Structural and magnetic properties of spin-$1/2$ dimer compound Cu$_2$(IPA)$_2$(DMF)(H$_2$O) with a large spin gap

TL;DR

This study synthesizes and characterizes a copper-based organic compound with a large spin gap, revealing its structural details and magnetic behavior consistent with a spin-1/2 dimer model, and confirms the absence of magnetic order at low temperatures.

Contribution

The paper provides a comprehensive structural and magnetic analysis of a new copper-organic compound with a large spin gap, including synthesis, crystallography, and magnetic measurements, highlighting its potential as a spin-dimer system.

Findings

Large spin gap of approximately 409 K confirmed.

No magnetic long-range order observed down to 2 K.

Structural analysis reveals spin dimers formed by Cu$^{2+}$ ions in a layered arrangement.

Abstract

We present the synthesis and a detailed investigation of structural and magnetic properties of metal-organic compound Cu$_2$(IPA)$_2$(DMF)(H$_2$O) by means of x-ray diffraction, magnetization, and heat capacity measurements. Single crystals of the title compound were synthesized by judicious selection of organic ligand and employing a selective hydrothermal reaction route. It crystallizes in an orthorhombic structure with space group $Cmca$. The structural analysis revealed that two Cu$^{2+}$ ions are held together by the organic component (-O-C-O-) in a square paddle-wheel to form spin dimers which are aligned perpendicular to each other and are further coupled through organic ligands (isophthalic acid) forming two-dimensional layers. Temperature dependent magnetic susceptibility $\chi(T)$ could be described well using spin-$1/2$ dimer model. The spin susceptibility $\chi_{\rm spin} (T)$ shows an exponential decrease in the low temperature region, below the broad maximum, confirming the singlet ground state with a large spin gap of $\Delta/k_{\rm B} \simeq 409$~K. The heat capacity $C_{\rm p}$ measured as a function of temperature also confirms the absence of magnetic long-range-order down to 2~K.

Tables

Table 1. Table 1: Crystal structure data of Cu 2 (IPA) 2 (DMF)(H 2 O) obtained from single crystal XRD experiment at room temperature.

Empirical Formula	C19H15Cu2NO10
Formula weight	544.40
Temperature	296 K
Wavelength	0.71073 Å
Crystal system	Orthorhombic
Space Group	$Cmca$
Lattice parameters	$a=28.059\left(3\right)$ Å
	$b=25.025\left(2\right)$ Å
	$c=15.272\left(2\right)$ Å
	$\alpha ={90}^0$
	$\beta ={90}^0$
	$\gamma ={90}^0$
Volume	10724(2) Å3
$Z$	16
Calculated density ${\rho }_{cal}$	1.349 (mg/mm3)
Absorption Coefficient	1.631 mm-1
$F$(000)	4384
Crystal size	$0.200\times 0.200\times 0.100$ mm3
$2\theta$ ranges for data collection	2.9020 to 53.9880
Index ranges	$-35\le h\le 35$
	$-31\le k\le 29$
	$-19\le l\le 15$
Reflections Collected	25810
Independent Reflections	5964 [$R_{\mathrm{int}}=0.0660$]
Data / restraints / parameters	5964 / 0 / 295
Goodness of fit on $F^2$	0.946
Final $R$-Indices, $I\ge 2\sigma$(I)	$R_1\simeq 0.0429$, $w{R}_2\simeq 0.1102$
Final $R$-Indices(all data)	$R_1\simeq 0.0954$, $w{R}_2\simeq 0.1355$
Largest diff. peak/hole	0.650 & -0.566 e Å-3

Table 2. Table 2: Atomic coordinates for Cu 2 (IPA) 2 (DMF)(H 2 O). The isotropic atomic displacement parameters (ADP) U eq subscript 𝑈 eq U_{\rm eq} are defined as one third of the trace of the orthogonal U ij subscript 𝑈 ij U_{\rm ij} tensor. The errors are from the least-square structure refinement.

