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Magnetic behavior of cobalt bromide hydrates including a deuterated form
Journal of Magnetism and Magnetic Materials 428 (2017) 158–164
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Magnetic behavior of cobalt bromide hydrates including a deuterated form ⁎
MARK
G.C. DeFotis , A.S. Hampton, M.J. Van Dongen, C.H. Komatsu, C.L. DeSanto, C.M. Davis Chemistry Department, College of William & Mary, Williamsburg, VA 23187, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: Antiferromagnet Magnetic susceptibility Magnetization Exchange interactions Ising model Metamagnetism
The magnetic properties of little examined CoBr2•2H2O and new CoBr2•H2O and CoBr2•D2O are studied. CurieWeiss fits, χM=C/(T-θ), yield θ of −9.9, 9.4 and 10.0 K, respectively, over a 30–80 K linear range for each. Higher temperature data are fit assuming two moderately separated low lying Kramers doublets, with exchange accounted for in a mean-field approximation. Susceptibility maxima appear at 9.5, 15.4 and 15.5 K, with χmax of 0.163, 0.375 and 0.435 emu/mol, respectively. Antiferromagnetic ordering is estimated to occur at 9.0, 13.7 and 13.8 K, in the same order. The ratio Tc/Tmax is 0.95, 0.89 and 0.89, respectively, suggesting little low dimensional magnetic character in singly hydrated systems. Data at lower temperatures for the dihydrate are fit with an antiferromagnetic 3D-Ising model. For singly hydrated systems the large size of χmax prevents this; weakened interchain antiferromagnetic interactions yield enhanced susceptibility maxima. Magnetization data exhibit field induced transitions near 13.5 kG for the dihydrate, and near 6.5 kG for singly hydrated systems with enhanced hysteresis. These transitions are interpreted as metamagnetic in nature.
1. Introduction
The crystal structure of CoBr2•2H2O is isomorphous with that of the Mn(II) bromide dihydrate [7]. Both are characterized by chemical and structural MBr2MBr2M… chains along the c axis of a monoclinic C2/m unit cell. The chains are not well isolated, neither structurally nor magnetically. The structure is the same as previously determined for the chloride dihydrates [8,9]. Magnetic properties of the bromide dihydrate are only modestly studied [10,11]; no susceptibility data have appeared, in contrast to the chloride dihydrate [12]. Our examination of CoCl2•H2O [13–15] also reviews prior work on the dihydrate, while its properties are relevant for comparison with the new bromide monohydrate studied here. Powder susceptibility data on the bromide dihydrate are also worthwhile for comparison with similar data on the monohydrate.
Standard references on the magnetism of transition metal compounds [1–3] contain many examples of 3d metal halide hydrates. Most common are di-, tetra- and hexahydrate forms. Dihydrates are the most thoroughly examined, and the most interesting regarding magnetic ordering properties at low temperatures. Among these bromides are less studied than chlorides, though often isostructural. They deserve more attention; fruitful comparisons of superexchange interactions via halide bridging ions of different size and polarizability could emerge. We have been preparing and making magnetic measurements on bromide compounds which have been little studied or not at all relative to chloride counterparts. One recent report was concerned with several such Mn(II) compounds [4]. Two belonged to the relatively new monohydrate series, MX2•H2O, one containing D2O in place of H2O. The effect of deuteration on the magnetic behavior of transition metal compounds containing waters of hydration is not extensively examined. Our study of the magnetic behavior in the deuterated versions MnCl2•D2O and CoCl2•D2O of the earliest reported Mn(II) and Co(II) chloride monohydrates, presents important magnetic and structural comparisons as well as background for both the monohydrate series specifically and deuteration effects generally [5]. Most recently a similar series of nickel bromide hydrates was also examined [6]. In this report we present magnetic susceptibility and magnetization data for CoBr2•2H2 O,CoBr2•H2 O and CoBr2•D2O. ⁎
Corresponding author. E-mail address: [email protected] (G.C. DeFotis).
http://dx.doi.org/10.1016/j.jmmm.2016.11.121 Received 27 October 2016; Accepted 25 November 2016 Available online 27 November 2016 0304-8853/ © 2016 Elsevier B.V. All rights reserved.
2. Experimental 2.1. Materials and methods In preparing CoBr2•2H2O and CoBr2•H2O high purity anhydrous cobalt dibromide was dissolved in deionized water and each solution placed in an oven for slow evaporation, with occasional grinding of the solid material forming in order to prevent occlusion of water. The temperature conditions for obtaining each hydrate were explored by trial and error. A temperature of 73 °C yielded the dihydrate, which is medium violet in color. To obtain the bromide monohydrate a higher temperature of 94 °C was needed; this substance is medium blue in
Journal of Magnetism and Magnetic Materials 428 (2017) 158–164
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color. These temperatures are comparable with those leading to the corresponding chloride hydrates. Fine grained polycrystalline material was obtained for each. Thermogravimetric analysis showed the hydration state in each case to be within 0.05 water unit of that intended (also applying to the D2O system below). This is comparable precision to that for many other hydrated transition metal halide systems examined by us in the past. Preparation and hydration state analysis of CoBr2•D2O occurred in similar fashion, but with use of fully deuterated D2O (99.8%, Acros Chemicals) as solvent in first a glove box, then a vacuum oven filled with Ar(g) for evaporation, in order to avoid contamination by atmospheric water. Trial and error determined 83 °C to be appropriate for obtaining this material; the color is a darker blue verging on purple. The temperature is virtually the same as that leading to MnBr2•D2O [4]. As for Mn(II) compounds, somewhat lower temperatures are needed to obtain a given D2O hydration state than for H2O with some difference in color also apparent. Despite much effort CoBr2•2D2O could not be reliably obtained. Data on samples with average 2D2O content exhibited features implying the presence of components of different magnetic character.
Fig. 1. Inverse molar magnetic susceptibilities vs. temperature for CoBr2•2H2O (small circles), CoBr2•H2O (large circles) and CoBr2•D2O (triangles). Lines are Curie-Weiss fits described in text. For clarity triangle data are shifted up 10 mol/emu, and small circle data 20 mol/emu.
In weak octahedral coordination the crystal field ground term of Co(II) is a 4T1 g level. Crystal field distortions and spin-orbit coupling split this into six Kramers doublets. Curie(-Weiss) behavior will result if only the ground doublet is significantly populated over the temperature range employed (e.g., 30–80 K here), or if temperatures are so high that any thermally accessible doublets are virtually equally populated. At sufficiently low temperature departures from such behavior occur because of short-range order resulting from exchange interactions. Spectroscopic information on doublet separations is rarely available, but values of a few hundred equivalent K are typical. We adopt here the approach applied previously [5,14] to chloride compound data, and assume that the first excited doublet is a moderate ΔE above the ground doublet, but that more excited doublets are far higher in energy and make negligible contribution to the susceptibility. Allowance is made for different g values, g1 and g2, characterizing the ground and excited doublets. The Van Vleck equation [2] applied to this situation, treating each of the two doublets as an effective S´= ½, yields
2.2. Magnetic measurements Magnetization and susceptibility measurements were made with a vibrating sample magnetometer and cryostat. Data shown are field cooled measurements except where otherwise indicated, and are corrected for the rather small effects of diamagnetism and demagnetization, and the minute contribution of the sample holder. Applied magnetic fields in susceptibility measurements range from 0.1 to 1.6 kG depending on the temperature. No field dependences of susceptibilities were seen, as expected for such modest field values. Polycrystalline samples of approximately 100 mg size were packed into nonmagnetic sample holders under dry conditions, weighed accurately, then screwed onto a nonmagnetic sample rod in immediate proximity to a calibrated Cernox resistance thermometer. Temperatures are accurate to ± 0.005−0.5 K depending on the range. Magnetic fields are accurate to ± max (2 G, 0.1%), and magnetization and susceptibility values to 1.5% absolute, with substantially better precision. In handling of the materials care was taken to minimize exposure to atmospheric water vapor.
