Heat capacity and thermodynamic properties of manganese monophosphide at temperatures from 5 K to 840 K: transitions

J. Chem. Thermodynamics 1998, 30, 117]127

Heat capacity and thermodynamic properties of manganese monophosphide at temperatures from 5 K to 840 K: transitions Svein Stølen, Fredrik Grønvold, a Haakon O. Haakonsen, Department of Chemistry, Uni¨ ersity of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway

Jadwiga T. Sipowska, b and Edgar F. Westrum, Jr. Department of Chemistry, Uni¨ ersity of Michigan, Ann Arbor, Michigan 48109, U.S.A.

The heat capacity of manganese monophosphide ŽMnP. has been determined by adiabatic shield calorimetry at temperatures from 5 K to 840 K. The heli- to ferromagnetic transition is noted only as a slightly enhanced heat capacity at T f 53 K. A l-type heat capacity contribution with maximum at T s 289.5 K is related to the transition from ferro- to paramagnetism in the compound. The clearly cooperative part of the transitional entropy is only 1.27 J . Ky1 . moly1 over the region T s 220 K to T s 400 K. Less cooperative magneticrelectronic contributions are present. The overall estimated transitional entropy amounts to 5.2 J . Ky1 moly1 at T s 800 K. Values of the thermodynamic properties at T s 298.15 K and T s 800 K are:

 Sm Ž T . y Sm Ž 0 . 4

 Ž Hm Ž T . y Hm Ž0. 4

K

C p, m y1 . . J K moly1

J . Ky1 . moly1

298.15 800

52.05 59.51

48.96 102.27

J . moly1 8406.8 35863.8

T

Q 1998 Academic Press Limited

KEYWORDS: manganese monophosphide; MnP; thermodynamic properties; transitions

1. Introduction Manganese monophosphide ŽMnP. is magnetically ordered below ambient temperature,Ž1 ] 4. with different types of ordering depending upon temperature, pressure, and magnetic field strength.Ž5 ] 8. Below Ttrs f 50 K, and in the absence of an external magnetic field, an antiferromagnetic double elliptical spiral,Ž9 ] 11. or a

To whom correspondence should be addressed. Present address: Department of Chemistry, University of Michigan-Flint, Flint, Michigan, 485022186, U.S.A. b

0021]9614r98r010117 q 11 $25.00r0rct970280

Q1998 Academic Press Limited

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bunching spiral,Ž12,13. spin structure exists. The magnetic properties are highly anisotropic and magnetic phase transformations are induced by application of a magnetic field. When applied in the b-axis direction the low-temperature spiral spin structure changes first to a fan structure for 0.48 F Ž HrMAmy1 . F 2.8, and then to a ferromagnetic structure.Ž5,6. The field necessary to maintain the latter structure decreases with increasing temperature and vanishes at the Curie temperature, TC s Ž290.59 " 0.02. K.Ž14. Other determinations are in the range T s Ž286 to 298. K.Ž2 ] 4,6,7,14 ] 18. In both ferro- and helimagnetic conditions the manganese atoms are in low-spin states with saturation moment f 1.3 m B Ž2,4,9,11. as derived from magnetization and neutron diffraction experiments Žor somewhat higher f 1.6 m B Ž10. .. The low magnetic moment is supported by theoretical calculations Ž19,20. leading to 1.2 m B . In the paramagnetic region effective magnetic moments in the range Ž2.6 to 3.7. m B were derived from magnetic susceptibility measurements,Ž1,4,21,22. i.e. considerably below the spin-only value 4.9 m B for Mn 3q. Heat capacity determinations have been made on MnP in the ferro- to paramagnetic transition region by Krasovskii and Fakidov,Ž16. and in a qualitative way by Whitmore.Ž15. Thermal expansivity Ž22,23. and compressibility Ž24. have also been determined in this temperature region. The low-temperature heat capacities for MnP in three differently ordered magnetic states have been measured by Takase et al.Ž25. Plots of values from T s Ž1.5 to 8.0. K were presented for the helimagnetically ordered phase in the absence of an external magnetic field, and for the ferromagnetic one after aligning the single crystal with the c-axis parallel to the field Ž Hm s 480 kAmy1 .. Related results were obtained for the fan phase when the b-axis was in the direction of the field Ž Hm s 796 kAmy1 .. Heat-capacity results at temperatures from T s Ž60 to 300. K have been reported by Baratashvili et al.,Ž17. while drop-calorimetric results were obtained from T s Ž383 to 1186. K by Makharadze et al.Ž26. The discrepancy between the results by Krasovskii and Fakidov,Ž16. and those by Baratashvili et al.Ž17. in the Curie-temperature region is considerable. Furthermore, the heat capacity of this magnetically interesting compound has not been measured in the region of the lower temperature heli- to ferromagnetic transition. In the present paper results of heat-capacity determinations by adiabatic shield calorimetry from T s 5 K to T s 840 K are reported.

