with the antiferromagnetic interlayer coupling H,r was found to be 800 Oe, whereas the anisotropies .... can may be (Woods) soldered together. By letting He gas ...
Physica
58 (1972)
277-304
MAGNETIC
o North-Holland
Publishing
MEASUREMENTS
Co.
ON (CzHsNH&
FERROMAGNETIC LAYERS COUPLED BY A VERY ANTIFERROMAGNETIC INTERACTION
CuQ WEAK
L. J. DE JONGH, W. D. VAN AMSTEL and A. R. MIEDEMA Natuurkundig
Laboratorium
der Universiteit
zlan Amsterdam,
Nederland
Received 5 July 1971
synopsis The differential magnetic susceptibility x = (&?~@H)T of (CzH5NHs)&uC14 has been studied as a function of an extra external field (O-2 kOe) and of temperature (l-30 K; T, = 10.20 K). The compound is a typical layer-type ferromagnet, with a very weak antiferromagnetic coupling between the Cu2+ layers. The magnetic phase diagram of the antiferromagnetic structure has been established. From this we have obtained quantitative information about the small deviations from the ideal 2-dimensional Heisenberg model present in this compound. The effective field associated with the antiferromagnetic interlayer coupling H,r was found to be 800 Oe, whereas the anisotropies within and perpendicular to the ferromagnetic layer have been obtained as HF m 75 Oe and Hiut FZ 1000 Oe, respectively. The ferromagnetic intralayer exchange field is some orders larger: Hf = 5.1 x 105 Oe. The fact that x is large enough to be measured differentially (a consequence of the fact that H,f < HP) facilitates a detailed study of a number of properties which are interesting from a theoretical point of view, viz. (1) the temperature dependence of ~1, near T, in zero external field and in a number of constant magnetic fields, (2) the divergence of x at the spin-flop transition, (3) the temperature dependence of the phase boundaries in the phase diagram.
1. Introdt.dion. In previous papers l-4) it has been reported that the Cu compounds of general formula (CnHzn+lNH3)z CuX4, where n = 1, 2, 3, 4, 5, 6, 10 and X = Cl or Br, may be considered as consisting of nearly isolated magnetic layers. The interlayer coupling J’ was expected to be some orders of magnitude smaller than the exchange interaction Jf between the Cu ions within the same layer, which has the ferromagnetic sign. This has been anticipated from the crystal structure, studied by Willett et a1.5) for the case of the methyl- and ethyl-chlorine compounds and by Barendregt and Schenks) for the propyl-chlorine compound. Briefly, the structure consists of sheets of CuClz- ions, separated by two layers of alkyl-ammonium groups. The successive layers are bound together by van der Waals forces acting between the carbon atoms of the alkyl groups. The space group is 277
L. J. DE JONGH, W. D. VAN AMSTEL AND A. R. MIEDEMA
278
. cu Cl
t‘
C3N QC c
lFig.
1. Crystal
ethyl-ammonium Cu atom
structure
of (CzHsNHs)2CuC14.
groups are shown.
in the center
of the upper
For the sake of clarity
The Cl environment face.
b
This
figure
only part of the
is shown completely has been kindly
for the
prepared
by
A. R. Kop of our laboratory.
Pbca. The cell constants of (CsHsNHa)s CuC14 are a0 = 7.47, be = 7.35, CO= 21.18 A. A drawing of the face-centered orthorhombic unit cell based upon the (unpublished) results of Steadman and Willett is given in fig. 1. For one of the Cu atoms the Cl environment is shown more clearly. In refs. l-4 the quadratic Heisenberg ferromagnet has been proposed as a model for these salts since the interaction between Cus+ ions is usually fairly isotropic and the Cus+ ions within a layer build up a nearly quadratic network (ao/ba = 1.02-l .04). It has been found 3116)that both the high-temperature (T > T,) susceptibility and the spin-wave contribution to the heat capacity (T < T,) do show the features expected for this particular model. On the other hand it is clear that the coupling between the layers J’ (and also the anisotropy) will come into play as the transition temperature is approached. In particular the susceptibility at temperatures T & T, will be completely dominated by J’. This may be understood by realizing that, no matter how small J’ is compared to Jf, the magnitude and behaviour of the susceptibility will be widely different whether J’ effectuates a parallel or an antiparallel ordering of the ferromagnetic planes. Thus, as far as the susceptibility is concerned, the system studied is at low temperatures essentially 3-dimensional in character.
MAGNETIC MEASUREMENTS ON (c~H~NH&c~c~~
279
For the ethyl-chlorine compound studied here the sign of J’ is negative. We will therefore denote the interlayer coupling by the symbol Jai in what follows. The transition temperature will be denoted by Tc rather than TN, however, a.o. because it is the ferromagnetic intralayer interaction that for major part determines the position of the transition point. One of the attractive points of investigating the properties of inter(CsHsNH s) s Cu Cl 4 is that as a consequence of the antiferromagnetic layer coupling we may obtain quantitative information about the anisotropy and Jaf by studying the field dependence of the susceptibility at T < T,. Values for these quantities can be derived from the critical fields at which transitions from the antiferromagnetic to the spin-flop state and from the spin-flop to the paramagnetic state occur. Since both the anisotropy and JQf are very small, these transitions occur at low fields (H < 3 kOe). The outline of this paper is as follows, After a description of the experimental details in section 2, the high-temperature susceptibility results and the a.c. measurements in zero external field are presented insection 3. In the following section the field dependence of the susceptibility is discussed. Finally, in section 5 some concluding remarks are given. One may have noted that the properties of (CsHsNHs)sCuC14 in many respects resemble those of CrCl s, a compound that has been extensively studied by Narath et al. 7). Also in CrCls the magnetic layers are separated by two layers of nonmagnetic ions. However, in the Cu compound the 2dimensional features turn out to be more pronounced as a consequence of the lower spin value. This may be inferred for instance from a comparison of the ratio of the Curie-Weiss temperature 8 to the actual transition temperature Tc, which equals t3/Tc R+ 2 for CrCls as compared to t9/Tc M 4 for the Cu compound. In ref. 8 a comparison has been made of the properties of the Cu compound with those of CrCls and other (nearly) 2-dimensional Heisenberg magnets. 2. Experiment.
A mutual inductance
bridge operating
at a frequency
of
119 Hz has been used to measure the a.c. susceptibility. With this method the initial susceptibility in the limit of zero field is fairly well approximated because the amplitude of the measuring field may be kept very small. In our case it did not exceed 1 Oe. No dependence of x on the amplitude has been observed for these values. As the transition temperature T, = 10.20 K is well outside the liquid 4He range, the sample has to be isolated from the helium bath. Fig. 2 shows how this has been accomplished. The measuring-coil system is put in a glass capsule which is suspended by three posts extending from the lower half of a can made of brass. With the aid of the heating coil (8) the two parts of the can may be (Woods) soldered together. By letting He gas inside the can, which is immersed in liquid 4He, the capsule can be cooled down to the
L. J. DE
280
JONGH,
W. D. VAN
AMSTEL
AND
A. R. MIEDEMA
El
-_-
-P
Sz(-)
6
-__
-
S31*)
-
s, I-1
5
Fig.
