EXCHANGE AND CRYSTALLINE FIELD IN METALLIC COMPOUNDS.Coexistence of superconductivity and long range magnetic order

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EXCHANGE AND CRYSTALLINE FIELD IN METALLIC COMPOUNDS.Coexistence of superconductivity and long range magnetic order

Ø. Fischer, M. Ishikawa, M. Pelizzone, A. Treyvaud

To cite this version:

Ø. Fischer, M. Ishikawa, M. Pelizzone, A. Treyvaud. EXCHANGE AND CRYSTALLINE FIELD IN

METALLIC COMPOUNDS.Coexistence of superconductivity and long range magnetic order. Journal

de Physique Colloques, 1979, 40 (C5), pp.C5-89-C5-94. �10.1051/jphyscol:1979534�. �jpa-00218951�

JOURNAL DE PHYSIQUE Colloque C5, supplément au n° 5, Tome 40, Mai 1979, page C5-89

EXCHANGE AND CRYSTALLINE FIELD IN METALLIC COMPOUNDS.

Coexistence of superconductivity and long range magnetic order

0 . Fischer, M. Ishikawa, M. Pelizzone and A. Treyvaud

Departement de Physique de la Matiere Condensee, Universite de Geneve, 32, boulevard d'Yvoy, 1211 Geneve 4, Switzerland

Résumé. — La découverte récente des composés supraconducteurs (RE)Mo

X

(X = S, Se) et (RE)Rh

B

(RE = terre rare) nous offre une possibilité unique d'étudier le problème de la coexistence de la supraconductivité et du magnétisme. Dans HoMo

S

et ErRh

B

on trouve que la supraconductivité est détruite dès l'apparition de l'ordre ferromagnétique. Par contre, dans plusieurs autres composés du type (RE)Mo

S

on trouve un anti- ferromagnétisme qui coexiste avec l'état supraconducteur. Une analyse des champs critiques de ces composés montre l'existence d'une augmentation anormale du pairbreaking en dessous de la transition magnétique.

Abstract. — The recent discovery of the superconducting compounds of the type (RE)Mo

X

(X = S, Se) and (RE)Rh

B

(RE = rare earth) offers unique possibility to study the problem of coexistence of superconductivity and magnetism since they contain a Tegular lattice of RE-ions. In HoMo

S

and ErRh

B

superconductivity is destroyed at the onset of a long range ferromagnetic order. In several other (RE)Mo

X

compounds one finds antiferromagnetic order and the superconducting state remains below the magnetic transition. An analysis of H data shows that in the (RE)Mo

S

compounds an anomalous increase of the pairbreaking occurs below the magnetic transition.

1. Introduction. — It is well known that none of the magnetic elements do become superconducting.

The first one to discuss this fact is probably Ginz- burg [1]. He argued that the absence of superconduc- tivity in the ferromagnetic elements is due to the fact that the total induction B = H + 4 nM is much bigger than the critical field H

that one would expect for these elements. This argument is certainly true for the type I materials that Ginzburg considered, but with today's knowledge of type II superconductors it is not too difficult to find materials where one would have H

> 4 nM

, M

being the spontaneous magnetization. So there must be another reason for the absence of substances where both phenomena are present. The early experiment of Matthias and Suhl [2] showed that small quantities of magnetic impurities (~ 1 %) in a superconductor is enough to destroy superconductivity. Since then many attempts have been made to find coexistence in super- conductors with small quantities of magnetic impu- rities [3]. These attempts have so far failed, mainly because in such systems the magnetic ions are not distributed homogeneously.

However, a few years ago it was found that the superconducting Chevrel phases [4, 5, 6] can be syn- thesized with a regular lattice of magnetic rare earth ions without destroying superconductivity [7]. This discovery triggered a series of new investigations on the problem of coexistence of magnetization and superconductivity and in this article we shall review some recent work in this field.

2. Is coexistence of magnetism and superconducti- vity possible ? Summary of earlier work. — The strong influence that magnetic impurities have on a super- conductor was successfully explained by Abrikosov and Gorkov (AG) [8] on the basis of the BCS-Theory.