2. Experimental SAMPLE

The MnP was prepared directly from the elements; manganese as high-purity flakes Ž0.9998 atomic mass fraction pure. and phosphorus as Ž0.99999 mass fraction. pure lumps ŽKoch-Light Laboratories, Colnbrook, England.. The calorimetric sample of 130 g polycrystalline MnP was prepared by mixing 60 smaller batches of MnP Žf 2 g.. The use of small masses in the synthesis facilitates the production of homogeneous samples. MnP was made by heating mixtures of the elements in

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Heat capacity of MnP TABLE 1. Unit cell dimensions of manganese monophosphide at ambient temperature arpm

brpm

crpm

Reference

591.7 591.9 590 591.8 591.9 591.93 " 0.04 591.7 " 0.1

526.0 526.1 525 525.8 525.9 526.01 " 0.04 525.7 " 0.1

317.3 317.6 316 317.2 317.2 317.41 " 0.02 317.1 " 0.1

Fylking Ž28. ˚ Arstad and Nowotny Ž29. Shchukarev et al.Ž30. Rundqvist Ž31. Roger and Fruchart Ž32. Fjellvag ˚ and Kjekshus Ž33. Present study

stoichiometric ratio in evacuated and sealed fused silica tubes. Since the tubes frequently crack during cooling, the sample tube is put into an outer evacuated and sealed fused silica tube in order to avoid oxidation. The temperature in the horizontally positioned furnace was increased slowly in steps of 30 K per 8 h to T s 1123 K to avoid too high reaction rates, i.e. explosions. After cooling the samples to room temperature during 1 day, they were crushed and subjected to a further annealing at T s 1123 K for 7 d. Room temperature powder X-ray photographs were taken by the Guinier]Hagg ¨ technique using CrK a 1-radiation and silicon as internal standard.Ž27. The orthorhombic unit-cell dimensions were derived by least-squares refinement. The mean values obtained for six samples among the 60 are a s Ž591.7 " 0.1. pm, b s Ž525.7 " 0.1. pm, and c s Ž317.1 " 0.1. pm, in good agreement with most earlier results, see table 1. Reflections from impurity phases were not observed. CALORIMETRY

The low temperature heat-capacity measurements at the University of Michigan, Ann Arbor, were performed in the Mark XIII adiabatic cryostat.Ž34. A sample mass of 106.345 g was loaded into the calorimeter with a mass of 29.463 g and an internal volume of 44.7 cm3. In order to facilitate rapid thermal equilibration, a pressure of 7.2 kPa at T s 300 K of He gas was introducted after prior evacuation of the calorimeter. The thermometer was calibrated by the U.S. National Bureau of Standards Žnow NIST. on the IPTS-48, and was considered to reproduce thermodynamic temperatures within 0.03 K between T s 5 K and T s 300 K. The heat capacity of the empty calorimeter represented about 10 per cent of the total heat capacity below T s 50 K, increasing to about 30 per cent at ambient temperature. The high-temperature calorimetric apparatus and measuring technique used at the University of Oslo have been described earlier,Ž35,36. along with results obtained for the heat capacity of a standard sample of a-Al 2 O 3 . The calorimeter is intermittently heated, and surrounded by electrically heated, and electronically controlled adiabatic silver shields. A heated guard system, also of silver, is outside the shields and the whole assembly is placed in a vertical tube furnace. The temperature differences between corresponding parts of the calorimeter and shield

