Evidence for the presence of a small weak-ferromagnetic ... No trace of weak ferromagnetism appeared at ... field susceptibility and magnetization measure-.
Physica 115B (1983) 190-204 North-Holland Publishing Company
M A G N E T I C PROPERTIES OF T H E W E A K F E R R O M A G N E T NH4MnFs J. B A R T O L O M E , R. B U R R I E L , F. P A L A C I O and D. G O N Z A L E Z Dpto, de Termologla, Facultad de Cieneias, Universidad de Zaragoza, Spain R. N A V A R R O a n d J . A . R O J O Dpto. de Ffsica, E.T.S.LI., Zaragoza, Spain LJ. DE JONGH Kamerlingh Onnes Laboratory, University of Leiden, The Netherlands Received 29 April 1982
The magnetic properties of NH4MnF3 have been studied by means of heat capacity, a.c. susceptibility at zero field and at H = 10 kOe as a function of temperature, and at T = 4.2 K as a function of field. Moreover, magnetization measurements were carried out at T = 4.2 K as a function of field up to 20 kOe in a vibrating sample magnetometer and up to 400 kOe in a pulsed-field magnet. The compound has the simple cubic perovskite structure at room temperature. At Tc = 182.1 -+0.1 K a structural transition to a pseudo-tetragonal symmetry occurs, which gives rise to a small change in the paramagnetic susceptibility. The onset of antiferromagnetic ordering takes place at TN = 75.1 _+0.1 K at zero field, and a spin-flop transition at T = 4.2K is detected at HSF = 3.7 -+0.2 kOe. Evidence for the presence of a small weak-ferromagnetic moment is found from an anomaly in X and from the presence of magnetic absorption near TN. From a comparison of the data to predictions for the s.c. Heisenberg antiferromagnetic model, a value of J/k - -3.11 K is obtained for the exchange interaction.
1. Introduction T h e cubic p e r o v s k i t e s A M n X 3 , w h e r e A = K, R b , TI an d X = F, C1, h a v e b e e n e x t e n s i v e l y s t u d i e d since they p r o v i d e g o o d e x a m p l e s of t h e s i m p l e cubic H e i s e n b e r g a n t i f e r r o m a g n e t with spin S = 5/2. T h e c o m p o u n d R b M n F 3 has t h e cubic Pm3m(O~,) s y m m e t r y at all t e m p e r a t u r e s . This, t o g e t h e r with th e high i s o t r o p y of the e x c h a n g e i n t e r a c t i o n b e t w e e n t h e M n 2+ S = 5/2 m a g n e t i c m o m e n t s , r e n d e r s this c o m p o u n d an a l m o s t p e r f e c t e x a m p l e of t h e H e i s e n b e r g magnetic model. Extensive experiments using different t e c h n i q u e s h a v e b e e n p e r f o r m e d on this c o m p o u n d v er i fy i n g t h e a b o v e s t a t e m e n t . T h e s e results w e r e r e v i e w e d by D e J o n g h a n d M i e d e m a [1], a n d in p a r t i c u l a r an e x c e l l e n t fit of th e magne ti c susceptibility u p to 150 K was r e p o r t e d [2]. N o trace of w e a k f e r r o m a g n e t i s m a p p e a r e d at any t e m p e r a t u r e . In t h e case of TIMnF3 t h e a v a i l a b l e d a t a is
m o r e scarce, but m a g n e t i c susceptibility a n d h e a t capacity m e a s u r e m e n t s a g r e e with t h e s a m e m o d e l . H o w e v e r , b e c a u s e of s t r u c t u r a l distortions, t h e b e h a v i o u r d e v i a t e s f r o m that of t h e ideal cubic H e i s e n b e r g a n t i f e r r o m a g n e t [3]. D u e to this type of d i s t o r t i o n s o m e of t h e s e c o m p o u n d s s h o w w e a k - f e r r o m a g n e t i s m . In particular, KMnF3 is a w e l l - k n o w n e x a m p l e with such a b e h a v i o u r a n d has a t t r a c t e d c o n s i d e r a b l e a t t e n t i o n . Its s y m m e t r y is r e d u c e d f r o m (O~,) to e l o n g a t e d t e t r a g o n a l I 4 / m c m ( D ] 8) at Tc~ = 1 8 6 . 6 K by a structural p h a s e transition. Furt h e r m o r e , a n o t h e r structural transition at To2 = 92.3 K gives rise to a s e c o n d t e t r a g o n a l phase. Finally, a third transition at To3 = 81.5 K d e f o r m s t h e system to a l o w e r s y m m e t r y p h a s e [5-7]. T h e low-temperature structure apparently depends on crystal size an d t h e r m a l history ]6-9]. T h e m a g n e t i c b e h a v i o u r of this c o m p o u n d is similar to R b M n F 3 d o w n to TN = 88 K w h e r e l o n g - r a n g e a n t i f e r r o m a g n e t i c o r d e r i n g occurs. B e l o w TN a
