Year: 2006
Type: article
Abstract: We present a model of homoionic, equal-spin ${s}_{1}$ dimer single molecule magnets exhibiting ${D}_{2h}$, ${C}_{2v}$, or ${S}_{2}$ molecular group symmetry, focusing upon the simplest ${D}_{2h}$ case. The spins within each dimer interact via the Heisenberg and the most general set of four quadratic anisotropic spin interactions with respective strengths $J$ and ${{J}_{j}}$, and with the magnetic induction $\mathbit{B}$. We solve the model exactly for ${s}_{1}=1∕2$, and analytically for $\mathbit{B}$ along the crystal directions and numerically for other $\mathbit{B}$ directions for ${s}_{1}=1$ and 5/2, and present $\mathbit{M}(\mathbit{B})$ curves at low $T$ for these cases with antiferromagnetic Heisenberg couplings $(J<0)$. Low-$T$ ${C}_{V}(\mathbit{B})$ curves for ${s}_{1}=1∕2$ and electron paramagnetic susceptibility $\ensuremath{\chi}(\mathbit{B},\ensuremath{\omega})$ for ${s}_{1}=1$ are also provided. For weakly anisotropic dimers, the Hartree approximation, or strong exchange limit, yields rather simple analytic formulas for $\mathbit{M}(\mathbit{B})$ and ${C}_{V}(\mathbit{B})$ at arbitrary ${s}_{1}$ that accurately fit the exact solutions at sufficiently low $T$ or large $B$. Low-$T$, large-$B$ formulas for the inelastic neutron-scattering cross section $S(\mathbit{B},\mathbit{q},\ensuremath{\omega})$ and $\ensuremath{\chi}(\mathbit{B},\ensuremath{\omega})$ with arbitrary ${s}_{1}$ and $\mathbit{B}$ in the Hartree approximation are also given. For antiferromagnetic Heisenberg couplings $(J<0)$ and weak anisotropy interactions $(\ensuremath{\mid}{J}_{j}∕J\ensuremath{\mid}\ensuremath{\ll}1)$, we provide analytic formulas for the $2{s}_{1}$ level-crossing magnetic inductions ${B}_{s,{s}_{1}}^{\mathrm{lc}}(\ensuremath{\theta},\ensuremath{\phi})$, at which the low-$T$ magnetization $\mathbit{M}(\mathbit{B})$ exhibits steps and the low-$T$ specific heat ${C}_{V}(\mathbit{B})$ exhibits zeroes, surrounded by double peaks of uniform height. Strong anisotropy interactions drastically alter these behaviors, however. Our results are discussed with regard to existing experiments on ${s}_{1}=5∕2\phantom{\rule{0.3em}{0ex}}{\mathrm{Fe}}_{2}$, ${s}_{1}=3∕2\phantom{\rule{0.3em}{0ex}}{\mathrm{Cr}}_{2}$, and ${s}_{1}=1\phantom{\rule{0.3em}{0ex}}{\mathrm{Ni}}_{2}$ dimers, suggesting the presence of single-ion anisotropy in three of them, but apparently without any sizeable anisotropic exchange interactions. Further experiments on single crystals of these and higher-spin dimers are therefore warranted, and we particularly urge further electron paramagnetic resonance and inelastic neutron-scattering experiments to be performed.
Source: Physical Review B
Authors: Dmitri V. Efremov, Richard A. Klemm
Institutions: Technische Universität Dresden, Kansas State University
Language: English
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2067462909