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are measured by means of Pt-ŽPt q 10 per cent Rh. thermopiles. The amplified signals are recorded and used for automatic control of the shield heaters to maintain quasi-adiabatic conditions during input and drift periods. The temperature of the guard body is kept at 0.4 K below that of the shield, while the temperature of the furnace is kept at 10 K lower to secure satisfactory operation of the control units. The mass of the sample used in the experiments was f 130 g. It was enclosed in an evacuated and sealed vitreous silica tube of about 50 cm3 volume, which fits tightly into the silver calorimeter. A central well in the tube served for the heater and the platinum-resistance thermometer which was calibrated locally, at the ice, steam, tin, zinc, and antimony points. The thermometer resistance was measured with an automatically balancing ASL18 a.c. bridge, operated by a Hewlett-Packard Vectra computer. Temperatures are judged to correspond with the ITS-90 to within 0.02 K from T s 300 to T s 800 K, whereas the resolution of the temperature determination is within 2 . 10y5 K. The energy inputs from a constant-current supply are measured with a Hewlett-Packard digital voltmeter with an accuracy of "0.025 per cent. The heat capacity of the calorimeter without a sample was determined in a separate series of experiments with a standard deviation of a single measurement from the smoothed heat-capacity curve of about "0.15 per cent. The heat capacity of the empty calorimeter represented approximately 60 per cent of the total heat capacity. Small corrections were applied for differences in mass of the empty and full vitreous silica containers and for the ‘‘zero’’ drift of the calorimeter. The computer-operated experiments are started after obtaining a low and steady instrumental temperature drift Žless than 1 mK per min for a long period.. Under ordinary conditions, i.e. when no phase transformation takes place in the sample, the calorimeter temperature reaches its new equilibrium value about Ž30 to 40. min after the end of the input in the ambient temperature range, and within 15 min at T s 800 K. In transformation regions longer equilibration intervals are used. The standard deviation of a single measurement from the smoothed heat capacity curve is within "0.2 per cent, whereas the accuracy of the determined heat-capacity values is judged to be within "0.3 per cent.

3. Results and discussion The experimental heat capacities are given in chronological order in table 2 and also shown in figure 1. The approximate temperature increments used in the determinations can usually be inferred from the adjacent mean temperatures in table 2. A l-type heat-capacity maximum connected with the ferro- to paramagnetic transition is observed at T f 290 K. The heat capacity rises to f 60.2 J . Ky1 . moly1 over a 1.5 K interval around T s 289.5 K. The molar enthalpy increment of four very reproducible determinations from T s 260 K to T s 320 K in the lowtemperature calorimeter is D Hm s Ž2596.9 " 1.7. J . moly1 Žtable 3.. The individual values agree well, irrespective of the previous thermal treatment.

121

Heat capacity of MnP

TABLE 2. Experimental values for the molar heat capacity of manganese monophosphide ŽMnP. Ž R s 8.3145 J . Ky1 . moly1 ; M ŽMnP. s 85.9118 g . moly1 . as a function of temperature T TrK

C p, m rR

TrK

C p, m rR

TrK

C p, m rR

TrK

C p, m rR

593.08 603.79 614.52 625.29 636.08 646.92 657.78 676.43 695.34 706.38 717.46 728.58 739.75 750.97 762.22

6.661 6.689 6.720 6.744 6.778 6.767 6.814 6.835 6.883 6.920 6.955 6.980 7.009 7.030 7.059

299.006 305.305 311.469 320.637 332.907 342.139 347.641

6.260 6.157 6.162 6.140 6.134 6.107 6.116

Series V 264.114 270.138 276.212 282.239 287.228 289.495 290.726 292.172 293.678 298.567 305.325 313.904