0378-4363/83/0000-0000/$03.00 © 1983 N o r t h - H o l l a n d
J. Bartolom~ et al. / Magnetic properties of NH4MnF3
second magnetic transition associated with the structural transition at To3 leads to the development of a weak-ferromagnetic moment superimposed upon the basic antiferromagnetic susceptibility. The magnetic anomalies appear to be caused by magnetoelastic effects [8, 9]. It appears that KMnCI3 and T1MnCI3 show a similar behaviour. For instance, weak ferromagnetism has been reported [10] for the lowt e m p e r a t u r e distorted phase of the TI compound. The present p a p e r deals with the magnetic properties of NHnMnF3 and reports on heat capacity, a.c. magnetic susceptibility and magnetization measurements. The compound belongs to the class of Mn 2÷ compounds mentioned above, but is also a m e m b e r of the series of a m m o n i u m compounds NH4MF3 (M = Zn, Co, Mn) which we have extensively studied in relation to their structural, NH~ reorientational, and magnetic phase transitions [11-15]. In all these compounds structural phase transitions occur from cubic to tetragonal symmetry below r o o m temperature. In NH4MnF3 the cubic lattice o p a r a m e t e r is a = 4 . 2 4 2 4 ( 4 ) A at room temperature. At Tc = 182.1 K, an abrupt tetragonai elongation is found, the distortion c / a - 1 amounting to 0.4%. Below Tc the distortion increases continuously with decreasing temperature, and at 4 . 2 K the limiting lattice parameters° are a = 4.2080(12) A and c = 4.2659(14) A. Neutron diffraction measurements evidence an antiferromagnetic spin structure of type G below the magnetic ordering temperature, TN= 75.1 K. No discontinuity is observed in the lattice parameters at this temperature in the X-ray data, the elongation appears to increase continuously through the magnetic transition [12]. In all compounds of the series, the Mn 2÷ ion is octahedrally coordinated by F- ions. The ground state is a 6S5/2 sextet which is split into three Kramers doublets due to spin-orbit coupling. From E P R m e a s u r e m e n t s at r o o m t e m p e r a t u r e we have obtained for the Land6 factor a value of g = 2.0015(5), as found in Mn2÷-doped KMgF3 [16], while the reported energy difference between the Kramers doublets are of the order of 6.5 × 10 -4 cm -1. As our measurements are made
191
at temperatures higher than 4.2K, we may neglect the small fourth order anisotropy term associated with these crystal field splittings. Since the ground state is an orbital singlet, the isotropic (S = 5/2) Heisenberg model is closely satisfied by the Mn 2÷ compounds; in particular we shall compare our results to the theoretical predictions for the simple cubic case. In the tetragonal phase a discrepancy with respect to the above model can be expected due to the resulting inequivalency of the exchange paths in the three crystallographic directions, and also due to the possible presence of a weakferromagnetic moment, as in other distorted AMnF3 systems. Indeed, we may expect such an effect for NHaMnF3 because it was detected also in the isomorphous NI-LCoF3 c o m p o u n d [11]. On the other hand, Co compounds are m o r e likely to show weak ferromagnetism because of the much more important c r y s t a l - field effects. Lowfield susceptibility and magnetization measurements were thus needed to answer these questions. The p a p e r consists of three sections. In section 2.1 the heat capacity measurements are described and analyzed in terms of the proposed magnetic model. A comparison is m a d e with available data in the literature. In section 2.2 a.c. susceptibility at zero d.c. field and at H = 10 k O e as well as magnetization m e a s u r e m e n t s are presented and analyzed. In section 3 the obtained results are discussed.
