The principal susceptibilities of praseodymium salts have been
measured from room temperature down to liquid air temperature, The results are discussed in terms of the crystalline electric field theory. It is found that (1) on the basis of a single Suitable cubic field the observed magnetic moment at all temperatures in the range studied can be explained satisfactorily. (2) The observed large anisotropies of the crystals point to the existence 0f  strongly asymmetric rhombic field. (3) a rough
estimate of the rhombic part of the field shows that the splitting by it is by no means small and compares favorably with the cubic splitting. (4) The X1-axis of praseodymium sulphate rotates by about 63 degrees in the range studied

Mookherji, A

English

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THE PRINCIPAL MAGNETIC SUSCEPTIBILITIES OF SINGLE CRYSTALS OF RARE EARTH SALTS AT LOW TEMPERATURES. PART II.PRASEODYMIUM SALTSBy a . MOOKHERJI(Rci'dvcd Joy pitbUcalioUi June 27, Hj2ij)ABSTRACT. The principal su.sceptibilities of praseodyuiiuHi sails liave leeii measured from room temperature down to liquid air temperature, The results are dis­cussed in terms of the crystalline electric field theory. It is found that (j) on the basis of a single Suitable cubic field the observed magnetic moment at all temperatures in the range studied can be explained satisfactorily. (2) The observed large anisotropies of the crystals point to the existence 0/ strongly asymmetric rhombic field. (3) a rough estimate of the rhombic part of the field shows that the splitting by it is by no means small and compares favourably with the cubic splitting. (4) The Xraxi.s of praseodymium sulphate rotates by about 63 degrees m the range studied.34T N T R O IMJ C T T 0  NFollowing Vau Vleck (1932), Penney and .Schlapp (1932) if one attributes all the observed deviations in the magnetic properties of the rare earth ion,  ^ from tlie ideal free ion behaviour, to the splitting of the energy levels of the P r " *  ion, under the influence of strong and generally asymmetric crystalline fields, one should expect the mean of the three principal susceptibil­ities to be determined almost wholly by the cubic part of the field. The rhombic part will have very little effect on the mean of the three susceptibil­ities though the individual susceptibilities will be affected considerably. This conclusion has been verified satisfactorily in the case of cerium sails (Mookheiji,1949).Though in most of the crystals the crystalline fields are predominantly cubic in symmetry," the small deviations from the cubic part of the field produce nearly as great an effect on the susceptibilities as cubic parts. On the other hand if we consider the mean of the three principal susceptibilities of the crystal, which is the one measured with crystal i)owder, the effect of the non-cubic part is not so conspicuous, owing to averaging out of the effect along the three principal axes, which are not all of the, same sign (Mookherji 1946, Bose. 1948). The measurements on powder will reveal only the effects of the cubic part of the field whereas measurement with single crystal can reveal the effects of both the cubic and the non-cubic part. That is why measurements on the principal susceptibilities of single crystals510 A .  