Spin canting and exchange in the two-dimensional antiferromagnets (C3H7NH3)2 and (C3H7NH3)2MnBr4
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Physica 98B (1979) 53-59 North-Holland Publishing Company
SPIN CANTING AND EXCHANGE IN THE TWO-DIMENSIONAL ANTIFERROMAGNETS (C3H7NH3)2MnCI4 AND (C3H7NH3)2MnBr 4
H. A. GROENENDIJK and A. J. van DUYNEVELDT Kamerlingh Onnes Laboratorium der Ri/ksuniversiteit Leiden, Leiden, The Netherlands
R. D. WILLETT Department of Chemistry, Washington State University, Pullmann, Washington 99164, U.S.A.
(Commun. Kamerlingh Onnes Lab., No. 440c)
Received 3 July 1979
The compounds (C3H7NH3)2MnC14 and (C3H7NHa)2MnBr 4 axe good approximations of the two-dimensional quad- ratic Heisenberg antfferromagnet. From measurements of the magnetic susceptibility the exchange constants at 80 K have been obtained, J/k = -4.45(5) K and -4.50(5) K, respectively. These exchange constants axe compared with theoretical results for the Mn-X-Mn superexchange path. A slight temperature dependence of J is observed, resulting in values which are about 5% lower at 300 K.
The chloride is found to show weak ferromagnetism below T e = 39.2(2) K, which is ascribed to an antisymmetric ex- change term. The canting angle of the spins is only 0.05 . The bromide compound orders at 47(3) K but shows no sign of weak ferromagnetism.
In recent years there is much interest in the static as well as in the dynamic properties of magnetic systems showing lower dimensional behaviour. Com- pounds with the general formula (C n H2n+INH3)2MX 4 with M = Cu, Mn, Fe and X = C1, Br crystallize in layer structures and form good examples of 2-dimensional magnets. The copper compounds of this series show ferromagnetic interactions while the iron and manga- nese salts are antiferromagnets [1 ].
The structure of the bis(propylammonium)tetra- chloromanganate(II), PA2MnC14, has been determined at room temperature by Peterson and Willett . The unit cell is shown in fig. 1. The crystals are ortho- rhombic w i tha = 7.29 A, b = 25.94 A, and c = 7.51 A, space group Cmca. Each Mn 2+ ion is coupled to its four nearest magnetic neighbours in the a-c plane via a Mn-C1-Mn superexchange path. The corner sharing MnC16 octahedra are canted alternatingly towards the
c and ~ direction, the angle with the b axis being 8 . The manganese compounds show many structural phase transitions that have been studied extensively; these transitions change the structure only in a minor way . Due to the large separation of the layers and the nearly tetragonal symmetry the dipolar part of the interlayer interaction is very small; this interaction was estimated as about 10 -5 times the intralayer coupling . The superexchange interaction between the layers is expected to be even smaller because of the many intervening nonmagnetic atoms. The detailed structure of~PA2MnBr 4 is not yet known but there is no reason to assume that it differs much from that of the chloride.
Measurements of the a.c. susceptibility on a pow- dered sample of PA2MnC14 by Gerstein et al.  showed a sharp peak at To, which is an indication of the occurrence of spin canting. From susceptibility measurements on a single crystal , it was found that, below Tc, the spins are oriented predominantly
54 H. A. Groenendijk et aL /Spin canting and exchange in two-dimensional antiferromagnets
(il Mn 0 CL
Fig. 1. Three-dimensional view of the crystal structure of (C3HTNHa)2MnC14 after . Only half a unit cell has been drawn. The canted MnC16 octahedra form a two-dimensional network in the a-c plane. For clarity only three of the propyl- ammonium groups are drawn.
along the b axis, thus perpendicular to the layers. The weak ferromagnetic moment, due to canting of the antiferromagnetic sublattices, occurs along the c axis.
In this paper we will discuss the susceptibility measurements on powdered samples of both PA2MnC14 and PA2MnBr 4. The exchange constant J and the aniso- tropy are derived from the measurements. A discussion of a possible temperature dependence of J and the origin of the weak ferromagnetic moment will be given. A comparison will also be made between our results for J and recent calculations for the 180 Mn- X-Mn (X = F, C1, Br) superexchange path.