The reason for the destruction of superconductivity by the magnetic ions is that the exchange interaction between the conduction electron spin a and the magnetic impurity with angular momentum J lift the degeneracy of the two states forming a Cooper- pair. Such an interaction is referred to as pairbreaking and its effect on the superconducting state can be described by a pairbreaking parameter, p.

For the rare earth's we describe the exchange interaction by :

K„ = ixn0-D(v) a)

where r is the exchange-constant, g the Lande gf-factor and N the total number of atoms. The sum j runs over all Nj sites of the magnetic ions.

With this interaction p becomes for independent magnetic moments

_ c.N(0)Gr

Ps

~ 8fe

r

where c = NJN is the concentration of magnetic ions, G the de Gennes factor, G = (g — l)

J(J + 1)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979534

C5-90 0. FISCHER, M. ISHIKAWA, M. PELIZZONE AND A. TREYVAUD

and N(0) the density of states at the Fermi level.

In terms of this parameter the equation for Tc becomes

Tco is the critical temperature in the absence of magnetic impurities. T,(p:) is a monotonously decreasing function and is zero above p: = 0.281.

Since such pairbreaking effects will be present in both the paramagnetic and the ferro- or antiferro- magnetic state, an essential condition to observe coexistence is that p,O is small. Experimentally one has tried to achieve this by choosing c small enough (typically 1 at %). Many such dilute systems have been reported to show both phenomena, but the observed magnetic order has always been of the short range spin glass or cluster type, because of the irregular distribution of the magnetic ions [3].

Thus to study this coexistence problem, one should have a superconducting compound where the magnetic ions form a regular lattice, but where the number of magnetic ions is small enough for p: to be small.

This condition is, however, not enough. Eq. (2) was derived on the assumption of independent ions and is certainly not valid close to or below the magnetic transition.

The most obvious change in p when the system goes into the ferromagnetic state is due to the pola- rization of the conduction electron by the magnetic ions. This leads to an important increase in p and may in many cases be one reason why a ferromagnet does not become superconducting. In an antiferro- magnet this term will be absent and so one might think that it is more likely to find an antiferromagnetic superconductor than a ferromagnetic one. We shall see that the coexisting systems which have been found so far are indeed all antiferromagnetic, but the analysis of the data presented in section 4 shows that the simple argument given above is not enough to explain the absence of superconductivity in the ferro- magnetic case.

In addition to this polarization effect one expects on theoretical grounds fluctuations near Tm to modify p . How p is influenced depends very much on the model used but generally one expects p to be enhanced near T,. Finally, below Tm one has a superconducting system interacting with spinwaves and defects in the lattice of magnetic moments, which may lead to a value for p quite different from P s -

3. The new materials. - The Chevrel phases have the composition MxMo,S8 or M,Mo6Se8 where M is a metal and x depends on the element M [6]. Of particalar interest to us here are the compounds with M = Rare Earth (x r 1) 17, 111, which form with all the rare earths and which are nearly all super- conducting. The crystal structure of these materials

is rhombohedral-hexagonal with the rhombohedral angle close to 890. The RE atoms which are situated at the origin of the rhombohedral unit cell form therefore a simple nearly cubic lattice. These materials are the first superconductors containing a regular lattice of magnetic ions and it is surprising that in spite of the high concentration of magnetic ions these materials are superconducting. In figure 1 we show the critical temperature of the (RE)Mo,S, and (RE)Mo6Se8 series. When RE is magnetic there is certainly some pairbreaking present. Tc is thus lower than it would have been in absence of magnetic moments and in order to understand these materials it is important to know how large this reduction is.

The most direct way to obtain this information is to compare with isoelectronic non magnetic com- pounds. If La, -xLuxMo6S8 is used for the sulfides one gets the dash-dotted line in figure 1 [12]. A study of Pb, -,RExMo,S8 [13] solid solutions indicated that Tco would rather follow the dashed line. Using this latter curve for Tco we find r

17 meV for GdMo,S8 assuming N(0)

0.18 stateslev spin atom [14, 151.

