Magnetic interaction between binuclear clusters in potassium trihalocuprates(II) and dimethylammonium trihalocuprates(II)

JOURNAL

OF MAGNETIC

RESONANCE

4, 337-346 (1971)

Magnetic Interaction betweenBinuclear Clusters in PotassiumTrihalocuprates(II) and Dimethylammonium Trihalocuprates(II) KEN-ICHI

HARA, MOTOMICHI INOUE, SHUJI EMORI, AND MASAJI

KUBO

Department of Chemistry, Nagoya University, Chikusa, Nagoya, Japan Received December 1, 1970; accepted January 19, 1971 The magnetic susceptibilities of potassium trichlorocuprate(II), potassium tribromocuprate(II), dimethylammonium trichiorocuprate(II), and dimethylammonium tribromocuprate(I1) were determined in a temperature range of 4.2-300°K and analyzed with the molecular field model, the Ising model, and the Heisenberg model. Spin interaction operates between copper atoms belonging to different dimer ions, [CuaX$-, as weil as between copper atoms within a diier ion, the energy of interaction between the dimers amounting to 520% of the interaction energy within the dimer for potassium trihaiocuprates(I1) and to about 50 % for dimethylammonium tribromocuprate(I1). INTRODUCTION

The X-ray analysis of potassium trichlorocuprate(I1) (1) and dimethylammonium trichlorocuprate(I1) (2) has shown that dimer ions, [CU,CI,]~-, are stacked obliquely in a one-dimensional array in the crystals. In view of the crystal structure, one would expect that spin interaction operates between copper atoms belonging to different dimer ions as well as between copper atoms within a dimer. In fact, the magnetic susceptibility of potassium tribromocuprate(II), which is isomorphous with potassium trichlorocuprate(II), conforms to a theoretical equation for a modified dimer model in a temperature range of 80-300”K, indicating the existence of a weak antiferromagnetic interaction between dimer ions (3). However, the exchange interaction energy has not yet been determined in a pair of copper atoms belonging to different dimer ions. Although a number of experimental results (magnetic susceptibility (4), ESR (5), optical property (2), etc.) have been reported on potassium trichlorocuprate( no extensive discussion has been carried out for magnetic interaction between the dimer ions. Therefore, we have determined the susceptibility of these compounds in a temperature range of 4.2-3OO”K, and analyzed the data with various models in order to estimate the exchange interaction energy between the dimer ions. PREPARATION

OF MATERIALS

A solution of copper(I1) chloride (2 mols) and potassium chloride (1 mol) was concentrated over a water bath. The hot solution was made up to four times by volume with hot concentrated hydrochloric acid. On standing in a sealed vessel, the solution separated red brown needle crystals. This method gave Potassium frichlorocuprate(ZZ).

337

338

HARA,

INOUE,

EMORI,

AND

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a higher yield than did the method of Willet ef al. (1). Found: Cu, 30.2; Cl, 50.8%. Calculated for KCuCl, : Cu, 30.4; Cl, 50.9 %. Potassium tribromocuprate(II). This compound was synthesized by a method described in our previous paper (3). Found: Cu, 18.6; Br, 70.0%. Calculated for KCuBr, : Cu, 18.6; Br, 70.0 %. Dimethylammonium trichlorocuprate(ZZ). A small quantity of concentrated hydrochloric acid was added to a solution of equimolar amounts of copper(I1) chloride and dimethylammonium chloride. When the mixture was concentrated over a water bath and was left overnight in a sealed vessel, red brown crystals separated. Found: Cu, 29.3; Cl, 49.0%. Calculated for (CH,),NH,CuCI, : Cu, 29.4; Cl, 49.2%. Dimethylammonium tribromocuprate(IZ). This was prepared in the same way as for potassium tribromocuprate(I1) using dimethylammonium bromide in place of potassium bromide. Found: Cu, 18.2; Br, 68.6 %. Calculated for (CH,),NH,CuBr, : Cu, 18.2; Br, 68.6%. The X-ray powder patterns of potassium trihalocuprates(I1) and dimethylammonium trichlorocuprate(I1) agreed with the crystal data reported in the literature (1, 2). MAGNETIC