	Atoms	$x$	$y$	$z$	$U_{\mathrm{eq}}$
		($\times {10}^4$)	($\times {10}^4$)	($\times {10}^4$)	($\times {10}^3$ Å2)
	Cu1	5000	1150(1)	1820(1)	33(1)
	Cu2	5000	1904(1)	3030(1)	35(1)
	Cu3	2187(1)	3997(1)	1857(1)	32(1)
	C1	3667(1)	2656(1)	1630(3)	39(1)
	C2	3937(1)	2284(1)	1171(3)	42(1)
	C3	3816(2)	2146(2)	321(3)	52(1)
	C4	3419(2)	2370(2)	-68(3)	60(1)
	C5	3145(2)	2732(2)	391(3)	52(1)
	C6	3265(1)	2880(1)	1235(3)	39(1)
	C7	2970(1)	3284(1)	1731(3)	35(1)
	C8	4356(1)	2017(1)	1628(3)	39(1)
	C9	1758(1)	5200(1)	3590(3)	37(1)
	C10	1326(1)	5374(1)	3250(3)	37(1)
	C11	6105(1)	826(1)	3613(3)	39(1)
	C12	6311(2)	1088(2)	4299(3)	56(1)
	C13	6745(2)	910(2)	4630(3)	65(2)
	C14	1970(2)	5473(2)	4279(3)	53(1)
	C15	2015(1)	4731(1)	3186(3)	35(1)
	C16	1359(2)	4438(2)	-839(4)	98(2)
	C17	1960(3)	3857(3)	-1584(4)	118(2)
	C18	1912(2)	3920(2)	7(4)	59(1)
	C19	5662(1)	1049(1)	3197(3)	36(1)
	N1	1753(2)	4067(2)	-779(3)	67(1)
	O1	4507(1)	1601(1)	1281(2)	49(1)
	O2	4504(1)	2231(1)	2309(2)	50(1)
	O3	5495(1)	1459(1)	3559(2)	52(1)
	O4	5500(1)	818(1)	2537(2)	45(1)
	O5	1829(1)	4528(1)	2515(2)	45(1)
	O6	2613(1)	4581(1)	1444(2)	44(1)
	O7	2617(1)	3467(1)	1338(2)	43(1)
	O8	3118(1)	3421(1)	2461(2)	45(1)
	O9	1749(1)	4054(1)	710(2)	53(1)
	O10	5000	551(2)	804(4)	84(2)
	O11	5000	2456(2)	4123(3)	86(2)
	H1	3754	2754	2195	47
	H2	4002	1903	13	62
	H3	3336	2277	-638	72
	H4	2875	2879	130	62
	H5	1184	5193	2786	44
	H6	6161	1384	4544	68
	H7	6885	1091	5097	78
	H8	2261	5360	4500	64

Table 3. Table 3: Parameters obtained from the fitting of M 𝑀 M vs. H 𝐻 H curves by the Brillouin function [Eq ( 4 )].

Temperature	$\chi$	$f_{\mathrm{imp}}$	${\theta }_{\mathrm{imp}}$
(K)	(cm3K/mol)	(mol%)	(K)
2.1	$\sim$8.7 $\times$ 10-4	$\sim$0.03759	$\sim$0.59
5	$\sim$6.6 $\times$ 10-4	$\sim$0.03759	$\sim$1.81

Equations

$$\chi (T)={\chi }_0+\frac{C}{T+{\theta }_{\mathrm{CW}}},$$

$$\chi (T)={\chi }_0+\frac{C_{\mathrm{imp}}}{T+{\theta }_{\mathrm{imp}}}+{\chi }_{\mathrm{dimer}},$$

$${\chi }_{\mathrm{dimer}}=\frac{N_{\mathrm{A}}{g}^2{\mu }_{\mathrm{B}}^2}{k_{\mathrm{B}}T[3+exp(\Delta /k_{\mathrm{B}}T)]}.$$

$$M=\chi H+f_{\mathrm{imp}}{N}_{\mathrm{A}}{g}_{\mathrm{imp}}{\mu }_{\mathrm{B}}{S}_{\mathrm{imp}}{B}_{S_{\mathrm{imp}}}(x),$$

Full text

I Introduction

The last few decades have witnessed enormous research in the field of low-dimensional quantum magnets.Lemmens et al. (2003) Model compounds especially with a gap in the excitation spectrum are extensively pursued. Spin gap is found in many low-dimensional quantum spin systems. Some examples include spin dimers,Sebastian et al. (2006); Rüegg et al. (2003); Koo and Whangbo (2000); Singh and Johnston (2007) integer spin chains,Shimizu et al. (1995) even leg spin ladders,Azuma et al. (1994) alternating spin chains,Johnston et al. (1987); Ahmed et al. (2016); Ghoshray et al. (2005); Tsirlin et al. (2011) spin-Peierls compounds,Hase et al. (1993) etc. Spin dimers are the simplest magnetic clusters, comprising of unified pair of magnetic ions, coupled antiferromagnetically. Such systems are characterized by a gap in their excitation spectrum and the energy difference between excited triplet states ($S=1$) and singlet ground state ($S=0$) constitutes the spin gap.

