Thermal properties of three nickel hexammine halides below 1°K

Physica 30 1131-l 140

van Kempen, H. Duffy jr., W. T. Miedema, A. R. Huiskamp, W. J. 1964

THERMAL PROPERTIES OF THREE NICKEL HEXAMMINE HALIDES BELOW 1°K by H. VAN KEMPEN,

W. T. DUFFY

jr. *), A. R. MIEDEMA

and W. J. HUISKAMP Communication

No. 338~ from the Kamerlingh

Onnes Laboratorium,

Leiden,

Nederland

Synopsis The heat capacity of Ni(NHs)&le, Ni(NHs)sBrs and Ni(NHs)sIs is studied below 1°K. Sharp maxima in the heat capacity, corresponding to a transition to the antiferromagnetic state, have been observed at 0.6”K and 0.305”K for the bromide and iodide, respectively. For the chloride the transition to the antiferromagnetic state is accompanied by two peaks in the heat capacity at 1.45”K and 1.02OK. We also observed a non-magnetic anomaly in the heat capacity, in which the entropy changes by 6R In 2 per mole. This anomaly may be attributed to a splitting of the energy states for the proton nuclear spins, due to a hindered rotation of the ammonia molecules.

1. Introdz&iort. The thermal properties of Ni(NHs)s(Hal)s (Hal stands for Cl, Br or I) are of special interest at low temperatures for two reasons. The magnetic behaviour of the nickel ions is expected to have a special character, since they form a face-centered cubic (f.c.c.) lattice. In a f.c.c. lattice each magnetic ion has twelve nearest magnetic neighbours, which are arranged in such a way that each of these has four nearest neighbours among the same group of twelve. Thus, no antiferromagnetic ordering is possible in which all pairs of nearest-neighbouring spins are mutually antiparallel. As explained by Anderson 1) there are a number of possibilities for the ordered state of a f.c.c. antiferromagnet (with predominantly nearest neighbour interaction) in which there are two energetically favourable pairs against one unfavourable pair. Which of the possible super-lattice structures has the lowest energy depends on the next-nearest neighbour interaction, which may be very weak. As a consequence of the fact that in a f.c.c. lattice no simple two-sublattice antiferromagnetic structure is possible, the transition temperature must be considerably lower than that of a simple two-sublattice structure with the same .zJ value (z is the coordination number and J is the exchange constant). *) Present address: Physics Dept. Univ. of Santa National Science Foundation Postdoctoral Fellow.

-

Clara,

1131 -

Santa

Clara,

California,

U.S.A.,

U.S.

1132

H. VAN

KEMPEN,

W. T. DUFFY

JR.,

A. R. MIEDEMA

AND W.

J. HUISKAMP

A second point of interest in the nickel hexammine halides is the presence of the ammonia groups, which themselves may give rise to heat capacity anomalies, corresponding to some degrees of freedom for the NHsgroups. Using proton resonance techniques Kim 2) found that at 1.6”K there was still some indication of rotational motion of the NHs-molecules. Static susceptibility measurements made by Palma-Vittorelli e.a.3) on the three nickel halides showed that the salts follow a Curie-Weiss law from room temperature down to helium temperatures. The values of the Curie constant observed agree with S = 1 and a g-value of about 2.18, whereas the Weiss constant 8 varied from -9°K for the chloride to -7°K and -3°K for the bromide and the iodide, respectively. Between 1 and 4°K the susceptibility of the chloride and the bromide become nearly independent of temperature. Susceptibility measurements of Ni(NH3)&12 have also been performed by Watanabe 4) who found 0 = -8°K. The heat capacities of the chloride and bromide have been studied between 1 and 4°K by U kei and K an da 5). They report a l-type anomaly for Ni(NHs)& at T = 1.5”K; this is consistent with the splitting of the proton-spin resonance line observed in a single crystal below 1.5”K by Poulis 6). At temperatures above 1.5”K the heat capacity is large (2.5 J/ mole OK) and nearly independent of temperature. For Ni(NHa)sBrz no sharp maximum has been found; the specific heat is practically constant between 1 and 2°K.

nl

Fig. 1. Crystal structure of Ni(NHs)e(Hal)z. The environment of one of the Ni-ions is shown

I

in detail.

In the present paper we report heat capacity measurements on these three nickel hexammine halides, which have been performed between 0.08”K

THERMAL

PROPERTIES

OF THREE

and 1.6”K. At these low temperatures rotational results.