2. Experimental results
The samples have been prepared by slow evapora- tion of a solution of propylammoniumchloride (or bromide) and manganese chloride (bromide) in ethanol. In this way both single crystals and powders could be prepared. The bromide was found to be very hygroscopic.
To measure the susceptibility we used a mutual inductance technique in the temperature range from 1
to 200 K. Static magnetic fields up to 50 kOe could be applied parallel to the a.c. field. Additional data of the magnetization were obtained with a Faraday balance and a vibrating sample magnetometer.
The magnetic susceptibility of a powdered sample of PA2MnC14 is plotted versus temperature in fig. 2. The data at low temperatures (o) were obtained in zero external magnetic field with the mutual induct- ance technique while those at higher temperatures (e) were measured with the Faraday balance using a field strength of 5 kOe. Both sets of data, which were obtained on the same sample, are seen to agree well.
The susceptibility has been corrected for a diamag- netic contribution of 2.1 10 -4 emu/mole, which has been estimated from the known susceptibilities of dia- magnetic compounds . This constitutes a correc- tion of about 1% to the susceptibility.
The broad maximum in the X0 versus T curve at about 80 K confirms the expected two-dimensional magnetic properties. An interesting feature is the very sharp peak in the zero-field susceptibility. The peak is much higher than shown in the figure, it reaches a value of 7.5 X 10 -2 emu/mole. The peak also makes it possible to determine the three-dimensional ordering temperature accurately; T c = 39.2(2) K. What is plotted in fig. 2 is the real part, X', of the complex sus- ceptibility. We mention that, at Tc, a peak was also measured in the imaginary part, X", whereas this quan- tity was zero at all other temperatures. We ascribe the peak in the susceptibility to the occurrence of the weak ferromagnetic moment below T c. The details of this discussion will be given in a following paper  where we present the susceptibility measurements on a single crystal of PA2MnC14.
The susceptibility of a powdered sample of PA2MnBr 4 was measured with the magnetometer using a field strength of 5 kOe and is plotted in fig. 3 (open circles). These measurements have been corrected for a diamagnetic contribution of 2.3 10 -4 emu/mole. The susceptibility of the bromide is similar to that of the chloride as far as the broad maximum is concerned. The susceptibility shown in fig. 3 increases below 20 K due to paramagnetic (manganese) impurities which will affect the susceptibility at low temperatures. A similar, but smaller increase is seen in fig. 2 for T< 10 K. There is no peak due to weak ferromagnetism, so T c is obtained from the temperature where do/dT is maximal . Here we should like to remark that the
H. A. Groenendi/k et al./Spin canting and exchange in two-dimensional antiferromagnets
i I r I I
0.5~- I I J I I T 100 200 K 300
Fig. 2. The susceptibility versus temperature for a powdered sample of PA2MnCI 4. o: a.c. susceptibility measurements; e: suscept- ibilities obtained with the Faraday balance. Drawn line: susceptibility calculated for the 2-d quadratic Heisenberg antiferromagnet with S = 5/2 and J/k = -4.45 K.
x 1'0 -2
i I ~ I r
~ o o 0
o.~ I ~ I 1 O0 200 K 300 T
Fig. 3. Susceptibi l i ty versus temperature for a powdered sample o f PA2MnBr 4. o: exper imental data obtained with a vibrating sample magnetometer; e: susceptibi l i ty corrected for paramagnetic impurities. Drawn line: susceptibi l i ty calculated for the 2-d quadratic Heisenberg antfferromagnet with S = 5/2 and J/k = -4 .50 K.
56 H. A. Groenendifk et aL /Spin canting and exchange in two-dimensional antiferromagnets
presence of a weak ferromagnetic moment cannot be deduced from magnetization measurements in high magnetic fields, because a small ferromagnetic moment will give a negligible contribution to the total mag- netization below T c. However, the occurrence of even a very small moment at H = 0 will have a drastic influ- ence on the a.c. susceptibility, and therefore we have also measured the susceptibility of the bromide using the a.c. technique in zero field. We do not give the results in fig. 3, as we did not detect a peak in either X' or X", which means that PA2MnBr 4 is not a weak ferromagnet, in contrast to the chloride.
