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Description
Previous single crystal studies of Cu(en)$_2$SO$_4$ (en = C$_2$H$_8$N$_2$) indicated the absence of phase transition to magnetic ordered state down to $0.3$ K [1]. Exponential decrease of specific heat at lowest temperatures indicated the presence of energy gap in the excitation spectrum. Detailed inspection of the crystal structure considering local symmetry of crystal field and spatial distribution of $d_{x^2-y^2}$ orbitals of Cu(II) ion expected formation of magnetic dimers within the $bc$ plane. The conjecture was confirmed by the analysis of thermodynamic data within the $S=1/2$ Heisenberg antiferromagnetic dimer model. As a manifestation of interdimer interactions, significant deviations from the simple dimer model appeared in the vicinity of the critical magnetic field $7$ T, associated with the gap closure. To tune the strength of magnetic dimerization, isomorphic compound Cu(en)$_2$CrO$_4$ was investigated in the present work. As a result of different molar masses, the scaling of lattice specific heat of Cu(en)$_2$SO$_4$ by a factor $1.08$ provides excellent agreement with Cu(en)$_2$CrO$_4$ data. Besides that, the analysis of thermodynamic data including specific heat, susceptibility and isothermal magnetization revealed reduction of the intradimer coupling from $5.5$ K in Cu(en)$_2$SO$_4$ to $4.5$ K in Cu(en)$_2$CrO$_4$. Corresponding critical field shifted from $7$ T to $5.5$ T and saturation field reduced from $11$ T (Cu(en)$_2$SO$_4$) to $8.5$ T. In both materials the magnetic phase diagrams are symmetric with a dome shape and the S-Cr substitution significantly shifted the induced ordered phase to lower magnetic fields and temperatures. To obtain better insight into the character of the magnetic subsystem in Cu(en)$_2$CrO$_4$, the first principle calculations of exchange interactions were performed. The studies confirmed expected distribution of magnetic dimers within the $bc$ plane and provided information about the distribution of interdimer couplings which are crucial for the setting of the ordered state. Considering the magnetic lattice within the $bc$ plane as predicted by first principle studies, quantum Monte Carlo simulations of thermodynamic properties were performed and the simulations were used for the analysis of experimental data.
Acknowledgements
The financial support of projects VEGA 1/0132/22, APVV-18-0197 and APVV-22-0172 is acknowledged. D.L. acknowledges project QM4ST no. CZ.02.01.01/00/22_008/0004572 from MEYS of the Czech Republic.
References
[1] O. Vinnik et al., “Magnetic field-induced phase transitions in Cu(en)2SO4 – A dimerized S = 1/2 quantum antiferromagnet,” Journal of Magnetism and Magnetic Materials, vol. 586. Elsevier BV, p. 171207, Nov. 2023. https://doi.org/10.1016/j.jmmm.2023.171207