(NHa)

heat

capacity

NICKEL

HEXAMMINE

both the magnetic

anomalies

appear

HALIDES

1133

(Ni++) and the

in the experimental

2. Crystal structwe. The structure of the nickel hexammine halides is of the KsPtC16 type 7). As shown in fig. 1 the Ni++-ions are on a face centered cube (dimensions ao). Every Ni ++-ion is surrounded by a cube (dimensions &ao) consisting of negative halide ions on the corners and NHagroups on the faces. For the three salts studied a0 is slightly different: a0 = 10.06 A, 10.34 A and 10.88 A for the Cl-, Br- and I-salt, respectively. 3. Experiment. The apparatus used has already been extensively described in reference 8. Briefly, the sample is connected by a brass strip to a CrK-alum cooling salt. The thermal resistance of the strip can be calculated from its electrical resistance measured in the liquid helium temperature range. The sample is in good thermal contact with both this strip and a cerium magnesium nitrate thermometer. After adiabatic demagnetization of the cooling salt the sample is cooled via the brass strip. The heat capacity is then determined from observations on the cooling rate. This technique has led to a rather accurate evaluation of heat capacities as, for instance, has been verified in measurements on Ho- and Tb-metal a). Sufficiently large single crystals, as were used in the older experiments, are not available for the nickel halides and thus powdered samples had to be used. The problem of attaining good thermal contact between sample and brass heat-link becomes more serious in this case. In the present experiment the sample (about 0.5 g) was mixed with Apiezon-N grease and the mixture was put in a Perspex box (1 x 1 x 2 cm). A brush of 50-100 copper wires of 0.4 mm diameter and 2 cm length was pressed into the mixture, so that a contact area of about 20 cm2 between copper and mixture was attained. When studying the heat capacity of the iodide, it was necessary to use a small amount of sample (about 50 mg). In this case 500 mg of diamagnetic Al alum was added in order to have the same total volume and the same amount of grease. From experiments on the heat capacity of powdered Cu(NH4)$&*2HsO for which salt single crystal data are available, we concluded that there was no appreciable influence of the contact resistance at temperatures above O.l”K. Below 0.08”K the apparent heat capacity of the powdered sample was systematically somewhat higher than that of single crystals, which indicates that at this temperature the thermal contact resistance becomes of the same order of magnitude as the resistance of the thermal-link (heat flow through the heat-link: & = lOs(TT - Ti) erg/s) where Ti and Ts are the temperatures at the warm and the cold ends of the brass heat-link, respectively. The contact resistance between a grease mixture and copper

1134

H. VAN

KEMPEN,

W. T. DUFFY

JR.,

A. R. MIEDEMA

AND

W.

J. HUISKAMP

wires is apparently not very different from, the contact resistance reported by Kur ti e.a.10) between glycerol mixtures and copper wires (& M 103(Tf-T$

erg/s per cm2 contact

area).

4. ExPerimental results. The experimental heat capacity versus temperature curve for Ni(NH&& is shown in fig. 2. The curve shows pronounced

Fig. 2. Molar

heat

capacity

of Ni(NHs),&.

15 c J moleOK 10

5 crtl II 0

L

T0.1

I -

--

0.3

l

0.5

I 1.0

I

3

I

I

5

OKlO

Fig. 3. Molar heat capacity of Ni(NH s) 6B r2. The dashed line shows the heat capacity after subtracting the low temperature anomaly. The part of the curve drawn above 1°K represents data of Ukei and Kanda.

THERMAL

maxima

PROPERTIES

OF THREE

at 1.45”K and 1.02”K. Below

pidly (roughly proportional

NICKEL

HEXAMMINE

1135

HALIDES

1“K the heat capacity

to T2.7) and reaches a minimum

decreases raat

T = 0.2”K

Our results agree with those of U kei and K anda 5) in that they also report a maximum in the heat capacity occurring at’ T = 1.5”K, however their heat capacity values are about 25% lower. No indication of an anomaly at l.O”K is found in the data of Ukei

and Kanda.

