University of Applied Sciences Bielefeld  Department of Engineering and Mathematics Prof. Dr. rer. nat. Christian Schröder

Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron Christian Schröder,^{1,}* HeinzJürgen Schmidt^{2},Jürgen Schnack^{2 }and Marshall Luban^{3} ^{1}Department of Electrical Engineering and Computer Science, University of Applied Sciences Bielefeld, D33602 Bielefeld, Germany and Ames Laboratory, Ames, Iowa 50011, USA ^{2}Universität Osnabrück, Fachbereich Physik, D49069 Osnabrück, Germany ^{3}Ames Laboratory & Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA The observation of hysteresis effects in single molecule magnets like Mn_{12}acetate has initiated ideas of future applications in storage technology. The appearance of a hysteresis loop in such compounds is an outcome of their magnetic anisotropy. In a recent article (Phys. Rev. Lett. 94 (2005), 207203, condmat/0501558) we report that magnetic hysteresis occurs in a spin system without any anisotropy, specifically, where spins mounted on the vertices of an icosahedron are coupled by antiferromagnetic isotropic nearestneighbor Heisenberg interaction giving rise to geometric frustration. At T=0 this system undergoes a first order metamagnetic phase transition at a critical field B_{c} between two distinct families of ground state configurations. The metastable phase of the system is characterized by a temperature and field dependent survival probability distribution. 1. Resuls for classical simulations at T=0 The behavior of classical spin systems subject to an applied magnetic field both at T=0 and finite temperatures can be very effectively studied with the help of a stochastic spin dynamics approach such as that proposed in [1]. Here, the spin system is coupled to a heat bath in a Langevintype approach by using a LandauLifshitzdamping term as well as a fluctuating force with white noise characteristics. Starting from an arbitrary initial configuration the spin system can be investigated either at zero temperature by observing the relaxation to its ground state or at finite temperature by following its time evolution (follow this link to learn about the method by reading my stochastic spin dynamics tutorial). In the following movies we have set T=0 and applied an external magnetic field pointing upwards. For watching the movies just click on the images below. 1.1. The icosahedron in a linearly ramped field (4.5 MB MPEG movie) Starting from random initial conditions the system is first allowed to relax to the ground state configuration of an applied field value of B=0. The external field value is then ramped up linearly to B_{max} > B_{c}=1 and ramped down again to B=0. One can clearly see the phase transition as an abrupt change of the spin configuration at B=1. Note that on the down cycle the system remains in the metastable decagonphase which has the unique property of 2 spins pointing exactly into the applied field direction whereas the other 10 spins arrange themselves (almost) perpendicular to the external field with a canting depending on the strength of the external field value. 1.2. Slow motion of the phase transition (2.2 MB MPEG movie) In order to study the phase transition in detail we have prepared a slow motion of the dynamics in the vicinity of critical field B_{c}. In the movie below the system starts from a field value slightly below B_{c}. At the critical field the system changes from the 4thetaphase to the decagonphase with the 'north pole' and 'south pole' spins pointing in the field direction. Note that the phase transition manifests itself as a simultaneous rearrangement of all spins.
2. Results for classical simulations at
T>0 (7.6 MB MPEG
movie) For a general stability and lifetime analysis we have performed simulations at finite temperatures. For doing so the spin system is coupled to the heat bath and the trajectory is being calculated. For the following movie we have ramped up the external magnetic field until the system switches to the decagonfamilyphase at B=1. After that the field is reduced so that the decagonfamily is no longer the configuration of lowest energy but becomes metastable (here we have chosen a field value of B=0.6). For such fields we calculate the time evolution of the system until it eventually decays to the configuration of lowest energy, i.e. the 4thetafamily phase. By monitoring and histogramming the corresponding decay times one can derive the survival probability function for a given pair of parameters (T, B). In the movie one can clearly see the effect of a heat bath as a "shaking" of all spins. But even with this perturbation turned on the decagonfamily phase does not decay immediately when the magnetic field is reduced.

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