Magnetic structure of cubic spinels MnxCr3−xO4 (x=1.0−1.6)

Journal of Magnetism and Magnetic Materials $ (1977) 41 - 50 North-ltolland Publishing Company

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MAGN~IC STRU~URE OF CUBIC SPINELS MnxCr3_xO4 (x = t . 0 - t . 6 ) S. VRATISLAV, J. ZAJI~EK Faculty o f Nuch'ar i'hysics and Physical Engineering, I lO O0 Prague I, Czechoslm'akia

z. Jm ,g Institute o f Solid State Physics, Czech. Acad. Sci., 162 53 Prague 6, Czechoslovakia

and A.F. ANDRESEN lnstitutt for A tomenergi, 200 7 K/eller, Norway

Received 26 May 1976, inrevised form ! September 1976 Neutron diffraction study on samples MnxCra_xO4 with x = 1.0, 1.2, ! .4 and 1.6 has been performed at temperatures below --40 K where magnetic ordering is present. At 5 K the structure of the MnCr204 compound was found to be a general LKI)M magnetic spiral with the propagation vector deviating by 13.3" from the ! i lOI axis. This result differs from previous findings. At about 16 K the structure becomes collinear, in samples wi~.h higher content of manganese the magnetic structure is collinear over the whole temperature region (5--40) K, i.e. in the sense of long range ordering. However. a short range ordering of the transverse components of the spins is present both in these samples and in MnCr204 above 16 K

1. Introduction

by Hastings and Corliss [2], Dwight et al. [5] and Plumier [61. In the former-two papers [4,5 ] the magnetic structure of MnCr204 was found to be consistent with the [110] conical spiral model theoretic ally predicted by Lyons, Kaplan, Dwight and Menyuk (LKDM) [7]. They investigated the classical exchange energy of spin arrangement in normal cubic spinels of formulae AB204 in which only nearest-nelghbour A- B and B-B interactions are assumed. In that case the ground state depends only upon the parameter u defined by

Solid solutions MnCr2Oa--Mn304 (MnxCra__xO4) have cubic or tetragonal spinel structure depending on the manganese concentration and on the temperature. The samples with lower content of manganese are cubic and the boundary at low temperatures is about x = 1.7 [1 ]. Due to the strong preference of the Mn 3+ and Cr 3+ ions for the octahedral (B) sites of the spinel lattice the cation distribution can be assumed to be Mn 2+")A["Mn x3+- ! Cr3+ • 0 2-. This distribution was 3--xlB confirmed by our neutron diffraction investigation for the whole system (x = 1.0--3.0) [2 ]. Cubic samples MnxCr3_xO4 show an ordered magnetic structure at temperatures below approximately 40 K. The overall spontaneous moment at 4.2 K varies from "-1.20/an for MnCr204 to "~1.05/a B for Mni.6Crt.404 [3]. Only the magnetic structure of the MnCr204 compound has been investigated previously. The neutron diffraction studies have been performed

u = 4.]p,e,Se,/3JAe_eSA •

The investigation by generalized Luttinger-Tisza method led to the construction of a conical spiral spin arrangement defined by

Sv

= sin ¢u [~7' cos(k • R,w + %) + P' sin(k - Rnv + %)]

+ e' cos ~ , , 41

(1)

42

S, I'ratislav ct al. ./ Magm'tic structure o.l" ('u/tic spim, fs MnxO" 3 x 0 4

was inferred that the magnetization lies in the [110] axis. On the other hand, in ref. 15] the direction of magnetization could not be unequivocally determined due to a weak correlation with the experimental results. A differer,! magnetic structure of Mn204 was reported by Plumier [6] who suggested a non-collinear spin model on the basis of a magnetic cell of size 3a, 3a. a.