χ
= 0. 0938
g12 +g 22 e-∆E/kT T(1 +e-∆E /kT)
(1)
where the numerical prefactor has dimensions emu K/mol. Exchange interactions, obviously present, are accounted for in a mean-field approximation, employing the expression [16]
3. Results 3.1. Magnetic susceptibilities
χex = χ/[1 - (2zJ/N0 g 2μ 2B)χ],
3.1.1. Moderate to high temperature data The inverse molar magnetic susceptibilities of CoBr2•2H2O, CoBr2•H2O and CoBr2•D2O appear in Fig. 1. The data are corrected for diamagnetism (−113, −99 and −99×10−6 emu/mol, respectively) and demagnetization, both quite small effects. Reliably linear ranges for moderate to high temperatures are not evident, as for CoCl2•H2O previously [14]. Instrumental effects are responsible for the highest temperature upturn in dihydrate data; such can appear absent perfect data collection, and are excluded from analysis. The range 30–80 K is the best common linear regime for all three, and Curie-Weiss form fits, χM=C/(T−θ), are represented by the lines in the figure. Data below 30 K are more densely spaced and influenced by short range order effects, hence not included in the fits. Parameter values appear in Table 1. The negative θ for dihydrate contrasts markedly with the positive values for the other two systems. Via the standard relation C = Nog2μB2S(S+1)/ 3k, and S =3/2, the corresponding g are 2.54, 2.50 and 2.51 respectively. These are plausible average g for Co(II) compounds, well above 2.0 because of orbital contributions. Assuming an effective S´= ½ (see below) the corresponding g are 5.67, 5.59 and 5.61 respectively. These are plausible average values for a highly anisotropic ground doublet [1].
(2)
where J is a mean interaction over z neighbors, and the exchange convention Hex =−2 J∑i > jSi·Sj. Susceptibility data were fit from 30 K to 300 K (250 K for dihydrate) employing Eqs. (1) and (2). The fitted curve appears in each of Figs. 2, 3 and 4, displayed in both chi and inverse chi vs T representations. Parameter values appear in Table 1. The rms fit deviations are 0.33%, 0.74% and 0.65% in the order the compounds appear in the table, and are similar to those obtained previously for chloride compounds [5,14]. The g values are plausible for such anisotropic doublets, with that for the excited doublet somewhat larger. The energy separation increases in the order 2H2O, D2O, H2O, though the variation is not large. This is also the order in which curvature in the inverse chi vs T representations increases. The zJ/k values are the same sign as the θ values. Moreover, substitution into the mean field relation [1,2]
θ = 2S (S + 1) zJ /3k
(3)
yields −7.5, 9.2 and 12.6 K respectively, similar to observation. Insufficient information is available to apply any multiparameter ligand field model, also involving idealized assumptions such as tetragonal distortion. Individual Kramers doublets are variably aniso159
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Table 1 Magnetic parameters for CoBr2•nH(D)2O data and fits; numbers in parentheses are estimated uncertainties in last significant digits. System
C (emuK/mol)
θ (K)
Tmax (K) Tc (K)
χmax (emu/mol)
ΔE/k (K)
g1 g2
zJ/k (K)
2H2O H2O D2O
3.02 (2) 2.93 (2) 2.96 (2)
−9.9 (4) 9.4 (4) 10.0 (4)
9.5 (2) 9.0 (2) 15.4 (2) 13.7 (2) 15.5 (2) 13.8 (2)
0.163 (5) 0.375 (5) 0.435 (5)
158 (10) 240 (10) 187 (10)
5.49 (5) 6.69 (5) 5.57 (5) 6.60 (5) 5.36 (5) 6.84 (5)
-15.0 (5) 18.5 (5) 25.2 (5)
Fig. 2. Molar magnetic susceptibility (left vertical) and its inverse (right vertical) vs. temperature for CoBr2•2H2O. Curves through data are a fit based on ground and excited Kramers doublets with a mean-field correction for exchange interactions, described in text.
Fig. 4. Molar magnetic susceptibility (left vertical) and its inverse (right vertical) vs temperature for CoBr2•D2O. Curves through data are a fit based on ground and excited Kramers doublets with a mean-field correction for exchange interactions, described in text.
Fig. 5. Molar magnetic susceptibility vs temperature for CoBr2•2H2O, and a fit to data using a 3D Ising model, described in text. The calculated curve is shown to somewhat lower temperatures than can be or were fit by the model.
Fig. 3. Molar magnetic susceptibility (left vertical) and its inverse (right vertical) vs temperature for CoBr2•H2O. Curves through data are a fit based on ground and excited Kramers doublets with a mean-field correction for exchange interactions, described in text.
these two, even though located at substantially higher temperatures than for the dihydrate. Estimates of Tmax and χmax appear in Table 1. Noteworthy is that the maximum susceptibility for the bromide dihydrate occurs at a much lower temperature, 9.5 K, than for the isomorphous chloride dihydrate, 17.5 K [12]. The maximum susceptibility in the bromide is 60% larger than in the chloride, consistent with lesser Tmax, hence weaker antiferromagnetic interactions. Maximum susceptibility values for the two singly hydrated forms in Fig. 6 are approximately four times larger than for chloride dihydrate, even though their Tmax are only slightly lower than for the chloride. The location of an inflection point (maximum dχ/dT) on the low temperature side of the maximum can be estimated. Although polycrystalline data are less ideal than easy axis single crystal data, such a feature can be taken as signaling an antiferromagnetic transition [17]. Such Tc estimates also appear in Table 1. The ratio Tc/Tmax is 0.95, 0.89
tropic dependent on detailed distortions, energy separations and other factors. This also justifies the large fitted g values, Ising like, of both ground and first excited doublet. That the present phenomenological model fits the data quite well over a rather broad temperature range, and involves a plausible minimum number of parameters, is attractive. 3.1.2. Low temperature data The molar magnetic susceptibilities at low temperatures appear in Figs. 5 and 6. That for CoBr2•2H2O also shows a fit employing a threedimensional s.c. Ising model, to be described. For each singly hydrated compound no plausible fit with any model was achievable. This is because of the unusually large size of the susceptibility maxima for 160
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Fig. 8. Molar magnetization vs applied field for CoBr2•H2O at various temperatures. For clarity vertical shifts of 1.2, 1.8 and 2.4×103 emu/mol are applied for successively higher temperatures. Closed symbols are for decreasing field.
Fig. 6. Molar magnetic susceptibilities vs temperature for CoBr2•H2O (small circles) and CoBr2•D2O (triangles).
and 0.89 in the same order as above. The first, well above 0.90, is characteristic of systems where exchange interactions operate with comparable strength in three spatial dimensions (3D magnetically). The latter two are slightly below the characteristic 3D range, but not low enough to imply typical low dimensional magnetic behavior, i.e., 2D (layered) or 1D (chain). For temperatures in the vicinity of the susceptibility maximum in CoBr2•2H2O only a 3D Ising model [18] yielded a plausible fit. The best fit obtained is shown in Fig. 3, with g =6.012 and J/k=−3.17 K. It is over the 9–25 K range (from just below Tmax but not below Tc to 2.5 times Tmax, as done by us for other systems), with rms deviation of 2.4%. It is approximate since powder data are being fitted. Fit parameters are only weakly sensitive to the choice of fitting range. The exchange interaction reproduces the observed Tmax very well, and the g value is typical of an isolated ground Kramers doublet with S´= ½. With z=6 for the s.c. 3D Ising model applied, substitution into Eq. (3) yields −9.5 K, agreeing very well with the observed θ.
Fig. 9. Molar magnetization vs applied field for CoBr2•D2O at various temperatures. For clarity vertical shifts of 1, 2 and 3×103 emu/mol are applied for successively higher temperatures. Closed symbols are for decreasing field.
