Neutron scattering studies at high pressure on rare earth intermetallic compounds

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Neutron scattering studies at high pressure on rare earth intermetallic compounds

D. Mcwhan, C. Vettier

To cite this version:

D. Mcwhan, C. Vettier. Neutron scattering studies at high pressure on rare earth intermetallic compounds. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-107-C5-111. �10.1051/jphyscol:1979537�.

�jpa-00218954�

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JOURNAL DE PHYSIQUE Colloque C5, supplément au n° 5, Tome 40, Mai 1979, page C5-107

Neutron scattering studies at high pressure on rare earth intermetallic compounds

D. B. McWhan

Bell Laboratories, Murray Hill, NJ 07974, U.S.A.

and C. Vettier

Institute Laue Langevin, 38042 Grenoble, France

Résumé. — Nous présentons une revue des résultats expérimentaux obtenus par diffusion neutronique sous haute pression, en insistant sur le magnétisme induit dans les systèmes dont l'état fondamental est un singulet.

En particulier, nous discutons la structure antiferromagnétique de PrSb ainsi que le comportement des excitons au-dessus de la pression critique.

Abstract. — A review of neutron scattering results at high pressure is given along with a review of induced moment magnetism in singlet ground state systems. Recent results on the pressure induced antiferromagnetism in PrSb are presented. The soft longitudinal exciton is found to saturate at a finite energy with decreasing temperature above the critical pressure.

Inelastic neutron scattering is almost a unique probe for the study of atomic excitations in rare earth intermetallic compounds. Many of these excitations can be understood using a model Hamiltonian containing a sum of single ion crystal field terms which are coupled by a wave vector dependent exchange. During the last decade interest has centered on the study of systems in which the lowest crystal field level is a nonmagnetic singlet and in which induced moment magnetism results when the ratio of the exchange to the crystal field exceeds a critical value [1, 2]. At ambient pressure it has been necessary to find a variety of model compounds which span the region from weak exchange to strong exchange. The classic examples of materials near the critical ratio are Pr metal and Pr3Tl [1, 2]. The former is on the verge of ordering magnetically while the latter orders ferro- magnetically at ~ 12 K. In order to study materials exactly at the critical ratio at ambient pressure, it is necessary to resort to alloys of for example Pi^-^Nd^

or Pra.^La^Tl [3-5]. During the last five years the techniques have been developed to do inelastic neutron scattering over a wide range of pressure and temperature. For example, we have recently taken single crystals to pressures of 3.6 GPa (1 GPa = 10 kbar) and temperatures of 5 K using a pressure cell made of externally supported aluminum oxide and a clamp device to retain the pressure. With pressure as a variable it is possible to scan the critical region in a controlled way in pure materials. For example, Tc in Pr3Tl decreases to 0 K at a pressure of ~ 1.2 GPa [6]

and Pr metal becomes antiferromagnetic with the application of a small uniaxial stress [7]. Both Pr3Tl

and Pr metal have features that make them less than ideal for the study of the critical region. It has not been possible to grow well-ordered single crystals of Pr3Tl, and the measurements to date have been limited to polycrystalline samples. As a result of this, it is not possible to study the long wavelength limit as q -» 0 where the interesting soft mode behavior is expected, and only the average exchange is measured rather than J(q). Pr metal is complicated by having the double hexagonal close-packed crystal structure with two crystallographically inequivalent sites. This leads to two sets of single ion crystal field levels and coupling terms within and between the two types of sites. A great deal of effort has been put into understanding Pr metal over the past two decades, and there is reaso- nable agreement between theory and experiment (see Ref. [8]). In the course of studies of the effect of pressure on crystal field splittings, we found a third system for the study of induced moment antiferromagnetism [9]. PrSb has the simple NaCl structure common to many of the rare earth pnictides and chalcogenides, and it has been possible to grow good quality single crystals. The cubic crystalline field partially lifts the 9-fold degeneracy of the 3H4 lowest Hund's rule multiplet to approach at low temperatures a singlet-triplet system. We found that the 3-fold degeneracy of the triplet is lifted along the [100]

direction to give a singlet-singlet system at the zone boundary at low temperatures. With increasing pressure the energy difference between the two singlets decreases until at a critical pressure of ~ 3 GPa there is a transition to a type 1 antiferromagnet in the limit of T -> 0 K [9]. We have determined the structure