,,vhe,e n identifies the unit cell. v = i , 2 . . . . 6 identifies 1he particular site within a primitive cell (~ of elementa~ ceil ): S,,,,is the s p i n o n the m,th site. Orientation of the k'. f"..~' coordinate system with respect to the crxstai axes is arbitrary. In this configuration the spins on ca~h sublattice v lie on a cone of hailXangle @vwith thci~ positions on this cone determined by a single propagation vector k. Phase shifts between the particu~ar sublattices are given by angles 7,. The results of LKI)M proved that in the region u < Uo = S/~1 the N6e] configuration is the ground st, ' At u = Uo the configuration is destabilized by the .,,?iral mode of type ( I ) with ko in the [ 110] directio~L This [I I0] spiral is locally stable up to u = u" = ].29S and may be even the ground state (the generalized Luttinger-Tisza method fails on this point). For u > t{' the [ i 10] spiral is unstable and cannot be the ground state. Calculated parameters of the [ I ! 0] spiral (ko. 0,,. 7,,) can be found in tee 171. Note only that the six cation sites in a unit cell are distributed 2 : 2 : 2 into three magnetic sublattices, one composed of A sites and the other two of B sites, each with its own half-angle of cone. The axis of the cones (.~'), i.e. direction of sponta~ e o u s m a g n e t i z a t i t m depends on the magnetic anisot rop,, and can be found experimentally by neutron diffractioq measurements. For example, in ~ef. [4] it

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2. Experimental The samples of MnxCr3_xO4 with x = 1.0, !.2, 1.4 and !.6 used in our investigation were prepared by a ceramic method from homogenized mixtures of Cr203 and MnCO3. The mixture was fired for 8 hr in air al: 700°C. This was followed by a final firing of 24 hr at 1400°C in air (for x = 1.0 in vacuum 10 - s mm Hg). From this temperature the samples were quenched into water. Only the spinel phase was detected by X-ray and neutron diffraction. The chemical analysis resulted in compositions equal to the above mentioned values o f x within an experimental error of 5 x = -+0.01. Neutron diffraction powder patterns were first obtained using the diffrzctometer KSN-2 in Re~ near

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li~. l. 4 part of lhe neutron diffraction pattern o f MnCr204 at 5 K (h = 1.873 A) obtained by stepscanning (step O.l°). CalcuIared positions of first additional lines are m a r k e d by unlabelled arrows. [The region 20 = ( 2 - 5 ) " was studied in a different a "rangcmcnt and no additkmal line,; v, ere observed there. ]

S. Vratislav et al. /Magnetic structure o f cubic spine[s MnxCr 3 _ x 0 4 !

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Prague and later completed using the high resolution diffractometer OPUS at Kjeller. The wavelengths of the neutron beams were !.023 and 1.873 A, respectively. Diffraction patterns were taken at room temperature and at temperatures of liquid N2 and He. Some diffraction lines were studied as a function of temperature between 5 K and the Curie point. The room temperature diffraction patterns consisted of Bragg peaks in positions given by the spinel structure of tile samples and of a background showing a weak diffuse peak in the neighbourhood of the line (! 11). This peak was studied previously by Dwight et al. [81 and was explained as a paramagnetic scattering. It shows that there is a certain correlation of the spins even at room temperature. On lowering the temperature the coherent lines remain unchanged down to the Curie point where their intensities increase abruptly due to magnetic contributions from ordered spins. The intensity of the diffuse peak (between 20 ~ (19-29) ° at k = 1.873 A) shows a steady slow increase with decreasing temperature and achieves a maximum at liquid He temperature ill samples with x > 1.0 and at "- 16 K in MnCr204. At the latter temperature the sample MnCr2Oq undergoes a second magnetic transition connected with the occurrence of a number of additional coherent peaks which cannot be indexed on the spinel cell or any simple multiplum of this (see fig. 1). This is consistent

with the result in ref. 4. These lines were not observed in the diffraction patterns of samples with a higher content of manganese as shown for example in fig. 2. The intensity of the diffuse peak in these samples decreases with increasing value of.v. The intensities of the additional lines observed in MnCr204 below 16 K increase with decreasing temperature (see fig. 3). However, their positions and relative _. i

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Fig. 3. Temperature dependence of the intensily of the strongest additional lines peaked at 20 = 25.0°