Assuming r to be the same for all RE, eqs. (1) and (2) would predict the values lying on the full line in figure 1. The pairbreaking is therefore very weak in these compounds. The reason for this is that the magnetic ions are situated relatively far away from the superconducting electrons (Mo-d-electrons) so that the exchange integral r is particularly low in these materials.

Recently another series of ternary compounds was found, (RE)Rh4B4 [16]. This time the structure is tetragonal and the RE atoms form a body centered

Fig. 1. -Critical temperatures for the series (RE),Mo,X, (X

S,

Se). Ref. [7, l l , 2 3 , 301.

COEXISTENCE OF SUPERCONDUCTIVITY AND LONG RANGE MAGNETIC ORDER C5-91

tetragonal lattice. Some of these compounds are superconducting with relatively high transition tempe- ratures (8.7 K for ErRh4B4).

That these two classes of compounds are very different from the dilute systems became clear where it was discovered that both ErRh4B4 [17] and HoMo,S, [18] did return to the normal state at a lower transition temperature TC2 (0.9 and 0.65 res- pectively for the two compounds). Susceptibility, magnetization and specific heat measurements indicated that at this temperature a long range ferromagnetic order sets in. This has more recently been confirmed by neutron scattering measure- ments [19]. This result demonstrates in a rather dramatic way that although the pairbreaking para- meter p is very small in the paramagnetic state it may become very big in the magnetic one.

In the RE(Rh4B4) series the Er compound is the only one to show this behaviour, the other members of the series are either ferromagnetic or super- conducting only. The change over from magnetism in HoRh B (T,

6.4 K) to superconductivity in ErRh,B4 * particularly striking. Among the (RE)Mo,S, and the (RE)Mo,Se, compounds, HoMo,S, also seems to be the only one which displays this reentrant behaviour. The other super- conducting Chevrel phases remain superconducting down to below 100 mK, and several of them do become antiferromagnetic without destroying the superconducting state [20, 21, 221.

However, since at the ferromagnetic transition in HoMo,S, the superconducting state is completely destroyed we do expect to see some anomaly in the superconducting properties at the antiferromagnetic transition too. In figure 2 we show the resistivity versus temperature in different external magnetic fields for the compound DyMo,S,. In zero field we only see one superconducting transition but in fields above 800 G there appears a second transition back to the normal state at T

0.4 K. The a.c.

susceptibility measured in a finite field shows at this temperature a peak indicating a magnetic transition.

L . . . . , . . . . , . , . . ! . . . . , . , . . , I

0 0 5 10 15 20 2 5

TEMPERATURE ( K )

Fig. 2.

Resistivity of Dy,,,Mo,S,

temperature for various external magnetic fields. Ref. [20].

SCdTTERIXG ANGLE ( 2 8 )

Fig. 3.

Powder neutron diffraction data for DyMo,S, above (T

0.7 K) and below (T

0.05 K) the antiferromagnetic ordering transition at T ,

0.4 K. The magnetic peaks have been hatched.

The insert shows the spin arrangement in the magnetic state.

Ref. [24].

Low temperature magnetization measurements [23]

and recent neutron scattering measurements [24]

show that this order is antiferromagnetic. In figure 3 the low temperature diffraction pattern is shown at 0.7 K and at 0.05 K as obtained by Moncton et al. [24].

The observed magnetic peaks can all be indexed in an A type antiferromagnetic structure in the Chevrel phase. In figure 4 we show the intensity of the (;,O,O) line which is proportional to the square of the staggered magnetization. The magnetic transi- tion temperature is in perfect agreement with the one deduced from the results presented in figure 2.

Note in particular the correspondence between the anomaly in the upper critical field (see also figure 6 ) and the magnetic order parameter.