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979537

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C5-108 D. B. McWHAN AND C. VETTIER

and the moment and the phase boundary in the pressure-temperature plane. Recently, we have studied the temperature renormalization of the soft mode above the critical pressure [lo]. In the following sections previous neutron scattering measurements at high pressure on rare earths are reviewed and the experimental techniques are summarized. Next the theoretical predictions for the singlet-singlet and singlet-triplet systems are presented chronologically.

Finally our pressure measurements on PrSb are presented.

1. Neutron scattering at high pressure. - Table I lists all the references, which we could find, on neutron scattering measurements at high pressure on rare earths. After the early work of Umbeyashi et al.

on the ordering temperature and turn angle in several heavy rare earth metals, there was almost nothing repo;teduntil the mid-1970s. By this time the emphasis in research on rare earths had shifted to the light rare earth metals, mixed valence materials, and crystal field effects. As there is a trend in crystal structure with increasing pressure from hcp -, Sm type ^-+dhcp -+ fcc [ll], a study of a well-understood metal such as Tb in the high pressure Sm type phase might help to elucidate the properties of the lighter rare earth metals.

Most of the papers listed in table I report studies made below a pressure of 1 GPa. This represents the limit of pressure cells made of unsupported aluminum alloys. All of the published work at higher pressures has used aluminum oxide cylinders which are externally supported. In these cells the present limitation is the unsupported tungsten carbide pistons used to

Table I.

1. Tb, Ho : H. Umebayashi, G. Shirane, B. C. Frazer, W. B. Daniels, Phys. Rev. 165 (1968) 688.

2. LaMnO, : N. N. Sirota and A. P. Karavai, Fiz. Tverd.

Tela 18 (1976) 2666 [Sov. Phys. Solid State 18 (1976) 15551.

3. CeSb, CeAs, CeP : H. Barthdlin, D. Florence, G. Parisot, J. Paureau, 0. Vogt, Phys. Lett. 602 (1977) 47.

4. Ce : B. D. Rainford, B. Buras. B. Lebech, Physica 86-88B (1977) 41.

5. CeSn, : J. Beille, D. Bloch, J. Voiron, G. Parisot, Physica 86-88B (1977) 231.

6. PrSb : C. Vettier, D. B. McWhan, E. I. Blount, G. Shirane, Phys. Rev. Lett. 39 (1977) 1028.

7. SmS : R. M. Moon, W. C. Koehler, D. B.

McWhan, F. Holtzberg, J. Appl. Phys. 49 (1978) 2107.

8. Pr : K. A. McEwen, W. G. Stirling, C. Vettier, Phys. Rev. Lett. (1978).

9. SmS : D. B. McWhan, S. M. Shapiro, J. Eckert, H. A. Mook, R. J. Birgeneau, Phys. Rev. B (1978).

10. Pr,Tl : J. K. Kjems, M. Nielson, W. J. L. Buyers, J. E. Crow (this conference), J. Physique

CoZloq. 40 (1979) C-5.

apply the pressure to the sample contained in the cylinder, and this limit is

-

4.5 GPa. One must further distinguish between samples immersed in a solid or liquid pressure transmitting medium. Pressures of 4-4.5 GPa have only been reached in solid systems as for example in the measurement of the compressibility of CeSb. The maximum pressure which we have attained using a fluid pressure transmitting medium is 3-3.5 GPa. In the study on PrSb, Fluorinert FC-75 was the medium, and it becomes glassy above

-

^{2 GPa}

as evidenced by the %fold increase in the width of the rocking curve between 2 and 3.6 GPa [lo]. In the earlier work on PrSb a special combination cryostat and hydraulic press was used to cool the pressure cell to

-

^{25 K}using a closed cycle helium refrigerator [9].