MookJkerjiare much more informative than the usual measurements, namely, on the crystal powder.It i.s true that the axes of the crystal fields associated with the different I)araiuagnetic ions in crystals will not in general be parallel to one another and even in an anisotropic crystal there is a partial averaging out of the contributions of the non-cubic parts of the crystalline electric field associated with different paramagnetic ions. But even so, such anisotropy as is left over can supply much information regarding the a.symmetric part of the crystalline field and the influence on tlie magnetic properties (Krishuan and Mookherji,1936).In this communication the results of magnetic ineasuremeuts on single crystals of salts of Pr '^^^ions from room temperature down to liquid air temperature are discussed from the point of view of the splitting of the energy levels by the cubic as well as the non-cubic part of the field and ultipialely of the magnetic behaviour of the ion.li X 1* R R 1 M K N T A hThe experimental methods used in these measurements were the Same as described in our previous paper (Mookherji, 1049) on cerium salts.Specimens of praesodymium salts in these investigations w’cre of high purity and were made available through the kindne.ss of Profe.ssor Trombe' of Paris University to whom we take this opportunity to express our thanks.R E S U L T  S*The results of measurements are collected in Tables 1 to IV. The same notations and diamagnetic corrections as adopted in the ])revioiis paper (Mookheiji, 1549) are used in the present communication. Figs. i to 5 show the nature of variation of magnetic anisotropy and square of principle moments with temperature.o— oPr.^ iS04);].8H20Principal Magnetic SusceptihibUes of Single etc. 3//;•Pro(SOi)i.SIljjO_ Mi3000l^ r2(SC)4)3.8H.O Gorlvr—O I’rcsciit author— .128 I/U2Pr9Mffq(NOM)i5*.3(2 A. MookjierjiF’ff' 5Pr2Mjr;,(N< )■ .)]?.rr2Mgs(N03)j2. n.)ll20l*Tr1 .FREE ION I CUBIC 1 RNOM&CI I ^ Fig. 6T H I<: M E A N  M A G N K T I C M O M E N T  A N D  T H E  C U H I C P A R T  O F  T H E  F I E L DI h e  ground state of the Pr'*'^  ^ ion is ’H i. The next higher level natnel.y the is removed by about 2100 cm~*-aud hence at all ordinary temperaturesPrincipal Magnetic SuscepUhilitics of Single Crystals, etc. 313the influence of the latter level on the magnetic behaviour of the ion will be negligible. The splitting of the ground level of ion under electricfields is given in Fig. 6 above.IMagnetic anisotropy at 30*0.Crystal Crystallo- gtaphic dataMode of suspension.Oricnlalion in the field. A xMagnetic/Vnisotropyrr^tSOilj-SIIjOMonocliiiicprisma :b :c2.986:1 ‘.i .99 iS-.-uS**‘ h ’ axis vertical } ' a ’ axis ) vertical > 0^01) plane ) horizontal )0=* + 3 \ l' b ' axis along field  ^' b * axis ) alongjlield >7951006iSoo( Xi“ X2=795\ X3“ Xi =T0051 + 25®.9 Cal. -f 26” .0IVjMgs (NOjha.aitTlaOi1Trigonal1TrigonalaxisTrig, axis normal lo 636 =636horizontal1field. a, ■Tablk IIAbsolute susceptil)ility along a convenient directionCrystalDirection along which susceptibi­lity was m easured.Temp."CDensity of the crystalVolume suscepi i- bility.CorrcwS-ponding gin. m oj, suscepti­bility.Corres­ponding gm. mol. suscepti­bility at 30 "C.Prj (804)3.81120 rraM galN O jlij.atllsOAlong xi-axis Normal to Trigonal axis28-53«S2.8372.1823S-17 9,6809,4309,6400.450We have already mentioned that the mean of the three principal susceptibilities is determined to a close approximation by the cubic part of the field alone. Taking the cubic part of the field b to be of the fourth order, the energy levels will be given by (Penney and Schlapj). 193®) the following equation (i)P7 i = 67aa( i )I7 a = JF,= W4= 336a Wr” W , - W , ‘= - 624aand the corresponding energy separations are o ,— 33601 “ S76<* ■—1296a,where ’ a’ is a constant determined by the magnitude of the cubic field, the5—1713 P.