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~ . An i,ntez~dng feature is that the sum t ~ m~emities of the additional fines in the region ~ = 23-27 ~ a l 5 K does not exceed substantially the ~led mtensi~ of the diffuse ~ at about 20 K

~eaty m - - ~ k diffr~tion diagram obtained with the Wave~h l.S73 A tins the same ratio between the coher~ ~ ~ e diffuse peak as at the wavelength !.023 A. ~ s ~ s ~b~ both ty~es of peaks have the same de~w~e~:c,: , ~ ~ e w~leng~h namely proportional to -~ I~ p~xes ~ha~ ~he dlffuse peak must be due to in:effere~>: e~\~c~s o n objects with a c e r t a i n ordering. ",,~:e ~,~ m ~be case of ~ramagnetic scattering the m = . e ~ a ~ m~ens~. ~s proportional to X2. ~ ~ ~ ~.rttegrated intensities of the diffrac~t~ ~ ~ r e evaJuated using a pmfde analysis of the ~ f L - ~ : ~ ~ : z e m s [9|. The ~ t e r s of the chem~,-a~~ ~ e ~ ~ c ~ u r e were refined by a LSQM ~ of ~he m e n , red attd calculated data. Some of ~ e pz~me,te~ are listed in table 1. Oxygen parameters were foaad to be practically independent of tempentture and__.~ f o r e . only the room temperature a ~ t ~ b ~ e ~ . Low temperature values of the ~ y e - W a ~ r ~emperature factor were --9 within the ex~n~ent~l errors for aI_!lthe ~ m p ! ~ .

x = 1,2 tL,~II) 8.433 8,433 0.3888 0.6 44 1.145

8A60 8.452 8,452 0,3887 1.2 47 1.045

for the additional lines (satellites)

of msnganese chromites

occur~nce of the additional lines in the diffraction ~ t ~ e ~ of MnCr204 at S K cannot be explained e ~ e r by any enlargement of the elementary cell up ~o _~. ~ , 3a or by a nonicat spiral model with the

x=' 1.6

propagation vector in any main crystailographical direction. Therefore, in the second step of our structure determination we assumed the appficability of a conical spiral model with the propagation vector k in a general direction. (We note that this was the only equal-relative.angle magnetic configuration [7] in qualitative accordance with our pattern.) The vector k was searched in a sector of the first Brillouin zone utilizing the symmetry of the Lc.c. structure. This sector was divided into approximately l0 s points [k~, k2, k3]. First, the points giving no possibility of reflection into the position of the strongest additional line (20 = 25 °) were eliminated. The elimination was repeated for the remaining strong additional lines except for the peak at 20 = 25.9 ° where the line (002) admitted in the LKDM [110] model is situated. It was found by this procedure that only a conical spiral model with with propagation vector k ' = 2n~/a, where • - [0.660, 0.595, 0.205] (or its other cubic "equivalents") can account for the positions of all strong additional lines. The other weak additional lines could be indexed on the basis of this model as well (see table 2). The diffracted intensity is a sum of the nuclear and magnetic contributions. The magnetic contribution is proportional to [4,7] sin 2 wlAa 2 , for the spinel lines (fundamentals), (1 + cos 2 00/4- IT! 2 ,

3, Magne~c s ~ ~

x t 1.4 8.449 8.443 8,442 0388? I.I 45 1.105

(a is the angle between the direction of the spontaneous magnetization and the scattering vector), where

A~kt = ~Jf~vktSv cos 0v exp {2ni(hxv +/~.v +/zv)} V

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S. I"ratislar et al. /Magnetic structurc o.f cubic Sl~bWls MnxCr 3 _ x 0 4

Table 2 (continuedJ line

20ca I

20 obs

lobs

Ical model !

?.-22+

48.01 48.09

24031313113322_0+ 222 + 3-11131 + 40231"!+ 004042113 +

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and

Th*rl'k~ r 2 ' l t r3 = ~vf f

ties of the fundamentals and satellites at 5 K showed that the cone angles and the phase angles must satisfy approximately the relations valid in the [1 IO] LKDM model, i.e.

