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Submitted on 1 Jan 1971
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HIGH FIELD DATA AND ANISOTROPY FOR Mn3O4
O. Nielsen
To cite this version:
O. Nielsen. HIGH FIELD DATA AND ANISOTROPY FOR Mn3O4. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-51-C1-52. �10.1051/jphyscol:1971110�. �jpa-00213912�
HIGH FIELD
DATAAND ANISOTROPY FOR Mn,04
0. V. NIELSEN
Laboratory for Electrophysics The Technical University, Lyngby, Denmark
R6sum6. - Les propriktks magnktiques statiques de monocristaux de MnsO4 ont kt6 mesurkes entre 4,2 OK et la temperature ambiante. En dessous du point de Nee1 (42 OK), l'axe c est une direction de difficile aimantation (Kc =
-
1,60 x 107 ergs. cm-3 a 4,2 OK). L'anisotropie persiste dans la phase paramagnktique entre le point de N b l et 100 OK. L'aimantation spontanke extrapolb a 0 OK est 1,84 p~lmole, suggkrant une structure de spin non colineaire.D'apres nos mesures nous proposons qu'en dessous du point de NCel les spins sont tous dans le plan de base.
Abstract. - The static magnetic properties of single crystals of Mn304 have been measured from 4.2 OK to room temperature. Below the Nee1 point (42 OK) the c-axis is a magnetically hard direction (Kc = - 1.60 X 107 ergs. cm-3 at 4.2 OK). The anisotropy persists in the paramagnetic phase from the Nkel point up to 100 OK. The spontaneous magne- tization extrapolated to 0 OK is 1.84 p~/mole, suggesting a canted spin arrangement. From our static measurements we propose that below the Nee1 point all spins lie in the basal plane.
Single crystals of Mn30, (hausmannite), have been grown. from a Borax-flux according to [I]. Below 1450 OK the crystal structure is a tetragonally distorted spinel, with c/a = 1.16 at room temperature. The following description however is given in t e e s of the chemical bc unit cell where c/a = 1.16 x 4'2 = 1.64.
I. Spontaneous magnetization. - From low field measurements (10 kG), Dwight and Menuyk [2]
showed the a-axis to be an easy direction of magneti- zation. We have measured the high field (max 60 kG) a-axis magnetization. The isotherms on figure 1 show a n anomaleous curvature for temperatures close to
FIG. 1. - Magnetization in an a-direction vs. applied field.
the transition point (420K), and in fact this point cannot be determined from the spontaneous magne- tization obtained by zero-field extrapolation. Figure 2 shows these extrapolations below 400K. The OOK extrapolation on figure 2 of 1.84 pB/mole agrees with the result from 121.
I 1 I I I I
0 100 200 300
T ( O K )
FIG. 2. - Zero-field extrapolated a-axis magnetization (= Ms) and inverse susceptibilities.
11. Anisotropy in (100). Paramagnetic susceptibility.
- In a c-direction the magnetization is linear with field over the whole temperature range except between 28 OK and 44OK, where a slight saturation effect is observed above 40 kG. Below the N6el point the anisotropy energy Ec referred to this direction can then be written Ec = Kc sin2 8, where 8 is the magne- tization inclination with c-axis. At 4.2 OK,
Kc =
-
1.60 x lo7 ergs cm-3 corresponding toKc/Ms = - 74 kG
.
From the reciprocal susceptibilities shown in figure 2 it follows that the NBel point is determined most accurately from the discontinuity in 1 / ~ , a t 42 OK. In the high temperature range our results agree satisfactory with Rosenbergs data on polycrystalline samples [3], and the paramagnetic anisotropy vanihs- ing at lOOOK has previously been observed by Moruzzi [4].
111. Neutron diffraction. - From previous measu- rements (Dwight [2], Jacobs [ 5 ] ) it is assumed that the magnetic structure below the N6el point is a canted arrangement. With raising temperature it fol- lows from molecular field theory that this state must
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971110
C 1 - 5 2 0. V. NIELSEN be superseded by another ordered state before reaching
the disordering temperature. In order to confirm this we have measured the neutron diffraction pattern at 4.20K. All magnetic reflexions could be indexed according to an orthorhombic doubling in an a- direction of the chemical unit cell, in agreement with Kaspers result 161. The most intense pure magnetic ((021)orthorhombic Or !lol)orthorhombic) fO1-
lowed with temperature and it showed a sharp disap- pearence at 42 OK. At 50 OK we made a new diffrac- tion pattern which neither revealed a magnetic super- structure nor a magnetic contribution to the nuclear peaks compared with room temperature intensities.
