Spin canting and exchange in the two-dimensional antiferromagnets (C3H7NH3)2 and (C3H7NH3)2MnBr4

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<ul><li><p>Physica 98B (1979) 53-59 North-Holland Publishing Company </p><p>SPIN CANTING AND EXCHANGE IN THE TWO-DIMENSIONAL ANTIFERROMAGNETS (C3H7NH3)2MnCI4 AND (C3H7NH3)2MnBr 4 </p><p>H. A. GROENENDIJK and A. J. van DUYNEVELDT Kamerlingh Onnes Laboratorium der Ri/ksuniversiteit Leiden, Leiden, The Netherlands </p><p>and </p><p>R. D. WILLETT Department of Chemistry, Washington State University, Pullmann, Washington 99164, U.S.A. </p><p>(Commun. Kamerlingh Onnes Lab., No. 440c) </p><p>Received 3 July 1979 </p><p>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. </p><p>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. </p><p>1. Introduction </p><p>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 ]. </p><p>The structure of the bis(propylammonium)tetra- chloromanganate(II), PA2MnC14, has been determined at room temperature by Peterson and Willett [2]. 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 </p><p>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 [3]. 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 [4]. 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. </p><p>Measurements of the a.c. susceptibility on a pow- dered sample of PA2MnC14 by Gerstein et al. [5] showed a sharp peak at To, which is an indication of the occurrence of spin canting. From susceptibility measurements on a single crystal [6], it was found that, below Tc, the spins are oriented predominantly </p><p>53 </p></li><li><p>54 H. A. Groenendijk et aL /Spin canting and exchange in two-dimensional antiferromagnets </p><p>c r </p><p>(il Mn 0 CL </p><p>N </p><p> C </p><p>Fig. 1. Three-dimensional view of the crystal structure of (C3HTNHa)2MnC14 after [2]. 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. </p><p>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. </p><p>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. </p><p>2. Experimental results </p><p>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. </p><p>To measure the susceptibility we used a mutual inductance technique in the temperature range from 1 </p><p>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. </p><p>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. </p><p>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 [20]. This constitutes a correc- tion of about 1% to the susceptibility. </p><p>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 [6] where we present the susceptibility measurements on a single crystal of PA2MnC14. </p><p>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&lt; 10 K. There is no peak due to weak ferromagnetism, so T c is obtained from the temperature where do/dT is maximal [7]. Here we should like to remark that the </p></li><li><p>H. A. Groenendi/k et al./Spin canting and exchange in two-dimensional antiferromagnets </p><p>emu/mole 2.5 </p><p>xlO -2 </p><p>2.0 </p><p>1.5 </p><p>i I r I I </p><p>0 </p><p>1.0 </p><p>0.5~- I I J I I T 100 200 K 300 </p><p>55 </p><p>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. </p><p>emulmole 2.,5 </p><p>x 1'0 -2 </p><p>2.0 </p><p>1.5 </p><p>i I ~ I r </p><p>~ o o 0 </p><p>1.0 </p><p>o.~ I ~ I 1 O0 200 K 300 T </p><p>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. </p></li><li><p>56 H. A. Groenendifk et aL /Spin canting and exchange in two-dimensional antiferromagnets </p><p>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. </p><p>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 [6], 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. </p><p>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. </p><p>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 [8]. 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 [9] </p><p>1 (O)-l+~a 1 S (2 + a)zSJ (1) </p><p>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. [10]. </p><p>The quantity e(a) is nearly independent of a [11 ], so we used the value e(0) = 0.632 given by Keffer [9]. 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. </p><p>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). </p><p>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). </p><p>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 &lt; T&lt; 110 K). The values forJ/k given in table I per- tain to this temperature range. A variation of J with </p><p>Table I Experimental values of the exchange constant, critical temperature and anisotropy </p><p>Compound T c (K) J/k at T= 80K </p><p>= HA/HE </p><p>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 </p></li><li><p>H. A. Groenendijk et aL /Spin canting and exchange in two-dimensional antiferromagnets 57 </p><p>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. </p><p>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 [3]. 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 [3]. 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. </p><p>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 [12] and by Gerstein et al. [13]. </p><p>3. Discussion </p><p>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 </p><p>distance becomes much smaller now, it changes from 5.23 A to 4.15 A, while the exchange is hardly differ- ent (table II...</p></li></ul>

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