5.928 6.092 6.181 6.349 6.537 7.244 6.776 6.518 6.441 6.213 6.142 6.134

High-temperature determinations ŽUniversity of Oslo. Series I 306.08 312.95 319.83 326.71 333.60 340.51 347.41 354.31 362.95

6.213 6.184 6.165 6.162 6.161 6.149 6.156 6.165 6.181

Series II 373.34 383.72 394.11 404.50

6.189 6.212 6.232 6.261

414.92 425.36 435.80 446.26 456.74 467.24 477.75 488.29 498.86 509.44 520.04 530.64 541.26 551.77 623.37 634.14

6.277 6.297 6.317 6.342 6.363 6.385 6.407 6.430 6.449 6.472 6.494 6.521 6.546 6.562 6.723 6.733

644.90 655.77 666.66 677.56 699.40 765.68 776.95 788.25 810.77 822.22 833.67

6.759 6.785 6.807 6.851 6.899 7.055 7.106 7.138 7.175 7.189 7.246

Series III 561.12 571.75 582.40

6.609 6.637 6.647

Low-temperature determinations ŽUniversity of Michigan. Series IV 4.949 5.844 6.783 7.501 8.508 9.586 10.882 12.101 13.393 14.719 16.066 17.458 18.872 20.291 21.697 23.197 24.789 26.364 30.966 32.591 34.399 36.207 38.030 39.869 41.894

0.0079 0.0094 0.0114 0.0134 0.0156 0.0174 0.0213 0.0253 0.0292 0.0338 0.0391 0.0453 0.0503 0.0583 0.0675 0.0779 0.0895 0.1073 0.1604 0.1829 0.2125 0.2444 0.2801 0.3167 0.3624

44.096 46.313 48.538 50.773 53.303 55.757 58.412 61.070 63.750 66.744 70.082 73.435 77.063 80.804 84.700 88.790 93.122 98.007 103.353 108.716 114.102 119.520 124.966 130.431 135.911 141.424

0.4152 0.4686 0.5343 0.6009 0.6902 0.7516 0.8450 0.9210 1.0157 1.1279 1.2372 1.3563 1.4819 1.6198 1.7634 1.924 2.070 2.237 2.420 2.600 2.782 2.950 3.117 3.285 3.442 3.587

146.948 152.486 158.041 163.597 169.178 174.770 180.359 185.964 191.568 197.183 202.814 208.457 214.307 220.351 226.390 232.434 238.480 244.523 250.564 256.615 262.658 268.694 274.720 280.726 286.701 292.741

3.732 3.868 3.997 4.141 4.235 4.362 4.473 4.573 4.699 4.788 4.878 4.990 5.075 5.178 5.273 5.371 5.466 5.572 5.682 5.765 5.887 6.004 6.152 6.323 6.509 6.562

Series VI DH determination Series VII DH determination

The transition region is very broad. Thus, in the absence of lattice-dynamics results only an estimate of the more cooperative part of the transitional heat capacity may be obtained. A measure of the lattice heat capacity plus the less cooperative part of the magnetic heat-capacity contribution was derived by fitting

122

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FIGURE 1. Molar heat capacity C p, m of manganese monophosphide: `, present results from University of Michigan; ^, present results from University of Oslo; \, results by Baratasvhili et al.;Ž17. - - - - -, results by Makharadze et al.;Ž26. ?????, results by Krasovskii and Fakidov,Ž16. ----, clearly noncooperative heat capacity; ---?---, estimated non-magnetic heat capacity.

the observed heat capacities in the regions 160 F TrK F 220 and 400 F TrK F 500 with a common third-order polynomial Žsolid line in figure 1.: C p , m Ž n.t.. r Ž J . Ky1 . moly1 . s 50.207 q 11.057 . 10y3 . Ž TrK . 2

y 478.145 . 10 3 . Ž KrT . .

Ž 1.