MEASUREMENTS

AND

RESULTS

The magnetic susceptibility was determined by means of a magnetic balance described in our previous paper (6). As the compounds were very hygroscopic, the samples were maintained in a dry argon atmosphere. The observed susceptibilities were corrected for diamagnetic contributions from all ions involved (in 10m6 emu/mol): CL?” (-ll), Cl- (-26), Br- (-36), K+ (- 13) (7), and (CH,),NH: (- 38) (8). The temperature-independent paramagnetism was assumed to be equal to 60 x 10e6 emu/m01 (9). From the corrected molar paramagnetic susceptibility x, the effective magnetic moment p,rr was calculated per copper ion (see Table 1):

PI

peff = 2.83(~7’)“~,

where Tis the absolute temperature. The observed susceptibilities are shown in Figs. 1, 2, and 3 as functions of temperature. The Curie-Weiss law holds for potassium trichlorocuprate(I1) above about 80°K and dimethylammonium tribromocuprate(I1) above about 200°K. Table 1 TABLE

1

EFFECTIVE MAGNETIC MOMENTS AT ROOM TEMPERATURE, CONSTANTS, AND THE TEMPERATURE OF THE MAXIMUM TRIHALOCUPRATES(II) AND DIMETHYLAMMONIUM

KCuC13 KCuBr3 a (CH,),NH,CuCI,

(CH&NH&uBr3 a The susceptibility

CONSTANTS, g-VALurq WEISS SUSCEPTIBILITYOF POTASSIUM TRIHAU)CUPRATES(II)

CURIE

&If (B.M.)

c (emu deg/mol)

9

1.75 1.52 1.83 1.64

0.415 0.415 0.429

2.10 2.10 2.14

does not obey the Curie-Weiss

(2) -22 0 -78

32 130 74

law in the temperature range invest&ted.

MAGNETIC INTERACTION

339

IN TRIHALOCUPRATES(I1)

TEMPERATURE,“K

FIG. 1. Reciprocal susceptibilities of potassium trichlorocuprate(I1) ( l ), dimethylammonium trichlorocuprate(I1) (O), and dimethylammonium tribromocuprate(I1) ( n ).

. /

0 TEMPERATURE,“K

FIG. 2. Magnetic susceptibility of potassium trichlorocuprate(I1). The broken curve shows the theoretical curve for binuclear clusters with J/k =- 256°K and g = 2.10. The dotted curve was calculated for the same model with g = 2.07. The solid curve was calculated for the molecular field model (Eq. [41, J,,/k = - 256”K, Jb/Ja = 0.05, and g = 2.09).

340

HARA,

INOUE,

., 01

EMORI,

AND

KUBO

t

100 TEMPERATURE,“K

200

300

FIG. 3. Magnetic susceptibility of potassium tribromocuprate(I1) (V) and dimethylammonhun tribromocuprate (II) (w). The broken curveswere calculatedassumingthe validity of the BleaneyBowers equation. The solid curves show theoretical curvesfor the molecular field model (Eq. [4])

shows the Curie constants C, g-values evaluated from C, and the Weiss constants 8. The g-values agree fairly well with 2.16 as determined by ESR (4, 5). The susceptibility of dimethylammonium trichlorocuprate(I1) conforms to the Curie law above about lOoK, below which deviation takes place. No maximum susceptibility was observed in the temperature range studied. (See Ref. (3) for potassium tribromocuprate(I DISCUSSION

Bleaney and Bowers (10) have proposed a theoretical equation for the susceptibility of isolated binuclear clusters : x =

N$

[I++-2JlkT]-1,

PI

where N is the Avogadro number, g is the electronic g-value, fi is the Bohr magneton, k is the Boltzmann constant, and J is the exchange integral within a cluster. The value of J/k can be determined directly from the temperature T, of the maximum susceptibility as J/k = -O.fiOT,. Since the exchange integral within the dimer ion is presumed to be predominant, the susceptibilities were calculated assuming the validity of Eq. [2] with exchange integrals estimated from T, and g-values evaluated from Curie constants (see Table 1). They are shown by broken curves in Figs. 2 and 3. (The curve for dimethylammonium trichlorocuprate(II) is missing because T, was not observed.) The observed susceptibilities are smaller than the calculated values at all temperatures investigated. The discrepancies are not due to the choice of diamagnetic corrections and temperatureindependent paramagnetism, because the observed susceptibilities cannot be fitted to the theoretical curves by a simple shift along the ordinate. Only the susceptibility