IV. Discussion. - The analvsis given here is based on the Yafet-Kittel model as &eatLd by Lotgering [7]
and extended by Dwight and Menuyk [2] to include magnetocrystalline anisotropy. Their notation is used throughout this discussion. The low spontaneous magnetization at 0 OK has previously been explained from a canted spin configuration : A-site spins are supposed colinear in the basal plane, and B-spins inclined an angle $ with the A-spins. The resultant of the B-spins is antiparallel with the A-spins. Subdi- viding the spin system into two A- and B-lattices respectively, the molecular fields may be written
hAr = - n[aaz
+
b,+
b,]h,, = - n[a,
+
a,+
$pb,+
pb,], etc.,
here a,, a,, b, and b, are the respective sublattice magnetizations,
I
a,I
=1
a,I
= a and I b,I
= I b2 I = b.Following [2] we suppose, that the octahedral coordinated B-site Mn3+-ions account for the obser- ved c-axis anisotropy energy. Further we suppose, that the magnetocrystalline energy for the B-spins can be written EB = KB cos2 $. Then the equilibrium angle $, is given by cos $, = a/b(P
+
K) wherefc = ~,/nb,. If a magnetic field H is applied in an a-direction, the equilibrium conditions for all indivi- dual ions lead to the following total magnetization :
M a = Ms
+
~res.H= 2 a l 1 - - - - I
P +
1+
n ( ~+ ~ c >
H (1)where Ms is the spontaneous magnetization and
x,,,
is the residual susceptibility for high fields. For a field applied in the c-direction we obtain
MC=xc.H=
[
- (COS nrc cos 2 $,ILo
-+ (*)
cos $, Xreq]In order to discuss the structure at 0 OK we need the paramagnetic assymptotic Curie temperature T, which is taken from our high temperature data. We find
-
- 640 OK. The theoretical expression for Ta is T, where CA and CB are the respective sublattice Curie constants. Now at 0 OK we must consider two cases :$, = 66.7 and $, = 31.8 degrees, bothangles result- ing in M, = 1.84 pB/mole. If $, = 66.7 degrees we find from (1) (neglecting rc) fl = 1.58 and n = 42.4.
Inserting these values in the expression for Ta, and assuming the spin-only values for the Curie constants, we find a = 6.4 and therefore ap % 1, showing that this state is impossible. If $, = 31.8 degrees we find
p
= 0.73 and n = 92 which yields a z 0. Considering eq. (2) forxC
we find that the last term equals 0.54xreS,
and from figure 2 we see that
xc -
4 . 8 . ~ ~ ~ ~ . This means that the first term in (2) must be posltlve which requires K to be negative. But in that case the B-spins will be in an energy minimum when they lie in the basal plane. Therefore we tentatively propose that all spins lie in the basal plane in contradiction to previous assumptions. However, with our values of n andp
and any reasonable value of a we at present can give neither a quantitative interpretation of the observed anisotropy in
x
for 42OK c T 2 100 OK nor of the detailed behaviour ofx
for T 7 100 OK.Acknowledgements. - The author wishes to express his gratitude to Prof. V. Franck for his valuable interest and to Dr G. B. Jensen and Dr J. Kjems for their helpful1 assistance in performing the neutron diffraction experiments.
References
[13 NIELSEN (0. V.), J. Cryst. Growth, 1969, 5 , 398. [41 MORUZZI (V. L.), J. Appl. Phys., 1961, 32, 59 S.
[2] DWIGHT (K.) and MENUYK (N.), Phys. Rev., 1960, [5] JACOBS (I. S.), Phys. and Chem. of Solids, 1959, 11, 1.
119,1470. [6] KASPER (J. S.), Bull. Am. Phys. Soc., 1959, 4 , 178.
[3] ROSENBERG (M.) and NICOLAE (I.), Proc. Int. Conf. [7] LOTGERING (F. K.), Philips Res. Rep., 1956, 11, 190.
on Magnetism, Nottingham, 1965, 561.
