Magnetic-field-induced ordered phase in the chloro-bridged copper(II) dimer system $\left[\mathrm{C}{\mathrm{u}}_2{\left(\mathrm{apyhist}\right)}_2\mathrm{C}{\mathrm{l}}_2\right]{\left(\mathrm{Cl}{\mathrm{O}}_4\right)}_2$

Specific heat and magnetization measurements of the compound $\left[\mathrm{C}{\mathrm{u}}_2{\left(\mathrm{apyhist}\right)}_2\mathrm{C}{\mathrm{l}}_2\right]{\left(\mathrm{Cl}{\mathrm{O}}_4\right)}_2$, where apyhist = (4-imidazolyl)ethylene-2-amino-1-ethylpyridine), were used to identify a magnetic-field-induced long-range antiferromagnetic ordered phase at low temperatures $(T<0.36\mathrm{K})$ and magnetic fields $(1.6<H<5.3\mathrm{T})$. This system consists of a Schiff base copper(II) complex, containing chloro-bridges between adjacent copper ions in a dinuclear arrangement, with an antiferromagnetic intradimer interaction $|J_{\mathrm{intra}}|/k_B\approx 3.65\mathrm{K}$ linked by an antiferromagnetic coupling $|J_{\mathrm{inter}}|z/k_B\approx 2.7\mathrm{K}$. The magnetic-field-induced ordering behavior was analyzed using the mean-field approximation and Monte Carlo simulation results. The obtained physical properties of the system are consistent with the description of the ordered phase as a Bose-Einstein condensation (BEC) of magnetic excitations. We present the phase diagram of this compound, which shows one of the lowest critical magnetic field among all known members of the family of BEC quantum magnets.

Figure 1

Spin levels scheme showing the zero-field gap due to the intradimer interactions. The levels are dispersed, forming bands due to the interdimer interactions that evolve in magnetic fields due to the Zeeman coupling.

Figure 2

Perspective view of the crystallographically $\left[\mathrm{C}{\mathrm{u}}_2{\left(\mathrm{apyhist}\right)}_2\mathrm{C}{\mathrm{l}}_2\right]{\left(\mathrm{Cl}{\mathrm{O}}_4\right)}_2$ unit with the atom labeling. The structure is consolidated by extensive intermolecular hydrogen bonds between binuclear species through the perchlorate ions, where each dimer interacts with six neighboring symmetry-related molecules.

Figure 3

Temperature dependence of the magnetic susceptibility. The line represents the fit to the numerical calculations represented by Eq. (3).

Figure 4

Specific heat as a function of the temperature measured under different applied magnetic fields. The dashed black and dotted red lines represent the lattice $C_l\left(T\right)=a{T}^3+b{T}^5+c{T}^7$ and nuclear $C_n\left(T\right)=\beta T^{-2}$ contributions with fitted coefficients $a=2.9\times {10}^{-2},b=-6.5\times {10}^{-5},c=6\times {10}^{-8}$, and $\beta =7.5\times {10}^{-3}$. The continuous lines are only provided to serve as guides.

Figure 5

Integrated electronic magnetic entropy obtained after the subtraction of the lattice and nuclear contributions to the specific heat. The inset shows the electronic specific heat and the red continuous line represents the calculated specific heat for isotropic Heisenberg $S=1/2$ dimers.

Figure 6

The inset shows the total specific heat measured under $H=3.5\mathrm{T}$ and the black line represents the nuclear contribution $C_n\left(T\right)=\beta T^{-2}$ with $\beta =2.1\times {10}^{-2}$. The main panel shows the electronic specific heat, which shows the $T^3$ behavior characteristic of antiferromagnetic magnons.

Figure 7

Magnetic field dependence of the specific heat measured at different temperatures as described in the text. The two peaks at $H_{c1}$ and $H_{c2}$ determine the boundary of the field-induced ordered phase.

Figure 8

The magnetic phase diagram of $\left[\mathrm{C}{\mathrm{u}}_2{\left(\mathrm{apyhist}\right)}_2\mathrm{C}{\mathrm{l}}_2\right]{\left(\mathrm{Cl}{\mathrm{O}}_4\right)}_2$ from the temperature and magnetic field scans of the specific heat showing the field-induced long-range antiferromagnetic (AF) ordered phase.