MAGNETIC

INTERACTION

IN

TRIHALOCUPRATES(I1)

341

of potassium trichlorocuprate(II) can be fitted fairly well with the theoretical curve calculated by Eq. [2] provided that one assumes that J/k = -256°K as evaluated from T, = 32°K and that g = 2.07. However, if one employs a more reasonable value of g = 2.16 as determined by ESR, discrepancy becomes considerable. In addition, the observed 101/T, equal to 0.69 of this complex is much larger than the value 0.40 expected from Eq. [2]. Figure 4a shows the arrangement of copper ions in a crystal of potassium trichlorocuprate(I1). If exchange interaction between S, and S,, 1 is disregarded, the lattice can be subdivided into two equivalent interpenetrating lattices, -S,- l-S,,,-Sn+ r- and

b 0: cu FIG.

0:

Cl

4. Binuclear clusters in the crystals of potassium trichlorocuprateiJ1)

ammonium

trichlorocuprate(II)

(a) and dimethyl-

(b).

-s,- ps”-Sm+ I-. Let us take it for granted that exchange interaction between dimer ions is much smaller than that within a dimer. Then in accordance with a molecular field model similar to that developed by Stout and Chisholm (II), the Hamiltonian for a pair of spins, S, and S,,, in the lattice is given by &’ = -25&,/S,-gfi(S,+S,)*H-gj?(S;H;+S;H;), 1131 where H is the external magnetic field and Hf is the mean internal field acting on the spin S,. By use of the Hamiltonian, the susceptibility can be formulated theoretically as (see Appendix) Ng2P2 ’ = kT(3+e-2JalkT)-4zJb’

[41

where z is the number of copper atoms that are closest to a copper atom in question and belong to the sublattice other than that comprising the copper atom (z = 2 for a and z = 1 for b in Fig. 4), and J,, is the exchange integral between copper atoms in neighboring dimers. The value of J,/k can be determined from T, as J,lk = -0.8OT,. Equation [4] based on the Heisenberg (i.e. isotropic) model can give a good approximation to the powder susceptibility of potassium trichlorocuprate because the g-value determined by ESR is nearly isotropic (5). The observed susceptibility of potassium trichlorocuprate(II) conforms to Eq. [4] with

342

HARA,

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AND

KUBO

JdJa= 0.05-0.20. The choice of

Jb/J, = 0.05 gives a g-value equal to 2.09, which is very close to the g-value 2.10 evaluated from the Curie constant. In Fig. 2, the solid curve shows the theoretical curve calculated from Eq. [4] with J,/k = -25.6”K, JdJa= 0.05, and g = 2.09 in good agreement with the observed values. In addition, reasonable values lf3l/T, = 0.48-0.72 and xmTm = 0.200-0.179 are obtained as shown in Table 2, indicating the presence of magnetic interaction between dimer ions. Figure 3 shows that the observed susceptibility of potassium tribromocuprate(II), which is isomorphous with potassium trichlorocuprate(II), also conforms to Eq. [4] with parameters listed in Table 3 for the molecular field model. If the exchange interaction between S, and Sm+l shown in Fig. 4a is disregarded, a mathematically rigorous equation can be obtained for the susceptibility of the TABLE

2

OBSRVED lf31/Tm AND xmT,,, FOR THREE COPPER COMPLEXES COMPARED WITH THOSE CALCULATED FOR VARIOUS MODEJJ

KCuCla KCuBrs (CH&NH&uBra Binuclear cluster Molecular field model b Jb/Ja = 0.05 Jb/Ja = 0.2 Two coupled Ising chains Jb/J,, = 0.1 Jb/J, = 0.2 Alternating linear Ising chain Jb/Ja = 0.3 Jb/Ja = 0.6 Alternating linear Heisenberg chain Jb/J. = 0.2 Jt,/Ja = 0.6

0.69 1.05 0.40

0.202 0.178 0.169 0.208

0.48 0.72

0.200 0.179

0.75 0.83

0.173 0.169

0.82 0.94

0.167 0.157

0.48 0.66

0.198 0.172

a Calculated values were obtained assuming that g = 2.10. b Calculated for the lattice shown in Fig. 4a (z = 2). TABLE EXCHANGE

INTEGRAL.YAND g-VArxss Molecular

KCuCla KCuBre (CH&NH&uBrs

3

FOR VARIOUS

field model

MODELS

OF

Ising model

SPIN INTERAC~ON Heisenberg model

;/)

JdJ..