-rl'*±r2't±r3 S,, sin 0v

X exp(-¥iy,)exp {2ni(hx,, + ky~, + lzL,)}

01

(h, k, I all even or odd). ttence, the intensities of the fundamentals depend on the longitudinal components of the spins SII ,, = S v cos Cv a~d !he intensities of the satellites depend on the transverse components S ~ = S,, sin ~,,, and on the phase angles %. Assuming the space group Fd3m, it can be shown that the magnitude of lTI for a set of phase angles 71,3'2, 3'3, "1'4, "t's and 76 is the same for -72, Y ~ , - - 3 ' 3 , -3'4, -3'5 and -"1'o. The same is valid for the classical Heisenberg energy of the conical spiral configuration. Therefore, there are two solutions in the structure determination generally. A preliminary evaluation of the integrated intensi-

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Fig, 4. The sites in r~rimitive cell of the spinel structure. The numbers =1,2 ..... 6 idcnlify the various calion sites.

=0:,

3'I-'3'2-0,

03 =04,

Os = 0 6 ,

3'3 = ....3'4, "Is =3'6 = n ,

(2)

(3)

where the sublaltice labelling is as shown in fig. 4. l,i. nal refinement was performed using LSOM. Atomic form factors for Mn 2~ ions have been taken from ref. [10], for Cr 3~ ions from ref. [!1] and for Mn J÷ ions in samples with x > 1.0 from ref. [ 12 ]. We found that with the restrictions (2) and (3) the fit of observed and calculated satellite inlensities was very poor (factor R "-- 0.30). Therefore, we tried two other models o f the magnetic structure of MnCraO4. In model I we assumed general phase angles 3'v and differen! cone angles on 3,4 and 5,6 (2 • 2) and in model !1 fixed phase relations (3j and general cone angles. The !a!!er model led to a division with approximalely equal angles on 4, 5, 6 and a different angle on 3 (1 • 3). Bolh models resulted in approximately the same factor R "-- 0.12 for satellites and R "-- 0.01 for fundamentals. Tile measured and calculated inlensilies ate compared in tables 71 and 3. in table 3 the calculated intensity is practically the same for model I and !1. The structural parameters are given in table 4. (One of the six phase

S. Vratislar et al. / Magnetic stnwture o f cubic spinels MnxCr 3 x 0 4 Table 3 Observed and c a l c u l a t e d intensities o f spinel lines o f M n C r 2 0 4 at 5 K Line

20

tnucl "cal

/ca~ g

(I l l) (220) (311) {222) {400) {331) {422) (51 I) (333)

22.22 36.65 43.26 45.29 52.78 57.94 65.95 70.52 70.52

2441 142
1306 490 63 84 201 214 104 8} 4

(440)

77.87

2898

I

trot "eal

lobs

3747 632 63 1850 4911 238 339 943

3739 629 60 1836 4923 244 339 951

2899

2903

angles % is arbitrary, thus we put 71 = 0.) The fit of the measttred and calculated satellite intensities was not much improved when no restriction was put on either the cone angles or the phase angles. All the calculations were performed for the direction of spontaneous magnetization along the 11 I0] axis. Any other direction yields very poor fit and was, therefore, excluded. This is in general agreemen! with the measureTable 4 Parameters of the conical spiral s t l u c t u t e of M n ( ' r 2 0 4 at 5 K (k eters are given in b r a c k e t s ) ('onical spiral Inodcl

1

Phase angles

or

i0o

~t6 =

Long|ludinal c o n t p o n e n l s o1 spills

....

~3 .... i 0 0 ° ~4 ~= " 180 ~'

3rs = Transverse c o m p o n e n t s of spins

ments of the anisotropy of unsaturated magnetization in MnCr204 [13] in which below "-17 K the easy direction was found to lie along [i 10]. Temperature dependence of the longitudinal components of the spins is drawn in fig. 5. it was determined on the basis of the temperature dependence of the magnetic contributions to the lines (111 ) and (220). The values of the spins in A and B sites are roughly proportional over the whole temperature region and show no irregularity in the neighbourhood of 16 K where tile magnetic transition occurs. This suggests that the transition is not conr, ected with a diminution of cone angles but rather with a disordering of the transverse components of spins. Below ~ 15 K the values of the longitudinal components of the spins decrease slightly with decreasing temperature. The second magnetic transition did not occur in samples with x I> 1.2. Calculated longitudinal componeff!s-of spins in A and B sites at 5 K are given for these samples in table 5. They do not differ much from those in MnCr204 (table 4). Especially, the values of spins on the B sites are much lower than the spin-only values of trivalenl chromiunl and manganese.