—7314 A . MookherjiT able JIITemperature variation of Magnetic AnisotropyCrystalPrj (804)3.811201T3MR3(N03)j2Suspension used for measurementTemp.“K axis vertical *a' axis verticalXl-Xi eX1-X2 X a - X i  - X 2  sin*«300 800 1 0 1 0 1010 +2.1868 1 0 7 0 1070 2 .1260 9 3 7 1 1 7 0 1 1 7 02 4 0 JOIO J32O 1 3 1 0 \  4-0220 JIOO 1500 1480 \ ^-7200 1 20() 1780 172 0 12 .5180 13 20 2 J20 J97O 19-5160 1480 2670 23/JO 28.01 4 0 1 7 4 0 3-160 2770 32.0120 2620 459 0 2960 52.0lOU 4 5 9 <-’ 1 5 7 1 0 ,2250 6u.2S5 68S0 6 7 5 0 1060 62.5Trigonal axis horijsontalXj.-11 30U 6601 280 802j  26<) 9 4 9i T08022f» a 22020t ) 1380t8o 15201 60 « 1690140 i8 6 0120 2020100 2 2 TO85 2340f^rincipcd Magnetic Susceptihililies of Single Crystals, etc. 5/5TABLIt IVTeniperalure variation of principal susceptibilities(d x\ X'.j x'eH300 gg6o gi6o 10970 10030 12.05 11.08 i3-«^7 12.13280 10500 9630 11570 10570 11.82 TO.87 13.06 11.92260 11140 10290 1231)0 11240 n.6? 10.79 12.89 11.78240 11770 10760 13080 11870 r^-39 10.42 12.66 il.49220 12470 11370 13960 125t)0 11.06 10.09 n,i8200 3^390 12190 1511^ -^ 13560 10.80 1 9.S30 12.18 IU.90180 14380 i3(t6o i<'\3.So 14600 in.43 9.4S.! 1 11.87 10.59i6o 17870 15S( 10 10,02 9.070 ^T1.53 10.21140 j6goo 15160 19670 17280 9.540 S.sfio 11 11. TO 0.73012f> J8510 15890 21460 18690 8.960 7.681 j 10.39 9.010100 20360 i6o(K) 22870 19S30 6.450 9.23 8.003a.s 22360 15480 22420 20420 7.66 ! 5-137 8.03 7.00>^'11 x' '‘1 M I300 lOllo y45'j 9890 12.23 ^^■ 43 11.962S0 10(510 t)8io 10340 li.yS 11,08 11.68260 11390 10440 11080 IJ.9I 10.94 n.6r240 T2I9c» 1 l in o111830 11.80 10.75 n.45220 12970  ^ J1750 T2570 n.50 10,42 n.14200 13830 1245<^’ ■ 13370 11.15 10.04 10.78380 15040 1552^ ^ 14540 10,91 9.830 10.54160 16550 ,,14860 15Q9‘^ 10,68 9-585 10.32140 18400 '' 16540 17780 10.39 9-337 10.04 ;1?0 20550 1853^ ^ 19880 9.920 8.964 g.oot)100 23090 20880 9-31^ 8.420 9.01085 259CK> 23560 33750 8.8S0i8.076 8.6ioCryKlal and direction along which ineasure- nient was takenrr3(S04):i8H20 Along >^ piixisPrj»Mg:j(NO;di2 241120 Along Xx /^'xis5/6 A . M ookherjimean of the three principal susceptibilities will then be given byX =  00926^3" + .o533c~^" — .o227e“ ‘^' — .oi99c~^ 4*')a+ (. 1302c’ + .oo52c~ 7'')] -i- [3c’ -'^ " + 2e~^’' + 3c” (a) Where hence conversely from the observed mean of the threerC JLprincipal susceptibilities at any given teinperatin;e we can calculate the field constant. It is gratifying that over the whole of the temperatnre range studied by us, the observed magnetic data for the mean susceptibility fit well with the value a— — .585 cm "'. The observed values of /u® and those calculated on the assumption of a cubic field of the fourth order with a=  —.585 cm"^ are given in Table V.Temp.T aw.e VPr^fSOJa-SHsO a = “  .585 cm"'"KCalculated 01)served300 12.74 12.T 0200 10.86 3 0 .g200 8.19 8 .0 35^ 7.18 7 .0The corresponding valuesfor the Pr2Mgs(N03)ia.24H20 are given in Table VI.T abi.e VIPr2M g3(N03)u24Hs()a= — .508 cm"‘ ’Temp.“K_l^Calculated Observed11.95 II.g6200 10.85 10.78loo 6.89 9.015^ S.( ;5 8,62Thus the magnetic data for the mean susceptibility for ,both the crystals can be satisfactorily explained on the basis of a suitable cubic field. The magni­tudes of the cubic field required for this purpose are reasonable since they will correspond to an overall separation of 756 cin“* in the sulphate and 66i cm"* in the double nitrate. These are of the order of separation in the absorption spectra.For the octahydrated sulphate data for the mean susceptibility at low temperature arc available from the measurements of Corter and de Haas . (1931)- Their values are given in Table VII, for comparisonPrincipal Magnetic Suscepiihilities of Single Cryst<ds, etc, 317T able  V I l3SS SA9-i i6i),6 J37<9 77.53 20.4 '•1-3911.03 10.R3 lO.T 9.06 8 .72 .