TABLE 3. Enthalpy of transition D trs Hm of the ferrorparamagnetic transition in manganese monophosphide ŽMnP. at T s 289.5 K Series

Determination

IV 8 V 11 VI 1 VII 1 Mean value T 310K y1 D 220K Hm ŽJ . mol . T y1 . Ž . D400K 310K Hm J mol

TirK a

TfrK b

y1 . Ž . DTT f HT m J mol

T y1 . Ž . D310K 260K Hm J mol

259.644 261.113 261.401 260.981

308.454 308.197 310.130 309.770

2537.3 2451.3 2534.8 2535.5

2599.0 2597.3 2596.2 2594.9 2596.9 " 1.7 1827.0

T y1 . c Ž . yD400K 220K Hm J mol y1 . . Ž D trs Hm r J mol D trs Sm rŽJ . Ky1 . moly1 . a

i s initial. b f s final. c n.t.s non-transitional.

4622.3 8676.3 370 1.27

Heat capacity of MnP

123

FIGURE 2. Molar heat capacity C p, m of manganese monophosphide plotted as C p, m rT against T : `, present results from University of Michigan.

The resulting transitional enthalpy is D trs Hm s 370 J . moly1 over the region T s 220 K to T s 400 K Žtable 3.. The corresponding entropy increment, 1.27 J . Ky1 . moly1 , is only a fraction of that expected for randomization of 3d electron spins on manganese. Assuming that 1.3 spins per Mn atom become completely randomized above T N , the spin-only magnetic entropy should be D mag Sm s R . lnŽ2 S q 1. s 6.9 ŽJ . Ky1 . moly1 . where S is the spin quantum number. This value is far above the observed one and indicates that magnetic excitations of less cooperative nature are present, see below. The magnetic order]order transition at T f 50 K is presumably of first order.Ž7,37. Electrical resistivity studies by Takase and KasuyaŽ38. show that the transition temperature increases with sample purity from T s 47 K to T s 53 K. In the present study only three determinations were made in this region. A plot of C p, m . Ty1 against temperature shows a slightly augmented heat-capacity value over a 2.5 K interval around T s 53.3 K Žsee figure 2.. This determination establishes the maximal heat capacity effect that can be ascribed to the magnetic transition and likewise provides an upper bound for the excess or magnetic enthalpy, about 0.3 J . moly1 . The presently measured heat capacities in the low-temperature region agree well with those reported by Takase et al.Ž25. for the helical phase in the region 1.5 F TrK F 8.0 Žsee figure 3.. They are fitted with polynomials in temperature by the method of least squares. The values of enthalpy and entropy are obtained by

124

S. Stølen et al.

FIGURE 3. Low-temperature molar heat capacity C p, m of manganese monophosphide plotted as C p,m rT against T 2 : `, present results from University of Michigan; -?-?-?-?-, results by Takase et al.Ž25. for helical phase, no magnetic field; ?????, for ferromagnetic phase, Hm s 796 kAmy1 along the b-axis; - - - - -, for fan phase, Hm s 480 kAmy1 along the c-axis.

integration of the heat-capacity polynomials and are given at selected temperatures in table 4. The standard entropy at T s 298.15 K is 48.96 J . Ky1 . moly1 . The heat-capacity results by Baratasvhili et al.Ž17. in the region T s Ž58 to 300. K agree well with the present ones Žsee figure 1.. The maximum heat capacity at the Curie temperature is not quite as high as observed here and is at a slightly lower temperature, 286 K. The results by Krasovskii and Fakidov Ž16. in the Curie temperature region are about 8 per cent lower. Baratasvhili et al.Ž17. derived a standard entropy at T s 298.15 K which is 0.4 per cent higher than obtained here, while their estimate at T s 60 K was 2.9 per cent higher. The entropy estimate by Myers et al.Ž39. is 10 per cent lower than obtained here. The value given by Myers was estimated from the entropies of manganese silicides and the experimental values are believed to be more correct. Drop-calorimetric results by Makharadze et al.Ž26. up to T s 1186 K lead to the heat capacities shown by a dotted line in figure 1 over the common region. Their estimated value at T s 298.15 K is 11 per cent lower than measured here. The heat capacity values rise to 1.2 per cent above ours at T s 500 K and falls to 4.3 per cent below at T s 800 K. The high heat capacity of MnP above ambient temperature indicates the presence of further magneticrelectronic excitations. Their influence may be determined by subtracting the contributions from harmonic and anharmonic lattice