2n/a 10.660, 0 . 5 9 5 , 0 . 2 0 5 J; standard d c v i a t i o n s of s o m e param-

II

1 t ~ O' 1,2 . . . . .

0" I0 o

...... I I f f - 17(V

0. . . . . . . 3o °

--

"II = ~2 = ~5 = 3'6 ' O° ) 3 = "~4 ~ 180°

I0" 20"

S~I = S~2 = 1.32 Sj3=S~4= 1.08

S j l = Si~ = !.3(} S l 3 =~ 0 . 2 9

SIS ~ Sl6 ~

1.31

$14 = S i S =: $ 1 6 =

S~! I ~ S~ 2 ~ S , j ~ S~I4 ~

!.70 O J,5

Sll t ~ .Si2 ~ 1.70 Sll 3 = 0.82

!,25

0.48

Magniludcs ol spln~

('one angles Spontaneous moment

S 1 ~S 2 S 3 =S 4 S s ~,S 6

:,~ 2,15 (18) ~= 1 2 6 (15) ~ 1,40{09)

S I =,S 2 = 2.14 ( 1 8 ) S 3 .... 0 . 8 7 t 2 ~ ) S 4 = 5 5 = S 6 = 1.34 (1)6)

03 Os

~60 ° = 70°

03 04

~04 =06

!.14 ( 0 8 ) u B

47

~ 20" =¢'s =06

1.14 (1 I) ~B

=7B"

4S

X I,'ratislar et al. /Magnetic structure oJ ('ul, ic sl,inels MnxCr 3 x 0 4 k

....

~

......

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/0 ,.0

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4. Discussion

0

\0

~0

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SB

o

05

I

i,

tO

20

,

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40

30

T (K)

I ig. 5. Tcmf, eralure dependence of the longitudinal componenl,; of spins S~,~ and S ~ = ;!( S B,,I + S'i~12) for M n C r 2 0 4.

~,e therefl~re think that the different behaviour of ~mples wifl~ higher cor:tent of manganese can be attributed to a disordering of the transverse components of the spins in the sense of long range ordering, in thai case there Js no nhysicat reason for the division of B sites into two sublatticcs. -iherefore, an equal distribution of the directions of the spontaneous magnetizaliorl over the cubic axes was assumed in the refinemcnt t)f the structural parameters. According to magnetic torque measurements the easy directions in manganese-rich cubic chromites lie along the [ I I 1] axes [14]. Temperature dependence of the longitudinal components of the spins in samples with x >t 1.2 are very similar to the curves in fig. 5 except at tempera-

Table 5 Par:am,..'t,ers ~t the magnetic structure of man~:anese rich chromites at 5 K (,~mpound

SA

SB

Spontaneous m o m e n t [,UB]

x 1.,."~ .v : 1.4 .v = 1.6

2.00 2.04 2.05

-0.67 --0.72 -0.73

1.3 1.2 1.2

:

tures beh)w "--15 K where the spin values are practically constant.

We have found that the magnetic structure of MnCr2 04 can be described by a conical spiral model with the propagation vector in a general direction. This result is in contradiction to those given in refs. [4], 5] where a [i 10] spiral with ko = 21r/a [0.59, 0.59, Ol and 2rr]a [0.64, 0.64, 0], respectively, were found and to the result in ref. [6]. This can be ascribed to the use of a longer wavelength and a better resolution which has made it possible to see more additional peaks and to determine their positions with greater accuracy. Note also that in ref. [4] some of the relatively strong additional lines could not be indexed. Nevertheless, the physical reason for the establishment of k' = 2n[a [0.660, 0.595, 0.205 ! as the propagation vector is not clear. An explanation has not yet been found in terms of the classical Heisenberg exchange energy *. The parameters of the magnetic structure of MnCr204 (cone angles, phase angles) could not be determined equivocally on the basis of our diffraction data. Itowever, certain considerations enable us to decide in favour of model ! in which the B sublattice is divided into two sublattices BI (sites 3 and 4) and B2 (sites 5 and 6). The exchange energy of model ! is considerably lower than the energy of model !i and only model I yields magnetic anisotropy with the easy di-