2. Experimental results and analysis 2.1. H e a t capacity
The sample used in the heat capacity measurements was a powder obtained by the method of Handler et al. [17]. The heat capacity was measured between 5 and 350 K in an adiabatic calorimeter described elsewhere [13], and the results are shown in fig. 1. At the t e m p e r a t u r e of the structural phase transition (T~ = 182.1-+0.1 K) a very strong and sharp anomaly (C-if,~ = 122R) is detected, originating from the simultaneous reorientation of
192
J. Bartolomd et al. / Magnetic properties of NH4MnF~ I
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Fig. 1. Heat capacity data for NH4MnF3versus temperature. A magnetic ordering anomaly is detected at TN= 75.1 K. The second anomaly at Tc= 182.1 K is associated to the structural phase transition (C~pa*= 122R). the NH~ groups. A second anomaly is found at TN = 75.1 + 0 . 1 K and is ascribed to the antiferromagnetic ordering. As the present paper deals only with the magnetic properties of this material, we will restrict ourselves to the analysis of the second anomaly; the NH~ reorientation transition will be treated in a forthcoming paper [18]. The heat capacity measured below 150 K (fig. 2) consists of a contribution of the lattice phonons, as well as magnetic and NH~-rotational contributions. Assuming all these contributions to be mutually independent, it is possible to estimate the non-magnetic base line via the following procedure. Firstly, the data below 2 5 K is fitted to a simple Cp = A T 3 law (see insert in fig. 2) because both phonons and magnons give rise to a cubic law-temperature dependence in the present case. We have obtained A = 0.556mJ/K 3, which is somewhat higher than A = 0.310 and 0.334mJ/K 3 found by Montgomery [19] for KMnF3 and RbMnF3, respectively. Secondly, we
have calculated the low-temperature spin-wave contribution for the s.c. Heisenberg S = 5/2 antiferromagnet from the Kubo prediction [20] C / R = (7r2/2 × 35/2× 54) ( k T / J ) 3, with J/k = - 3 . 0 2 K as deduced from TN (see belo'~). The magnon result is shown as the dashed line in the insert of fig. 2, and the difference with the experimental data can be assigned to the phonon T 3 contribution. We can extend this estimation to higher temperatures by fitting the phonon base line deduced below 25 K to our data for the non-magnetic KZnF3 c o m p o u n d and applying the corresponding states law at higher temperatures [13]. Proceeding in this way, we find that the equation Cph .... (T, NH4MnF3)= Cp (fT, KZnF3) is verified for f = 0.92 below 25 K and we obtain curve d (fig. 2) for the phonon contribution up to higher temperatures. Finally, as a check, we have applied the same procedure to our data of NI-I4ZnF3 below 60 K, and we obtain the same curve d if we take f = 1.11 (for T < 60 K the contribution to the heat capacity of the NH~-libration is negligible).
193
J. Bartolora6 et al. / Magnetic properties of NH~VInF3 I
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T(K) Fig. 2. H e a t c a p a c i t y d a t a n e a r TN. C u r v e a: A T 3 fit of t h e e x p e r i m e n t a l data. C u r v e b: c a l c u l a t e d s p i n - w a v e c o n t r i b u t i o n . C u r v e c: n o n - m a g n e t i c b a s e line. C u r v e d: p h o n o n c o n t r i b u t i o n as o b t a i n e d f r o m c o r r e s p o n d i n g s t a t e s l a w f r o m Cp(KZnF3).
On the other hand, the librational contributions will definitely b e c o m e important above 100K, and have to be accounted for in the determination of the non-magnetic base line. We have applied a reverse procedure above 100 K assuming that the magnetic heat capacity tail will be given by the high-temperature limit for the s.c. Heisenberg model, i.e. C f f R = 4 ( S ( S + 1))2(j/k)2T -2. Using the same value of J / k = - 3 . 0 2 K as for the magnon contribution at low temperatures, we subtract this magnetic contribution from the measured points, obtaining curve c (fig. 2). By simple interpolation (dashed line) between curves c and d in the range 60 K < T < 100 K we obtain the estimated lattice contribution over the whole t e m p e r a t u r e range (fig. 2), and from the differences with the data, the anomalous magnetic Cp in the region near to and below the transition t e m p e r a t u r e TN is found. The m a x i m u m in this A anomaly reaches a value of 2.5R, and the entropy content is A S / R = 1.71. The difference of 4.6% in entropy from the theoretical value In 6, is small enough to conform
the validity of the procedure followed to estimate the non-magnetic contributions. The estimated magnetic heat capacity of NI-LMnF3 is depicted in fig. 3 and c o m p a r e d with the available data of KMnF3 [21] and RbMnF3 [22]. For the latter two cases we have deduced base lines from the published data by similar procedures. All data are plotted versus the relative t e m p e r a t u r e T/TN. T h e shape of the anomalies is similar although the heights and widths near Tr~ are somewhat different. W e explain these differences as being due to, e.g., the use of single crystals, and the application of special techniques for critical exponent studies in those other compounds. In Table I we have compared our critical entropy and energy parameters with the hight e m p e r a t u r e series predictions for the simple cubic Heisenberg S = ~ ferro- or antiferromagnet [23], since the available n u m b e r of terms for the specific heat series with S = 5/2 [24, 25] do not allow a reliable determination of those quantities. We have added for both cases the TN/O values which have been obtained by means
J. Bartolom6 et al. / Magnetic properties of NH4MnF~
194
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of the Pad6-approximants analyses [26] of the singularities in the staggered susceptibility [27] series yielding IJI/kTN= 0.0402(1). The prediction for the location of TN and the experimental value Try= 75.1K enables us to determine the exchange constant value J/k = - 3 . 0 2 K, used already in the above lattice estimation.