2. Apparatus
1) to high-vacuum capsule
for
measuring
pump
with high-vacuum
consisting
of a primary
thermometer; 9) feed-throughs,
a.c.
susceptibilities
or He gas reservoir; joint; coil
(P)
7) Wood’s_soldered connected
4) sample, and
three
joint.
by constantan
in the
2) heat
mounted
wires;
(copper
on sample
secondary
Heating
region
shield coils
is provided 10) epibond-
holder;
(S)
1 < T < 50 K. disk);
3) glass
5) coil system
as sketched;
by
8);
8) heating
or epoxy
resin
6) Gecoil; feed-
throughs.
bath temperature whereafter the can is evacuated (lo-6 mm Hg). In this way the capsule is isolated from the bath and may be heated by a heater wound upon the copper foil in which the capsule is thightly wrapped. We used “coil foil” to avoid eddy-current effects. The foil, together with a small amount of He gas with which the capsule is filled, ensures that the capsule and its contents retain a uniform temperature. The uniformity has been checked by measuring the temperature simultaneously at different places inside the capsule, while varying the degree of vacuum in the can on purpose. The feedthroughs of the capsule and the can are connected by constantan wires in order to minimize the heat leak. The heat input required to keep the capsule at a temperature of about 10 K is of the order of lo-4 W. The sample holder rests on the coil system as shown. It is readily acces-
MAGNETIC
MEASUREMENTS
ON (CzH5NH3)2CuCla
281
sible by removing the upper cap of the capsule. The position of the sample may be adjusted by the screw-like arrangement sketched. The sample itself is fixed on a thin disk, which may be rotated about two mutually perpendicular axes. The different parts of the sample holder have been made of lucite or nylon. As shown in fig. 2 the coil system
used is of the conventional
kind. The
coils are wound on a holder made of Epibond 100 A. The dimensions are on scale, the length of the primary coil P being 8 cm. The secondary coil consists of three parts. Si and Ss together having the same number of turns but being oppositely wound as Ss, in which the sample is placed. This has been done a.o. to minimize the empty-apparatus signal. The field of the primary coil has been made homogeneous within 1y. over the length of the three secondary coils for the same purpose. The secondary coils have been wound of Povin D copper wire of 0.07 mm diameter and have a total of 14,200 turns together. The primary consists of three layers of 0.17 mm diameter wire with a total of 1250 turns. Extra turns at the ends of P provide the mentioned homogeneity. To further minimize the empty-apparatus signal, the Ge thermometer has been put at a position where the field of the primary is essentially zero. Also soft-soldered joints inside the capsule have been avoided. The susceptibility x(T) is obtained from the bridge readings N(T) according to the relation N(T) = ax(T) + No + AN&‘). The last two terms in the right-hand side of this equation represent the empty-apparatus signal, due a.o. to incomplete compensation of the secondary coils. The constant No varies only slightly for successive measuring days. The temperature-dependent part ANo( caused a.o. by the thermal expansion of the coils, proved to be reproducible and could thus be obtained with reasonable accuracy. Moreover, the magnitude of diva(T) between 8 and 20 K was only 100 bridge units whereas in general the measured susceptibilities reach 103-106 units below T,. In the case of a measurement on a small single crystal the constant No is determined by comparing its x at temperatures T M 2T, with the measurements on a large powdered sample of the same material (a few grams), for which No has been obtained by extrapolation methods at temperatures T w 4T,. The constant a has been determined by calibrating the coil system by means of chromic potassium alum. Crystals of various sizes and shapes were used, in order to eliminate remaining uncertainties related to the actual position of the sample with respect to the pick-up coil. TO provide for the extra constant field in the field-dependent measurements, a 32 cm long solenoid was constructed producing 500 Oe/A. It is suspended in the liquid Ns surrounding the helium dewar. This field is homogeneous within 0.05% over a length of 2 cm. It has been calibrated with a Hall probe which in turn has been calibrated by means of proton resonance. The largest misalignment of the axis of the solenoid with respect
282
L. J. DE JONGH,
W. D. VAN
AMSTEL
AND
A. R. MIEDEMA
to the chosen orientation of the crystal will be about 8”. For the a.c. measuring-coil system the error in the orientation is only 3” at most. Crystals of (CsH5NHa)sCuC14 have been prepared at our laboratory by slow evaporation of aqueous or alcoholic solutions of C2H5NHaC1 and CuC12 (stoichiometric mixture). The sample used in these experiments is a thin platelet weighing 0.06055 f 0.04% grams, of dimensions 7.36 x 7.62 x 0.62 mms. The c axis is perpendicular to the plane of the platelet. The a and b axes have been located with the aid of a microscope using polarized light and proved to be the bisecting lines of the angles formed by the sides of the platelet. Other crystals grown from the same solution have been analysed. In all cases the weight percentages of Cu and Cl were found to be in accordance with the calculated values, the error in the analysis being about 1%. The Ge thermometer used in these investigations and those used by Bloembergen in his heat-capacity experiments have been carefully compared. Furthermore, absolute calibration has been accomplished by comparison with a Pt resistance standard in the region T > 10 K. In the range T < 4 K the susceptibility of a crystal of chromic potassium alum was used as a reference, the temperature being calculated from the formula x = C/(T + 19) (0 > 0). The constants 0 and C have been determined using temperatures derived from measurements of the vapour pressure of the 4He bath, in the temperature regions where the errors involved are small. The 4He 1958 scale was used. The value of f3 derived from least-squares fits to the data is consistent within 2 mK with that obtained by Durieux et al. for this salt 9) in the experiments used in the determination of the 1958 scale. The region 4 < T ( 10 K was spanned by using both the magnetic thermometer and a carbon resistor la). Estimates of the deviations from the absolute scale are: a few mK for 1 < T < 4 K, 0.3% for 4 < T < 10 K, 0.2% for 10
20 K. For the sake of completeness we shall also present in section 3 the susceptibility resultsa) at temperatures T > Tc, where they have been obtained from magnetization measurements in fields of 4 and 10 kOe with a force method. Powdered samples were used, weighing about 50 mg. The values for the Curie constants C used in the following sections have been calculated from the g values measured by Vega at our laboratory ll). For all Cl compounds (YZ= l-6) in the series the value along the c axis was found to be ge = 2.05 & 0.01. In the ab plane no anisotropy could be detected: g,,, = 2.16 f 0.0 1. These values have been used in order to calculate the susceptibility as x/C along the various crystallographic axes. For the powdered samples we took giowd. = Q(g2,+ 2g&). We remark that the same g values as measured by Vega have also been reported by Furlani et aZ.12) for the compound (CHaNHs)sCuC14. For (CHaNHs)sCuC14 and (CsHaNHa)sCuC14 Willett et al. 13) have found gc = 2.05 and g,b = 2.14.
MAGNETIC
MEASUREMENTS
283
ON (CsHsNH3)sCuC14
0 0.5
0
1.0
1.5 -=-XT
Fig. 3. The susceptibility
The transition
wersus J/kT. = 4 kOe;
x
of (CsHsNHs)sCuC14 temperature
: H = 0 (a.c.-susceptibility
s.q. Heisenberg magnet
ferromagnet;
in the region
is J/kT,
T >
T, plotted
as C/XT
1.81. n : H = 10 kOe; o : H = measurements) ; 1 : susceptibility series for the
2: susceptibility
(abscissa scaled by a factor C/XT =
1 -
=
series for the b.c.c. 2)
; 3 : molecular
Heisenberg
ferro-
field prediction
2JIkT.