TABLE

I

Properties

of three nickel hexammine

Ni(NH3)eClz

halides

1&OK) 1TN(“K) 1 ~/TN 1;;_iz$?;

1 a&

salt

I

10.06

-9

1.45

-6

0.025

-9 --II

0.19

- 10

5

Ni(NH3)8Brs

10.34

--7

1.02 0.61

Ni(NHs)&

10.88

-3

0.305

The results obtained for Ni(NHs)GBrs as given in fig. 3 show a pronounced peak at T = 0.61”K. The maximum is much higher than that for the chloride (14 J/ mo 1e “K compared to 7.2 J/mole OK). Also, for the bromide the heat capacity increases again on the low temperature side, proportional approximately to T-2.The proportionality constant is much larger for the bromide than for the chloride, as may be seen in table I. The part of the curve drawn above 1°K represents data of U kei and Kanda. One may see that the results of Ukei and Kanda and our results can be connected in a satisfactory way. Assuming that the heat capacity versus temperature curve consists of the sum of a magnetic contribution and an anomaly due to the ammonia molecules one may separate the two anomalies as indicated by the dashed line in fig. 3. The above assumption I

I

I

I

I

I

I

I

I

I

I

I

40 3 m&K 30

20

10

cm I I

0

I

T

I

I

I

I

I

0.5

Fig. 4. Molar heat capacity of Ni(NH3).&

I OK

1

1.0

1136

H. VAN

KEMPEN,

W.

T. DUFFY

JR.,

A. R. MIEDEMA

AND

W.

J. HUISKAMP

appears to be correct since the entropy corresponding to the high temperature anomaly fits nicely to R In 3, the value expected for spin 1. The curve for Ni(NHa)& differs from that found for the bromide in that the two anomalies are no longer separated (see fig. 4). The heat capacity reaches very high values, a sharp maximum of more than 40 J/mole “K occurring at T = 0.305”K. The total entropy gain for the iodide, evaluated from fig. 4 with the aid of extrapolation on both the low and the high temperature sides, equals 5.3 R. This clearly proves that there is a contribution to the heat capacity which is not due to the ordering of the magnetic moments of the nickel ions. 5. Discussion. In each of the three nickel hexammine halides two anomalies are present. One of these corresponds to an ordering of the magnetic moments of the nickel ions, as may be deduced from the results on the bromide. The second anomaly, occurring below O.l”K for the bromide and chloride and around 0.3”K for the iodide, must be attributed to the ammonia molecules, The value of the total entropy gain found for the I-salt precludes the possiblity that it is due to electric quadrupole interaction of the halogen nuclei. Further, there is only a remote possibility of magnetic h.f.s. interaction, such as, for instance, the transferred h.f.s. interaction between halogen nuclei and Ni-ions. Moreover, the temperature region in which the heat capacity anomaly occurs, would require effective magnetic fields at the halogen nuclei of the order of 106 Oe, which are much larger than hitherto observed in salts like NiFs etc. I A-

I

I

I

,

I

I

I

m&K

go-

Fig.

0

T

5. Magnetic

heat

I 1

capacity

I

I 2

of Ni(NHs)eBr2.

1°K represents

data of Ukei

I

The part

I .3

of the curve

and Kanda.

I OK

drawn

above

An accurate value for the magnetic heat capacity for the bromide.

For the iodide, the magnetic

has been obtained only

and non-magnetic

anomalies

occur in the same temperature region, whereas for the chloride the data of Ukei and Kanda disagree with the data reported here. This may be related to the presence of the two maxima found for this salt which may suggest inhomogeneity of the sample due to chemical instability. Two transition temperatures may occur if part of the sample has lost some of its ammonia; since a reliable extrapolation of the heat capacity on the high temperature side is not possible, no entropy check has been made. For the bromide the magnetic heat capacity, shown on a linear scale in fig. 5, nicely corresponds to an entropy of R In 3. Since for a f.c.c. antiferromagnet with nearest neighbour interactions only, 8 nearest neighbours of a given magnetic ion become ordered antiparallel to each other while 4 are parallel, the energy gain (at T = 0) will be according to molecular field theory E/R = J can be estimated

-4JSz/k.

from the Curie-Weiss 8 = 2 zJS(S +

constant 1)/3k

(1) 8 using: (2)

where z equals 12. Using 8 = -7°K 3) we obtain J/k = - (7/16) “K and according to formula (1) E/R must be (7/4)“K. This fits nicely to the experimental value E/R = 2.0 “K. Neglecting next nearest neighbour interactions molecular field theory further predicts 8 = -~TN. Experimentally, however, we found 8 = - 11TN for the bromide and 0 = - 10T~ for the iodide which agrees remarkably well with data available on other f.c.c. antiferromagnets. For MnS (ZnS type, S = 5/2) Carter and Stevens 11) report 8 = -9.4T N, while Cooke e.a.is) report for two f.c.c. chloroiridates (S= l/2), 8=-10.5 TN for KsIrCl6 and 8=-9.4T~ for (N&)sIrCl6. This may suggest that quite generally, independent of spin, 8 = -1OTn for f.c.c. antiferromagnets with predominantly nearest neighbour interactions. The existence of such a rule is rather unexpected if (~/TN is determined by the relative magnitude of the next nearest neighbour interactions. In E.S.R. experiments on the three halides Palma e.a.3) is) observed a very strong increase in line width when the crystal was cooled below a well defined temperature, namely T = 80°K for the Cl, T = 34°K for the Br and T = 19.5”K for the I-salt. For instance in the Ni(NHs)& the line width increased by roughly a factor 10 (to a value of about 1.5 kOe) when cooling from 20 to lO”K, while the increase was steepest at the above mentioned temperature. On the other hand, the center of the line did not noticeably shift and neither was an indication of line splitting observed.