125

Heat capacity of MnP TABLE 4. Molar thermodynamic properties of manganese monophoside ŽMnP. Ž R s 8.3145 J . Ky1 . moly1 . TrK

0 5 10 15 20 25 30 35 40 45 50 53

C p, m rR

0 0.0075 0.0189 0.0345 0.0575 0.0930 0.1472 0.2230 0.3199 0.4397 0.5778 0.6615

DT0 Sm rR

DT0 Hm rR . K

M ŽMnP. s 85.9118 g . moly1 helimagnetic 0 Ž0.006. 0.0146 0.0250 0.0378 0.0542 0.0756 0.1037 0.1396 0.1840 0.2374 0.2736

0 Ž0.0164. 0.0814 0.2127 0.4388 0.8085 1.400 2.317 3.666 5.556 8.093 9.999

fm rR a

0 Ž0.003. 0.0065 0.0108 0.0159 0.0219 0.0289 0.0375 0.0480 0.0605 0.0755 0.0850

ferromagnetic 53 60 70 80 90 100 120 140 160 180 200 220 240 260 280 289.5

0.6615 0.8921 1.2366 1.5947 1.954 2.307 2.968 3.550 4.045 4.467 4.837 5.172 5.493 5.839 6.290 7.236

289.5 298.15 300 350 400 450 500 550 600 650 700 750 800 840

7.236 6.260 6.207 6.162 6.230 6.337 6.455 6.572 6.684 6.792 6.900 7.015 7.147 7.273

0.2743 0.3699 0.5330 0.7215 0.9300 1.1553 1.6344 2.136 2.644 3.146 3.636 4.114 4.577 5.029 5.478 5.694

10.035 15.408 26.034 40.185 57.932 79.245 132.12 197.45 273.53 358.76 451.87 552.0 658.6 771.9 893.0 954.6

0.0850 0.1131 0.1611 0.2192 0.2863 0.3629 0.5334 0.7256 0.9344 1.153 1.377 1.604 1.833 2.060 2.289 2.396

paramagnetic

a

5.694 5.887 5.925 6.876 7.703 8.443 9.136 9.737 10.314 10.853 11.360 11.840 12.297 12.649

954.6 1011.1 1022.7 1330.4 1640.0 1954.1 2273.8 2599.5 2931.0 3267.9 3610.2 3958.0 4312.0 4600.3

2.396 2.496 2.516 3.075 3.603 4.100 4.569 5.011 5.429 5.825 6.203 6.562 6.907 7.172

fm is defined as yGm ŽT . y Hm Ž0.4rT.

vibrations and that from the conduction electrons. The lattice heat capacity at constant volume may be extrapolated with a value of the Debye temperature

126

S. Stølen et al.

obtained in the lower temperature region, where the other contributions have been determined. Thus, Takase et al.Ž25. obtained values for the electronic heat-capacity coefficient g in the range Ž5.4 to 7.6. mJ . Ky2 . moly1 considering two limiting expressions for the magnetic heat capacity. The intermediate value 6.5 mJ . Ky2 . moly1 is used here. The dilation contribution is derived from the expression Cd s C p y C V s Ž a 2rk . Vm T ,

Ž 2.