3. High-temfieratzwe and zero-field suscefitibilities. In fig. 3 the x measurements in the high-temperature region (T > T,) are presented. The susceptibility is dominated by the ferromagnetic intralayer exchange interaction Jr in this range. It has been plotted as C/XT versus J/kT( J= Jf), so that the molecular-field result appears as the straight line (labelled 3 in fig. 3) : C/XT = 1 - 0/T (0 = 2 J/k for the quadratic lattice with S = 3). As discussed in ref. 3 the experimental data have been fitted to a theoretical curve, which is the full line labelled 1 drawn through the experimentalpointsin the region J/kT 1 K, Colpai6) of our laboratory has derived values that are about 10% lower. The possible origins of this systematic difference are extensively discussed in ref. 16. Fig. 3 shows that the deviation of x from the molecular-field result is very large for the 2-dimensional Heisenberg model. Eor comparison the series results for the b.c.c., s = 4, Heisenberg ferromagnetr7) has also been included: the dotted curve labelled 2. The abscissa has to be scaled by a factor 2 for the 3-dimensional lattice as the number of neighbours is doubled in going from the s.q. to the b.c.c. lattice. It is obvious that even in the 3dimensional case the usual procedure of obtaining a 0 value by drawing a straight line through the measuring points at T > T, introduces serious errors, unless one really goes to very high temperatures. The susceptibility is seen to become field dependent at JIkT > 0.8. Therefore, we have included some points measured with the a.c. bridge (zerofield method) on a powdered sample ( FZ 2.3 g). These results coincide with those measured in 4 kOe for J/kT < 1.O. As the transition point (J/kTc = 1.81) is approached the effects of the interlayer coupling and the anisotropy will gradually come into plays), and for T 5 T, they will dominate the magnitude and the behaviour of the susceptibility. In (CsH5NHa)&uC14 this coupling is negative, which leads to the remarkable result that while at T> T, x shows the characteristics of a
II IK‘
34
If 5 ._
Fig. 4. The susceptibility of antiferromagnetic (C~H~NH~)&UC& in the region T e T, plotted as x/C WYSUSTIT,. The insert shows the spin structure as deduced from
the magnetic
measurements.
The
data have effects.
been
corrected
for demagnetizing
MAGNETIC
2-dimensional
MEASUREMENTS
ferromagnet,
becomes of a 3-dimensional In fig. 4 the susceptibility
its behaviour
ON (CzHsNH3)&uC14
is changed
at T m Tc, where it
antiferromagnetic nature. results measured in the low-temperature
have been plotted as x/C veys%usthe reduced in the insert of fig. 4, x was measured along The transition temperature T, was taken the maximum in the specific heat occurs : T,
285
region
temperature T/T,. As indicated the three crystallographic axes. as the temperature at which = 10.20 * 0.01 K, as obtained
by Bloembergen 15). The susceptibility shows the behaviour to be expected for a simple two-sublattice antiferromagnet, the preferential axis for the spins being the a axis, which is the longest crystallographic axis within the Cuz+ plane. This direction is favoured by the dipole-dipole interaction. The difference between the two perpendicular susceptibilities x\ and XT originates from the out-of-plane anisotropy Hiut. Apparently there is an orthorhombic anisotropy in this compound with the b axis as the next-preferred direction. The anisotropy within the Cuz+ plane (between the a and the b axes) will be denoted by Hii in what follows. From the values of & and XT extra-polated to T = 0 K, values for Hyt and for the antiferromagnetic interlayer coupling Jaf will be derived in section 4. A peculiarity to note from fig. 4 is that at both sides of T, the susceptibility (for T -=c T,, xi,) drops very steeply. At the low-temperature side this indicates that the sublattice magnetization quickly rises to near-saturation values, which implies a low value for the exponent ,J in the power law MS N (1 - T/T@. This is indeed expected for a nearly 2-dimensional latticeis). The steep fall for T > T, is a consequence of the fact that Jaf is very small as compared to the intra-sublattice interaction Jf. This point may be clarified by considering that the antiferromagnetic configuration sketched in the insert of fig. 4. is not unusual in itself and may also occur in cubic lattices for instance. A b.c.c. antiferromagnet, subdivided into two sublattices, may also be seen as a system of antiferromagnetically coupled ferromagnetic layers. However, in “normal” antiferromagnets the ferromagnetic intrasublattice interaction Jf is much smaller than the antiferromagnetic interaction Jaf, so that the transition temperature T, is for most part determined by Jaf. In our case Jt- >>Jaf, the latter causing only a small upward shift of T, as compared with the transition temperature corresponding to the intralayer interaction Jf. This is illustrated in fig. 5, where we have compared the parallel susceptibility of the ethyl compound with the x of (CHsNH 3) 2 Cu Cl 4 and (CiaHsiNHa)sCuC14. The susceptibility is plotted as x/C versus kT/J, where J stands for the ferromagnetic intralayer interaction. In the methyl and decyl compounds the coupling between the ferromagnetic layers is positive, in contrast to the situation in (CzHsNHa)zCuC14. As we shall discuss in a subsequent paper, in the RTIJ region shown in fig. 5 the x of the methyl and decyl compounds is essentially the susceptibility of the ideal (isolated) ferromagnetic layer. The transition temperature corre-
286
L. J. DE JONGH,
W. D. VAN
AMSTEL
AND
A. R. MIEDEMA
0.5
1.0 -"T/J
Fig. 5. Comparison o
of the susceptibility
of three Cu compounds.
: (CsHsNHs)sCuC1zr;
The susceptibility layer interaction.
is plotted
B : (CH3NH3)2CuC14; q : (C10H21NH3)2C~C14. as x/C versus kT/J, where J is the ferromagnetic
The interlayer
and ferromagnetic
Fig. 6. The susceptibility
coupling
is antiferromagnetic
for the methyl
behaviour
i&a-
for the ehtyl compound
and decyl compounds.
in the neighbourhood
of the transition
plotted
as
x/C versus T. The symbols a, b and c denote the crystallographic axes along which measurements were taken. The following temperatures indicated in the figure are of interest. 1 : T, = 10.200 maximum in the specific heat; 2: To = 10.235 maximum in ax;/aT; 3: T = 10.245 maximum in ~5; 4: T = 10.270 maximum in x$ ; 5: T =
10.305 maximum
in ~8.
MAGNETIC
MEASUREMENTS
ON (C2H5NH3)2CuC14
287
sponding to this ideal 2-dimensional ferromagnet has been estimated to be kT,/ J w 0.442). Thus we may regard the upper curve in fig. 5 as representing the susceptibility of the isolated ferromagnetic sublattices of the antiferromagnet (CsHsNHs)sCuC14. The lower curve is obtained by “switching on” the weak antiferromagnetic inter-sublattice interaction. Since Jar is so small, the resulting upward shift of kTc/J is only about 20% and the maximum value of the antiferromagnetic susceptibility, which depends on the ratio of correlations Jai to Jr, is unusually high (XT& w, 85). The antiferromagnetic are seen to decay rapidly with increasing temperature. For kT/J> 0.8 the influence of the interlayer coupling has become negligible. In “normal” antiferromagnetic substances Jf T, also results in a very small difference T max at which xl/ reaches its maximum value and between the temperature the temperature To at which the slope of the ~11 velsas T curve is highest. The difference (T,,, - To)/Tmax may in “normal” cases (Jf < Jef) be seen as a measure of the amount of antiferromagnetic short-range order still present in the system for T > T,lg). For the nearly a-dimensional antiferromagnets like KsNiF4 and isomorphous compounds the difference is typically of the order of SO%, while in 3-dimensional compounds it is only 5-l 5% because short-range order effects become less pronounced in going to the higher dimension. In the case of (CsHbNHs)sCuC14 the difference amounts to only 0.70/. This may be observed from fig. 6 in which the susceptibility behaviour in the immediate neighbourhood of the transition is displayed. The maximum in +;“/aT occurs at To = 10.235 f 0.01 K, as indicated by the tangent to the xc/C ZMYSUST curve, while T,,, = 10.305 K. From the above discussion, however, it is clear that we may not attribute the fact is so small solely to lack of antiferromagnetic that (Max - To)/T,,, correlations above T,, but also to the fact that Jaf Q Jf. As a result, the behaviour of the ~11 above T, reflects the temperature dependence of the
288
L. J. DE JONGH,
W. D. VAN
ferromagnetic sublattice lation function.
rather
than
AMSTEL
that
AND
A. R. MIEDEMA
of the antiferromagnetic
corre-
The value Ta = 10.235 K also differs from the transition temperature T, = 10.20 f 0.01 K, derived from the specific-heat maximum. To avoid confusion we emphasize that what concerns us in this comlection is the contribution of the 3-dimensional antiferromagnetic ordering to the specific heat. This appears
as a small spike on the low-temperature
side of a
broad maximum (maximum at T m 2T,) that represents the contribution of the short-range ferromagnetic ordering processes within the Cusf layers29 4). It may be seen from fig. 6 that the difference To - T, = 35 mK is well outside the experimental error. The error introduced by the fact that different thermometers were used in the heat-capacity and the susceptibility experiments is estimated by us to be 0.1 o/oonly (10 mK at T = 10 K), in view of the careful comparison we made of them. We have two possible explanations for the observed difference. Firstly we observe that the connection between To and T, stems from the relation between the magnetic specific heat C, and the temperature derivative of ~1, of an antiferromagnet, viz.