1138

H. VAN

KEMPEN,

W.

T. DUFFY

JR.,

A. R. MIEDEMA

AND

W.

J. HUISKAMP

For the iodide crystal a heat capacity maximum was observed at the same temperature 14) ; if the normal lattice heat capacity is subtracted from this maximum, the remaining heat capacity corresponds to an entropy change of K In 3 per Ni-ion. A simple explanation for the heat capacity anomaly might be sought in a removal of the (2.S + I)-fold- degeneracy of the ground state of the Ni-ion, but this is in contradiction to: 1) the heat capacity data at low temperatures; 2) susceptibility data; 3) the order of magnitude of overall crystalline field splittings in other salts, ranging from 0.1 cm-r in the highly symmetric NiSiFse6HzO to about 5 cm-i in very asymmetric environments; and 4) the fixed position of the peak in the E.S.R. spectrum and the absence of line splitting. On the other hand the E.S.R. experiments may be explained by assuming a transition of the crystal to a structure of lower than cubic symmetry, inducing ,for instance, axial components in the crystalline field potential, varying among the Ni-ions. However, this does not explain the rather sharp peak in the heat capacity, occurring at such high temperatures. A satisfactory explanation for the specific heat anomaly has been given by Stevens 15)) who emphasized the peculiar situation that the Ni-ion (at relatively high temperatures) obviously maintains a predominantly cubic environment in spite of the presence of 6 triangular NHs-molecules. He suggested that the transition at 20°K for the I-salt is due to vanishing of rotational degrees of freedom for the NHa-molecules with a concurrent loss of cubic symmetry. The latter, as said before, may qualitatively explain 13) the E.S.R. data, while the R In 3 entropy gain has to be provided by the NHs-groups. Stevens suggests that the 24 operations of the cubic symmetry group on an arbitrary configuration of the 6 NHs-groups (therefore, in particular also the configuration having lowest potential energy) lead to 4 energetically equivalent states. These can, by taking proper linear combinations, be grouped into two irreducible representations of the cubic group, namely one singlet and one triplet. If further these states are not precisely orthogonal, but for instance show some overlap, a splitting between singlet and triplet will occur. If it is assumed that the singlet is higher and is widely separated from the triplet, then the specific heat anomaly may be explained by a splitting of the triplet at the forementioned transition temperature, leading to an entropy loss of K In 3 per Ni(NH 3) 6I 2 molecule if the temperature is sufficiently decreased. The splitting of the triplet signifies a loss of cubic symmetry or a freezing of the motion from one configuration of 6 NHs-molecules to other configurations (derived from the former one by cubic symmetry operations). It is quite plausible that such a freezing effect is produced in a cooperative fashion with neighbouring groups of (NHs)a-molecules, such that a sharp transition temperature is obtained (similar to the freezing of rotational motions observed for organic molecules in various molecular crystals). An explanation can be given of the 5.3 k entropy loss per Ni-ion when further de-

THERMAL

creasing

PROPERTIES

the temperature.

OF THREE NICKEL

Although

HEXAMMINE

the originally

cubic

HALIDES

configuration

1139 of

the 6 NHa-molecules may be deformed, there is still left a threefold spatial degeneracy for each NHa-group separately. Similar to the removal of the inversion degeneracy in a NHa-molecule, there remains the possibility of tunneling of one configuration of 3 protons to other configurations, which are rotated & 120” with respect to the former one. This will, as is well known from the theory of hindered rotations