Recently, many new magnetic materials composed of antiferromagnetic spin dimers have been discovered. Because of different inter-dimer exchange networks, a variety of magnetic excitations have been observed under external magnetic field. Bose-Einstein-Condensation (BEC) of magnons in BaCuSi2O6, TlCuCl3, (Ba,Sr)3Cr2O8, NiCl2-4SC(NH2)2 etcSebastian et al. (2006); Aczel et al. (2009a, b); Zapf et al. (2006); Rüegg et al. (2003), magnetization plateaus in Ba3Mn2O8,[Ref. Uchida et al., 2002] and magnetization plateaus and Wigner crystallization of magnons in SrCu2(BO3)2[Ref. Kodama et al., 2002; *Kageyama3168] are the best known examples. These discoveries have accelerated the search for new spin dimer compounds and interesting quantum phenomena.

Unlike the inorganic materials (as discussed above), the metal-organic compounds are not explored well despite being easier to synthesize. In magnetically active metal-organic systems, the organic moieties bond the metal ions in a wide variety of forms leading to structurally and magnetically diverse systems.Jain et al. (2007); Carlin (1986) We have recently demonstrated that the organic moieties can modulate both the structural and magnetic features between metal ions significantly as the organic ligand NIPA leads to the formation of a hourglass nanomagnet Cu5(NIPA)4(OH)2.11H2O with two antiferromagnetic (AFM) and one ferromagnetic (FM) couplings between Cu2+ ionsNath et al. (2013) while another similar ligand leads to the formation of a quasi-two-dimensional (2D) AFM with weakly anisotropic spin-$1/2$ square lattice.Nath et al. (2015) Cu(1,3-$bdc$) is another well studied compound where Cu2+ ions are connected via IPA forming a perfect Kagom$\acute{e}$ lattice with strong magnetic frustration.Nytko et al. (2008); *Chisnell214403; *Marcipar132402 It undergoes a magnetic long-range-order (LRO) at $T_{\rm N}\simeq 1.77$ K. We have reported that in such Kagom$\acute{e}$ lattices by changing the ligand it is possible to tune the magnetic ground state keeping the crystal structure intact.Ajeesh et al. (2015) Thus, the organic ligands play a vital role in stabilizing different ground states in the metal-organic complexes.

Herein, we report synthesis, crystal structure, and magnetic properties of a new spin-$1/2$ compound Cu2(IPA)2(DMF)(H2O) [IPA = isophthalic acid and DMF = dimethyl formamide]. Cu2+ ions in the compound form spin dimers which are weakly coupled via long ligands. Our magnetic susceptibility measurements revealed an activated behavior at low temperatures with a large spin gap of $\Delta/k_{\rm B}\simeq 409$ K.

II Experimental details

All the reagent quality chemicals were obtained from Sigma-Aldrich and used without further purification. Single crystals of Cu2(IPA)2(DMF)(H2O) were prepared by the hydrothermal route. In this process, an aqueous solution of Cu(NO3)2.3H2O (0.5 mM, 0.12 g) was mixed with same equivalent of isopthalic (1,3-benzenedicarboxylic) acid (0.5 mM, 0.08 g) in 10 mL of DMF. The mixture was heated at 90 0C in a 25 mL teflon capped autoclave. Big plate like blue crystals were collected from the walls of the vial after 3 days. The crystals after washing in water and acetone and then drying in air were found to be the phase pure form of Cu2(IPA)2(DMF)(H2O). The yield was 72.6% (based on Cu).