Cm(T)= V)
a[xT/cl aT
.
In this formula F(T) is a relatively slowly varying function of temperature of order unity near T,. The theoretical situation has been explained by Fisher is), and the relation has been tested for a variety of antiferromagnets ls, 20). It follows from (2) that To = T, if C, and the susceptibility gradient rise to infinity at T,. However, if these quantities remain finite, as will be the case experimentally, a function F(T) that is monotonically decreasing with T for T > T, will shift To with respect to T, to a somewhat higher value. This situation is found in most of the experimental tests of relation (2). The explanation seems therefore to be a plausible one, were it not that for T > T, relation (2) perhaps does not apply here because of the fact that Jf > Jar. As we have seen in the above, the behaviour of x at T > Tc reflects the temperature dependence of the x of the ferromagnetic sublattice rather than that of the antiferromagnetic correlation function. A comparison of the differentiated x,,TIC versus T curve with the specificheat peak which may throw some light upon this question will be made by Bloembergen in a forthcoming paper. The second possibility would be the presence of a small amount of Br contamination in the sample used in our x measurements. Since the transition temperature of the isomorphous Br compound is TC = 10.85 K3), this could have the effect of shifting T, upward by a small amount. A similar effect has been observed by Renard et al. 21) in the case of Cu(NH4)sBrd. 2H20.
MAGNETIC
We remark,
however,
Cu compounds,
MEASUREMENTS
289
ON (CzH5NH3)&uC14
that in the case of the other members
where the same arguments
of the series of
apply, we have hitherto
always
found agreement within 0.1% between the T,‘s derived from the specific heat and the x measurements. This is the more surprising since in the case of these other members the difference between the T, of the chlorine and of the isomorphous bromine compound is much larger : 3-4 K 3) compared with 0.65 K for the ethyl compound. There is another argument in favour of the first explanation. Following the same lines as in deriving relation (2), Fisher has predicted that the parallel susceptibility measured as a function of temperature in a finite constant field should display a sharp peak at the (field-dependent) transition temperature. At the end of the following section we shall show that this seems to be verified by the experiment. We are thus inclined to believe that relation (2) holds for T & T, even for this unusual type of antiferromagnet, though probably not for T > T,. 4. Field-dependent wsce~tibility. As is well known221 sa), in general two different phase transitions will occur if a field is applied parallel to the preferential axis of an antiferromagnet. Theexpected behaviour of the magnetization and the differential susceptibility x= (SI/~H)T as a function of field at a temperature T M 0 is sketched in fig. 7. At a critical field Hr a first-order transition will occur, when the spins suddenly flip over to a direction perpendicular to the field because the gain in magnetic energy, &(xl - ~1,) HT, exceeds the anisotropy energy that favours the parallel orientation. A further increase of H will gradually rotate the moments of each sublattice until at a field Hs their mean direction is parallel to the field. At this
Fig. 7. The expected x =
behaviour
of the magnetization
and the differential
susceptibility
(aM/aH)rr as a function of field for a weakly anisotropic antiferromagnet applied parallel to the preferential direction. Temperature is T m 0.
if H is
L. J. DE JONGH,
290
W. D. VAN
AMSTEL
0
The numbers
indicate
been measured.
dimensions
value
susceptibility
to the a axis (preferred
therms indicated
2
-u
-
parallel
have
A. R. MIEDEMA
1
Fig. 8. The real part x’ of the complex field applied
AND
the values
of the relative
Note
that
l/DC is the calculated
(D = demagnetizing
factor).
x = x’ -
axis) at different temperature
x’/C is plotted limit
ix” as a function constant
of a
temperatures.
T/Tc at which the iso-
on a logarithmic
for a ferromagnetic
For obvious
isotherms
lko.1
sample
scale. The of the same
reasons only half of the measured
are shown.
-H 0
1
0.5
(kOe)
(K-l)
G50
t 0 Fig. 9. The imaginary of a field
applied
part x” of the complex
parallel
susceptibility
to the a axis. The numbers
x = x’ -
indicate
the
ix” as a function values
of
T/T,.
MAGNETIC
MEASUREMENTS
transition from the spin-flop order, the antiferromagnetic
ON (CsHsNHs)sCuC14
291
to the paramagnetic phase, which is of second interaction is balanced by the applied field
and the anisotropy field. Both critical fields will depend on temperature and will vanish as the transition temperature is approached. In fig. 8 we have plotted the differential susceptibility measured as a function of a field applied parallel to the preferential axis (u axis) of the Cu compound. The numbers indicated in the figure give the relative temperatures, T/T,, at which measurements were taken. These isotherms do show the expected behaviour. Instead of the complex susceptibility x = x’ - ix”, we have plotted the real part x’ which differs slightly from x because at the critical fields Hy there also occur large peaks in the imaginary part x”. These are shown in fig. 9, the numbers again indicating the relative temperatures. At all other field values x” vanishes, which is to be expected for an antiferromagnet. We also point out that at Hy the x’ reaches values that are very near to the estimated ferromagnetic value, which is the inverse of the demagnetizing factor D. These findings lead to the conclusion that at Hy, where the susceptibility tends to infinity, a limit is set to x, which is the same as in the ferromagnetic case. One may imagine that some sort of domain structure is formed. In this picture the variation of the height of
al 2 H IkO.1 Fig. 10. The susceptibility as a function of a field applied parallel to the b axis (nextpreferred axis) at constant temperature. The numbers again indicate T/T, values. The apparent difference in behaviour from the high-field part of fig. 8 is caused by the fact that in fig. 8 x is plotted on a logarithmic scale. Only half of the measured isotherms are shown. The data have not been corrected for demagnetizing effects. 0
1
-
292
DE JONGH, W. D. VAN
L. J.
AMSTEL
AND
A. R. MIEDEMA
the x” peak with T can be ascribed to a decrease in the domain-wall when the temperature is lowered.
mobility
Inbet ween Hy and Hz, x attains values nearly equal to those of x”, in zero field as shown in fig. 4. As a matter of fact the temperatureedependence of x at H = 0 is that of the parallel susceptibility in fig. 4. Before discussing the temperature dependence of H;” and Htj we present in fig. 10 the results for x obtained when the field is applied parallel to the b axis, which is the next-preferred direction. Again the isotherms are labelled by the values of the relative temperature. Obviously the spin-flop 3 [kOe!
P-
H
t
nl-
\\
’
I
2
b
1
c-
0 0
10
05 -
Fig.