9

;[)

JalJa

g

Jdk cKj

-25.6 -105 -58

0.05 0.1 0.6

2.09 2.00 2.11

-35 -150 -85

0.2 0.1 0.6

2.20 2.05 2.14

-25 -105 -60

JdJa

g

0.2 0.2 0.5

2.08 2.00 2.03

MAGNETIC

INTERACTION

IN

343

TRIHALOCUPRATES(I1)

Ising model, the Hamiltonian for which is given by N/2 z =,n~1[-2Jn~~Snl-2J,(S~S:+,+S,‘S~+1)-gPH(S:,+S;;)].

PI

From Eq. [5], the zero-field parallel susceptibility can be formulated by the implicit differentiation method (12). eZKb(eKaR - sinh 2K,) Ng2P2 II61 ’ = 4kT [ (R - eKnsinh 2K,)(cosh2 K, cash’ 2K, - sinh2 2Kb)1’2 ’ where R = cash K, cash 2K, + (cosh2 K, cosh2 2K, - sinh2 2K,)‘12,

1

K, = J,/2kT, K, = J,/2kT.

The perpendicular component should be taken into account in the Ising model as well. However, the parallel susceptibility can give a fairly good approximation to the susceptibility of polycrystalline powders especially in a high temperature region. Figure 5 shows that the theoretical Eq. [6] can be fitted to the observed susceptibilities of potassium trichlorocuprate(I1) and potassium tribromocuprate(I1) except for the region of very low temperature. Duffy and Barr (13) have calculated the susceptibility of an alternating Heisenberg chain consisting of 10 spins in order to estimate the behavior of an infinite alternating chain shown in Fig. 4b. If only the interaction between S, and S,,,+i is taken into account as an interaction between the dimer ions (the exchange integral being denoted by Jb), the lattice shown in Fig. 4a is identical with that in Fig. 4b. In spite of the

1.5

1.0

2.0

2.5

klhl

FIG. 5. Theoretical susceptibilityof two coupled king chains (Eq. [6], Jb/Ja = 0.1 and 0.2) and observed susceptibilities of potassium trichlorocuprate(I1) (0) and potassium tribromo-

cuprate0r) (W.

344

HARA,

INOUE,

EMORI,

AND

KUBO

simplifying assumption, the theoretical calculation fits the susceptibilities of the copper complexes (see Fig. 6). The values of J,/k and J,jJ, obtained from the three models agree fairly well with one another as shown in Table 3, indicating that the energy of magnetic interaction between dimer ions amounts to 5-20x of the energy of interaction within a dimer ion in the trihalocuprates(I1). The g-values 2.00-2.05 of potassium tribromocuprate(I1) obtained for the three models are somewhat smaller than the values of other copper(I1) complexes, suggesting the presence of a more complicated mechanism of spin interaction.

I.0

1.5

2.0

1.5

klilll

FIG. 6. Susceptibility calculated by Duffy and Barr for an alternating and the observed susceptibilities of potassium trichlorocuprate(I1) cuprate (v), and dimethylammonium tribromocuprate(I1) (m).

Heisenberg (Jb/JG = 0.246) (a), potassium tribromo-

For dimethylammonium trichlorocuprate(II), no maximum susceptibility was observed in the temperature range investigated. The Weiss constant is nearly equal to 0°K indicating that apparently no spin interaction operates between copper ions in the complex, although the structure of [CU,CI,]~- ions closely resembles that in potassium trichlorocuprate(I1). Possibly, the very weak interaction is a result of an almost complete annihilation of the antiferromagnetic effect by some ferromagnetic interactions. The susceptibility versus temperature curve of dimethylammonium tribromocuprate(I1) exhibits a maximum at about 74°K. Since no crystal data have been reported as yet, it was assumed that the complex is isomorphous with the corresponding chlorine compound, the copper ions in which are arranged in the lattice shown in Fig. 4b. As shown in Fig. 3, Eq. [4] for the molecular field model reproduces the observed susceptibility with reasonable values for parameters listed in Table 3. For the susceptibility of an alternating linear Ising chain shown in Fig. 4b, the