To reach 5 K a clamp device has been used. One version of this has been published [I21 and a second one is shown in figure 1. The aluminum shell has left-

Fig. 1. -Clamp device for neutron scattering at pressures up to 4.5 GPa (45 kbar) and low temperatures. (1) Steel shoe on (2) Tungsten carbide piston ; (3) Locking sleeve of A1 alloy 7075-T6 ; (4) High density A1,0, cylinder, (5) Beryllium copper cap and (6) Extrusion rings ; (7) Pressure transmitting medium of fluorinent PC-75 ; (8) Sample cell of Al 5052 ; (9) Single crystal sample ; (10) Locking nuts of Vascomax 300 for external support of A1,0,;

(1 1) Back up block of tungsten carbide in steel support ring.

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NEUTRON SCAnERING STUDIES AT HIGH PRESSURE ON INTERMETALLIC COMPOUNDS C5-109 and right-handed threads so that the external support

load or the pressure on the sample can be increased by a hydraulic press and then the load transferred to the locking nuts. The oriented single crystal plus fluid is mounted in a small aluminum container which fits inside the A1203 cylinder. The volume of the crystal used is typically 0.1 cc, and the volume of the pressure transmitting fluid is minimized by filling the space around the crystal with Pb or NaC1. This also serves as an independent check on the pressure as the equa- tions of state of both materials are known.

2. Singlet-singlet and singlet-triplet models. -

There have been a number of review articles published on induced moment magnetism [I, 21 and only the chronological development of theory and experiment is summarized below. In the cubic crystal field of the NaCl structure the 9-fold degeneracy of the ³ ^~ ^, configuration is lifted to give at the zone center the sequence of levels : I',(l), r,(3), r,(2), I',(3). The neutron scattering cross-section is proportional to the matrix element ( n

1

J , ( m ) coupling the nth and mth crystal field levels and to p, the population factor of the nth state. From measurements made at two temperatures on polycrystalline samples, the allowed transitions were found to be T,-T, (73 K), I',-T3 (52 K), I',-T, (1 14 K) and T,-T, (160 K) [13].

At low temperatures the system will approach a singlet-triplet system as only the T I state becomes populated. If the degeneracy of the triplet is substan- tially lifted as a function of q, then it is possible to have a singlet-singlet system at low enough temperatures.

The usual Hamiltonian used to derive the crystal field levels discussed above is of the form

where Vi is the single ion crystal field potential. In the simplest molecular field approximation for a singlet- singlet system the resulting inverse magnetic susceptibility is :

where A is the singlet-singlet separation,

is the matrix element coupling the ground and excited states

I

o, ) and

I

I, ), and

It is clear that as 4 3(q) a2/d approaches one, the susceptibility will diverge and that there will be a phase transition to an ordered phase in which the ground state is a mixture of the two crystal field

singlets. The exact value for the critical ratio of 3(q)/A varies slightly for more complicated models, but the basic nature of the transition remains unchanged [2]. A similar result is found for the singlet- triplet model. Measurements such as magnetic susceptibility and heat capacity on the system Pr, - .La,Tl are consistent with this model for induced moment ferromagnetism [4, 51. An effective boson approximation for the spin dynamics of a singlet-singlet system or singlet-triplet system predicts a soft mode behavior for the temperature dependence of the dispersion relation for the magnetic exciton [2].

Subsequent neutron scattering results failed to find any temperature dependence to the dispersion relation in Pr3TI [14]. It was pointed out that there were processes which could couple TI-T, excitations to excitations within the triply degenerate 1', [15]. In the ferromagnetic case this would result in the growth of critical scattering at E = 0 near the ordering temperature and a finite energy gap for the TI-T, excitation at q = 0. This critical scattering was subsequently observed, and there was qualitative agreement with RPA theories [16]. This mechanism for the absence of soft mode behaviour is only valid at finite temperatures where there is thermal occu- pation of the

r,

level. Studies on the variation of the critical scattering as T , is decreased with increasing pressure are discussed in Ref. [17] and a theory for the pressure dependence of T, is given in Ref. [IS]. At the present time the predicted full soft mode behavior in the limit of T + 0 K has not been observed experi- mentally in a singlet-singlet or singlet-triplet system.