with values for the molar volume Vm , the thermal expansivity a , and the isothermal compressibility k , reported in references 21, 23, and 24. The Debye temperature was taken as its maximum value ŽT s 500 K. calculated from each individual heat capacity determination against temperature. The maximum was obtained at T f 130 K after which the apparent Debye temperature decreases rapidly due to contributions from the magnetic order]disorder transition. The dash-dotted curve in figure 1 represents the total non-magnetic heat capacity of MnP. The resulting magnetic entropy increment over the temperature range Ž140 to 800. K is D trs S m s 5.2 J . Ky1 . moly1 . REFERENCES 1. Bates, L. F. Phil. Mag. 1929, 8, 714]732. 2. Guillaud, C.; Creveaux, H. Compt. rend. Paris 1947, 224, 266]268. ´ 3. Fakidov, I. G.; Krasovskii, V. P. Zh. Eksper. Teor. Fiz. SSSR 1959, 36, 1063]1067; So¨ . Phys. JETP 1959, 9, 755]758. 4. Huber, E. E., Jr.; Ridgley, D. H. Phys. Re¨ . 1964, A135, 1033]1040. 5. Komatsubara, T.; Suzuki, T.; Hirahara, E. J. Phys. Soc. Japan 1970, 28, 317]320. 6. Komatsubara, T.; Isizaki; A.; Kusaka, S.; Hirahara, E. Solid State Commun. 1974, 14, 741]745. 7. Shapira, Y.; Becerra, C. C.; Oliveira, N. F, Jr., Chang, T. S. Phys. Re¨ . 1984, B24, 2780]2806. 8. Shapira, Y.; Oliveira, N. F., Jr.; Becerra, C. C.; Foner, S. Phys. Re¨ . 1984, B29, 361]373. 9. Felcher, G. P.; J. Appl. Phys. 1966, 37, 1056]1058. 10. Forsyth, J. B.; Pickart, S. J.; Brown, P. J. Proc. Phys. Soc. 1966, 88, 333]339. 11. Obara, H.; Endoh, Y.; Ishikawa, Y.; Komatsubara, T. J. Phys. Soc. Japan 1980, 49, 928]935. 12. Hiyamizu, S.; Nagamiya, T. Int. J. Magnetism 1971, 2, 33]50. 13. Moon, R. M. J. Appl. Phys. 1982, 53, 1956]1957. 14. Terui, T.; Komatsubara, T.; Hirahara, E. J. Phys. Soc. Japan 1975, 38, 383]390. 15. Whitmore, B. G. Phil. Mag. 1929, 7, 125]129. 16. Krasovskii, V. P.; Fakidov, I. G. Fitz. Met. Metallo¨ ed. SSSR 1961, 11, 477]479; Phys. Metals Metallogr. USSR 1961, 11, 148]150. 17. Baratashvili, I. B.; Makharadze, I. A.; Varazashvili, V. S.; Tsarakhov, MM.S.; Tsagareishvili, D.Sh. Soobshch. Akad. Nauk Gruz. SSR 1977, 85, 625]628. 18. Kamigaichi, T.; Okamoto, T.; Iwata, N.; Tatsumoto, E. J. Phys. Soc. Japan 1968, 24, 649. 19. Perkins, G.; Marwaha, A. K.; Stewart, J. J. P. Theor. Chim. Acta 1981, 59, 569]583. 20. Yanase, A.; Hasegawa, A. J. Phys. C 1980, 13, 1989]1993. 21. Selte, K; Birkeland, L.; Kjekshus, A. Acta Chem. Scand. 1978, A32, 731]735. 22. Selte, K.; Fjellvag, ˚ H.; Kjekshus, A. Acta Chem. Scand. 1979, A33, 391]395. 23. Okamoto, T.; Kamigaichi, T. Iwata, N.; Tstsumoto, E. J. Phys. Soc. Japan 1968, 25, 1730. 24. Iwata, N.; Okamoto, T. Japan J. Appl. Phys. 1975, 14, 248]252. 25. Takase, A.; Yashima, H.; Kasuya, T. J. Phys. Soc. Japan 1979, 47, 531]534. 26. Makharadze, I. A.; Baratashvili, I. B.; Tsagareishvili, D. S; Gvelesiani, G. G. Iz¨ . Akad Nauk SSSR Neorg. Mater. 1975, 11, 599]601; Inorg. Materials USSR 1975, 11, 515]517. 27. Deslattes, R. D.; Henins, A. Phys. Re¨ . Lett. 1973, 31, 972]975. r 44, A17, No. 7, 1]9. r 35, B11, No. 48, 1]6; ibid. 1943r 28. Fylking, K. E. Arki¨ Kemi Mineral. Geol. 1933r

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