L K I ) M 17 ] proved that the [1 lOl spiral is the mininmnl-energy magnetic spiral of type ( ] ) for u at least up to 1.35. Our calculations performed up to u = 4 show that the energy of the [ i 10] spiral is always lower than the minimum energy o f a spiral with the propagation vector k' (the energy difference is very small - about 0.01 of the energy of the I I lOI spiral; see ref. 171). This conclusion is valid even if next neighbour inleracti,,ns J~a.B and next-to-next-neigh. bour interactions J~E I are involved. Only the parameters o f the m i n i m u m energy ] 110] spiral are changed. The calculalions wcre performed for IJ]3BI, IJ[H:II < JIIEI. Real magnitudes of the exchange interactions cannot be determined at this stage because of the failure of the theoretical explanation of ou! spiral configuration. In ref. 14,5 l the parameter u describing the strength of the B - B relative to the A - B in~teraction was estimated within the framework of the LK D:'i ILheory to It = 1.6 and 2. !, respec~tively.

49

s. l'ratislav ¢'t al. / Magnetic structure o f cubic spinels MnxCr 3 _ x 0 4

rection of magnetization along the [! I0] axis I-. NMR results on MnCr204 are in accordance with model ! as well [171. Assuming only nearest A - B and B- B interactions the optimization o f the exchange energy of the magnetic spiral configuration having the propagation vector k' gives values fo- the cone angles ¢~Jll and ¢ ~ which are practically the same as in the LKDM [! I0] spiral. There is a great difference between the cone angles on the Bi and B2 sublattices. This is in disagreement with our experimental values for model ! given in table 4. ! lowever, this disagreement can be removed by including next-neighbour exchange interactions. Their contributions to the exchange energy of ions on the Bt and B: sublattices are nearly the same. Hence, these interactions tend to make the cone angles in B t and B2 equal. Optimization o f the exchange energy for our configuration with respect to phase angles gives two solutions 7t = 0,

72 = - 3 0 ° , 3'3 = 1 0 3 ° ,

Y¢ = 210°,3'5 = 1 4 ° , Y 6

= -20°

"~"There is experimental evidence that in samples with x -, 0 the cubic anisotropy is very small at liquid IIc temperature [ 12]. We note, however, that both n:odcls 1 and ii led to a non-cubic anisotropy arising from contributions of Cr 3÷ ions. in model !, in which the subvision of B sites into B I and B2 sublattices take place, the anisotropy energy calculated within the one-ion model of anisotropy is orthorhombic 1151 /','A.... 2C°~I°t2 , where otI, °t2 are direction cosines of magnetization in coordinate system of cubic axes of the sample and the purameler C i.'~given 'at zer,a tempcrato.re hy C = 3/4D N(cos 2 @BI -. cos2 0B2) . EPR results [16] indicate that in spiqeis it is the spin hamiltonian parameter D(Cr 3+) ", 0 which leads to easy direction along the [ 110] axis and tt~ hard direction along the I 1 i0] axis. In the case of ad,.eqttac~ O|" model Ii the one-ion model gives easy direction in the [ I f I ] axis and hard plane of magnetization ( I l l ).

and y~ = 0 , 3'4

=

3'2 = --30°,3'3 =

133 °,

120 °, 3's = - 16 °, 3't, = - I 0 °.