3. Pressure induced antiferromagnetism in PrSb. - In a recent Physical Review Letter we reported inelastic neutron scattering measurements on a single crystal of PrSb at 1 atm and at

-

1.6 GPa [9]. The measurements were originally made to verify that the crystal field splitting decreased with decreasing interatomic spacing contrary to the variation expected on the basis of a point charge model. The first evidence for this decrease came from NMR measurements. As they are summarized in the following paper at this conference [19], this aspect of the problem will not be discussed here. The single crystal neutron scattering results were far richer than had been expected on the basis of earlier measurements on polycrystalline samples. Instead of a simple dispersion relation resulting from isotropic bilinear exchange, there was a lifting of the degeneracy of the triply degenerate T, level along [loo], suggesting a large anisotropy in the exchange (see figure 2). By studying the q dependence of the excitations, it was established that the singly degenerate longitudinal mode was lowest at (110).

With increasing pressure the separation between the singlet ground state and the singlet first excited state decredses. If the longitudinal exciton goes soft, then symmetry considerations suggest that a type 1 antiferromagnet with the moment parallel to the c-axis

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C5-110 D. B. McWHAN AND C. VE'ITIER

Fig. 2. - The lifting of the triple degeneracy of the T I T , exciton in the 4f2 configuration of Pr3+ in PrSb. Note splitting is only along [001] and not along 111 11. The lines are guides to the eye.

should result. We observed the appearance of a magnetic (1 10) reflection (and absence of a 100 reflection) at low temperature and reported a critical pressure of

-

3.5 GPa. On the basis of an improved

I I I I I J

0 1 2 3 4 ₅

PRESSURE (GPO)

Fig. 3. - Phase diagram for pressure induced antiferromagnetism in PrSb and variation with lattice parameter or pressure of the exciton energies (labelled in figure 2) at T < 5 K. a(0) is lattice parameter at T = 5 K and P = 1 atm.

pressure calibration the critical pressure is closer to PC = 3.0 +_ 0.2 GPa [lo]. From measurements, done at the Institute Laue Langevin, of the intensity of the 110 reflection as a function of temperature at several pressures, the phase boundary between the nonmagnetic and the antiferromagnetic phase was established. The results are shown in figure 3 along with the energy of the different excitons (labelled in figure 2) as a function of pressure at T

<

5 K. (The points from Ref. [9] at Aala, = - 0.009 8 were taken at T = 28 K but showed almost no temperature dependence contrary to the results near PC reported below.) The points at P = 2.3 GPa were taken at I.L.L. and the points at P = 3.4 GPa at Brookhaven National

~aboratory. In the latter experiments the crystal was mounted to give an hkO scattering plane, and because of the nature of the pressure distribution, there was a small uniaxial component along [OOl]. This resulted in the crystal being 88

%

in the single q state with the moment perpendicular to the scattering plane in the ordered phase. The elastic scattering measurements are consistent with the type 1 structure as is observed in many other rare earth pnictides and chalcogenides.

The moment is

-

^1.3^f^0.3^pBwhich is larger than that observed in Pr,Tl (0.8 pB) but less than half the free ion value of 3.2 p,. We have recently studied the temperature dependence of the dispersion relation along [I101 from 5 K to 40 K, and the results are shown at selected points in figure 4 [lo]. A large softening is observed but the exciton appears to saturate at a finite energy below the ordering tempe-

20 40

1

TEMPERATURE (K1

Fig. 4. - Temperature dependence of the magnetic excitons above the critical pressure [lo]. Ordering temperature is T, = 18 K.