There is a good agreement between the experimental entropy values above TN and the theoretical ones for S = ~. Below TN the comparison with the S---:~ model is not adequate because the functional form with temperature of the reduced magnetization is different to that for finite spin, and Cp tends to a finite value at
Table I Entropy and energy parameters of NI-i4/VInF3 in comparison with the Heisenberg model S NH4MnF3 s.c. ferro or antiferro s.c. antiferro
5
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TN(K)
Tn/O
75.1 0.72 0.710(2)
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0.40 -+ 0.02 0.42
1.52 -+ 0.07
0.68 -+ 0.03 0.69
J. Banolom~ et al. / Magnetic properties of NHaMnF3
T = 0 K, violating the Nernst principle [23]. We have used the high-temperature specific heat series for S = 5/2 to obtain a theoretical prediction as close to TN as possible. In order to do this, direct Pad6-approximants have been used as extrapolation of the truncated series for S = 5/2 and the results for J/k = - 3 . 0 2 K are plotted in fig. 3 (curve a). Furthermore, in fig. 3 (curve b) we have drawn the extrapolation of the S = ~ high-temperature series in the s.c. model using the expression
CJR = P.A.[H.T.S.(S = oo) + B(1 - K/K~) -~] -
B(1
-
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with K c = 0.2313(1), B = +12.0, and ot = - 0 . 1 4 , [28] for the critical exponent. Within the experimental errors a reasonable agreement is obtained. A comparison of the data below TN to K u b o ' s [20] free spin-wave low-temperature theoretical prediction is included in fig. 3. However, the validity of this simple model extends up to T/TN=0.3 only, leaving a large gap ( 0 . 3 < T/TN < 1.2) for which a reliable theoretical prediction is lacking.
2.2. Magnetic measurements T h e magnetic measurements have been performed on the powdered sample used in the specific heat experiment, as well as on single crystals grown in gels by the method of Leckebush [29]. Additional powder samples obtained by crushing single crystals were studied. The zero-field susceptibility has been measured by means of a mutual inductance technique described elsewhere [30]. The t e m p e r a t u r e range covered was 4.5 K < T < 250 K; for the m e a s u r e m e n t s shown in fig. 4 the a.c. frequency was 332 Hz and the a.c. field amplitude 0 . 5 0 e . In agreement with the heat capacity measurements, the susceptibility data indicate an ordering t e m p e r a t u r e of TN= 7 5 . 1 ± 1 K , as derived from the observed small peak. In case of weak-ferromagnetic behaviour as observed here,
195
the transition t e m p e r a t u r e should be defined by the peak in the susceptibility, as in the molecular field theory. W e shall first proceed to compare our results with predictions for T > TN obtained from the Pad6-approximant analyses of the hight e m p e r a t u r e susceptibility series for the S = 5/2 Heisenberg s.c. antiferromagnet [24,25]. As the Land6 factor has been determined to be g = 2 . 0 0 1 4 , we adopt g = 2 and leave the exchange constant J/k as the only adjustable parameter. In the region from 250 to 180 K the best fit is obtained for J/k = - 3 . 2 7 K a n d is shown in fig. 5 as a 1/X versus t e m p e r a t u r e plot. This region corresponds to the cubic phase, i.e. to the ideal s.c. S = 5/2 magnetic model. At the structural phase transition which takes place at T = 182.1 K a small discontinuous increase in x ( T ) is detected. As a consequence, a new fit is needed below this t e m p e r a t u r e yielding J/k = - 3 . 1 1 ( 1 ) K (see fig. 5). With this value we explain our measurements within the experimental error of 1% down to TN. Short-range ordering is evidenced by the typical smooth antiferromagnetic m a x i m u m with a value Xmax= 19.20 × 10 -3 e m u / m o l at Tm,x= 82---1K. From these results and using the theoretical [31] predictions gmxlJ.]/NAg2lz~ = 0.0394(1) and kZmax/IJIS(S + 1) -- 3.07 ___0.01(1) we obtain the values of the exchange constant J/k = - 3 . 0 7 ± 0 . 0 3 ( 3 ) K and J/k = - 3 . 1 ± 0 . 1 ( 1 ) K , respectively. Considering all the errors involved, we obtain J/k = - 3 . 1 1 ± 0 . 0 1 ( 1 ) K as the best estimate, and a comparison of the theoretical curve with the experimental points is shown in fig. 4. At TN = 75.1 ± 1 K an abrupt increase in x ( T ) takes place, coinciding exactly with the magnetic ordering t e m p e r a t u r e determined in our Cp measurements. Since no structural change is found at this temperature, this indicates that the ordered state will correspond with a m o r e complicated spin structure than the simple twosublattice antiferromagnet. The most probable explanation of the peak at TN is the occurrence of some canting between the magnetization axes of the two sublattices, giving rise to weak-ferromagnetism, which is a c o m m o n feature in the distorted perovskites, as already mentioned in the introduction. However, in our previous neu-
196
J. Bartolom# et al. / Magnetic properties of NH4MnF~
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T(K) Fig. 4. Zero-field magnetic susceptibility versus temperature for N I ~ F 3 . A(S)~ Different series on milled crystals. A~7 Randomly oriented single crystals. The two series differ in sample mass, m = 0.6398 and 0.2804 g, respectively. • Stacked single crystals with two faces perpendicular to the c axis, m = 0.1453 g.--Theoretical prediction for the Heisenberg antiferromagnetic s.c. S = ~ model calculated by the Pad6-approximants analysis of the H.T.S. for J/k = -3.11 K.