3.2. Magnetization
hydrated systems. Their appearance must be influenced, of course, by the much lower Tmax and Tc of the dihydrate. Modest hysteresis is evident for the three temperatures below Tc in CoBr2•2H2O. Significant convex upward curvature appears in the 8.08 K isotherm, slightly below the estimated Tc =9.0 K, and small hysteresis. This contrasts with the linear behavior without hysteresis at 12.00 K, above Tc. For the two lowest temperatures in Fig. 7a field induced transition is evident near 13.5 kG, with somewhat larger hysteresis than at 8.08 K. This result is close to that reported previously [11]. The highest temperature isotherms in Figs. 8 and 9, taken slightly above the estimated Tc for these compounds, exhibit a clear S-shape; hysteresis is negligible. For the next lowest temperatures, modestly below the Tc estimates, curvature changes are stronger, though hysteresis remains small to negligible. In each of Figs. 8 and 9 the approximately 8 K and 4.2 K isotherms suggest field-induced transitions, with significant hysteresis evident. Approximate locations of these are at 5.5 and 6.0 kG for the H2O system, increasing slightly with decreasing temperature; and 5.0 and 5.5 kG for the D2O compound, about 10% smaller values than for H2O. At 1.843 K for CoBr2·H2O, Fig. 10, the transition is estimated to occur at 6.5 kG, with notably enhanced hysteresis. Quite similar behavior occurred for the D2O system at 1.8 K. Both here and at the higher 4.236 K in Fig. 8a small residual magnetization persists on lowering the applied field to zero value; it is approximately 455 and 85 emu/mol (0.082 and 0.015 µB/ ion) at these two temperatures respectively. A barely detectable residual value of 5 emu/mol occurs for 8.04 K. In weakly anisotropic antiferromagnets (as for Mn(II) compounds) a spin flop transition occurs for temperatures below Tc. In a randomly
In Figs. 7, 8 and 9 appear the molar magnetization for each compound for a range of temperatures. The contrast in general behavior for dihydrate versus monohydrate and monodeuterate is striking. The latter two are quite similar in appearance, though not identical. Slightly larger magnetization for comparable field and temperature occurs for the D2O than for the H2O compound. Magnetization values for the 2H2O compound are several times smaller, and isotherm shapes quite different from those of the singly
Fig. 7. Molar magnetization vs applied field for CoBr2•2H2O at various temperatures. For clarity vertical shifts of 150, 250 and 350 emu/mol are applied for successively higher temperatures. Closed symbols are for decreasing field.
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hydrated compounds are of course suggestive of metamagnetism as well. Substituting the estimated critical field of 6.5 kG for CoBr2·H2O at 1.843 K, and assuming the same, and plausible, g =6.0 as for dihydrate, yields z´J´/k=−2.62 K. The smaller value is in line with prior findings that interchain exchange is generally weaker in monohydrates than in corresponding dihydrates. The metamagnetic scenario is more plausible. 3.3. Thermoremanent magnetization Instrumental limitations prevented extensive study of irreversibility effects as for CoCl2•H2O previously [15]. One indicator of such is the presence and decay of a thermoremanent magnetization (TRM). This is measured on cooling a sample in fixed applied field from a temperature in the paramagnetic regime to a desired measuring temperature, typically below a spin glass [19] or other transition associated with disorder. The applied field is quickly decreased to zero and any residual magnetization followed in time. For conventional equilibrium ordered magnetic systems the TRM is nil. For nonequilibrium magnetic systems, spin glasses especially, substantial residual magnetization exists and shows significant time dependence. The TRM for the cobalt monohydrate at 1.84 K after field cooling in 500 G is shown in Fig. 11. Probably the most commonly observed form for the TRM decay is a stretched exponential,
Fig. 10. M magnetization vs applied field at a lowest 1.843 K for CoBr2•H2O; closed symbols are for decreasing field.
oriented polycrystalline sample such appear as an inflection in M(H), rather than the sharp increase if measuring along the easy axis. The spin flop field at 0 K is expressible in terms of effective exchange and anisotropy fields in a mean-field approach as [1,2]
HSF (0) = [2HE HA –HA2]1/2
(4)
HE = 2z J S / gμB
(5)
MTRM (t ) = M0 exp [−(t / τ )n ].
HA = 2 D (S –½)/ gμB
(6)
The time constant τ is characteristic of a particular material, while the exponent n (not unity) assumes values which tend to be characteristic of the class of glassy system involved. For spin glasses n values near or somewhat above 1/3 are typical. The curve in Fig. 11 is a fit using Eq. (8), with M0 =7.40 emu/mol, τ=7.74×105 s, and n =0.403. The size of the TRM is rather similar to that of the chloride monohydrate for closely similar cooling field and measuring temperature [15]. The relaxation parameters τ and n differ only moderately from chloride values.
Here J is the main intrasublattice antiferromagnetic exchange interaction and D is the anisotropy constant in the standard zero-field splitting Hamiltonian ĤZFS=D[Ŝz2 – S(S+1)/3]. However, in Co(II) compounds where anisotropy is usually strong, field induced transitions in ordered antiferromagnets are often metamagnetic in character. Mean field theory yields an expression for the metamagnetic critical field Hc=AM, where M is the sublattice magnetization N0gµBS/2 and A is a mean field coefficient given by 4z´|J´|/ N0g2µB2, with z´ and J´ the number of neighbors and antiferromagnetic interaction between ferromagnetically aligned sublattices (the standard metamagnetic scenario). These are often layers, and J´ an interlayer interaction. For the present systems, the properties of CoCl2· 2H2O suggest that the sublattices are arrays of ferromagnetic chains, one set oppositely directed from the other. In this case Jʹ is an interchain interaction. The above equations yield for the metamagnetic critical field
Hc = 2z′ J ′ S / gμB.
(8)
4. Discussion 4.1. Magnetic comparisons Certain relations connecting the ordering temperature and other quantities can be applied. The theoretical ratio Tc/|J/k| (in the present exchange interaction convention) ranges from 0.759 to 1.821 for various spin-1/2 2D Ising models, and from 1.352 to 4.898 for spin1/2 3D Ising models [20]. A range of experimental values [1] is from 1.10 to 1.28 for the former, and from 1.36 to 2.34 for the latter case. For CoBr2•2H2O here, using the ordering temperature and fitted J, the
(7)
The susceptibility of the dihydrate compound has a more typical appearance for an antiferromagnet than for the H2O and D2O systems, and the fit in Section 3.1.2. gives an estimate of the exchange interaction. We compare application of the above two interpretations. Substitution of the 3D Ising model fit parameters into Eq. (5) yields HE =47.1 kG. Employing this in Eq. (4), taking 13.5 kG as close enough to a 0 K value since 1.8 K is far below Tc, gives HA =1.94 kG. This is plausible for a Co(II) system. Examples are few; for CoBr2·6H2O an HA of 1.0 kG was reported [1]. With effective S´= ½ Eq. (6) does not apply, and no zero field splitting occurs. The anomalously large susceptibilities of the singly hydrated compounds cannot be fit by any standard model, but from the much larger Tmax a larger exchange interaction, hence also HE, is implied. Yet observed critical fields are less than half that of the dihydrate. The anisotropy field HA obtained on substitution is then substantially smaller. This seems implausible since the coordination geometry in singly hydrated systems must be less symmetrical. From this perspective a spin flop interpretation appears dubious. Substituting into Eq. (7) the same 13.5 kG critical field value and g =6.012 from the susceptibility fit yields z´J´/k=−5.45 K. The sharpness and large hysteresis of the field induced transitions in the singly
Fig. 11. Thermoremanent magnetization (TRM) for CoBr2•H2O at 1.843 K after field cooling in 500 G. The fitted curve is a stretched exponential form described in text.