Single-crystal x-ray diffraction (XRD) was performed using a Bruker APEX-II diffractometer (MoKα1 radiation with wavelength $\lambda_{\rm avg}\simeq 0.71073$ Å) on a good-quality single crystal of Cu2(IPA)2(DMF)(H2O) at room temperature and the crystal structure was solved. The phase purity of crystals was also confirmed through powder XRD performed on the crushed powder sample at room temperature using a PANalytical (Cu$K_{\alpha}$ radiation, $\lambda_{\rm avg}\simeq 1.5418$ Å) powder diffractometer. Magnetic susceptibility $\chi$ was measured as a function of temperature (2 K $\leq T\leq$ 380 K) using the vibrating sample magnetometer (VSM) attachment to the Physical Property Measurement System [PPMS, Quantum Design]. For high temperature measurements ($T\geq 380$ K), a high-$T$ oven (Model CM-C-VSM) was attached to the VSM. Our measurements were done upto 500 K, above which the sample was found to be decomposed. From the thermo gravity analysis, the decomposition temperature was indeed confirmed to be $\sim 500$ K. Heat capacity, $C_{\rm p}(T)$ was also measured using heat capacity option of the PPMS on a small piece of sintered pellet, adopting relaxation technique.

III Results and Discussion

III.1 Crystallography

Crystal structure of Cu2(IPA)2(DMF)(H2O) was solved from single crystal XRD. It crystallizes in a orthorhombic structure with space group $Cmca$. The obtained structural parameters are tabulated in Table 1 and  2. Figure 1 shows projection of the crystal structure in the $ab$-plane obtained from the single crystal XRD. It consists of paddle wheel like units, each containing two closely held Cu2+ ions. In each paddle wheel, Cu2+ ions are coupled via O-C-O path forming a spin dimer. It is to be noted that there are three inequivalent Cu sites [Cu(1), Cu(2), and Cu(3)] in the crystal structure which form two different dimers (type 1 and type 2). The intra-dimer distances are Cu(1)-Cu(2) $\simeq 2.641$ Åand Cu(3)-Cu(3) $\simeq 2.633$ Åfor type 1 and type 2 dimers, respectively. Each dimer is connected to the adjacent dimers through the organic ligand (isophthalic acid, IPA) leading to either a coupled dimer or a quasi-2D layered structure in the $ab$-plane. The dimers are of course far apart ($\sim 8$ Å) from each other where the inter-dimer interaction would be almost negligible compared to the intra-dimer interaction. Interestingly, in each layer the type 1 and type 2 dimers are aligned nearly perpendicular to each other. These 2D layers are well separated along the crystallographic $c$-direction.

Le-Bail fit of the observed powder XRD pattern was performed using the ullProf package.\cite{Carvajal55} The initial structural parameters for this purpose were taken from the single crystal XRD data. igure 2 shows the powder XRD pattern of Cu2(IPA)2(DMF)(H2O) at room temperature along with the calculated pattern. All the peaks could be fitted using the orthorhombic ($Cmca$) structure. The obtained best fit parameters are $a=28.275(1)$ Å, $b=25.231(1)$ Å, $c=15.3701(5)$ Åand the goodness-of-fit $\chi^{2}\simeq 8.27$. These lattice parameters are close to the values obtained from the single crystal XRD.

III.2 Magnetic Susceptibility

Magnetic susceptibility $\chi(T)$ ($\equiv M/H$, where $M$ is the magnetization) measured in an applied field of $H=1$ T is shown in the upper panel of Fig. 3. As the temperature decreases, $\chi(T)$ increases and passes through a broad maximum near $T_{\chi}^{\rm{max}}$ $\simeq 200$ K, a short range magnetic order which is fingerprint of low dimensional antiferromagnetic spin systems. At very high temperatures ($T\gg$ exchange coupling, $J/k_{\rm B}$), usually spins are randomly oriented and $\chi(T)$ behaves like a paramagnet. However, in our compound $\chi(T)$ does not seem to have reached the paramagnetic region even at $500$ K. Thus, persistence of magnetic correlations upto such a high temperature clearly reflects a strong antiferromagnetic exchange coupling between Cu2+ ions. At low temperatures ($T\lesssim 70$ K), $\chi(T)$ shows a clear upturn, possibly due to extrinsic paramagnetic impurities and/or defects present in the sample. No signature of any magnetic long-range-order (LRO) is observed down to 2 K.