tron diffraction study of the magnetic structure of NI-LMnF3, no evidence of a non-compensated m o m e n t was detected [12], and consequently the associated ferromagnetic component must be very small. We recall that a similar situation was met previously for NI-LCoF3 [11, 12] in which the same type of structural distortion occurs. A canting angle of 1° deduced from magnetization m e a s u r e m e n t s extrapolated to H - - 0 , could not be detected by the neutron experiment. The peak observed at TN in x(T) is somewhat smaller than the sharp and narrow peaks found in other Mn weak-ferromagnets [30]. As a matter of fact, the peak amplitude measured depends on the size of the particles (fig. 4). For crystallites less than l ~ m the peak is at most 1% of the value of Xm~, while an oriented collection of
cubic single crystals yields an increase up to 10% of the peak amplitude. We have p e r f o r m e d heating and cooling runs in order to detect possible hysteresis effects, but the value of TN and the sharp tail above TN always remained the same although some minor differences, amounting to a few percent, were detected in the low-temperature tail. There appears thus to be no drastic hysteresis effect associated with the transition. U p o n a further decrease of the temperature, x ( T ) is found to approach smoothly a lower limiting value. Two different measurements reported in fig. 4 show qualitatively a similar behaviour; however, for a r a n d o m arrangement of crystals a higher value of x ( T = 0) is measured than with an arrangements of cubes stacked with
J. Bartolomd et al. / Magnetic properties of NH4MnF3
197
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Fig. 5. Reciprocal magnetic susceptibility versus temperature of N-H4MnF3. The full lines represent the theoretical fits above and below To.
the faces perpendicular to the axis of the a.c. field. As we shall see below, this can be explained in terms of the statistics in the random orientation of large crystals divided into crystallographic domains. Another set of zero-field susceptibility experiments near TN were performed in order to study the size dependence of the weak-ferromagnetic peak. The results for randomly oriented single crystals (average width d - - i mm), crushed crystals ( d - - 0 . 1 mm), and directly synthesized powder (d = 0.5 ~m) are shown in fig. 6, in which the same a.c. field amplitude was used in the three cases. The ordering temperature remains the same in the first two cases (within the experimental errors), while an increase of 0.1 K in Tr~ is observed in the latter one. The heights of the peaks show a strong size effect increasing from a mere 1% of Xm~x to 10% for the larger crystals. Finally, in a separate set of experiments performed on the single crystals, the
a.c. field amplitude was varied between 0.05 Oe and 5 . 0 0 e , yielding variation in the heights of the peaks too small to be significant. Furthermore, we have measured differential susceptibility at T = 4.2 K in a uniform field up to H = 10kOe, on a collection of randomly stacked single crystals. The frequency and a.c. field amplitude were the same as in the previous experiments. We show the results in fig. 7, where we observe a peak, and a tendency to a constant value at H > 7 kOe, which is ~y(H = 0). Both facts indicate the occurrence of the spin-flop transition at HsF = 3.7 +- 0.2 kOe, the height of the X-peak being so low because it is the directional average of the crystals. (One only expects XII(HsF) = 1/D, with D the demagnetizing factor, in the case of a single-domain crystal oriented parallel to the field.) Thus, the susceptibility measured above 7 k O e corresponds to x ± ( T = 4.2 K). From the values of the spin-flop field and the exchange constant derived from TN, and
J. Bartolomd et al. / Magnetic properties of NHaMnF3
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using t h e r e l a t i o n
Hsv =
(2HEHA + H~A)/(1 -- XII/X±),
w h e r e HE = 21J]zS/gl.tB is t h e e x c h a n g e field a n d H A t h e t o t a l a n i s o t r o p y field, we o b t a i n c t HA~HE = 1.2 x 10 -3. Moreover, we have measured the susceptibility as a f u n c t i o n of t e m p e r a t u r e at H = 10 k O e , i.e. in t h e s p i n - f l o p p e d state, o b t a i n i n g t h e results shown in fig. 8. A s e x p e c t e d , we o b s e r v e the x±(T) v a l u e up to t h e p a r a m a g n e t i c r e g i o n . T h e weak-ferromagnetic peak has disappeared b e c a u s e t h a t c o m p o n e n t of t h e m a g n e t i c m o m e n t has o b v i o u s l y b e e n s a t u r a t e d . T h e m a x i m u m s l o p e of t h e c u r v e is o b s e r v e d at T = 75 ± 1. K, thus n o a p p r e c i a b l e v a r i a t i o n of the o r d e r i n g t e m p e r a t u r e is d e t e c t e d . A s we k n o w a , w e m a y c a l c u l a t e t h e s p i n - w a v e p r e d i c t i o n for X±(0) [20] for t h e s a m e J/k=-3.11K, y i e l d i n g 1 9 . 0 8 x 10 -3 e . m . u . / m o l , which is l o w e r than the