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NEUTRON SCATTERING STUDIES AT HIGH PRESSURE ON INTERMETALLIC COMPOUNDS C5-111

rature rather than showing typical soft mode behavior, i.e. going to zero energy at T, and then increasing below. Reaching pressures of 3.4 GPa and temperatures of 5 K has not been achieved without a cost in damage to the crystal in the form of a mosaic spread of FWHM = 1.7O. This results in a large uncertainty in the energy at (110) of the lowest branch at low temperatures. We believe that there is a finite energy gap, but the shape of the curve is uncertain in the limit of T + 0 K. There is a large amount of elastic scattering which appears with decreasing temperatures at (110). It is resolution limited, and it is not clear at this time if it is critical scattering or if it results from a range of ordering temperatures resulting from the lack of perfect hydrostatic conditions. In summary, we have established pressure induced antiferroma-

gnetism in PrSb resulting from a softening of the longitudinal exciton at (1 10). We observed temperature renormalization of this mode, but it is not completely consistent with a simple soft mode pic- ture. At present we are trying to make measurements as close to the critical pressure as possible to establish the nature of the transition in the limit of T 0 K.

Acknowledgments. - The work on PrSb has been done in collaboration with E. I. Blount, R. Young- blood and G. Shirane, and the crystals were grown by L. D. Longinotti. We have also had many illuminating discussions with P. Bak, R. J. Birgeneau, R. A. Cowley, P. A. Lindgard, and we thank A. L. Stevens for technical assistance.

References

[I] BIRGENEAU, R. J., in Magnetism and Magnetic Materials, AZP Con5 Proc. No. 10, edited by C. D. Graham, Jr and J. J. Rhyne (American Institute of Physics, New York) 1973, p. 1664.

[2] COOPER, B. R., in Magnetism and Metallic Compounds, edited by J. T. Lopuszanski, A. Pekalski and J. Przystawa plenum Publishing Co., New York) 1976, p. 225.

[3] LEBECH, B., MCEWEN, K. A. and LINDGARD, P. A., J. Phys.

C 8 (197.5) 1684.

[4] BUCHER, E., MAITA, J. P. and C ~ O P E R , A. S., Phys. Rev. 8 6 (1972) 2709.

[5] ANDRES, K., BUCHER, E., DARACK, S. and MAITA, J. P., Phys. Rev. B 6 (1972) 2216.

[6] HUANG, S. and CHU, C. W., Bull. Amer. Phys. Soc. 19 (1974) 174.

[7] MCEWEN, K. A., STIRLING, W. G. and VEITIER, C., Phys.

Rev. Lett. 41 (1978) 343.

[8] JENSEN, J., J. Physique Colloq. 40 (1979) C-5.

[g] VETTIER, C., MCWHAN, D. B., BLOUNT, E. I. and SHIRANE, G . , Phys. Rev. Lett. 39 (1977) 1028.

[lo] MCWHAN, D. B., VETTIER, C., YOUNGBLOOD, R. and SHI- RANE, G., TO be published.

[I 11 MCWHAN, D. B., Science 176 (1972) 751.

[12] BLOCH, D., PAUREAU, J., VOIRON, J. and PARISOT, G., Rev.

Sci. Znstr. 47 (1976) 296.

1131 TURBERFIELD, K. C., PASSELL, L., BIRGENEAU, R. J. and BUCHER, E., J. Appl. Phys. 42 (1971) 1746.

[I41 BIRGENEAU, R. J., ALS-NIELSON, J. and BUCHER, E., Phys.

Rev. Lett. 27 (1971) 1530 ; Phys. Rev. B 6 (1972) 2724.

[15] SMITH, S. R. P., J. Phys C 5 (1972) L-157.

[I61 ALS-NIELSON, J., KJBMS, J. K., BUYERS, W. J. L. and BIRGE-

NEAU, R. J., Physics 86-88B (1977) 1162.

[I71 KJEMS, J. K., NraSON, M., BUYERS, W. J. L. and CROW, J. E., J. Physique Colloq. 40 (1979) C-this conference.

[18] YANG, D. and LINDGARD, P. A., J. Physique Colloq. 40 (1979) C-5.

[I91 SHIRBER, J. E. and WEAVER, H. T., J. Physique C0ll0q. 40 (1979) C-5.