In the following we will also need the value of the spin-flop field HSF. This field value was obtained from a measurement of the a.c. susceptibility as a function of external magnetic field at a temperature of 1.2 K. For the PA2MnC14 we used a stack of small single crystals oriented with the b axis, which is the easy axis , parallel to the magnetic field. A rather broad but clear peak was observed at a field value of 16.3(2) kOe, which we identify with HSF.
To determine the spin-flop field of PA2MnBr 4 we used a powdered sample; HSF was now indicated by a small peak in the susceptibility at a field strength of 29.0(3) kOe.
In order to derive the exchange constant J from the experimental data, the impurity contribution has to be subtracted from the measured susceptibilities. To do this we first compared the raw data with the theoretical x(T) curve as calculated by Navarro for the S = 5/2 Heisenberg quadratic layer antiferromagnet . This yields a first estimate for J. Then the susceptibility at T--- 0 K is calculated from the prediction for the per- pendicular susceptibility from spin wave theory 
1 (O)-l+~a 1 S (2 + a)zSJ (1)
In this equation X 0 = Ng2ll2/4zlJI is the molecular field prediction for the perpendicular susceptibility of an antiferromagnet at T = 0 K and z is the number of nearest neighbours, a is the anisotropy parameter which was calculated from the spin-fiop field by using the relation: H2F = 2a//2, where H E = 2zJS/gtl B is the exchange field. AS(a) and e(a) are corrections arising from the effects of zero-point spin deviations. We used the values of AS(a) calculated by Colpa et al. .
The quantity e(a) is nearly independent of a [11 ], so we used the value e(0) = 0.632 given by Keffer . The susceptibility of a powder (1/3 1 + 2/3 X) at T = 0 K can now be calculated with eq. (1) because Xll(0) = 0. The result is subtracted from the experi- mental data at low temperatures and this yields the impurity contribution to the susceptibility, Xi. This impurity contribution is fitted to a relation of the form: i = Ci/(T- 0i) in order to enable a correction over the whole measured temperature range. The so- corrected susceptibility is compared to the theoretical x(T) curve and a better estimate for J/k is obtained. The whole procedure can be repeated if necessary.
The calculated powder susceptibility at T = 0 K for PA2MnC14 is found to be 1.23 X 10 -2 emu/mole, which is only slightly below the measured value. This means that only about 0.1% of the Mn 2+ ions are present as paramagnetic impurities. As a consequence the correction for the impurities becomes negligible above 50 K. The resulting values of J/k and a are -4.45(5) K and 3.0 10 -4, respectively (see table I).
The amount of paramagnetic impurities present in our PA2MnBr 4 sample is clearly much larger (fig. 3). The corrected values for X, obtained in the way des- cribed above, are plotted as closed circles in this figure. The estimated impurity content is about 0.9%. The resulting parameters are: J/k = -4.50(5) K and a = 9.4 X 10 -4 (table I).
In the above analysis it proved to be impossible to fit the corrected susceptibility data to the theoretical curve over the whole temperature range from 50 K to 300 K with a single value for J/k, within the accuracy of the measurements (~ 1%). The fits, shown by the drawn lines in figs. 2 and 3, have been made to the data in the temperature range of the maximum (50 K < T< 110 K). The values forJ/k given in table I per- tain to this temperature range. A variation of J with
Table I Experimental values of the exchange constant, critical temperature and anisotropy
Compound T c (K) J/k at T= 80K
PA2MnC14 39.2(2) -4.45(5) 3.0 X 10 -4 EA2MnC14 43.1(2) -4.60(5) 10 X 10 -4 MA2MnC14 45.3(5) -5.0(2) 11 X 10 -4 PA2MnBr 4 47(3) -4.50(5) 9.4 10 -4
H. A. Groenendijk et aL /Spin canting and exchange in two-dimensional antiferromagnets 57
temperature is also seen for some other two dimen- sional antiferromagnets [1 ] and may indicate a small decrease of J with increasing temperature, due to thermal expansion of the lattice. Comparing our sus- ceptibilities at high temperatures (300 K) with the theoretical prediction, we find a value of 4.2(1) K for J/k, for both PA2MnC14 and PA2MnBr 4.
