%0 Book Section %1 statphys23_0462 %A Tanaka, S. %A Miyashita, S. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K antiferromagnets arrhenius kagome law relaxation slow statphys23 topic-9 %T Entropy-driven slow relaxation of easy axis anisotropic kagome antiferromagnets in exotic ferromagnetic ordered state %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=462 %X We study slow relaxation process in the ordered state of easy axis type anisotropic kagome antiferromagnet: $H=-J\sum_łefti,j \right\rangle łeft(S_i^x S_j^x + S_i^y S_j^y+ \Delta S_i^z S_j^z \right)$, where $łefti,j \right\rangle$ denotes the nearest neighbor pair on the kagome lattice and $\Delta ( > 1)$ denotes Ising-like anisotropy. Properties of thermodynamic phase transition of this system were investigated by Kuroda and Miyashita2 and Bekhechi and Southern3. The ground state of this system is the set ($S_\alpha$, $S_\beta$, $S_\gamma$) on the triangle cluster. $S_= (0,0,1)$,$S_= (\sinþeta\cos\phi,\sinþeta\sin\phi,-\cosþeta)$, \\ $S_= (-\sinþeta\cos\phi,-\sinþeta\sin\phi,-\cosþeta)$, where $\cos= \Delta\Delta+1$. The angle $\phi$ is any angle denoting the freedom of rotation $2\pi$. The spontaneous magnetization of each unit triangle cluster is $m = (1-2\cosþeta)$. The symmetry breaking of the magnetization exists which causes the thermodynamic phase transition where the Z$_2$ symmetry is broken in spite of no sublattice long range order takes place at finite temperature. We call this low temperature phase ``exotic ferromagnetic phase''. If we connect $S_\beta$ and $S_\gamma$ in the ground state, the closed loops are formed which we call ``weathervane loops''. Entropy per weathervane loop is $2\pi$ at $T 0+$. We study the relaxation of the magnetization and the number of the weathervane loops $n_loop$4. We found that the relaxation of $n_loop$ is an entropy-driven process and is much slower than the one of the magnetization and energy. The relaxation consists of reconnections of the weathervane loops and thus we found the Arrhenius type relaxation $e^\beta\Delta E$ of $n_loop$4, although the process occurs in equal energy subspace. The characteristic energy barrier $\Delta E$ is the order of the interaction $J$. We also estimated the equilibrium $n_loop$ as a function of the temperature. 1) A.S. Wills et al., Phys. Rev. B, 62 R9264 (2000).\\ 2) A. Kuroda and S. Miyashita, J. Phys. Soc. Jpn., 64 4509 (1995).\\ 3) S. Bekhechi and B.W. Southern, Phys. Rev. B, 67 144403 (2003).\\ 4) S. Tanaka and S. Miyashita, J. Phys. Condens. Matter, 19 145256 (2007), cond-mat/0703148.

@incollection{statphys23_0462, abstract = {We study slow relaxation process in the ordered state of easy axis type anisotropic kagome antiferromagnet: $\mathcal{H}=-J\sum_{\left\langle i,j \right\rangle} \left(S_i^x S_j^x + S_i^y S_j^y+ \Delta S_i^z S_j^z \right)$, where $\left\langle i,j \right\rangle$ denotes the nearest neighbor pair on the kagome lattice and $\Delta ( > 1)$ denotes Ising-like anisotropy. Properties of thermodynamic phase transition of this system were investigated by Kuroda and Miyashita[2] and Bekhechi and Southern[3]. The ground state of this system is the set ($S_\alpha$, $S_\beta$, $S_\gamma$) on the triangle cluster. $S_\alpha = (0,0,1)$,$S_\beta = (\sin\theta\cos\phi,\sin\theta\sin\phi,-\cos\theta)$, \\ $S_\gamma = (-\sin\theta\cos\phi,-\sin\theta\sin\phi,-\cos\theta)$, where $\cos\theta = \frac{\Delta}{\Delta+1}$. The angle $\phi$ is any angle denoting the freedom of rotation $2\pi$. The spontaneous magnetization of each unit triangle cluster is $m = \pm (1-2\cos\theta)$. The symmetry breaking of the magnetization exists which causes the thermodynamic phase transition where the Z$_2$ symmetry is broken in spite of no sublattice long range order takes place at finite temperature. We call this low temperature phase ``exotic ferromagnetic phase''. If we connect $S_\beta$ and $S_\gamma$ in the ground state, the closed loops are formed which we call ``weathervane loops''. Entropy per weathervane loop is $2\pi$ at $T \to 0+$. We study the relaxation of the magnetization and the number of the weathervane loops $n_{\mathrm{loop}}$[4]. We found that the relaxation of $n_{\mathrm{loop}}$ is an entropy-driven process and is much slower than the one of the magnetization and energy. The relaxation consists of reconnections of the weathervane loops and thus we found the Arrhenius type relaxation $\tau \propto \mathrm{e}^{\beta\Delta E}$ of $n_{\mathrm{loop}}$[4], although the process occurs in equal energy subspace. The characteristic energy barrier $\Delta E$ is the order of the interaction $J$. We also estimated the equilibrium $n_{\mathrm{loop}}$ as a function of the temperature. 1) A.S. Wills et al., Phys. Rev. B, {\bf 62} R9264 (2000).\\ 2) A. Kuroda and S. Miyashita, J. Phys. Soc. Jpn., {\bf 64} 4509 (1995).\\ 3) S. Bekhechi and B.W. Southern, Phys. Rev. B, {\bf 67} 144403 (2003).\\ 4) S. Tanaka and S. Miyashita, J. Phys. Condens. Matter, {\bf 19} 145256 (2007), cond-mat/0703148.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Tanaka, S. and Miyashita, S.}, biburl = {https://www.bibsonomy.org/bibtex/22f3e7e8f9616cee35d45c4d2b94b4ac1/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {cecd33901f9018d40534d1d168700848}, intrahash = {2f3e7e8f9616cee35d45c4d2b94b4ac1}, keywords = {antiferromagnets arrhenius kagome law relaxation slow statphys23 topic-9}, month = {9-13 July}, timestamp = {2007-06-20T10:16:20.000+0200}, title = {Entropy-driven slow relaxation of easy axis anisotropic kagome antiferromagnets in exotic ferromagnetic ordered state}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=462}, year = 2007 }