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polarizability of the bromide ion should increase the size of superexchange interactions involving it. Arguably, this is less significant than larger lattice separations in bromide systems, which might be expected to decrease interaction strengths. Lattice parameter variations from chloride to bromide differ only very slightly for the manganese and cobalt systems. The volume per formula unit for MnCl2•2H2O and MnBr2•2H2O is 119.0 and 134.2 Å3 respectively, a difference of 15.2 Å3 or 12.8% [23]. For CoCl2•2H2O and CoBr2•2H2O the values are 109.6 and 124.9 Å3, for a difference of 15.3 Å3 or 14.0% [23]. The smaller cobalt than manganese volumes are consistent with tabulated ionic radii [24]. A more detailed comparison can be made. Lattice parameters for CoBr2•2H2O are from 2.3% to 5.9% larger than for isomorphous CoCl2•2H2O; in detail, the monoclinic b axis is 0.195 Å larger in the bromide, or 2.3%; the c axis is 0.211 Å larger, or 5.9%; and the a axis is 0.374 Å larger, or 5.2%. Oxygen-oxygen contacts occur along b; the MX2MX2M… chain direction is along c; halide-halide contacts also occur along a. The smallest enhancement, relatively and absolutely, is along b where halide-halide contacts are expected to matter least. The rms lattice parameter enhancement from chloride to bromide is 0.272 Å over all three axes, or if restricting to the ac plane where bromides reside, 0.304 Ǻ. A standard compilation [24] gives ionic radii as 1.67 and 1.82 Å for Cl- and Br-, respectively. It is plausible to expect average distances determined by Br-Br contacts to be 0.30 Å larger than for Cl-Cl contacts, that is by twice the ionic radius difference. This is the same as the second rms estimate above. Thus lattice parameter enhancements are in line with ionic radius expectations. Along the c (chemical chain) axis the expansion is less than twice the radius difference, while along a it is more. In neither direction are the Br-Br overlaps along their internuclear separation. Plausible is that along the a axis there is an exchange interaction reduction from chloride to bromide while along the c axis enhancement occurs. It is very difficult to predict what the net outcome will be. Certain unexpected findings emerge from a comparison of the previously studied chloride dihydrate and monohydrate and the bromide counterparts here. As already noted, the diminution in Tmax and Tc from chloride to bromide dihydrate is extraordinary. Atypical to begin with for chloride-bromide counterparts, the nearly factor of two reduction is larger than for any other such pair. Not less surprising, instead of the modest reduction in the above two characteristic temperatures seen from chloride dihydrate to monohydrate, for the corresponding bromides a major increase occurs. Yet the general behavior including major hysteretic effects and irreversibility is quite similar in CoCl2•H2O and CoBr2•H2O, and Tmax and Tc differ only slightly. Previous estimates of the ferromagnetic intrachain interaction in the chloride and bromide dihydrates have been rather indirect [9]; the former is estimated to be J/k=9.3 K and the latter 6.0 K. The reduction is opposite in sense to that of the separation argument in the previous paragraph, presumably too naïve. In any case, if significantly weaker intrachain and interchain interactions characterize the bromide dihydrate, yielding the significantly smaller Tmax and Tc, it is striking that hardly any such effects distinguish the chloride and bromide monohydrates. Also intriguing is the relationship among metamagntic critical fields in the four materials. The reduction from 31.6 to 4.5 kG in chloride dihydrate and monohydrate respectively reflects a general weakening of antiferromagnetic exchange between ferromagnetically coupled chains. However, there occurs both intrachain and interchain structural reorganization on passing from dihydrate to monohydrate [5]. Single crystal work in multi-Tesla fields revealed a complicated situation in CoCl2•2H2O [11] with the difference between two antiferromagnetic interchain interactions determining the observed 31 kG transition. It is plausible that an analogous phenomenon determines the 4.5 kG transition in CoCl2•H2O; the altered crystal structure (relative to dihydrate) admits at least two different significant interchain interactions. Neither single crystal nor sufficiently high field data are available
ratio is 2.84, evidently more 3D-like. Since the J value is from a fit employing a 3D model, it may be preferable to compare with a ratio involving only observed quantities. For several spin-1/2 2D and 3D Ising compounds the experimental ratio Tc/|θ| has been tabulated. It ranges from 0.55 to 0.64 for the former and from 0.62 to 0.79 for the latter [1]. For CoBr2•2H2O here the ratio is 0.91, much above 2D values. Comparisons with magnetic behavior in related materials can be made. As already noted, CoBr2•2H2O is isomorphous [7] with MnBr2•2H2O, both also isomorphous with the corresponding chlorides. Our report [4] on various manganese bromide hydrates revealed that antiferromagnetic MnBr2•2H2O is characterized by Tmax and Tc values moderately lower (14% and 12% respectively) than those of the chloride dihydrate. Comparable decreases appeared for nickel bromide dihydrates relative to chloride counterparts [6]. Such changes are in contrast to the trend [1,2] for the great majority of bromide-chloride pairs, as reviewed by us [4], where the bromide displays higher Tmax and Tc. For cobalt dihydrates reductions in these quantities are a remarkable 46% and 48% from chloride to bromide. To a much lesser degree the above finding regarding bromide vs chloride characteristic temperatures extends to the singly hydrated forms. For each of CoBr2•H2O and CoBr2•D2O, Tmax and Tc values in Table 1 are smaller than for corresponding chlorides [5], and as for chlorides virtually indistinguishable. Bromide Tmax values are 4–5% smaller than for corresponding chlorides, and Tc values 8–9% smaller. For nickel monohydrate compounds it was also found that bromide Tmax and Tc were moderately less than for corresponding chlorides [6]. There are interesting similarities and differences between magnetization isotherms obtained here for CoBr2•H2O and CoBr2•D2O and for the corresponding chlorides previously [5,14]; for either halide behaviors for H2O and D2O containing systems are virtually identical. The temperatures of enhanced susceptibility maxima in chloride and bromide monohydrates (D2O and H2O forms essentially indistinguishable) differ by only 5%, 16.2 and 15.4 K respectively. But the metamagnetic critical field at 2 K is significantly higher in the bromide, 6.5 kG, than in the chloride, 4.5 kG. For both chloride and bromide the substantial hysteresis is markedly enhanced between 4.2 and 2 K. Interestingly, the shape of M(H) on decreasing the applied field toward zero differs significantly between chloride and bromide. Also, in the chloride the 2 K residual magnetization is about twice as large as the 455 emu/mol seen here for the bromide. These differences between chloride and bromide monohydrates contrast markedly with dihydrate properties. For the bromide dihydrate Tmax is not slightly smaller but almost a factor of two smaller than for the chloride dihydrate. And the metamagnetic critical field of 13.5 kG for bromide is less than half as large as the 31.6 kG of the chloride [11]. Nevertheless, these fields are much larger than in the monohydrates. An explanation for the small reductions in Tmax and Tc for each cobalt halide monohydrate relative to dihydrate suggests itself. Ferromagnetic intrachain exchange along a Co-X-X-Co pathway is virtually the same in the two forms. This was demonstrated for MnCl2•H2O [21,22] vs MnCl2•2H2O, despite structural changes in the MnCl2MnCl2Mn… chains [5]; in these systems intrachain exchange is antiferromagnetic. The same structural relations hold for the corresponding cobalt systems. Weakened interchain antiferromagnetic interactions in monohydrates are evident from reduced metamagnetic critical fields and enhanced susceptibility maxima. But ferromagnetic intrachain exchange dominates ordering properties, and so characteristic temperatures are only modestly reduced. 4.2. Overview and conclusions The reductions in Tmax and Tc for bromide counterparts of chloride compounds (seen here for cobalt but also previously for manganese [4] and nickel [6]) are contrary to the expectation that the greater 163
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Chemistry Program, DMR-NSF. (grant number 0085662) and from the Donors of the American Chemical Society Petroleum Research Fund (grant number 43296-B10). He has also benefitted from a Plumeri Faculty Award from the College of William and Mary.
to permit detailed analysis. Since the four manganese or cobalt, chloride or bromide, dihydrates are isomorphous, it is likely from the similarity in susceptibility, magnetization and TRM of CoBr2•H2O relative to CoCl2•H2O that it shares the latter's crystal structure. For the chloride and bromide dihydrate pair, and the monohydrate pair, the same two (different) structures are involved. Thus the seven-fold reduction in Hc for the chloride forms becoming merely two-fold between CoBr2•2H2O and CoBr2•H2O can be understood as an accidental result of increased cancellation in a difference between two interchain antiferromagnetic interactions in the bromide monohydrate. A review of the limited literature concerning the effect of deuteration on the magnetic properties of transition metal complexes with waters of hydration has appeared [5]. Modest but larger than expected differences between Tmax and Tc for MnCl2•H2O and MnCl2•D2O were seen. Such were also found for MnBr2•H2O and MnBr2•D2O [4], though with differences in detail from chlorides. MnCl2•H2O and MnCl2•D2O were found to be isostructural [5], with only minute lattice parameter differences; hence magnetic differences cannot be attributed to structural differences. Replacing H2O by D2O in nickel chlorides and bromides, both dihydrate and monohydrate forms, also produced significant magnetic differences [6]. For CoBr2•H2O and CoBr2•D2O the negligible difference in Tmax and Tc can be considered more typical. Structural or even only unit cell determinations for corresponding H2O and D2O containing compound are rare. From CuCl2•2H2O to CuCl2•2D2O the unit cell volume increases by 1.6%, without structural change [25]. For α-CoC2O4•2H2O and α-CoC2O4•2D2O the increase is 0.7% on deuteration, also with the same structure [26]. Although the unit cell of MnBr2•2D2O differs [4] from that of MnBr2•2H2O, a similar increase in volume per formula unit appears as in these earlier examples. A substantial change in magnetic behavior resulted from the structural change. In the case of NiBr2•2D2O [6], also with a structural change relative to NiBr2•2H2O, the volume per formula unit again increases slightly. A variation in magnetic behavior, less pronounced than for the manganese systems but significant, also appears.