To extract the magnetic parameters, $\chi(T)$ at high temperatures was fitted by the following expression

[TABLE]

where $\chi_{0}$ is the temperature independent contribution consisting of core diamagnetic susceptibility ($\chi_{\rm core}$) of the core electron shells and Van-Vleck paramagnetic susceptibility ($\chi_{\rm VV}$) of the open shells of the Cu2+ ions present in the sample. The second term in Eq. (1) is the Curie-Weiss (CW) law with the CW temperature ($\theta_{\rm CW}$) and Curie constant $C=N_{\rm A}\mu_{\rm eff}^{2}/3k_{\rm B}$, where $N_{\rm A}$ is Avogadro number, $k_{\rm B}$ is Boltzmann constant, \mu_{\rm eff}=g\sqrt{S(S+1)}$$\mu_{\rm B} is the effective magnetic moment, $g$ is the Land$\acute{\rm e}$ $g$-factor, $\mu_{\rm B}$ is the Bohr magneton, and $S$ is the spin quantum number. As shown in the lower panel of Fig. 3, we fitted the $1/\chi(T)$ data in the temperature range 400 K to 500 K using Eq. (1). Since the compound is not completely paramagnetic in this temperature range, we fixed the value of $C$ to 0.375 cm3K/mol-Cu2+ (expected $C$ value for spin-$1/2$ systems taking $g=2$ to give $\mu_{\rm eff}=1.73$ $\mu_{\rm B}$/Cu2+) and tried to vary other parameters. The fit yields $\chi_{0}\simeq 7.94\times 10^{-5}$ cm3/mol-Cu2+ and $\theta_{\rm CW}\simeq 204.84$ K. The positive value of $\theta_{\rm CW}$ indicates that the dominant exchange couplings between Cu2+ ions are antiferromagnetic in nature. Such a large value of $\theta_{\rm CW}$ also suggests a strong exchange interaction between Cu2+ ions.

In order to get an estimation of the exchange coupling and to have a better view of the spin-lattice, we fitted the observed $\chi(T)$ data to the following expressionJohnston et al. (2000)

[TABLE]

where, $C_{\rm imp}$ represents the impurity concentration and $\theta_{\rm imp}$ provides the effective interaction strength between impurity spins. $\chi_{\rm dimer}$ is the expression for exact spin susceptibility of a spin-$1/2$ dimer model which can be written asSingh and Johnston (2007); Nakajima et al. (2006)

[TABLE]

The dimers have a spin gap $\Delta/k_{\rm B}$ ($=J/k_{\rm B}$) between the singlet ground state and the triplet excited states. Here, $J/k_{\rm B}$ is the intra-dimer exchange coupling.

The low temperature upturn of $\chi(T)$ below 70 K originates from the isolated Cu2+ ions possibly due to lattice defect. The second term (CW term) is included in Eq. (2) to account for this low temperature upturn. Overall, Eq. (2) has six fitting parameters: $\chi_{0}$, $C_{\rm imp}$, $\theta_{\rm imp}$, $g$, and $J/k_{\rm B}$. As shown in the upper panel of Fig. 3, Eq. (2) fits very well to the $\chi(T)$ data over the whole temperature range. The obtained best fit parameters are $\chi_{0}\simeq 7.50\times 10^{-5}$ cm3/mol-Cu2+, $C_{\rm imp}\simeq 0.015$ cm3K/mol-Cu2+, $g\simeq 1.91$, $\Delta/k_{\rm B}\simeq 409.83$ K, and $\theta_{\rm imp}\simeq 0.96$ K. This value of $C_{\rm imp}$ corresponds to a spin concentration of nearly 4.0 %, assuming the impurity spins as spin-$1/2$. In order to demonstrate the non-magnetic ground state, $\chi_{0}+\frac{C_{\rm imp}}{T+\theta_{\rm imp}}$ was subtracted from the $\chi(T)$ data and the obtained intrinsic spin susceptibility $\chi_{\rm spin}(T)$ is presented in the upper panel of Fig. 3. It is evident that $\chi_{\rm spin}(T)$ decreases rapidly towards zero at low temperatures which unambiguously establishes a spin gap in the excitation spectrum.Tsirlin et al. (2011, 2008)