m e a s u r e d v a l u e of 1 9 . 9 ± 1 × 10 -3 e . m . u . / m o l . C o n v e r s e l y , f r o m this v a l u e we m a y d e r i v e a new d e t e r m i n a t i o n of t h e e x c h a n g e c o n s t a n t , o b t a i n ing J/k = - 2 . 9 8 ( 1 ) K. In fig. 8 we h a v e i n c l u d e d t h e s p i n - w a v e t h e o r e t i c a l p r e d i c t i o n s for x I ( T ) f o l l o w i n g t h e m e t h o d of Keffer [32], for both values of t h e e x c h a n g e c o n s t a n t , as well as the h i g h - t e m p e r a t u r e series t h e o r e t i c a l curve for the paramagnetic phase. Within the experimental e r r o r s t h e fit is s a t i s f a c t o r y a b o v e TN, h o w e v e r , t h e e x p e r i m e n t a l X± is m u c h a b o v e the t h e o r e t i cal p r e d i c t i o n at low t e m p e r a t u r e s . Such an effect has also b e e n f o u n d in K M n F 3 ( m e a s u r e d at H = 9 . 6 4 0 k O e [33]) and its origin can b e t r a c e d to t h e s t r u c t u r a l c h a n g e s o c c u r r i n g in t h e s e m a t e r i a l s . In o u r case, it c o u l d just b e d u e to a c o n t i n u o u s v a r i a t i o n of the t e t r a g o n a l cell p a r a m e t e r s as a function of t e m p e r a t u r e . M a g n e t i z a t i o n m e a s u r e m e n t s in fields up to 2 2 k O e on a collection of r a n d o m l y o r i e n t e d single crystals h a v e b e e n p e r f o r m e d at T = 4.2 K
199
J. Bartolomd et al. / Magnetic properties of NH4MnF3 i
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T(K) Fig. 8. (O) Magnetic susceptibility of NH4MnF3 at constant magnetic field H = 10 kOe, as a function of temperature. (El) Value obtained from measurements shown in fig. 7. Curve a: H.T.S. prediction of X for J/k = -3.11 K. Curve b: Spin-wave prediction for J/k = - 3 . 1 1 K. Cm-ve c: idem for J/k = - 2 . 9 8 K.
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J. Bartolomd et al. / Magnetic properties of NH4MnF3
in a vibrating sample magnetometer. In fig. 9 we show the results for H < 1 0 k O e on a more expanded scale. A linear increase in the magnetization is found up to 2.2 kOe. A change in curvature indicates the occurrence of the spin-flop transition. Taking the inflexion point as the critical field we get Hsv = 4 + 1.0 kOe. A b o v e 7.5 kOe the behaviour is again linear with its slope corresponding to the X± susceptibility. The value of Hsr obtained in this way and the ratio between the high- and low-temperature linear parts of the magnetization corresponds roughly to 3/2, in agreement with the X versus H measurements shown above. Interestingly, both the high- and low-field parts of the magnetization curve in fig. 9 can be extrapolated to the origin, so that no measurable evidence for a spontaneous weak-ferromagnetic moment is found, in contrast to the results
obtained for NH4CoF3 [11]. Considering that the resolution of the extrapolation is better than 10-3glxBS, the above result implies a canting angle of less than 0.1 °. Moreover, magnetization measurements, obtained with a pulsed-field magnetometer, were also performed at T = 4.2 kOe, on a collection of randomly oriented single crystals and on powders. A linear behaviour is detected up to 400 kOe. The slope of the magnetization curve equals that for H > 7 . 5 kOe in fig. 8 and has a value of X ± = 2 0 . 5 - + 0 . 5 x 10 3e.m.u./mol. As a check similar pulsed-field measurements were performed on RbMnF3 powder yielding a slope of 17.66 x 10 .3 e.m.u./mol, which compares satisfactorily with X± = 17.43 x 10-3 e.m.u./mol obtained previously in susceptibility measurements [2] (see fig. 10). We may now compare the value of X± deduced
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201
J. Bartolomd et al. / Magnetic properties of NH4MnF3 ,
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Fig. 10. Pulsed-field magnetization measurements of at T = 4.2 K. Curve a: NH,tMnF3 randomly oriented single crystal. Curve b: RbMnF3 powder. from the magnetization extrapolation with the zero-field x ( T ) measurements near T = 0 (of fig. 4). For both data sets shown, one with parallel stacked crystals and the second with randomly oriented ones, differences are found with the expected powder susceptibility for a uniaxial antiferromagnetic, 2Xl, which would be in between both series of measurements. The experimental results may be explained as follows: one possibility is that upon distortion each crystallite selects one of the three equivalent quaternary axis. As a consequence, we have for the parallel stacked sample a finite number of crystals with distortions along any of the three space directions, and in the second case we get a collection of randomly oriented distorted crystals. A n o t h e r possibility is that each crystallite divides at Tc into a large number of crystalline domains, each of which selects at random the distortion axis among the three quaternary ones. We think the latter cause is the most probable one because we have observed the existence of domains directly by birefrigence and Raman experiments. In both cases, we should expect a magnetic susceptibility approaching the powder
value, as actually f o u n d . - H o w e v e r , differences from )Co may occur since the susceptibility will depend on the particular ratio of the total volumes of perpendicular to parallel domains. The ratios needed to fit the data are 0.7 and 0.6 for the random and stacked collections of cubic crystallites as compared to 0.67 for a powder.