^8 4.3-1Temp. *KAmong the other prasoedymium salts for which magnetic data at low temperatures are available arc :—(1) P r2 (C a H 5 S 0 4 )fi iS H g O ......  ...B 'araday rotation of this crysta l hasbecu studied by Becquerel (1936).(2) The anhydrous sulphate whose meen susceptibility in the powder state has been measured by Gdrter and de Haas (1931).In both these salts th e  tem perature variation  o f /x® is n early  the same as in th e h yd ra ted  su lp h a te , w h ich  po in t to a crysta llin e  field of nearly the sam e m agn itu d e in all of them . T h is  is to be exp ected  since in all of them th e fie ld  is  pre.sum ably due to  an octahedron o f s ix  n e ga tiv e ly  charged  o x y g e n  atom s, su rro u n d in g  th e  Pr^**^ion, b e lo n gin g  to  the w ater m olecules in one case an d  to SO— * gro u p s in th e o th er; bu t their distances from  the ion w ill be n e arly  th e sam e in both  the cases.We have seen that the cubic part of the field determines to a first approximation the mean square moment i.c., its deviation from the free ion value of 12.81, of Hund, and that the rhombic part will have very little effect on ju®, though the whole of observed anisotropy is due to it.In the above discussions we have for simplicity taken the cubic field to be of the fourth degree. This is justifiable at least in the case of Ce ion (Mookherji, 1949). In Pr**^ ions also the sixth degree terms of the cubic field, of any reasonable magnitude that may be present will not much affect the mean magnetic moment- This can be seen fioro the following Table V III  taken from a paper by Kynch (1937) which gives the energy levels under a cubic field involving respectively (r) the fourth degree terras only, (2) the fourth and sixth degree terms, the magnitudes of these two groups being chosen on the basis of the known distance of the negatively charged atoms surrounding the ion in the crystal.3 lB A .  Mooh_herjiT able VIIIO n l y  F o u rth  d e gree  teriiLsSixth degree terms nlso included101 .8  j j6.7374-521^ 0392.74 t'3-3c mIt will be seen that the two sets of values are not very different, showing that ilic effect of the sixth degree terms,on the energy levels and hence on the magnetic moment is quite small.It is observed that - axis of Pig (S04);i 8HaO rotates through about 63“ as the temperature is lowered from 300 to 85 degrees Kelvin.M  A  G  N  IC T I C  A N I S O T R O P Y  A N D  T  H  E  R  H  O  M  l U  C  P A R  T  O  !•' T  H  E  P' I  l i  L  D^11Though tlie rhombic part of the field does not to a first approximati affect the mean susceptibility, it is the rhombic that is responsible for the observed auisoliopy of the crystal, and from the known anisotropy it should be possible with suitable simplifying assumptions to estimate the rhombic part. The assumptions referred to are ;—(i) The principal axes of the rhombic field concide with those of the cubic field( 3 )  The field axes associated with dilTerent paramagnetic i^ous in the unit cell are all oriented parallel to one another.