It is to be noted that our attempt to fit the $\chi(T)$ data using coupled dimer model didnot improve the fitting significantly and the obtained value of inter-dimer coupling ($J^{{}^{\prime}}$) was not at all reliable. This implies that the spin-lattice behaves more like isolated dimers rather than coupled dimers. Typically, in isolated dimers, the strength of intra-dimer coupling quantitatively reflects the magnitude of spin gap. Moreover, the value of spin gap can be reduced immensely by the inter-dimer coupling, upto a threshold value, above which there is a transition to magnetic LRO.Tsirlin et al. (2011); Arjun et al. Thus, such a large spin gap in Cu2(IPA)2(DMF)(H2O) also implies a negligible inter-dimer coupling in the compound. This finding is in reasonable agreement with the structural data where the dimers are well separated ($\sim 8$ Å) from each other and are connected via a long and extended path. As one can see from Fig. 1 that Cu2+ dimers are formed through a complex path of -O-C-O- and the arrangement of Cu2+-O-C-O-Cu2+ is not in one line. Usually, one expects a strong exchange interaction for the interaction path involving only O between metal ions and $\sim 180^{0}$ metal-oxygen-metal bond angle. Despite having a complex interaction path within the dimers, this compound shows a large spin gap of $\Delta/k_{\rm B}\simeq 409$ K which is a surprising feature of the compound. It is worth mentioning that spin dimer compounds such as TlCuCl3, (Sr,Ba)3Cr2O8 etc where the super-exchange involves only oxygen/chlorine atom between metal ions gives a rather small value of the spin gap.Singh and Johnston (2007); Nakajima et al. (2006); Rüegg et al. (2003)

There are a few spin-$1/2$ metal-organic complexes based on Cu2+ reported to have paddle-wheel like dimer units but with different ground states. For instance, [Cu2(OOCC5H11)4(urea)2], [$\{{\rm Cu}_{2}({\rm OOCC}_{5}H_{11})_{4}({\rm urea})\}_{2}$], [Cu2(OOCC5H11)4]n, and Cu2(O2CCH=CHCH3)4(DMF)2 show singlet ground state with a spin gap of $\sim 342$ K, $\sim 375$ K, $\sim 333$ K, and $\sim 220$ K, respectively.Kozlevčar et al. (2004); Schlam et al. (2000) The compound tetrakis($\mu_{2}$benzoato-O,O′)-bis(dimethyl sulfoxide)dicopper(II) which also has paddle-wheel like dimer units but with a different ligand show one-dimensional character with a exchange coupling $J/k_{\rm B}\simeq 405$ K.Reyes-Ortega et al. (2005) It undergoes a FM ordering at $T_{\rm C}\simeq 9$ K. Recently, another compound Cu(IPA)(H2O) is reported to have paddle-wheel like spin dimers coupled through IPA ligand, similar to our compound. The crystal lattice forms a Kagom$\acute{e}$ structure with a very large spin gap of $\Delta/k_{\rm B}\simeq 410$ K.Šimėnas et al. (2016) From the above examples it is clear that though all these compounds are having paddle-wheel like spin dimers but different connecting ligands between dimers lead to diverse ground states. Thus, in these compounds one can tune the ground state properties and even the magnitude of the spin gap/exchange coupling by simply changing/modifying the connecting ligand.

III.3 Magnetic Isotherm

As one can see in the upper panel of Fig. 3, the magnitude of $\chi_{\rm spin}(T)$ is nearly zero below 50 K. Thus, the low temperature upturn observed in $\chi(T)$ below 50 K is purely extrinsic in nature. Therefore, one can precisely estimate the extrinsic contribution to $\chi(T)$ by analyzing the magnetic isotherms ($M$ vs $H$) at low temperatures. Figure 4 shows the magnetic isotherms measured at different temperatures. At $T=200$ K (inset of Fig. 4), it is a nice straight line. As the temperature is lowered, it shows a pronounced curvature typically observed for paramagnets. In order to quantitatively estimate the paramagnetic impurity contribution, we fitted the $M$ vs $H$ data at $T$ = 2.1 K and 5 K by the following equationNath et al. (2009)

[TABLE]

where $\chi$ is the intrinsic susceptibility of the sample, $f_{\rm imp}$ is the molar fraction of the impurities, $N_{\rm A}$ is the Avogadro’s number, $g_{\rm imp}$ impurity $g$-factor, $S_{\rm imp}$ is the impurity spin, $B_{S_{\rm imp}}(x)$ is the Brillouin function,Kittel (1986) and the modified argument of the Brillouin function is $x=g_{\rm imp}\mu_{\rm B}S_{\rm imp}H/[k_{\rm B}(T-\theta_{\rm imp})]$.