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Acknowledgements
[26]
G.C.D. gratefully acknowledges grants from the Solid State
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Magnetic behavior of cobalt bromide hydrates including a deuterated form ⁎
MARK
G.C. DeFotis , A.S. Hampton, M.J. Van Dongen, C.H. Komatsu, C.L. DeSanto, C.M. Davis Chemistry Department, College of William & Mary, Williamsburg, VA 23187, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: Antiferromagnet Magnetic susceptibility Magnetization Exchange interactions Ising model Metamagnetism
The magnetic properties of little examined CoBr2•2H2O and new CoBr2•H2O and CoBr2•D2O are studied. CurieWeiss fits, χM=C/(T-θ), yield θ of −9.9, 9.4 and 10.0 K, respectively, over a 30–80 K linear range for each. Higher temperature data are fit assuming two moderately separated low lying Kramers doublets, with exchange accounted for in a mean-field approximation. Susceptibility maxima appear at 9.5, 15.4 and 15.5 K, with χmax of 0.163, 0.375 and 0.435 emu/mol, respectively. Antiferromagnetic ordering is estimated to occur at 9.0, 13.7 and 13.8 K, in the same order. The ratio Tc/Tmax is 0.95, 0.89 and 0.89, respectively, suggesting little low dimensional magnetic character in singly hydrated systems. Data at lower temperatures for the dihydrate are fit with an antiferromagnetic 3D-Ising model. For singly hydrated systems the large size of χmax prevents this; weakened interchain antiferromagnetic interactions yield enhanced susceptibility maxima. Magnetization data exhibit field induced transitions near 13.5 kG for the dihydrate, and near 6.5 kG for singly hydrated systems with enhanced hysteresis. These transitions are interpreted as metamagnetic in nature.
1. Introduction
The crystal structure of CoBr2•2H2O is isomorphous with that of the Mn(II) bromide dihydrate [7]. Both are characterized by chemical and structural MBr2MBr2M… chains along the c axis of a monoclinic C2/m unit cell. The chains are not well isolated, neither structurally nor magnetically. The structure is the same as previously determined for the chloride dihydrates [8,9]. Magnetic properties of the bromide dihydrate are only modestly studied [10,11]; no susceptibility data have appeared, in contrast to the chloride dihydrate [12]. Our examination of CoCl2•H2O [13–15] also reviews prior work on the dihydrate, while its properties are relevant for comparison with the new bromide monohydrate studied here. Powder susceptibility data on the bromide dihydrate are also worthwhile for comparison with similar data on the monohydrate.
Standard references on the magnetism of transition metal compounds [1–3] contain many examples of 3d metal halide hydrates. Most common are di-, tetra- and hexahydrate forms. Dihydrates are the most thoroughly examined, and the most interesting regarding magnetic ordering properties at low temperatures. Among these bromides are less studied than chlorides, though often isostructural. They deserve more attention; fruitful comparisons of superexchange interactions via halide bridging ions of different size and polarizability could emerge. We have been preparing and making magnetic measurements on bromide compounds which have been little studied or not at all relative to chloride counterparts. One recent report was concerned with several such Mn(II) compounds [4]. Two belonged to the relatively new monohydrate series, MX2•H2O, one containing D2O in place of H2O. The effect of deuteration on the magnetic behavior of transition metal compounds containing waters of hydration is not extensively examined. Our study of the magnetic behavior in the deuterated versions MnCl2•D2O and CoCl2•D2O of the earliest reported Mn(II) and Co(II) chloride monohydrates, presents important magnetic and structural comparisons as well as background for both the monohydrate series specifically and deuteration effects generally [5]. Most recently a similar series of nickel bromide hydrates was also examined [6]. In this report we present magnetic susceptibility and magnetization data for CoBr2•2H2 O,CoBr2•H2 O and CoBr2•D2O. ⁎
Corresponding author. E-mail address: [email protected] (G.C. DeFotis).
http://dx.doi.org/10.1016/j.jmmm.2016.11.121 Received 27 October 2016; Accepted 25 November 2016 Available online 27 November 2016 0304-8853/ © 2016 Elsevier B.V. All rights reserved.
2. Experimental 2.1. Materials and methods In preparing CoBr2•2H2O and CoBr2•H2O high purity anhydrous cobalt dibromide was dissolved in deionized water and each solution placed in an oven for slow evaporation, with occasional grinding of the solid material forming in order to prevent occlusion of water. The temperature conditions for obtaining each hydrate were explored by trial and error. A temperature of 73 °C yielded the dihydrate, which is medium violet in color. To obtain the bromide monohydrate a higher temperature of 94 °C was needed; this substance is medium blue in
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color. These temperatures are comparable with those leading to the corresponding chloride hydrates. Fine grained polycrystalline material was obtained for each. Thermogravimetric analysis showed the hydration state in each case to be within 0.05 water unit of that intended (also applying to the D2O system below). This is comparable precision to that for many other hydrated transition metal halide systems examined by us in the past. Preparation and hydration state analysis of CoBr2•D2O occurred in similar fashion, but with use of fully deuterated D2O (99.8%, Acros Chemicals) as solvent in first a glove box, then a vacuum oven filled with Ar(g) for evaporation, in order to avoid contamination by atmospheric water. Trial and error determined 83 °C to be appropriate for obtaining this material; the color is a darker blue verging on purple. The temperature is virtually the same as that leading to MnBr2•D2O [4]. As for Mn(II) compounds, somewhat lower temperatures are needed to obtain a given D2O hydration state than for H2O with some difference in color also apparent. Despite much effort CoBr2•2D2O could not be reliably obtained. Data on samples with average 2D2O content exhibited features implying the presence of components of different magnetic character.
Fig. 1. Inverse molar magnetic susceptibilities vs. temperature for CoBr2•2H2O (small circles), CoBr2•H2O (large circles) and CoBr2•D2O (triangles). Lines are Curie-Weiss fits described in text. For clarity triangle data are shifted up 10 mol/emu, and small circle data 20 mol/emu.
In weak octahedral coordination the crystal field ground term of Co(II) is a 4T1 g level. Crystal field distortions and spin-orbit coupling split this into six Kramers doublets. Curie(-Weiss) behavior will result if only the ground doublet is significantly populated over the temperature range employed (e.g., 30–80 K here), or if temperatures are so high that any thermally accessible doublets are virtually equally populated. At sufficiently low temperature departures from such behavior occur because of short-range order resulting from exchange interactions. Spectroscopic information on doublet separations is rarely available, but values of a few hundred equivalent K are typical. We adopt here the approach applied previously [5,14] to chloride compound data, and assume that the first excited doublet is a moderate ΔE above the ground doublet, but that more excited doublets are far higher in energy and make negligible contribution to the susceptibility. Allowance is made for different g values, g1 and g2, characterizing the ground and excited doublets. The Van Vleck equation [2] applied to this situation, treating each of the two doublets as an effective S´= ½, yields
2.2. Magnetic measurements Magnetization and susceptibility measurements were made with a vibrating sample magnetometer and cryostat. Data shown are field cooled measurements except where otherwise indicated, and are corrected for the rather small effects of diamagnetism and demagnetization, and the minute contribution of the sample holder. Applied magnetic fields in susceptibility measurements range from 0.1 to 1.6 kG depending on the temperature. No field dependences of susceptibilities were seen, as expected for such modest field values. Polycrystalline samples of approximately 100 mg size were packed into nonmagnetic sample holders under dry conditions, weighed accurately, then screwed onto a nonmagnetic sample rod in immediate proximity to a calibrated Cernox resistance thermometer. Temperatures are accurate to ± 0.005−0.5 K depending on the range. Magnetic fields are accurate to ± max (2 G, 0.1%), and magnetization and susceptibility values to 1.5% absolute, with substantially better precision. In handling of the materials care was taken to minimize exposure to atmospheric water vapor.