11. Phase diagram
anisotropy bourhood
of antiferromagnetic
in this compound. of the transition
extrapolation
The insert
(CsHsNHs)sCuC14, shows the region
point. The position
of the H$ transition
K‘
reflecting
the biaxial
in the immediate
neigh-
of the triple point has been indicated
by
curve. The point lying on the T/Tc axis corresponds
to To, i.e. the temperature at which the slope of the ~11 1Jeysu.sT curve reaches its maximum. o, 0: HI spin-flop transitions; field parallel to the a axis (preferred axis). Symbols
refer to different
a axis. Symbols
measurements;
refer to different
A, A: Hk transitions;
measurements;
q
field
: Hg transitions;
parallel
to the
field parallel
to
the b axis (next-preferred axis) ; A : H$ transitions; field parallel to the c axis (hard direction). The error bars indicate the uncertainty in the position. The point at T = 0 has been calculated from ~7 (H = 0, T = 0). For the other directions the uncertainty in the transitionpoints is too small to be seen in the figure.
MAGNETIC MEASUREMENTS
transition
ON (CzH5NH3)2CuC14
at HI is now absent, and the zero-field
293
values of x are those of
& in fig. 4. Along this axis higher fields Hi are needed to bring the spin system into the paramagnetic phase, because the anisotropy now oppo ses the applied field, instead of adding to it. The temperature dependence of the various critical fields is shown in the phase diagram of fig. 11. Only a few values for H,C have been obtained, applying the field parallel to the c axis, because our current-supply limited the field region to 2.5 kOe. Also the transition is not so clearly indicated in this case, resulting in large error margins. The point H,C at T = 0 has been calculated from the perpendicular susceptibility ~7 measured in zero field (see below). The orthorhombic anisotropy in this compound is reflected in the higher values of H,” as compared to those of Hi(Hiut > H?). The values for the critical fields in fig. 11 have been corrected for demagnetizing effects using the formula H corr. = Happl._(l + %J-l.
(3)
The relatively low values for the critical fields in this compound reflect the extreme instability of the spin system. As may be seen from the insert of fig. 11 we have also observed transitions in the region Tc < T < To, To being the point on the T/Tc axis. The highest temperature at which we could detect an HZj transition was T/Tc = 0.9945. We estimate that the Hfj curve intersects the H’f curve at T/Tc = 0.997. This point in the H-T diagram is a triple point, as the three different phases are coexistent there. At the phase boundary extending from the triple point to the T/T, axis there occurs a transition from the antiferromagnetic phase directly into the paramagnetic phase. From the above we estimate the triple point to be at T/T,=0.997, H= 135 Oe. To obtain expressions for the various critical fields at T = 0 we use a simple molecular field model, in which the magnetic moments of the ferromagnetic sublattices are treated as classical vectors. The antiferromagnetic coupling is taken to be isotropic, the biaxial anisotropy is introduced in the form of terms KS; and LSZ, where K > L > 0 and the y and z axes are the crystallographic b and c axes, respectively. Applying the external field successively in the a, b and c directions, the following expressions for the critical fields are derived (Hy)z = 2H$Ht H; = 2Hz
-
-
(H:)2,
(4)
H?,
(5)
H2” = 2H$ + H’,n,
(6)
H; = 2HiFt + Hiut.
(7)
In these equations
the antiferromagnetic
coupling
and the anisotropy
294
L. J. DE JONGH, W. D. VAN AMSTEL AND A. R. MIEDEMA
have been introduced
in the form of the effective fields Hz = 24JaflS/ga,+4g;
HzFt=2z,f IJai S/g,,u~; H: = 2KS/g,, b,UBand Hyt = 2LS/&UB, the g values and the anisotropy fields having been defined in sections 2 and 3, respectively. As the transition at Hy is of first order one might have expected hysteresis effects to occur 2s), especially because HA and H,f are of the same order of magnitude, as we shall see in the following. any of these effects and we have therefore
However, we did not observe taken expression (4) for the
critical field Hy, which is obtained by minimizing the free energy with respect to the angle between the spins and the field direction. The explanation for the absence of hysteresis may be that both HA and Hsf are very small as compared to the thermal energy, even at the lowest temperature at which measurements were taken. The extrapolated values for the critical fields at T = 0 are Hy = 345 Oe, Hi = 1510 Oe and Hi = 1690 Oe. With the aid of (5) and (6) we obtain Hz = 800 f 10 Oe and Hii = 90 + 10 Oe. Substituting this value for H,f in (4) yields H% = 75 f 5 Oe. The difference between the two values for H: can be due to a difference in the anisotropy when going from the antiferromagnetic to the paramagnetic phase, although the assumption of a small anisotropy in the exchange term may also account for its4). From the zero-field susceptibilities xy and XT another value for H,f and also an estimate of Hrt may be derived. In the calculation we make use of the molecularfield expressions xl = x”i(l + HA/2H&1,
(8)
x”l = Ng/&/2H,f,
(9)
where & denotes the perpendicular susceptibility corrected for anisotropy effects. Firstly we calculate xt from &, using the results H$ = 800 Oe, H? = 80 Oe. The extrapolated value to T = 0 K being $‘JC = 8.65 K-l we obtain x0,/C = 9.05 K-1. We mention that the value of xa/C in the flop phase is 9.13 K-l at T = 1.30 K. Substituting for &C in eq. (9) yields Hs = 762 Oe, in reasonable agreement with the value obtained from the field-dependent measurements. Next we calculate HFt from eq. (8) using value xl/C = 9.05, H:Ft = H’‘,“,g,, b/gc = 843 Oe and the extrapolated x:/C = 5.75 K-r. We thus obtain H,Out= 968 Oe, from which the value for the critical field HC, = 2650 Oe at T = 0 K was calculated included in fig. 11. We note that the Curie constants in the above have been calculated with the appropriate g value for the various directions. Recently, Bloembergen and Franse of our laboratory have also obtained values for the spin-flop field, the interlayer coupling and the anisotropy at T = 1.2 K from magnetic torque measurements. They found Hy = 335 Oe, H,f = 805 Oe, H’,” = 70 Oe, Hrt m 1100 Oe15) agreeing nicely with our results. Our final values are therefore
H,f = 800 Oe, HP M 75 Oe, HFt
m 1000
MAGNETIC Oe.
These
MEASUREMENTS
fields are to be compared
the ferromagnetic
interaction
295
ON (CsHsNHs)&n&
with the effective
within the layers.
field representing
From Jf/k =
18.6 K, with
the choice g = ga, b = 2.16 we calculate this field to be Hr = 5 13 kOe. As mentioned in the preceding section the value for J/k may be about 10% too high in view of the specific-heat results. It is obvious from these results that both the anisotropy and the interlayer coupling are several orders of magnitude smaller than the 2-dimensional interaction. From the isotherms shown in fig. 8 we may also derive the behaviour of x as a function of T in various fixed magnetic fields. This is of importance, because from general arguments Fisher lg) has argued that x in a constant nonzero field should display a sharp peak at the (field-dependent) transition temperature T,(H), superimposed on the continuous zero-field behaviour. This feature of the antiferromagnetic susceptibility follows from the same considerations that yield relation (2) between the temperature derivate of x and the specific heat mentioned in section 3. In fact the peak at T,(H) reflects the specific-heat singularity la). The phenomenon has been rigorously established for the 2-dimensional super-exchange Ising modelss).
I
I
I
t” ; I
%+ /
1K-'I
]
’
I
I I
I
\
parallel susceptibility in the neighbourhood
H = IL3
TiKl
measured in constant fields of the transition temperature
the lowest three fields the anomaly in x at T,(H) At H =
lo.5-
10.0
9.5
Fig. 12. The temperature,
’
’
I
i
t
’
I
143 Oe there occurs a spin-flop
predicted by Fisher is clearly seen.
transition
real effect).
as a function of T, (H = 0). For
(the flattening
of the peak is a
296
L.