(3) That the rhombic lerms which can be put in the usual formV = A x^ + By^~i A + B)z~ (:0have either(a) Some symmetry, corresponding, say to the two constants A and B being equal hi which case the expression for Vr reduces toVr =A( x^ + y^-2Z^) (4)Or(b) Extreme asymmetry, corresponding to the coefiicieut of 2* being zero, in which case the expression for Vr reduces tol^  = / lU 2 -y= ) (5)W e shall refer to these two alternatives as case (n) and ca.se ib) respectively.With these assumptions, as Penney and Kynch (1939) have, shown, the separations of the energy levels produced by the rhombic field will be as given in Fig. 7Case (a)— Denoting by numbers 1 to 4, the four split levels split by the cubic part of the field as shown in Fig. 7, the overall splittiug produced byPrincipal Magnetic Susceptibilities of Single Crystals, etc. 3/9the rhombic part will be z8w for level (2 ) and 8m for level U), where w is: h:>31F ig. 7a constant determined by the rhombic field. The conespoudinj. expressions for the princii>al susceptibilities at room temperature will be1^2.14 + .osSiu) uf = 12.14 -  .116111)Case U»)— Here the overall separations of (2) and (4) will be 280! and 8m respectively. The .strscepUbility at room temperature is ^iven by12.14+ .058 m(6)/xf = 1:M? = i 2. i4.14- ■ 'osSm ) (7)12.14 represents tlie mean susceptibility of the cry.stal at room teinperalure. It is indejjendenl of 111 and is determined by the cubic fiehl alone.In actual crystals the simplifying assumptions (i) to (.3) will not hold at all. But the order of magnitude of the rhombic part of the field can still be estimated roughly.From equations (6) and (7) it will be seen that A/x® is equal to 0.174 m in case of (a) and equal to o.ii6m  in case of (h). In both cases the separations are equal to 28m and 8m respectively for levels (2) and (4). For any rhombic field in general, we may calculate the order of magnitude of the separations by taking A/x  ^ to be of the order of 0.15/11, and the separations to be of the order of lom . Now in Pr2(S04)38H20, is about 12 cm“  ^ and the Ag»anisotropy is about 0.2 from which we obtain A/x^  = 2.5 cm~F SinceA/x2^o. 15m, this gives /«^o.i6 cm” \  and the separation produced by the rhombic field, which we have taken to be of the order io?», should be about 160 cm "'. This is not much smaller than the separations by the cubic part of the field.A C K N O W1/E D G M E N TThe work was carried out at the laboratories of the Indian Association for the Cultivation of Science, Calcutta, and the author wishes to express320 A. Mookherjihis thanks to its committee of management for affording all facilities. The author also expresses his tJianks to Sir K . S. Krishnan* K t., D.Sc., F .R .S.,F .N .I., for his keen interest and valuable help and advice. Thanks are also due to Dr. A. Bose, D.Sc., for his valuable discussions.R K F E R E N C R vSBacqncrcl, J. iQ3(>, Physics 3 , 705,Tiosc. A, Jour. Phys.  ^2 2 , 1Q5.Gorter C. J. and dt* TTaap, W. J, ig^ i, Proc, Roy. AcatP 2 4 , iz^qJackson I/. C., Proc. Roy. Soc. A., 1 7 0 , 266.Krisiman, K. S. and Mooklieiji, A. 1936, Phill. Trans Roy. Soc. A., 2 3 7 , 135 Kynch J. O., 1937, Trans, Farail. Soc.  ^ 3 3 , i/]o21Mookherji A., 'H)46, ]m1. Jour, Phys., 2 0 , 9.,, , 1949, Ind. Jour. Phy,. 2 3 , 217-Tenney W. G, and Kynch, 1939, Proc. Roy. Sco. A., 1 7 0 , 112.Penney, W, G. and Schlapp. R, 1932, Phys, Rev. 4 1 , 794.2^, 666.Van Vleck J, H., 793 The Theory of Electric and Magnetic vSusccptibililics, Oxford, Clarendon Press, Chapter XI, 1\

The Principal Magnetic Susceptibilities of Single Crystals of Rare Earth Salts at Low Temperatures. Part II. Praseodymium Salts

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The Principal Magnetic Susceptibilities of Single Crystals of Rare Earth Salts at Low Temperatures. Part II. Praseodymium Salts

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