χ
= 0. 0938
g12 +g 22 e-∆E/kT T(1 +e-∆E /kT)
(1)
where the numerical prefactor has dimensions emu K/mol. Exchange interactions, obviously present, are accounted for in a mean-field approximation, employing the expression [16]
3. Results 3.1. Magnetic susceptibilities
χex = χ/[1 - (2zJ/N0 g 2μ 2B)χ],
3.1.1. Moderate to high temperature data The inverse molar magnetic susceptibilities of CoBr2•2H2O, CoBr2•H2O and CoBr2•D2O appear in Fig. 1. The data are corrected for diamagnetism (−113, −99 and −99×10−6 emu/mol, respectively) and demagnetization, both quite small effects. Reliably linear ranges for moderate to high temperatures are not evident, as for CoCl2•H2O previously [14]. Instrumental effects are responsible for the highest temperature upturn in dihydrate data; such can appear absent perfect data collection, and are excluded from analysis. The range 30–80 K is the best common linear regime for all three, and Curie-Weiss form fits, χM=C/(T−θ), are represented by the lines in the figure. Data below 30 K are more densely spaced and influenced by short range order effects, hence not included in the fits. Parameter values appear in Table 1. The negative θ for dihydrate contrasts markedly with the positive values for the other two systems. Via the standard relation C = Nog2μB2S(S+1)/ 3k, and S =3/2, the corresponding g are 2.54, 2.50 and 2.51 respectively. These are plausible average g for Co(II) compounds, well above 2.0 because of orbital contributions. Assuming an effective S´= ½ (see below) the corresponding g are 5.67, 5.59 and 5.61 respectively. These are plausible average values for a highly anisotropic ground doublet [1].
(2)
where J is a mean interaction over z neighbors, and the exchange convention Hex =−2 J∑i > jSi·Sj. Susceptibility data were fit from 30 K to 300 K (250 K for dihydrate) employing Eqs. (1) and (2). The fitted curve appears in each of Figs. 2, 3 and 4, displayed in both chi and inverse chi vs T representations. Parameter values appear in Table 1. The rms fit deviations are 0.33%, 0.74% and 0.65% in the order the compounds appear in the table, and are similar to those obtained previously for chloride compounds [5,14]. The g values are plausible for such anisotropic doublets, with that for the excited doublet somewhat larger. The energy separation increases in the order 2H2O, D2O, H2O, though the variation is not large. This is also the order in which curvature in the inverse chi vs T representations increases. The zJ/k values are the same sign as the θ values. Moreover, substitution into the mean field relation [1,2]
θ = 2S (S + 1) zJ /3k
(3)
yields −7.5, 9.2 and 12.6 K respectively, similar to observation. Insufficient information is available to apply any multiparameter ligand field model, also involving idealized assumptions such as tetragonal distortion. Individual Kramers doublets are variably aniso159
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Table 1 Magnetic parameters for CoBr2•nH(D)2O data and fits; numbers in parentheses are estimated uncertainties in last significant digits. System
C (emuK/mol)
θ (K)
Tmax (K) Tc (K)
χmax (emu/mol)
ΔE/k (K)
g1 g2
zJ/k (K)
2H2O H2O D2O
3.02 (2) 2.93 (2) 2.96 (2)
−9.9 (4) 9.4 (4) 10.0 (4)
9.5 (2) 9.0 (2) 15.4 (2) 13.7 (2) 15.5 (2) 13.8 (2)
0.163 (5) 0.375 (5) 0.435 (5)
158 (10) 240 (10) 187 (10)
5.49 (5) 6.69 (5) 5.57 (5) 6.60 (5) 5.36 (5) 6.84 (5)
-15.0 (5) 18.5 (5) 25.2 (5)
Fig. 2. Molar magnetic susceptibility (left vertical) and its inverse (right vertical) vs. temperature for CoBr2•2H2O. Curves through data are a fit based on ground and excited Kramers doublets with a mean-field correction for exchange interactions, described in text.
Fig. 4. Molar magnetic susceptibility (left vertical) and its inverse (right vertical) vs temperature for CoBr2•D2O. Curves through data are a fit based on ground and excited Kramers doublets with a mean-field correction for exchange interactions, described in text.
Fig. 5. Molar magnetic susceptibility vs temperature for CoBr2•2H2O, and a fit to data using a 3D Ising model, described in text. The calculated curve is shown to somewhat lower temperatures than can be or were fit by the model.
Fig. 3. Molar magnetic susceptibility (left vertical) and its inverse (right vertical) vs temperature for CoBr2•H2O. Curves through data are a fit based on ground and excited Kramers doublets with a mean-field correction for exchange interactions, described in text.
these two, even though located at substantially higher temperatures than for the dihydrate. Estimates of Tmax and χmax appear in Table 1. Noteworthy is that the maximum susceptibility for the bromide dihydrate occurs at a much lower temperature, 9.5 K, than for the isomorphous chloride dihydrate, 17.5 K [12]. The maximum susceptibility in the bromide is 60% larger than in the chloride, consistent with lesser Tmax, hence weaker antiferromagnetic interactions. Maximum susceptibility values for the two singly hydrated forms in Fig. 6 are approximately four times larger than for chloride dihydrate, even though their Tmax are only slightly lower than for the chloride. The location of an inflection point (maximum dχ/dT) on the low temperature side of the maximum can be estimated. Although polycrystalline data are less ideal than easy axis single crystal data, such a feature can be taken as signaling an antiferromagnetic transition [17]. Such Tc estimates also appear in Table 1. The ratio Tc/Tmax is 0.95, 0.89
tropic dependent on detailed distortions, energy separations and other factors. This also justifies the large fitted g values, Ising like, of both ground and first excited doublet. That the present phenomenological model fits the data quite well over a rather broad temperature range, and involves a plausible minimum number of parameters, is attractive. 3.1.2. Low temperature data The molar magnetic susceptibilities at low temperatures appear in Figs. 5 and 6. That for CoBr2•2H2O also shows a fit employing a threedimensional s.c. Ising model, to be described. For each singly hydrated compound no plausible fit with any model was achievable. This is because of the unusually large size of the susceptibility maxima for 160
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Fig. 8. Molar magnetization vs applied field for CoBr2•H2O at various temperatures. For clarity vertical shifts of 1.2, 1.8 and 2.4×103 emu/mol are applied for successively higher temperatures. Closed symbols are for decreasing field.
Fig. 6. Molar magnetic susceptibilities vs temperature for CoBr2•H2O (small circles) and CoBr2•D2O (triangles).
and 0.89 in the same order as above. The first, well above 0.90, is characteristic of systems where exchange interactions operate with comparable strength in three spatial dimensions (3D magnetically). The latter two are slightly below the characteristic 3D range, but not low enough to imply typical low dimensional magnetic behavior, i.e., 2D (layered) or 1D (chain). For temperatures in the vicinity of the susceptibility maximum in CoBr2•2H2O only a 3D Ising model [18] yielded a plausible fit. The best fit obtained is shown in Fig. 3, with g =6.012 and J/k=−3.17 K. It is over the 9–25 K range (from just below Tmax but not below Tc to 2.5 times Tmax, as done by us for other systems), with rms deviation of 2.4%. It is approximate since powder data are being fitted. Fit parameters are only weakly sensitive to the choice of fitting range. The exchange interaction reproduces the observed Tmax very well, and the g value is typical of an isolated ground Kramers doublet with S´= ½. With z=6 for the s.c. 3D Ising model applied, substitution into Eq. (3) yields −9.5 K, agreeing very well with the observed θ.
Fig. 9. Molar magnetization vs applied field for CoBr2•D2O at various temperatures. For clarity vertical shifts of 1, 2 and 3×103 emu/mol are applied for successively higher temperatures. Closed symbols are for decreasing field.