3. Discussion In the cubic phase, the exchange interaction path is of the collinear M - F - M type. We can compare our results of J / k with the predictions for its dependence on the M - M distance, given by de Jongh and Block [34], who found that for XMnFa and X2MnF4 manganese fluorides the J / k values follow approximately a r -'2 power law. Our determination of J / k = - 3 . 2 7 K in the cubic phase °with corresponding lattice constant a = 4.242 A is in agreement with the trend observed for the other Mn fluorides mentioned. However, below 180K a seeming inconsistency occurs because the average M n - M n dis-
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J. Bartolomd et al. / Magnetic properties of NH4MnF~
tance diminishes, so a larger J/ku value should be expected instead of the lower one actually found. This same effect is known to occur for KMnF3 [33], for example. The reason must be found in the nature of the structural transition producing the distorted pseudo-tetragonal low-temperature structure. A detailed analysis requires knowledge of the atomic positions, while for NH4MnF3 only powder X-ray data is available. In the absence of this, we can invoke the generally observed behaviour using the simplified model proposed by Glazer [35] for distorted perovskites, based upon coherent rotations of basically regular MX6 octahedra. According to this model the lowt e m p e r a t u r e structure would be compatible with symmetry groups involving a single tilt around the c axis of these octahedra. In that case,o the pseudo-tetragonal cell p a r a m e t e r c = 4.2659 A implies a tilt angle of 9.4 °. Though this is only a rough estimate it seems a reasonable assumption in view of the observed tilt angles of 8.7 ° for NH4MnCI3 [36], as detected by X-ray diffraction on a single crystal, and 5.2 ° for TIMnCI3 and 8.8 ° for KMnF3, as derived from birefringence m e a s u r e m e n t s [37]. Within this model, the superexchange paths will now consist of two collinear ones along the ¢ axis, and four paths with an M - F - M angle of 161 °. For these last pathways the departure from collinearity implies a reduction of a few percent in the strength of the antiferromagnetic interaction, for the same length in the M - F segment [38]. We have averaged the distortion effects on the magnetic interaction assuming six collinear pathways with M - M distances of 4.266 A. By using the roomt e m p e r a t u r e values for J/k and M - M distance, and the r -12 law, we obtain J/k = - 3 . 0 6 K for the distorted phase, in fair agreement with the values of J/k determined in our low-temperature experiments. Considering the approximations involved, this model explains satisfactorily the reduction of J/k in the distorted phase. The peak in the susceptibility that appears at TN indicates that the ordered spin-structure is m o r e complicated than a simple two-sublattice antiferromagnet. This peak is accompanied, even for H = 0, by the appearance of an imaginary c o m p o n e n t in the complex susceptibility, imply-
ing the presence of a non-zero (local) magnetization. These facts point towards the presence of a canting of inequivalent Mn spins, giving rise to a non-compensated moment. We observe a weakferromagnetic behaviour similar to that detected in KMnF3 [7] or TtMnCI3 [39], the origin of this canting is probably due to single-ion anisotropy. From the spin-flop field of HsF = 3.7 kOe, one calculates an anisotropy field HA = 1 4 . 0 0 e and a corresponding anisotropy energy of ( K ~HAM~)--2.0 × 10~ erg/mol. A rough estimate of the dipolar anisotropy field is an order of magnitude higher, implying the presence of other sources of anisotropy such as crystal-field splittings, which compensate in part the dipolar anisotropy. In view of the lack of precise crystallographic information we do not pursue this matter further. The presence of crystalline domains in the single crystals has been mentioned in the previous section in connection with the low-temperature susceptibility and also plays an important role in the discussion of the X anomaly at T~. As we said in the above, their presence in NHaMnF3 has been checked experimentally, but their size could not be well determined. From our preliminary R a m a n m e a s u r e m e n t s we can say that they are of the order of 100 #,m, which seems to be similar to the size of single domain regions in KMnF3 [40]. Actually, the sizes may depend on the rate of t e m p e r a t u r e decrease and also may differ from one part of the crystal to the other. In this connection, it is noteworthy to mention a detailed report on NH4MnC13 [36], in which the distribution of domains was described as being not random, the three possible domains with distortion axes along the quaternary ones occupying 20, 53 and 27% of the crystal. In our directly synthesized powder sample each particle had a size less than 1 ~,m, so it is certainly a single domain. On the other hand, the particles in the crushed single crystal samples were of average size 100 #,m, so they may be single or multi-domain, whereas the large crystals of 1 m m width are definitely divided into several crystalline domains, as observed. The magnetic properties of the m e m b e r s of