As mentioned in the introduction, the compound PA2MnC14 shows several crystallographic phase transi- tions, two of them occurring in the temperature range where we performed susceptibility measurements, at 110 K and 165 K . To see whether these transi- tions can be detected in the susceptibility, we per- formed accurate measurements near these tempera- tures. No effect on the susceptibility was seen, a change of about 0.5% should have been detected. This is not surprising since the structural phase transitions are known to arise due to rearrangements in the propyl groups . This will affect only the small interlayer interaction while the susceptibility in this temperature range is determined by the strong superexchange coup- ling in the layers.
In addition to the results described above we have also measured the susceptibility versus temperature of a powdered sample of bis(ethylammonium)tetrachloro- manganate(II), EA2MnC14. The X0 versus T curve mea- sured with the a.c. technique shows a large peak at a temperature of T c = 43.1(2) K indicating that this compound is also a weak ferromagnet. The exchange constant around 80 K was found to be: J/k = -4.60(5) K, while at 300 K a value of -4.4(1) K resulted. From a measurement of X versus H the spin-flop field, HSF , was found at 31.0(3) kOe, yielding an anisotropy par- ameter a of 10 X 10 -4. These data have been included in table I together with those obtained for the methyl- ammonium salt: MA2MnC14 by Van Amstel and De Jongh  and by Gerstein et al. .
The exchange constant for PA2MnBr 4 reported above is the first experimental determination of the exchange via a 180 Mn-Br-Mn superexchange path. It is surprising that although the Mn-Mn distance is much larger than in the chloride, 5.56 against 5.23 A, the magnitude of the exchange is the same. A similar effect is seen when CI is replaced by F, the Mn-Mn
distance becomes much smaller now, it changes from 5.23 A to 4.15 A, while the exchange is hardly differ- ent (table II). The small change in J is related to the larger extension of the valence shell when e.g. C1 is replaced by Br, this leads to more overlap of the wave functions and thus an enhancement of the exchange . In table II the experimental values of J/k taken from room temperature data are compared with the exchange as calculated by De Jongh and Block on the basis of their effective electron model . The ex- change for the bromide has been calculated using a value of 0.62 a.u. for the parameter kBr,  which determines the effective extension of the various orbitals. The theoretical values are reasonably in accord with the experimental ones.
As mentioned in the experimental section a small decrease of J was found with increasing temperature. For both PA2MnC14 and PA2MnBr 4 we obtain the ratio: J(300 K)/J(80 K) = 0.94(4). From the measure- ments of Van Amstel and De Jongh on MA2MnC14 we deduce a ratio of 1.00(5) , for EA2MnC14 we found a ratio of 0.95(4). Using the dependence of the exchange on the distance between Mn ions, J = r -12 , and the lattice parameters for MA2-, EA 2- and PA2MnC14 which are known as a function of tempera- ture , the change in J caused by the lattice con- traction can be calculated. From this calculation we find the ratio J(300 K)/J(80 K) to be 0.91 for these salts. This result is in reasonable agreement with the experimentally determined temperature dependence of J. The temperature dependence of J was also cal- culated by Zaspel and Drumheller for compounds with general formula (CnH2n+INH3)2MX4 . By taking the thermal average of J using the vibrational states of an anharmonic oscillator these authors cal-
Table II Experimental and calculated values for J/k in some com- pounds with a 180 Mn-X-Mn superexchange path
Compound r(A) J/k (K) J/k (K) experimental calculated (at T= 300K) [14, 15]
K2MnF4 a 4 .15 -4.13(5) -4.2 PA2MnC14 5.23 -4.2(1) -4.0 PA2MnBr 4 5.56 -4.2(1) --3.7
a References to the experimental data can be found in ref. 14.
58 H. A. Groenendijk et al./Spin canting and exchange in two-dim ensional anti ferromagnets
culated a ratio of 0.66, which is much smaller than our measured values.