3.2. Magnetization
hydrated systems. Their appearance must be influenced, of course, by the much lower Tmax and Tc of the dihydrate. Modest hysteresis is evident for the three temperatures below Tc in CoBr2•2H2O. Significant convex upward curvature appears in the 8.08 K isotherm, slightly below the estimated Tc =9.0 K, and small hysteresis. This contrasts with the linear behavior without hysteresis at 12.00 K, above Tc. For the two lowest temperatures in Fig. 7a field induced transition is evident near 13.5 kG, with somewhat larger hysteresis than at 8.08 K. This result is close to that reported previously [11]. The highest temperature isotherms in Figs. 8 and 9, taken slightly above the estimated Tc for these compounds, exhibit a clear S-shape; hysteresis is negligible. For the next lowest temperatures, modestly below the Tc estimates, curvature changes are stronger, though hysteresis remains small to negligible. In each of Figs. 8 and 9 the approximately 8 K and 4.2 K isotherms suggest field-induced transitions, with significant hysteresis evident. Approximate locations of these are at 5.5 and 6.0 kG for the H2O system, increasing slightly with decreasing temperature; and 5.0 and 5.5 kG for the D2O compound, about 10% smaller values than for H2O. At 1.843 K for CoBr2·H2O, Fig. 10, the transition is estimated to occur at 6.5 kG, with notably enhanced hysteresis. Quite similar behavior occurred for the D2O system at 1.8 K. Both here and at the higher 4.236 K in Fig. 8a small residual magnetization persists on lowering the applied field to zero value; it is approximately 455 and 85 emu/mol (0.082 and 0.015 µB/ ion) at these two temperatures respectively. A barely detectable residual value of 5 emu/mol occurs for 8.04 K. In weakly anisotropic antiferromagnets (as for Mn(II) compounds) a spin flop transition occurs for temperatures below Tc. In a randomly
In Figs. 7, 8 and 9 appear the molar magnetization for each compound for a range of temperatures. The contrast in general behavior for dihydrate versus monohydrate and monodeuterate is striking. The latter two are quite similar in appearance, though not identical. Slightly larger magnetization for comparable field and temperature occurs for the D2O than for the H2O compound. Magnetization values for the 2H2O compound are several times smaller, and isotherm shapes quite different from those of the singly
Fig. 7. Molar magnetization vs applied field for CoBr2•2H2O at various temperatures. For clarity vertical shifts of 150, 250 and 350 emu/mol are applied for successively higher temperatures. Closed symbols are for decreasing field.
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hydrated compounds are of course suggestive of metamagnetism as well. Substituting the estimated critical field of 6.5 kG for CoBr2·H2O at 1.843 K, and assuming the same, and plausible, g =6.0 as for dihydrate, yields z´J´/k=−2.62 K. The smaller value is in line with prior findings that interchain exchange is generally weaker in monohydrates than in corresponding dihydrates. The metamagnetic scenario is more plausible. 3.3. Thermoremanent magnetization Instrumental limitations prevented extensive study of irreversibility effects as for CoCl2•H2O previously [15]. One indicator of such is the presence and decay of a thermoremanent magnetization (TRM). This is measured on cooling a sample in fixed applied field from a temperature in the paramagnetic regime to a desired measuring temperature, typically below a spin glass [19] or other transition associated with disorder. The applied field is quickly decreased to zero and any residual magnetization followed in time. For conventional equilibrium ordered magnetic systems the TRM is nil. For nonequilibrium magnetic systems, spin glasses especially, substantial residual magnetization exists and shows significant time dependence. The TRM for the cobalt monohydrate at 1.84 K after field cooling in 500 G is shown in Fig. 11. Probably the most commonly observed form for the TRM decay is a stretched exponential,
Fig. 10. M magnetization vs applied field at a lowest 1.843 K for CoBr2•H2O; closed symbols are for decreasing field.
oriented polycrystalline sample such appear as an inflection in M(H), rather than the sharp increase if measuring along the easy axis. The spin flop field at 0 K is expressible in terms of effective exchange and anisotropy fields in a mean-field approach as [1,2]
HSF (0) = [2HE HA –HA2]1/2
(4)
HE = 2z J S / gμB
(5)
MTRM (t ) = M0 exp [−(t / τ )n ].
HA = 2 D (S –½)/ gμB
(6)
The time constant τ is characteristic of a particular material, while the exponent n (not unity) assumes values which tend to be characteristic of the class of glassy system involved. For spin glasses n values near or somewhat above 1/3 are typical. The curve in Fig. 11 is a fit using Eq. (8), with M0 =7.40 emu/mol, τ=7.74×105 s, and n =0.403. The size of the TRM is rather similar to that of the chloride monohydrate for closely similar cooling field and measuring temperature [15]. The relaxation parameters τ and n differ only moderately from chloride values.
Here J is the main intrasublattice antiferromagnetic exchange interaction and D is the anisotropy constant in the standard zero-field splitting Hamiltonian ĤZFS=D[Ŝz2 – S(S+1)/3]. However, in Co(II) compounds where anisotropy is usually strong, field induced transitions in ordered antiferromagnets are often metamagnetic in character. Mean field theory yields an expression for the metamagnetic critical field Hc=AM, where M is the sublattice magnetization N0gµBS/2 and A is a mean field coefficient given by 4z´|J´|/ N0g2µB2, with z´ and J´ the number of neighbors and antiferromagnetic interaction between ferromagnetically aligned sublattices (the standard metamagnetic scenario). These are often layers, and J´ an interlayer interaction. For the present systems, the properties of CoCl2· 2H2O suggest that the sublattices are arrays of ferromagnetic chains, one set oppositely directed from the other. In this case Jʹ is an interchain interaction. The above equations yield for the metamagnetic critical field
Hc = 2z′ J ′ S / gμB.
(8)
4. Discussion 4.1. Magnetic comparisons Certain relations connecting the ordering temperature and other quantities can be applied. The theoretical ratio Tc/|J/k| (in the present exchange interaction convention) ranges from 0.759 to 1.821 for various spin-1/2 2D Ising models, and from 1.352 to 4.898 for spin1/2 3D Ising models [20]. A range of experimental values [1] is from 1.10 to 1.28 for the former, and from 1.36 to 2.34 for the latter case. For CoBr2•2H2O here, using the ordering temperature and fitted J, the
(7)
The susceptibility of the dihydrate compound has a more typical appearance for an antiferromagnet than for the H2O and D2O systems, and the fit in Section 3.1.2. gives an estimate of the exchange interaction. We compare application of the above two interpretations. Substitution of the 3D Ising model fit parameters into Eq. (5) yields HE =47.1 kG. Employing this in Eq. (4), taking 13.5 kG as close enough to a 0 K value since 1.8 K is far below Tc, gives HA =1.94 kG. This is plausible for a Co(II) system. Examples are few; for CoBr2·6H2O an HA of 1.0 kG was reported [1]. With effective S´= ½ Eq. (6) does not apply, and no zero field splitting occurs. The anomalously large susceptibilities of the singly hydrated compounds cannot be fit by any standard model, but from the much larger Tmax a larger exchange interaction, hence also HE, is implied. Yet observed critical fields are less than half that of the dihydrate. The anisotropy field HA obtained on substitution is then substantially smaller. This seems implausible since the coordination geometry in singly hydrated systems must be less symmetrical. From this perspective a spin flop interpretation appears dubious. Substituting into Eq. (7) the same 13.5 kG critical field value and g =6.012 from the susceptibility fit yields z´J´/k=−5.45 K. The sharpness and large hysteresis of the field induced transitions in the singly
Fig. 11. Thermoremanent magnetization (TRM) for CoBr2•H2O at 1.843 K after field cooling in 500 G. The fitted curve is a stretched exponential form described in text.