A similar behaviour has been found in TbMo,S,, where the magnetic structure turns out to be identical to the one found in DyMo,S, [25]. In both cases

"

- (1/2 0 0 )

0 HEATING COOLING

TEMPERATURE (K)

Fig. 4.

The temperature dependence of the

3, 0, 0 ) anti-

ferromagnetic peak shown together with the anomaly of the critical

field. Ref. [20, 241.

C5-92 0. FISCHER, M. ISHIKAWA, M. PELIZZONE AND A. TREYVAUD

as well as for HoMo6S8 one finds the magnetic moment in the rhombohedra1 [I 111 direction. It has furthermore been found that also ErMo6S, [20] and GdMo6S, [23] order antiferromagnetically at 0.15 K and 0.95 K respectively. In corresponding selenides metallurgical problems have made the identification of magnetic order in the Chevrel phase difficult [26].

Very careful low temperature specific heat [22]

have now shown that GdMo6Se, does order anti- ferromagnetically at T,

0.75 K.

4. Analysis of the upper critical field.

In view of these new and to a certain extent unexpected results it is interesting to analyse the data in terms of different pairbreaking mechanisms. We shall do this by analysing the critical field HC2 of some of the (RE)Mo,S,. The materials we are dealing with are known to be in the dirty and strong spin-orbit inter- action limit 161. In this case Hc2 is determined by eq. (2) but with p,O replaced by the following pair- breaking parameter [27, 61

Here the quantities H,*Z(O) and cc can be obtained from (dHC2ldT)TC by using

and from eq. (7)

p, is determined from the estimated Tco using eq. (3).

For T,, we shall take the dashed line in figure 1.

We should point out however that this choice is not of importance here. We have in fact also per- formed the calculation using the dash-dotted line and the change in the result is of the order of a few

I percents.

p(7; HC2) = + ^0.281 - ~ ~ ( 0 1 (Hc2(T)

The magnetization is taken directly from experi- ment. This is possible since we deal with extreme

+ 4 nM(Hc,, T)) + ^0.281 - 1 ^0.022 a type I1 materials and there is no difficulty to obtain H:(o) A,, Tco the susceptibility or the magnetization close to HC,.

X

(He, + q(H(2p TI)2 + ^Ps - ^{(4) Eq.} (7) still contains two parameters : A,,, the spin- orbit scattering parameter and r, the exchange The first term describes the pairbreaking due to

the total induction B in the sample and the second term results from the polarization of the conduction electron spins due to the external field and the internal exchange field H,. This latter field is given by the average over X,, which is then written as

g, p, HJ o, :

The first term in eq. (4) describes the exchange scattering. We shall write p, = p,O + pi(T), where pi(T) describes the temperature dependence due, for instance to fluctuations near T,. Since different expressions for pi(T) available in the literature are very model dependent, we shall perform the calcula- tion of HC2 with pL(T) = 0 and then in a second step we determine pi(T) from the discrepancy between the calculated critical field and the measured one.

H,*,(T) is the orbital critical field obtained from eq. (2) by putting

In terms of H,*2(T) we may use eq. (4) to write the

equation for Hc2(T) : (with

in units

Fig. 5.

Critical field versus temperature for Er,,,Mo6S,. The

of kG) full line is the theoretical curve as explained in the text. The insert shows the susceptibility determined 800 G at low temperature.

Hc2(T) = H,*Z(T)

3.56 HZ(0) p, - Ref.

COEXISTENCE OF SUPERCONDUCTIVITY AND LONG RANGE MAGNETIC ORDER 0 - 9 3

constant. However, since in these compounds we have HC2 << HJ there is in reality only one constant, T2/Aso, to determine. This one we shall fix by fitting to one experimental point between Tm and T,.

In figure 5 we show the results for ErMo6S8.

r 2/As, were determined by fitting at T = 1.05 K and M was taken from the observed susceptibility (M

xH). The excellent fit shows that it is not necessary to involve any new pairbreaking mecha- nism in order to explain the data. The reentrant behaviour starting below 1 K is a result of the pola- rization of the Er magnetic moments by the external magnetic field. We can therefore safely take pb(T)

0 in the paramagnetic regions. What happens in the magnetically ordered phase cannot be determined clearly by these measurements since Tm is very low, we can however conclude that the increase of HC2 below Tm is a result of the reduced susceptibility.