In order to reduce the number of fitting parameters, in the Brillouin function fit using Eq. (4), we fixed $g_{\rm imp}$ and $S_{\rm imp}$ to 1.9 [obtained from the $\chi(T)$ analysis] and $1/2$, respectively. The fitting parameters ($\chi$, $f_{\rm imp}$, and $\theta_{\rm imp}$) obtained at $T=2.1$ K and 5 K are tabulated in Table 3. The value of $f_{\rm imp}$ obtained from the analysis of 2.1 K data was fixed while analysing the 5 K data. Using the value of $f_{\rm imp}$ in $C_{\rm imp}=f_{\rm imp}N_{\rm A}g_{\rm imp}\mu_{\rm B}S_{\rm imp}(S_{\rm imp}+1)$, we calculated the Curie constant of the paramagnetic impurities to be $C_{\rm imp}\approx 0.0127$ cm3 K/mol. This value of $C_{\rm imp}$ corresponds to $\sim 3.4\%$ of spin-$1/2$ impurity spins which is close to that obtained from the $\chi(T)$ analysis.

III.4 Heat Capacity

The heat capacity $C_{\rm p}$ of Cu2(IPA)2(DMF)(H2O) is measured as a function of temperature at zero applied field in the temperature range from 2 K to 90 K (see Fig. 5). No indication of magnetic LRO was observed down to 2 K, which is in accordance with our $\chi(T)$ data. In a magnetic insulator, $C_{\rm p}(T)$ has two major contributions: one due to phonon excitations and the other due to magnetic part. We refrained from doing any quantitative analysis of the $C_{\rm p}$ data since it was not possible to subtract the phonon contribution without a non-magnetic analogue compound.

IV Summary

We have synthesized a novel paddle-wheel type Cu2+ spin-$1/2$ dimer compound Cu2(IPA)2(DMF)(H2O) and investigated its crystal structure and magnetic properties. It crystallizes in an orthorhombic ($Cmca$) crystal structure. Analysis of $\chi(T)$ revealed dimer model for the spin lattice with a large spin gap of $\Delta/k_{\rm B}\simeq 409$ K. The paramagnetic impurity concentration was estimated to be $\sim 4$% which is likely due to defects present in the sample. No signature of magnetic LRO was observed down to 2 K from the $C_{\rm p}(T)$ data, further supporting the gapped behaviour. In magnetic insulators, strongest super-exchange interaction between magnetic ions is usually expected via non-magnetic ions such as oxygen.Motoyama et al. (1996) However, in our compound, despite having a long and complex interaction path Cu-O-C-O-Cu, the intra-dimer interaction is surprisingly very large. For a comparison, the highest value of spin gap is found to be reported for SrCu2O3 ($\Delta/k_{\rm B}\simeq 420$ K)Azuma et al. (1994) among the inorganic compounds and for Cu(IPA)(H2O) ($\Delta/k_{\rm B}\simeq 410$ K) among the metal-organic compounds.Schlam et al. (2000) Thus, the value of spin gap found for Cu2(IPA)2(DMF)(H2O) is nearly same in magnitude to the highest values reported so far.

As pointed out earlier, the crystal structure contains quasi-2D layers of orthogonal Cu2+ dimers. Such a crystal lattice is reminiscent of the magnetic sub-lattice reported for SrCu2(BO3)2 where Wigner crystallization of magnons and magnetization plateaus were observed in an applied magnetic field.Kodama et al. (2002) Thus, a large spin gap and orthogonal arrangement of dimers in the 2D layer make Cu2(IPA)2(DMF)(H2O) a unique system for further investigations. Furthermore, the value of spin gap is very sensitive to the inter-dimer couplings which tend to reduce the spin gap and heavily affect the properties under high magnetic field. In such a context, this compound serves as a starting point to synthesize further new compounds where one can tune the spin gap simply by changing the organic ligand.

V Acknowledgement

We would like to acknowledge IISER Thiruvananthapuram for providing necessary experimental facilities.