J. Bartolomd et al. / Magnetic properties of NH4MnF3
this series so far studied have been shown to depend exclusively on the structural distortions [7-10]. In fact, the weak-ferromagnetic moment measure of ms-~4.0x 10-3e.m.u./mol in both KMnF3 [7] and T1MnCI3 are due to the tilts of the octahedra mentioned above. As we have the same type of structural distortions we may expect the same behaviour. However, our magnetization measurements do not show a spontaneous ferromagnetic moment, and the A anomaly in X does not reach by far the value 1 / D which should be associated to it. This difference could be due to a much smaller value of ms in our compound, but it is more likely that it is caused by the division into crystallographic domains. So, if we take the ms found in the other two compounds as an upper limit, each crystallographic domain becomes a magnetic domain as ordering takes place and, as a consequence, has a non-zero net moment. Since equipartition of crystallographic domains in all directions is expected to occur, compensation of the moments takes place and no spontaneous moment appears. The magnetic domains are thus separated by lattice defects and magnetic alignment of the moments can only take place if we remove them. Nevertheless, it is clear from our measurements that we have not achieved this situation by means of the applied magnetic fields. It is interesting to mention that a similar behaviour is reported for T1MnCI3 [10] in which it was possible to obtain magnetic single domains by means of a uniaxial stress. Since incomplete equipartition of crystallographic domains may happen, as was argued above, the difference in magnetization may not be exactly zero. This small net moment would give rise to an extra susceptibility that shows a peak as the magnetic domains appear at TN. When the magnetic structure is established and fixed below TN the walls cannot be moved by the small a.c. field and the susceptibility becomes once more antiferromagnetic, as observed. The height of the anomaly will depend strongly on the size of the particles and their distribution. So, in the case of very fine powder, each crystallite is probably a single domain, but the distribution of their orientations is at random
203
and the height of the anomaly in X is the smallest. For the larger crystals, 1 mm width, the distribution of the d e f e c t s - which give rise to the crystallographic d o m a i n s - can be very inhomogeneous and equipartition is less probable, giving rise to the largest amplitude in the peak. This explanation is consistent with the fact that different amounts of crystals or different arrangements give rise to variations in the peak height (fig. 6). Even in the ordered region, the magnetic susceptibility already depends on the particular arrangements of the crystals, the experiments yielding curves at both sides of the powder prediction, which again can be explained by the unequal distribution of the crystallographic domains. A similar dependence on particle size of the excess susceptibility due to weak ferromagnetism has been found in KMnF3 at low temperatures by Maartense and Searle [8]. In that case, the critical size of the particle needed to suppress the anomaly was 20 txm, which is of the order of our estimates. Although this precedent gives support to our interpretation, an actual determination of the magnetic and/or crystalline domain sizes would be welcome. Finally we mention that the tetragonal symmetry evidenced by the X-ray measurements cannot support weak ferromagnetism, by magnetic group theory, so the actual symmetry must be lower. As mentioned for NH4CoF3 [11], the symmetry could be orthorhombic. However, a careful single-crystal X-ray determination of the low-temperature crystal structure would be needed to establish this more firmly.
Acknowledgments We are very grateful to H.J.M. de Groot (K.O.Lab.) for providing us with the high-field and pulse-magnet data up to 40 T. We thank Dr. Van Duyneveldt and Dr. Groenendijk (Kamerlingh Onnes Laboratorium, Leiden) for their expert advice regarding the susceptibility experiments and discussions. Dr. Pu6rtolas' assistance in the susceptibility measurements under field, and Dr. Calleja's (Universidad
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J. Bartolom~ et al. / Magnetic properties of NH4MnI~
Aut6noma de Madrid) preliminary report on Raman measurements are thanked. Financial support for this project has been provided by the Spanish Comision Asesora de Investigaci6n and the Volkswagen Foundation.
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