which are in satisfactory agreement with tile experimental vahles for model I in table 4. "these values were determined for the parameter value u = 2. I:or other vaiues of u in the region (8/9 4) the solutions are practically identical. The magnitude of spins on A sites are equal to the reduced spin value of Mn 2÷ ions Sxln2, - 2.15 reported in ref. [5 ! on the basis ,ff magnetic susceptibility measurements on MnCr2Oa. The magnitude of spins on B sites are close to the spin only value ol'Cr 3. ions Scr3+ = 1.5. The observed difference can be caused by the fact that our spiral conliguration is only a first approximation to the ground state or that (ordered) transverse components of spins are lowered due to a phase disordering of the magnetic spiral in places of lattice defects. Both facts can also explain the poor fit between observed and calculated intensities of additional lines even for strong and medium lines. The experimental values of the I,mgitudinal components of the spins are in good accordance with the saturation magnetization. At about 16 K the additional lines in the diffraction patterns of MnCr204 disappear, signifying a transition to a collinear magnetic structure. This ter~perature is slightly lower than the temperature T = IL K reported in ref. [41. Furthermore, at about 36 K, the magnetic contributions to the spinel lines vanish as any long range orderin,,, of spins cease to exist. This value of tl'e ('uric point is also lower than Tt,. = 43 K given in ref. 141. No additional coherent lines were observed in samples with higher content of manganese even at 5 K. According to magnelic torque measurements [ 181 the limiting composition for the transition to spiral configuration is x --- 1.05. Nevertheless, the wavelength dependence of the ii~tensity of the diffuse peak in neighbourhood of the ( I I 1) line is a sign of short range ordering of the transverse ccnnponents of the spins for samples with x > i.05. The same is valid for MnCr204 above 16 K. The Curie points of Mn t.2Crl js04, Mnt.4Crt .604 and Mn i.c,Crt .404 given in table I are substantially higher than the Curie point of MnCr204.

50

S. I "ratislar et al. / Magnetic sttacture o]'cubic spineis M n x C r 3 _ x O 4

Acknowledgement

I71 D.ti. Lyons, T.A. Kaplan, K. Dwight and N. Menyuk,

The authe, rs express their thanks to Dr. M. Nevfiva for preparation of samp!es, to Dr, V. Roskovec for magnetic measurements and to Drs. S. Krupff:ka and P, Nov~ik for useful discussions.

181 K. Dwight, N. Menyuk and T.A. Kaplan, J. Appl. Phys.

Phys. Rev. 126 (1962)541). 36 (1965) 1090.

191 Z..lirtlk, Czech. J. Phys. A26 (1976) 273. Ii01 J.M. Hastings, N. Elliott and L.M. Corliss, Phys. Rev. 115 (1959) 13.

I111 R.E. Watson and A.J. Freeman, Acta Cryst. 14 (1961)

References Ill !'. pollcrt and Z. Jir,ik, Czech. J. Phys. B26 (1976)481. 121 Z Jir,'ik, S. Vratislav, J. Zajicck, Phys. Status Solids 37 ( ! 976) K47. 131 V. Ro.skt,~cc (unpublished results). 141 J.M. tlastings and L.M. Corl ~s, Phys. Rev. 126 (1962) 556. [51 K. Dw~ht, N. Menyuk, J. Feinleib and A, Wold, J. Appl. Phys. 37 (1966) 962. 16 [ R. Plumier, ('oml~tes Rcndus B265 (1967) 726.

27.

It21 G.B. Jensen and O.V. Nielsen, J. Phys. C7 (1974). [131 T. Tsushima, Y. Kino and S. Funahashi, .I. Appl. Phys. 39 (1968) 626.

1141 V. Roskovcc and M. Nev~ipa, 3rd Conf. of Czech. Physicists (Academia, Prague, 1974), pp. 268-269.

1151 P. Nov~ik and Z. Jir~ik (unpublished results). 1161 S.A. Altschuler and B.M. Kozirev, Elektronnyj paramagnitnyj resonans (Nauka, Moscow, 1972), pp. 391-392.

[171 H. Nagasava and T. Tushima, Phys. Lett. 15 (1965) 205, 1181 S. Krupi~:ka, Z. Jirfik, P. Nov,'ik, V. Roskovcc and F. Zounov;i, (to be presented in ICM 76, Amsterdam).