MAGNETIC

INTERACTION

IN

345

TRIJL4LOCUPRATES(II)

following equation has been derived (12): Ng21J2

eV,+Jd12kT

1

PI cash [(J,-J,)/2kT] . As shown in Fig. 7, the observed susceptibility conforms to Eq. [7] with Jb/Ja = 0.3-0.6 provided that the g-value is assumed to be equal to 2.14 as evaluated from the Curie constant. The theoretical curves calculated by Duffy and Barr with Ja/Ja equal to 0.4 and 0.6 agree well with the observed susceptibility as shown in Fig. 6. The interaction energy between dimer ions is estimated to be about 50% of the interaction energy within a dimer ion. Regardless of the choice of models, the interaction energy between dimer ions amounts to about 50% of the exchange energy within a dimer ion as shown in Table 3. it = 4kT

0.16

0

0.5

1.0 kl/lll

1.5

2.0

2.5

FIG. 7. Susceptibility of an alternating linear king chain (J@,, = 0.3 and 0.6) and the observed susceptibility of dimethylammonium tribromocuprate(I1) (0 : Ja/k = - WK, n : J,/k = - 95°K).

APPENDIX

Hz and HF in Eq. [3] are given by

H: = Y(%J + (&O), H: = Y(-- (P(O)+ <&d), CA-11 where y is the Weiss coefficient, p0 is the magnetic moment of a sublattice in the absence of external field, and (6~) is the induced magnetic moment of a sublattice in an external field. Since spontaneous magnetization does not take place for a one-dimensional lattice, Eq. [A-l] leads to H,M = H,M = y(@)

= y~H/2.

CA-21

Therefore, the interaction energy is obtained as shown in Table A, and the zero-field

346

HARA,

INOUE,

EMORI,

AND

KUBO

susceptibility is given by log C ,-K%MsW S,MS TABLE

s

MS

0

0

1

1

1

0

1

. 1 Ii =0

iA-

A

US, MS) IJ@

- BJa

-1

By use of the interaction energy given in Table A, the susceptibility can be formulated as

L-A-41 Since (y~)~ is negligible (yx c 0.5), Eq. [A-4] leads to

Ng2P2

X= kT(e- 2JaikT+3)-yg2~2’ The molecular field model (14) gives 425, y=

Ng2jj2’

Substituting Eq. [A-6] into Eq. [A-5], one gets Eq. [4]. If a lattice shown in Fig. 4b is subdivided into two linear sublattices, which are parallel to each other, the same equation is derived by substituting z = 1 for z = 2. REFERENCES C. DWINGGINS, JR., R. F. KRUH, AND R. E. RKJNDLE, J. Chem. Phys. 38,2429 (1963). 2. R. D. WILLETT, J. Chem. Phys. 44, 39 (1966). 3. M. INOIJE, M. KISHITA, AND M. KUBO, Znorg. Chem. 6,900 (1967). 4. G. J. Mm, B. C. GERSTEIN, ANJJ R. D. WILLETT, J. Chem. Phys. 46,401 (1967). 5. J. E. HY~s, B. B. GARRETT, AND W. G. MOULTON, J. Chem. Phys. 52,267l (1970). 6. M. INOUE, S. EMOIU, AND M. KIJBO, Znorg. Chem. 7, 1427 (1968). 2nd Ed., Interscience, New York, 1956. 7. P. W. SELWOOD, “Magnetochemistry,” 8. G. Foisx, “Con&antes Sblectiom&s, Diamagnktisme et Paramagn&isme,” Masson, Paris, 1957. 9. B. N. FroGIs AND R. L. MARTIN, J. Chem. Sot. 3837 (1956). 10. B. BLEANEY AND K. D. BOWERS, Proc. Roy. Sot. London A 214,451 (1952). Il. J. W. STOUT AND R. C. CHJSHOLM, J. Chem. Phys. 36,979 (1962). 12. M. INOUE AND M. KIJBO, J. Mugn. Resonance 4, 175 (1971) 13. W. DUFFY, JR., AND K. P. BARR, Phys. Rev. 165,647 (1968). 14. J. SMART, “Effective Field Theories of Magnetism,” Saunders, Philadelphia, 1966. 1. R. D. WILLEXT,