J. DE JONGH,
We point
out that
W. D. VAN
the transition
AMSTEL
AND
curve in the
A. R. MIEDEMA
H-T diagram of fig. 11
to which these arguments apply is the boundary separating the antiferromagnetic from the paramagnetic phase, which is the curve extending from the triple point to the T/Tc axis. From the location of the triple point it follows that the phenomenon may be observed for fields smaller than H= 135 Oe only. For higher fields the system is no longer brought directly from the antiferromagnetic
into the paramagnetic
phase, as the first-order
spin-flop
transition is no longer avoided. In fig. 12 we have plotted the x/C versz4s T curves derived from fig. 8 for the four lowest field values. The behaviour in the fields H = 52, 97 and 122 Oe shows a striking resemblance to Fisher’s theoretical curvess). In going from H = 122 Oe to H = 143 Oe, which is above the estimated triple point value, the character of the curve is abruptly changed. According to the arguments given above this should be due to the occurrence of a spin-flop transition. We now turn to the temperature dependence of the critical fields Hz. From spin-wave theory it follows 22~23) that Hz(T)=2H,f(O)R(T) for HA=O, where R(T) is the factor with which the spin-wave spectrum is renormalized. In the case of an antiferromagnet at the transition to the paramagnetic phase, R(T) is expected to vary like the magnetization, so that in a low-temperature approximation Hz(T) should behave as Hz(T)/H2(0)
1-
=
ao(T/T,)” -
where the as are constants power-law
dependence
0.32
&
0.02
(10) we have observed
a
T/Tc)o,
and A =
(11) 1.08 F 0.08.
This may be seen in fig. 13
[l
-
:$I
’
dependence of the critical fields Hz at which the system is brought phase. A : Hg = 2Hs - H%; q : H% = 2Hi? + H2; 0 : gz =
= *(Hz + Hi) = 2H5. a double
....
and Hz(O) = 2H,r(O). Instead
---xzFig. 13. Temperature into the paramagnetic
-
of the form
Hz(T)/Hz(O) = A(1 with ,!I =
UI(T/T#
logarithmic
The fields are plotted as Hz(T)/Hz(O) versus (1 - T/T,) scale. The fit to the power law yields B = 0.32 & 0.02.
on
MAGNETIC
MEASUREMENTS
ON (CzHsNHs)sCuC14
297
where Hz(T)/Hz(O) is plotted VCYSUS(1 - T/T,) on a double-logarithmic scale. For both H; and Hi the power law is obeyed over the whole investiAlso the quantity as gated temperature range 0.05 < T/T, < 0.99. -_ i(H;+
Hi)
that,
according
to
(5) and
(6), should be equal to Hz(T)
= 2H,f(T) fits the same curve. In most magnets the power-law dependence gives a good description of the magnetization near the critical point. The excellent fit of our data to (11) may be understood in this picture by considering that .zrtrIJsrl/k is only e 9 at T = 1 K already. It follows that even 0.115 K, so that kT/z,flJ,fl at the lowest temperatures reached, the thermal energy is much too high as compared to lJafl for the low-temperature spin-wave approximation to be applicable. The fact that the antiferromagnetic coupling results in a 3dimensional ordering of the system makes it acceptable that the exponent ,9 is approximately &, which is the common “3-dimensional” value for the magnetization. After having established this special feature of the system we once more draw attention to the behaviour of x near the critical fields Ht and HE in figs. 8 and 10. From the fact that x peaks at Ha a nonlinear behaviour of the magnetization is deduced, a peculiarity that has also been observed in other investigations 26127). Jacobs and Silversteins6) have attributed it to the gradual suppression of zero-point spinreduction when the spins are rotated by the field from the antiferromagnetic to the ferromagnetic configuration. From spin-wave calculations they obtained a x-H curve that is at least qualitatively similar to the experimentally observed isotherms. They also mentioned the strain-dependence of the exchange energy as a possible source. Though these effects may account at least partly for the deviations from linearity in other systems, they are not likely to explain our results. Carara et al. 27) have attributed the nonlinear behaviour observed in the metamagnet
FeCls
to the fact
that
the anisotropy
HA is comparable
in
1
Fig. 14. Temperature netic measurements.
dependence of the anisotropy fields as derived from the mag0: Hyt; a: HF, The power-law fit yields j3 = 0.43 for Hyt and p w 0.65 for H’i.
298
L. J. DE JONGH,
W. D. VAN
AMSTEL
AND
A. R. MIEDEMA
magnitude to the total exchange HE = Hf + H,f. relevant here because HA/HE M IO-3 - 1O-4.
This effect
is also not
The results of Feder and Pytte, howeverss), seem to be at least in qualitative agreement with our findings. From spin-wave theory they obtained for the susceptibility near the phase boundary the term x = A(T) x [Hz- HI-S, where A (T) is a linear function of temperature. Such a behaviour may be qualitatively understood by inspection of the evolution of the spinwave spectrum of the flop phase as H + Hz (fig. 1 of ref. 28). As Hz is approached it is seen to cost less energy to create (antiferromagnetic) spin waves, resulting in an extra increase in magnetization. A more detailed analysis will be given in a subsequent publication. We have also tried to deduce the temperature dependence of the anisotropy fields. From (5) and (6) one obtains H% as the difference +(Hi -- Hg), while Hyt may be derived from the temperature dependence of x’;, using
(8). Also for the anisotropy fields one may expect, to hold or, in a low-temperature approximation, HA(T)/HA(0)
=
1-
b(T/T,)‘.
either the power law (11) a formula of the form
(12)
The fit to the power law is shown in fig. 14. The agreement is reasonably good, especially in the case of Hy’, yielding the exponent values /3m 0.65 and ,9 = 0.43 for Hii and Hyt, respectively. However, a fit to formula (12) is equally well possible, giving Y = 1.72 for both fields. In any case it is clear that the temperature dependences of H% and Hyt are not completely the same. This may have to do with the fact that there are different origins of anisotropy. The dipolar interaction, which for a ferromagnetically ordered layer results in a strong preference for an orientation within the plane, introduces the following anisotropy fieldsl6): out = 930 Oe, H*
Hi”A = 5 . 5 Oe .
Apparently, there is an additional contribution from the anisotropy in the exchange, resulting in the measured Hyt w 1000 Oe and nearly completely accounting ]for Hii m 75 Oe. It follows that the effects of the long-range interactions will only be reflected in Hiut, while for the temperature dependence of H: solely near-neighbour interactions must be responsible. The spin-flop field Hi” decreases with temperature, in contrast with what is mostly observed. From it we have obtained another estimate of the temperature variation of H a~, using formula (4) corrected for the fact that for T > 0 no longer is XI/ = 0 23). The result for H,f was in qualitative agreement with the curve shown in fig. 13. Finally we investigate the divergence of the susceptibility at the spin-flop transition HI in more detail (we omit the superscript a in what follows). As we have seen in fig. 8 in practice x’ remains finite, the highest value reached being near the value l/D, where D is the estimated demagnetizing factor.
MAGNETIC
MEASUREMENTS
/L
299
ON (CsHsNHs)sCuC&
lo3
I
lo2
10
1
10-l .2
10
1
--- 1 lo-’
H
Fig.
15. Field for
x:T=4.023K; +:
dependence H >
o:
0:
v:T=9.746K.
V~YSUS(H -
Hl)Hl
H,
real part
T =
o:T=5.046K;
T=8.876K;
plotted
of the
HI.
x’ of the
at the
spin-flop
: T = 2.980 K; n :T=8.034K;
q
T=6.115K; A: T=7.049K; The (corrected) values for the susceptibility
on a double-logarithmic
0.2 and F = 0.06 i
susceptibility
n: T = 2136K;
1.30K;
X’IC N F[(H with p = 2.3 *
1N3
Hl
[ transition
.2
10
scale.