From our measurements we concluded that the compound PA2MnC14 is a weak ferromagnet with a small canting angle. Magnetization measurements on a single crystal at T = 4.2 K lead to a value of about 30 gauss/mole for the ferromagnetic moment . This small moment yields a canting angle of 3' = M(O)/M S = 8 10 -4 rad (0.05), M s being the saturation mag- netization.
The possible occurrence of canting of the spins depends on the symmetry of the crystal structure . In the case of PA2MnC14 there exists no center of symmetry between the manganese ions due to the tilting of the MnC16 octahedra, so that canting is allowed.
A canted spin arrangement may occur due to the presence of an antisymmetric coupling. Two possible causes for such a coupling are antisymmetric exchange and single-ion anisotropy . In the case of anti- symmetric exchange the hamiltonian contains a term of the form: 2Zdi/"[S i X Sj]. The order of magni- tude of this interaction is J(g - 2)/g, where J is the iso- tropic superexchange . From the g values along the a axis, determined from ESR measurements , we obtain: Idl = 2 10 -3 IJI. It is easy to show that the energy at T = 0 K will be minimal when the cant- ing angle 3' is equal to ~ Id/JI. Using the value of d obtained above, we find: 3' = 10 10 -4, which is close to the value of 8 10 -4 as deduced from the magnetization measurements.
We will now discuss the possible contribution of the anisotropy to the spin-canting. An important contri- bution to the total anisotropy arises from the dipolar interaction. The dipolar anisotropy field, HAD, that results from this interaction was calculated to be 1226 Oe for PA2MnC14 and is directed along the crystal b axis . The effective anisotropy field H A which is obtained from the measured value of a = HA/H E is: H A = 200 Oe. From the large difference existing between these two values it must be concluded that another, competing source of anisotropy is present, that lowers the net anisotropy. This competing source might well be the single-ion anisotropy. The related anisotropy field HAS must then be about 1000 Oe if this single-ion anisotr0py, caused by the zero-field splitting, is directed along the axis of the MnC16 octa- hedron, which is only 8 away from the b axis. This
anisotropy field corresponds with a zero-field splitting of  : D/k =H,ssgllB/4k ~ 4 X 10 -2 K, a reason- able value for Mn 2+ ions . The above description with competing anisotropies gives a reasonable explan- ation of the observed small effective anisotropy. This effective anisotropy field, H A = 3 X 10-4 HE is about a factor of ten smaller than the field resulting from the antisymmetric exchange: H d = 2 X 10-3 HE so the antisymmetric exchange dominates the spin canting in PA2MnC14.
For PA2MnBr 4 the dipolar anisotropy field was cal- culated to be 1072 Oe , also larger than the effec- tive anisotropy field obtained from the anisotropy par- ameter: H A = 630 Oe. This indicates that a zero-field splitting is present in this case too.
If canting were present in PA2MnBr 4, it is expected to be of the same order of magnitude as in the chloride. However, no peak occurs in the zero-field susceptibility and hence the bromide is not weakly ferromagnetic. A possible explanation for this would be the absence of a canting of the MnBr 6 octahedra. This is unlikely however, as there is no known example of a (CnH2n+I- NH3)2MX 4 salt without canting of the MX 6 octahedra in the low-temperature phase. Another explanation might be that spin canting exists but that the coupling between the layers is such that the moments in adja- cent layers are directed in opposite directions which leads to a situation of hidden canting. In this case also no ferromagnetic moment occurs below T c. Whether or not the MnBr 6 octahedra are canted will be known when the crystal structure is determined. It will be very difficult, however, to obtain direct evidence for hidden canting in this case as a small canting angle (a value of the order of 0.1 is expected) has virtually no influence on the susceptibility.
We would like to thank Prof. N. J. Poulis and Dr. L. J. de Jongh for their interest in the present work and D. W. Engelfriet for performing the measurements with the Faraday balance. We also thank Dr. F. H. M. Mischgofsky for providing us with a sample of PA2MnC14.
H. A. Groenendiik et aL /Spin canting and exchange in two-dimensional antiferromagnets 59
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