in organic

molecules, in general lead to a splitting of the ground state, as was for instance demonstrated in microwave experiments of Heller 16) on CHagroups, who found a splitting of a few cm-i. It was pointed out to us by Prof. Stevens, that the proton spins impose symmetry requirements on the spatial wave functions such that the total number of possible states per NH3 group is 8. These 8 states are according to group theory not equivalent, but belong to two representations, each of them spanning 4 states, one quartet having a total spin I = 312 and the other one total spin I = l/2. If the potential barrier between one configuration and another one, rotated by 120”, is not infinitely high, quantum mechanical tunneling is expected to occur with a certain frequency, which corresponds to an energy splitting between the two quartets. At low temperature only the lowest quartet remains populated, giving a change in the entropy of 6R In 2 per mole. The results obtained on the iodide are in excellent agreement with this theory; the experimental value of the entropy gain is 5.3 & 0.3 R which practically equals the theoretical value of R In 3 + 6 R In 2 = 5.26 R (R In 3 representing the magnetic entropy of the nickel ions). Since the tunneling frequency is very sensitively dependent on the height of the potential barrier, the size of the halide ion may have considerable influence on the temperature, at which the specific heat anomaly occurs. The observed heat capacity tails correspond to energy/k splittings between the two quartets of 0.045”K for the chloride, 0.12”K for the bromide and 0.72 “K for the iodide. For a free rotation of the NHa-molecule about the fixed trigonal axis, the energy difference between the I = 2 ground state and the I = + first rotational state would be 9.3”K. The observed level splittings are much smaller as a result of the hindering potential barriers. The phenomenon observed is rather similar to the ortho-para transition in molecular hydrogen, where states with even and odd spins are energetically separated. 6. Conclusion. In the three hexammine halides the transition to the antiferromagnetic state is observed. For the bromide and the iodide the Weiss constant 8 is about ten times the Neel temperature TN, as is also found in other f.c.c. antiferromagnetics with predominantly nearest neighbour interaction. This makes it less probable that the ratio of the nearest

1140

THERMAL

PROPERTIES

6~

THREE

NICKEL

HEXAMMINE

HALIDES

neighbour and next nearest neighbour interaction is the determining factor for ~/TN for these salts. Besides the heat capacity anomaly of magnetic origin, another anomaly is observed in the three salts. This anomaly can be attributed to the splitting of the eight possible proton-spin states of a NHs-group into two quartets (one quartet with total spin I = $, the other with I = 4). The splitting is due to the possibility of tunneling of one proton configuration to another. It may be noticed that at temperatures corresponding to energies low compared to the splitting (e.g. at O.l”K for the iodide) one third of the protonspin entropy is removed. One can expect that the substitution of the protons by deuterons affects both the temperature region where the anomaly occurs as well as the total entropy gain. So measurements on the deuterated salts may be interesting 16). Acknowledgements. This investigation is part of the research program of the “Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.)” which is financially supported by the “Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (Z.W.O.)“. We are sincerely indebted to Prof. K. W. K. Stevens for discussions and suggestions and to Prof. C. J. Gorter for his continuous interest. Received

REFERENCES

1) 2)

Anderson,

3)

Palma-Vittorelli, M. B., Palma, M. IJ., Drewes, G. W. J. and Koerts, Kamerlingh Onnes Lab., Leiden No. 323~; Physica 26 (1960) 922.

4)

Watanabe,

5) 6)

Ukei, K. and Kanda, Poulis, N. J., Private

7)

Wyckoff,

3)

X, table page 34. Haseda, T. and Miedema,

9)

Van

Kim,

P. W., Phys. Rev. 79 (1950) 705.

P. H., J. phys. Sot. Japan

15 (1960) 445.

T., J. phys. Sot. Japan

R. W. G., Crystal Structures

Kempen,

16 (1961)

E., J. phys. Sot. Japan communication.

1131.

Leiden

Publishers,

Inc.,

New York,

No. 329~; Physica

A. R. and Huiskamp,

Physica 30 (1964) 229. Kurti, N., Robinson,

Commun.

16 (1961) 2061.

(Interscience

A. R., Commun.

H., Miedema,

W.,

1948) Chapt.

27 (1961)

W. J., Commun.

Leiden

1102. No. 336~;

F. H. N., Simon, F. and Spohr, D. A., Nature 178 (1956) 450. 10) W. S. and Stevens, K. W. H., Proc. phys. Sot. 869 (1956) 1006. 11) Carter, J. and Wolf, W. P., Proc. roy Sot. A. H., Lazenby, R., McKim, F. R., Owen, 12) Cookes, 250 (1959) 97. M. B., Palma, M. U. and Persico, F., J. phys. Sot. Japan 17 (1962) 13) Palma-Vittorelli, Suppl. B 1, 475. Miss H. M., Unpublished. 14) Voorhoeve, K. W. H., Private communication. 15) Stevens, H., To be published. 16) Van Kempen,