The data fit the power
are law
-- H1)/H1]-P
0.02 K-r
over more
than
three
decades
in x’/C.
We have therefore corrected the experimental values in the usual way [formula (I)]. For H > HI the zero level of x was taken to be x1, for H < HI the value of x at H = 0 was taken. In fig. 15 we have plotted x’/C veY.szts (H - HI)/HI for fields H > HI on a double-logarithmic scale, in order to see to which extent a power-law description of the form X’IC N F I(H -
Hi)/HiP’
(13)
applies. Here F and p are constants. Fig. 15 shows that (13) is valid over nearly four decades in x/C, with p = 2.3 f 0.26 and F = 0.06 f 0.02 K-r. The measurements taken at nine different temperatures may be fitted to the same curve for (H - Hl)/Hl > > 0.015. The agreement to[(13) extends to lower relative field values for the isotherms taken at T M 6 K, at which temperatures the x’/C in fig. 8 reaches
300
L. J. DE JONGH,
W. D. VAN
AMSTEL
AND
A. R. MIEDEMA
the highest values. But for the isotherms at which the maximum of x’/C is lowered deviations from the power law occur at higher field values already, as may be seen in fig. 15 from the results taken at T = 1.30 and T = 9.784 K. For fields (H - Hr)/Hr < 0.005 the points have no real meaning because of the rounding of the x peak. We also remark that for (H - Hr)/Hr > 0.02 the applied correction according to formula (1) is negligible in fig. 15, and that it also makes no appreciable difference if, instead of x’, 1x1= lx’ -- ix”1 is taken. Fig. 16 shows the same quantities but now for fields H -c HI. The powerlaw fit is less impressive here; however, the results are not too much different from those at the high-field side, as is indicated by the heavy line which is the curve obtained in fig. 15. For j(H - Hl)/Hll > 0.05 another contribution to the susceptibility seems to be superimposed on the divergent part of x. The magnitude of this contribution decreases as the temperature is lowered. This fact, together with the effects of rounding, tends to obscure the critical behaviour. Concerning the value of p = 2.3 there is little theoretical information available. Feder and Pyttes*) have derived p = 4 from spin-wave theory. H1 -H -p [ Hl lo4
1
(K-'1
Fig. 16. The same quantities as in fig. 15 but now for the case H < HI. The results are seen to agree qualitatively
with the curve obtained for H > HI, which is indicated by the heavy line.
MAGNETIC
The same divergence
ON (CzH5NH3)2CuC14
301
for the case of non-interacting
spin waves
MEASUREMENTS
is predicted
in an isotropic 3-dimensional ferromagnet, where at zero temperature x NH-‘, with L z 3 near the phase boundary (which is the line HI = 0) 18). Also for the spherical model this type of divergence has been found is). A similarity in behaviour near the phase boundary is not unlikely in view of the analogy between the spin-flop transition and the liquid-gas and ferromagnetic transitions, as pointed out by Anderson and Callena”). From spin-wave theory for a 2-dimensional isotropic ferromagnet we derive from a formula on page 90 of ref. 23 for small fields : x - H-l. At the transition temperature2gp 30) i = y-l, where y is the exponent with which the susceptibility diverges as T, is approached from above, according to the power law x N (1 - T,/T)-“. Thus, it was found for the 2- and 3-dimensional Ising modelsss) that L increases slowly from the value y-i at T, (y-1 = 0.57 and 0.80, respectively) to the value L = 1 at T = 0. For the 3-dimensional Heisenberg modelao) 1 = y-l m 0.7 (S = 4) at T,. The value found for p is therefore considerably higher than those obtained for the corresponding exponent in the analogous ferromagnetic models. We note that the observed behaviour of the susceptibility implies that the magnetization for H > H1 behaves as M(H) P=T-[ C
LH
(PF
l)][
(H;lHi)](p-‘)
(p>
1).
(14)
Because of the smallness of the amplitude F the second term on the righthand side of (14) will manifest itself only in the immediate neighbourhood of the transition. In concluding this section we comment on the fact that we did observe the spin-flop transition although the uncertainty in the orientation of the applied field with respect to the preferential axis was relatively large (maximum 8”). For the case of a uniaxial antiferromagnet, Rohrer and Thomas al) have recently deduced that the maximum angle with respect to the easy axis under which the spin-flopping may be observed is given by # = 28.6” x (H*/Haf). 0 ne may expect a similar result in the orthorhombic case with the applied field perpendicular to the hard direction. In most antiferromagnets the exchange energy is much larger than the anisotropy energy so that #may be even smaller than lo. In our compound HA and H,r are of the same magnitude, which explains the insensitivity to a possible misalignment. 5. ConclzGding remarks. In the foregoing sections we have reported magnetic investigations on (CsH~NHs)sCuCl~, a member of a series of compounds in which the magnetic structure very nearly approximates the 2-dimensional Heisenberg ferromagnet. The possible existence of a phase transition at which the susceptibility diverges for the ideal 2-dimensional system is a problem that has drawn considerable attention both theoretically
302
L. J. DE JONGH,
W. D. VAN
AMSTEL
AND
A. R. MIEDEMA
and experimentally (a discussion of the ordering problem is given in ref. 8). It is therefore interesting to study the antiferromagnetic ordering of (CsH5NHs)sCuC14, because in that way quantitative information is obtained about the deviations from the 2-dimensional Heisenberg model. We have established that the system orders at kTc/J L= 0.55, at least partly under the influence of an iltterlayer coupling H,f :: 800 Oe and of anisotropy fields H% w 75 Oe and HTt !a 1000 Oe. Considering the fact that in some of the other chlorine compounds of the series the transition temperature kTc/ J is lower by 10 to 20% s), while preliminary results indicate that at least in some of them the anisotropy is not much different, we think H,f to be the dominant mechanism that establishes the 3-dimensional orderings). This contrasts with the situation in the 2-dimensional antiferromagnets of the KsNiF4 type, where in most cases the onset of long-range ordering may be ascribed to the anisotropy 3% 3s). In ref. 8 the possible existence of a transition temperature for the susceptibility of the ideal 2-dimensional Heisenberg model is discussed in view of the experimental results obtained on a number of layer-type magnets. Because H,f, H: and Hyt are some orders of magnitude smaller than the ferromagnetic intralayer exchange Hf = 5.13 x 105 Oe, the system shows at high temperatures (T 3 T,) the behaviour expected for a 2-dimensional Heisenberg ferromagnet. Large short-range order effects are observed in the susceptibility. The quantitative results for the anisotropy are a justification a posteriori for the use of the susceptibility series for the isotropic Heisenberg model in fitting the x at T > T,. However, very near to T, the fact that Hyt m 10 H? may have the consequence that the critical