For DyMo6S8 we have done a similar calculation (figure 6), determining r2/ils0 by fitting at 0.8 K.

Here it was necessary to take into account the complete magnetization curve. Since precise low temperature data have not yet been obtained we used the experi- mental M(H/T) curve obtained between 1.41 K and 1.99 K and used it to make molecular field calculation with Tm = 0.4 K. The fit obtained in the paramagnetic region is very good. To demonstrate that this is not a trivial result we also plot in figure 6 the curve we obtained using a Brillouin function B,,,,(H/T) rather than the experimental magnetization.

TEMPERATURE ( K )

Fig. 6.

The critical field versus temperature for Dy,,,Mo,S, and Ho,,,Mo,S,. The full line shows the calculated field using the experimental magnetization curves. The dash-dotted line was obtained using a Brillouin function for the magnetization rather than the measured one.

Below the magnetic transition temperature there is a clear discrepancy between the calculated and the measured critical field. Since we use a fitting procedure one might think that by changing the parameter r2/Aso somewhat one might get a better fit. It is however easy to see that this is not the case, since there is no anomaly in M at 0.4 K and H z 1.2 kG. In fact the magnetic moments are essentially aligned under these conditions and there is nothing in eq. (7) except pi(T) which can produce such an abrupt decrease in HC2.

The parameter r/AiL2 found in this analysis was 12 meV, 3.5 meV, and 11 meV for TbMo6S8, DyMo6S8 and ErMo6S, respectively.

As explained above, we now express the discrepancy between the calculated and the measured Hc2 values in terms of an additional pairbreaking parameter p;(T). The result is shown in figure 7. We can see that in both DyMo6S8 and TbMo6S8 p;(T) increases below Tm and then seems to saturate at low tempe- rature. It thus behaves qualitatively as the magnetic order parameter. The errobars shown in figure 7 account for the different uncertainties in the fitting procedure. Fluctuation effects, which should show up as an anomaly in p,' close to Tm, seem to be absent in these compounds. However the results are not precise enough to completely exclude the existence of such effects, and more careful measurements in samples with narrow transitions will be necessary in order to decide on this question. The origin of this additional pairbreaking parameter is at the present time unclear. A possible explanation could be the reduction of the effective electron-electron inter- action due to the exchange of virtual magnons [28,29].

Finally we want to make a remark about HoMo6S,.

We have not made detailed measurements of HC2

TEMPERATURE (K)

Fig. 7.

Additional pairbreaking parameter versus temperature

for Tb,.,Mo,S, and Dy,.,Mo,S,.

C5-94 0. FISCHER, M. ISHIKAWA, M. PELIZZONE AND A. TREYVAUD

yet but in figure 6 some values are plotted. If we make an approximate calculation we find a similar situation as in DyMo,S,. The abrupt decrease of HC2 just above T, cannot be explained by the polarization on the conduction electrons since in a field of 1 I ~ G ^the

Ho-ions are already nearly polarized even above T,.

In other words the superconductor sees the diffe- rence between the spins polarized by interaction only (just below T,) and spins polarized with the help of an external magnetic field (just above T,).

conductivity. The analysis of the Hc2-data of some of these materials shows that there is an anomalous increase in the pairbreaking parameter below the magnetic transition. This leads to a reduction of the critical field in the antiferromagnetic case, but in the ferromagnetic case it is strong enough to completely destroy superconductivity. More careful work has to be performed in order to completely understand the observed interaction between super- conductivity and long range magnetic order.

5. Conclusions.

Among the (RE)Mo,X, (X = S, Acknowledgment. - We thank D. E. Moncton, Se) we find the first materials showing coexistence W. Thomlinson and G . Shirane for communicating of long range antiferromagnetic order and super- their neutron results prior to publication.

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