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polarizability of the bromide ion should increase the size of superexchange interactions involving it. Arguably, this is less significant than larger lattice separations in bromide systems, which might be expected to decrease interaction strengths. Lattice parameter variations from chloride to bromide differ only very slightly for the manganese and cobalt systems. The volume per formula unit for MnCl2•2H2O and MnBr2•2H2O is 119.0 and 134.2 Å3 respectively, a difference of 15.2 Å3 or 12.8% [23]. For CoCl2•2H2O and CoBr2•2H2O the values are 109.6 and 124.9 Å3, for a difference of 15.3 Å3 or 14.0% [23]. The smaller cobalt than manganese volumes are consistent with tabulated ionic radii [24]. A more detailed comparison can be made. Lattice parameters for CoBr2•2H2O are from 2.3% to 5.9% larger than for isomorphous CoCl2•2H2O; in detail, the monoclinic b axis is 0.195 Å larger in the bromide, or 2.3%; the c axis is 0.211 Å larger, or 5.9%; and the a axis is 0.374 Å larger, or 5.2%. Oxygen-oxygen contacts occur along b; the MX2MX2M… chain direction is along c; halide-halide contacts also occur along a. The smallest enhancement, relatively and absolutely, is along b where halide-halide contacts are expected to matter least. The rms lattice parameter enhancement from chloride to bromide is 0.272 Å over all three axes, or if restricting to the ac plane where bromides reside, 0.304 Ǻ. A standard compilation [24] gives ionic radii as 1.67 and 1.82 Å for Cl- and Br-, respectively. It is plausible to expect average distances determined by Br-Br contacts to be 0.30 Å larger than for Cl-Cl contacts, that is by twice the ionic radius difference. This is the same as the second rms estimate above. Thus lattice parameter enhancements are in line with ionic radius expectations. Along the c (chemical chain) axis the expansion is less than twice the radius difference, while along a it is more. In neither direction are the Br-Br overlaps along their internuclear separation. Plausible is that along the a axis there is an exchange interaction reduction from chloride to bromide while along the c axis enhancement occurs. It is very difficult to predict what the net outcome will be. Certain unexpected findings emerge from a comparison of the previously studied chloride dihydrate and monohydrate and the bromide counterparts here. As already noted, the diminution in Tmax and Tc from chloride to bromide dihydrate is extraordinary. Atypical to begin with for chloride-bromide counterparts, the nearly factor of two reduction is larger than for any other such pair. Not less surprising, instead of the modest reduction in the above two characteristic temperatures seen from chloride dihydrate to monohydrate, for the corresponding bromides a major increase occurs. Yet the general behavior including major hysteretic effects and irreversibility is quite similar in CoCl2•H2O and CoBr2•H2O, and Tmax and Tc differ only slightly. Previous estimates of the ferromagnetic intrachain interaction in the chloride and bromide dihydrates have been rather indirect [9]; the former is estimated to be J/k=9.3 K and the latter 6.0 K. The reduction is opposite in sense to that of the separation argument in the previous paragraph, presumably too naïve. In any case, if significantly weaker intrachain and interchain interactions characterize the bromide dihydrate, yielding the significantly smaller Tmax and Tc, it is striking that hardly any such effects distinguish the chloride and bromide monohydrates. Also intriguing is the relationship among metamagntic critical fields in the four materials. The reduction from 31.6 to 4.5 kG in chloride dihydrate and monohydrate respectively reflects a general weakening of antiferromagnetic exchange between ferromagnetically coupled chains. However, there occurs both intrachain and interchain structural reorganization on passing from dihydrate to monohydrate [5]. Single crystal work in multi-Tesla fields revealed a complicated situation in CoCl2•2H2O [11] with the difference between two antiferromagnetic interchain interactions determining the observed 31 kG transition. It is plausible that an analogous phenomenon determines the 4.5 kG transition in CoCl2•H2O; the altered crystal structure (relative to dihydrate) admits at least two different significant interchain interactions. Neither single crystal nor sufficiently high field data are available
ratio is 2.84, evidently more 3D-like. Since the J value is from a fit employing a 3D model, it may be preferable to compare with a ratio involving only observed quantities. For several spin-1/2 2D and 3D Ising compounds the experimental ratio Tc/|θ| has been tabulated. It ranges from 0.55 to 0.64 for the former and from 0.62 to 0.79 for the latter [1]. For CoBr2•2H2O here the ratio is 0.91, much above 2D values. Comparisons with magnetic behavior in related materials can be made. As already noted, CoBr2•2H2O is isomorphous [7] with MnBr2•2H2O, both also isomorphous with the corresponding chlorides. Our report [4] on various manganese bromide hydrates revealed that antiferromagnetic MnBr2•2H2O is characterized by Tmax and Tc values moderately lower (14% and 12% respectively) than those of the chloride dihydrate. Comparable decreases appeared for nickel bromide dihydrates relative to chloride counterparts [6]. Such changes are in contrast to the trend [1,2] for the great majority of bromide-chloride pairs, as reviewed by us [4], where the bromide displays higher Tmax and Tc. For cobalt dihydrates reductions in these quantities are a remarkable 46% and 48% from chloride to bromide. To a much lesser degree the above finding regarding bromide vs chloride characteristic temperatures extends to the singly hydrated forms. For each of CoBr2•H2O and CoBr2•D2O, Tmax and Tc values in Table 1 are smaller than for corresponding chlorides [5], and as for chlorides virtually indistinguishable. Bromide Tmax values are 4–5% smaller than for corresponding chlorides, and Tc values 8–9% smaller. For nickel monohydrate compounds it was also found that bromide Tmax and Tc were moderately less than for corresponding chlorides [6]. There are interesting similarities and differences between magnetization isotherms obtained here for CoBr2•H2O and CoBr2•D2O and for the corresponding chlorides previously [5,14]; for either halide behaviors for H2O and D2O containing systems are virtually identical. The temperatures of enhanced susceptibility maxima in chloride and bromide monohydrates (D2O and H2O forms essentially indistinguishable) differ by only 5%, 16.2 and 15.4 K respectively. But the metamagnetic critical field at 2 K is significantly higher in the bromide, 6.5 kG, than in the chloride, 4.5 kG. For both chloride and bromide the substantial hysteresis is markedly enhanced between 4.2 and 2 K. Interestingly, the shape of M(H) on decreasing the applied field toward zero differs significantly between chloride and bromide. Also, in the chloride the 2 K residual magnetization is about twice as large as the 455 emu/mol seen here for the bromide. These differences between chloride and bromide monohydrates contrast markedly with dihydrate properties. For the bromide dihydrate Tmax is not slightly smaller but almost a factor of two smaller than for the chloride dihydrate. And the metamagnetic critical field of 13.5 kG for bromide is less than half as large as the 31.6 kG of the chloride [11]. Nevertheless, these fields are much larger than in the monohydrates. An explanation for the small reductions in Tmax and Tc for each cobalt halide monohydrate relative to dihydrate suggests itself. Ferromagnetic intrachain exchange along a Co-X-X-Co pathway is virtually the same in the two forms. This was demonstrated for MnCl2•H2O [21,22] vs MnCl2•2H2O, despite structural changes in the MnCl2MnCl2Mn… chains [5]; in these systems intrachain exchange is antiferromagnetic. The same structural relations hold for the corresponding cobalt systems. Weakened interchain antiferromagnetic interactions in monohydrates are evident from reduced metamagnetic critical fields and enhanced susceptibility maxima. But ferromagnetic intrachain exchange dominates ordering properties, and so characteristic temperatures are only modestly reduced. 4.2. Overview and conclusions The reductions in Tmax and Tc for bromide counterparts of chloride compounds (seen here for cobalt but also previously for manganese [4] and nickel [6]) are contrary to the expectation that the greater 163
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Chemistry Program, DMR-NSF. (grant number 0085662) and from the Donors of the American Chemical Society Petroleum Research Fund (grant number 43296-B10). He has also benefitted from a Plumeri Faculty Award from the College of William and Mary.
to permit detailed analysis. Since the four manganese or cobalt, chloride or bromide, dihydrates are isomorphous, it is likely from the similarity in susceptibility, magnetization and TRM of CoBr2•H2O relative to CoCl2•H2O that it shares the latter's crystal structure. For the chloride and bromide dihydrate pair, and the monohydrate pair, the same two (different) structures are involved. Thus the seven-fold reduction in Hc for the chloride forms becoming merely two-fold between CoBr2•2H2O and CoBr2•H2O can be understood as an accidental result of increased cancellation in a difference between two interchain antiferromagnetic interactions in the bromide monohydrate. A review of the limited literature concerning the effect of deuteration on the magnetic properties of transition metal complexes with waters of hydration has appeared [5]. Modest but larger than expected differences between Tmax and Tc for MnCl2•H2O and MnCl2•D2O were seen. Such were also found for MnBr2•H2O and MnBr2•D2O [4], though with differences in detail from chlorides. MnCl2•H2O and MnCl2•D2O were found to be isostructural [5], with only minute lattice parameter differences; hence magnetic differences cannot be attributed to structural differences. Replacing H2O by D2O in nickel chlorides and bromides, both dihydrate and monohydrate forms, also produced significant magnetic differences [6]. For CoBr2•H2O and CoBr2•D2O the negligible difference in Tmax and Tc can be considered more typical. Structural or even only unit cell determinations for corresponding H2O and D2O containing compound are rare. From CuCl2•2H2O to CuCl2•2D2O the unit cell volume increases by 1.6%, without structural change [25]. For α-CoC2O4•2H2O and α-CoC2O4•2D2O the increase is 0.7% on deuteration, also with the same structure [26]. Although the unit cell of MnBr2•2D2O differs [4] from that of MnBr2•2H2O, a similar increase in volume per formula unit appears as in these earlier examples. A substantial change in magnetic behavior resulted from the structural change. In the case of NiBr2•2D2O [6], also with a structural change relative to NiBr2•2H2O, the volume per formula unit again increases slightly. A variation in magnetic behavior, less pronounced than for the manganese systems but significant, also appears.
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