not superconductor When disorder is added the system becomes a superconductor!

7 Spin Glasses In ‘pure’ frustrated magnetic systems: no ordering In ‘pure’ frustrated magnetic systems: no ordering Experiments observe a transition! Experiments observe a transition! Transition very similar to “spin glasses” Transition very similar to “spin glasses” Normal spin glasses: large proportion of impurities (>10%) Normal spin glasses: large proportion of impurities (>10%) Frustrated magnets: very small proportion of impurities (<3%) Frustrated magnets: very small proportion of impurities (<3%) Explaining this unique behaviour has been a problem for the past 15 years Explaining this unique behaviour has been a problem for the past 15 years System cooled with no applied field System cooled with an applied field Transition Temperature Zn 1-x Cd x Cr 2 O 4

8 Monte Carlo Algorithm - Probabilistic method for finding ground states of complex systems Monte Carlo Algorithm - Probabilistic method for finding ground states of complex systems Parallel Tempering – advance on Monte Carlo – that simulates the system ‘faster’ than real life Parallel Tempering – advance on Monte Carlo – that simulates the system ‘faster’ than real life Computer Simulations T min T1T1 T2T2 T3T3 T max Compare energies of systems that are adjacent in temperature. Swap them if probabilistically favourable This allows us to simulate very complex systems quickly – though it uses up to 24 CPUs at the same time! This allows us to simulate very complex systems quickly – though it uses up to 24 CPUs at the same time! Feed back new systems and run again…

Spins cooled down with impurities present Phase Transition Temperature Temperature Numerical Results

10 Summary We have explained the experimental observations using a physically sensible model We have explained the experimental observations using a physically sensible model The coupling between the frustration and the impurities is the essential ingredient The coupling between the frustration and the impurities is the essential ingredient Understanding this ‘simpler’ system should enable us to make progress on more difficult frustrated systems such as high-temperature superconductors Understanding this ‘simpler’ system should enable us to make progress on more difficult frustrated systems such as high-temperature superconductors

11 Superconducting Layers