behaviour is better described by the XY model (planar Heisenberg model). In the introduction we have already mentioned that the properties of the Cu salt resemble those of CrCls7) in several respects. Also in CrCls the magnetic structure consists of ferromagnetic layers coupled by a weak antiferromagnetic interaction. A comparison has been made in ref. 8. It turns out that the deviations from the 2-dimensional Heisenberg model viz. H,f, H?, Hyt are equal or even smaller in CrCls. Yet in the Cu compound the transition temperature T, is much lower with respect to the molecularfield value 8. The ratio T,# is 0.28 for the Cu compound, while it is 0.43 for CrCla. The larger reduction may be attributed to the lower spinvalue of the Cus+ ion (S = +) as compared to S = g for Crs+ 8). Besides the ordering problem the compound (CsHsNHs)sCuCl4 is an interesting object of study because it is such an unusual antiferromagnetic system. Since Jaf is very small as compared to Jf, x is high enough to be measured by a mutual inductance method. This facilitates the measurements of field-dependent properties and other features that are of theoretical of the phase diagram in detail, interest, namely : 1) the establishment 2) a test of Fisher’s relation between the energy and susceptibility of an anti-
MAGNETIC
ferromagnet,
MEASUREMENTS
ON (CzH5NH3)aCuC14
3) the study of the divergence
4) the verification the susceptibility (field-dependent)
of Fisher’s
prediction
303
of x at the spin-flop transition,
that, if measured in a constant
field,
versus temperature curve should display an anomaly at the transition temperature, superimposed on the zero-field
behaviour. As mentioned before, all these interesting antiferromagnetic properties may be studied within the easily accessible field region H < 2.5 kOe. Concerning the origins of the anisotropy fields Hi2 m 75 Oe and out m 1000 Oe, we have already mentioned that the dipole interaction H* introduces the anisotropy fields Hii = 5.5 Oe and Hrt = 930 Oe16), favouring the longest crystallographic axis within the Cu layer. Clearly also an anisotropy in the exchange must be present. We shall discuss the origins of the anisotropy in detail in a subsequent paper, comparing the results for some of the Cu compounds. At this point we only remark that there must be at least two competing mechanisms of exchange anisotropy, because the anisotropy in the g tensor introduces a field of a few kOe that also favours the Cu plane, while H,Outis only 1 kOe experimentally. We feel that the super-exchange mechanism via the Cl ion must be responsible for an anisotropy that favours the direction perpendicular to the plane, partly compensating the combined effects of the dipolar interaction and the g anisotropy. The presence of this contribution manifests itself clearly when the Cl- ion is replaced by the Br- ion, as we have observed in preliminary measurements on salts of the Br series. Similarc onclusions have also been drawn by Narath 7), comparing CrC13 and CrBr3. Acknowledgement. We are very much indebted to J. H. P. Colpa, P. Bloembergen and E. P. Maarschall for many fruitful discussions about these experiments and their own work in this field. The invaluable assistance of the technical staff of our laboratory is also greatfully acknowledged. They have carefully constructed the various pieces of apparatus and supplied us with a nearly continuous flow of liquid helium. We express our gratitude to Professor G. de Vries for a critical reading of the manuscript. This work is part of the research program of the “Stichting F.O.M.” and was made possible by financial support from the “Nederlandse Organisatie voor Z.W.O.“. REFEKENCES 1)
De Jongh,
2)
Phys. 40 (1969) 1363. Bloembergen, P., Tan, Int. Conf.
3)
De Jongh, J. Phys.,
L. J., Botterman,
Magn.,
A. C., De Boer,
K. G., Lefkvre,
Grenoble
suppl.
no. 2-3,
F. H. J. and Bleyendaal,
1970. J. Phys.,
L. J. and van Amstel, Tome
F. R. and Miedema,
suppl.
W. D., Proc.
32 (1971)
880.
no. 2-3,
Int. Conf.
Tome Magn.,
A. R., J. appl. A. H. M., Proc. 32 (1971) GrenBble
879. 1970.
304 4) 5)
MAGNETIC
MEASUREMENTS
Miedema,
A. R., Proc.
Int. Conf. Magn.,
32 (1971)
305.
Willett,
R. D., J. them.
Steadman, 6)
Chem. (1966). Barendregt, F. and Schenk,
7)
Narath, Narath,
8)
De Jongh,
9)
Durieux,
M., thesis
Durieux,
M., Van
Publ.
H., Physica
Corp.
Dijk,
49 (1970)
Furlani,
137
of Leiden,
(New York,
in Science
J. H. P., Physica
H. and Van
E. P., private
C., Sgamellotti,
A., Magrini,
Jr., G. A., Gilbert,
H. E., Eve,
15)
25A (1967) 3. Bloembergen, P., private
16)
Colpa,
J. H. P., in Physica
57 (1972)
17)
Baker
Jr.,
C. in Temperature,
M. B. M., Physica
H. E.,
18)
164 (1967) 800. See for instance
38 (1968) 287.
D., J. molecular
C., Inorg.
Chem.
J. and Rushbrooke,
Spectrosc.
6 (1967)
1885.
G. S., Phys.
Letters
communication.
Gilbert,
Fisher,
347.
Eve,
M. E., Rep.
J. and
Progr.
Phys.
Fisher, M. E., Phil. Mag. 7 (1962) 173 1. Wolf, W. P., Wyatt, A. F. G., Phys. Rev. Love,
Rijn,
Vol. 3, Part I, 383, Reinhold
F. and Cordischi,
Baker
H.,
305.
communication.
13)
Forstat,
58 (1972)
1960).
1962).
14)
20)
to Inorg.
465.
and Industry.
24 (1967) 270. Willett, R. D., Liles Jr., 0. L. and Michelson,
19)
no. 2-3,
( 1965) 163.
B. M., Van Dissel, W. J. J. and Jacobs,
G. A.,
suppl.
submitted
The Netherlands,
H., Ter Harmsel,
and Control
S. and Maarschall,
12)
communication,
P. and Colpa,
(University
1970. J. Phys.,
(1964) 2243.
R. D., private
L. J., Bloembergen,
IO) Boerstoel, Vega,
41
GrenBble
A., Phys. Rev. 131 (1963) 1929. A. and Davis, H. L., Phys. Rev.
its Measurement
11)
Phys.
J. P. and Willett,
ON (CzHsNHs)aCuC14
N. D.,
McElearney,
Letters J. and
Rushbrooke,
G. S., Phys.
vol. 30, 2 (1967) 13 (1964)
Rev.
800.
368.
Weinstock,
H.,
Phys.
Rev.
145
R. D., Phys.
Rev.
164
( 1966) 406. Skalyo,
J., Cohen,
A. F., Friedberg,
S. A. and Griffiths,
(1967) 705. Breed,
D. J., Gilijamse,
Wright, 21)
J. C., Moos,
K. and Miedema,
H. W., Collwell,
Phys. Rev. B 3 (1971) 843. Renard, J. P. and Velu, E., Proc. suppl.
no. 2-3,
22)
See for instance
23)
For
a review
Teil 2, Springer
24) Blazey, 25) 26)
Fisher, Jacobs,
27)
Carrara,
Tome
32 (1971)
Anderson,
Int. Conf.
45 (1969)
Magnetism,
Grenbble
D. D.,
1970. J. Phys.
1154.
F.,
( 1966).
K. W. and Rohrer,
H., Phys.
Rev.
173 (1968)
574.
M. E., Proc. Roy. Sot. A254 (1960) 66. J. S. and Silverstain, S. D., Phys. Rev. Letters P., De Gunzbourg,
J. and Allain,
13 (1964)
Y., J. appl.
Phys.
28) Feder, 29) ‘Gaunt,
J. and Pytte, E., Phys. Rev. 168 (1968) 168. D. S. and Baker Jr., G. A., Phys. Rev. B 1 (1970)
30) ‘Baker
Jr., G. A., Eve,
J. and Rushbrooke,
31)
Rohrer,
H. and Thomas,
32)
Matsuura,
33)
Letters 33 A (1970) 363. Birgenau, R. J., Skalyo Jr., J. and Shirane,
M.,
205.
B. W. and Thornton,
F. B. and Callen, H. B., Phys. Rev. 136 (1964) A 1068. Handbuch der Physik, Band XVIII, Sp inwaves,
see Keffer, Verlag
A. R., Physica
J. H., Mangum,
Gilijamse,
H., J. appl. K.,
Phys.
Sterkenburg,
G. S., Phys. 40 (1969)
272.
40 (1969)
1035.
1184. Rev.
B 2 (1970)
706.
1025.
J. E. W. G., J. appl.
and
Breed,
Phys.
41
D.
J.,
Phys.
(1970) 1303.
