Ground state properties and energy parameters of the Anderson lattice system, CeAl2

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Ground state properties and energy parameters of the Anderson lattice system, CeAl2

R. Parks, L. Kupferberg, M. Croft, S. Shapiro, E. Gurewitz

To cite this version:

R. Parks, L. Kupferberg, M. Croft, S. Shapiro, E. Gurewitz. Ground state properties and energy parameters of the Anderson lattice system, CeAl2. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-323-C5-325. �10.1051/jphyscol:19795110�. �jpa-00218894�

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JOURNAL DE PHYSIQUE Colloque C5, supplkment au no 5, Tome 40, M a i 1979, page (25-323

Ground state properties and energy parameters of the Anderson lattice system, CeAl,

R. D. Parks (*) and L. C. Kupferberg (*) University of Rochester, Rochester, NY 14627, U.S.A

M. C. Croft

Rutgers University, Piscataway, NJ 08804, U.S.A.

S. M. Shapiro and E. Gurewitz

Brookhaven National Laboratory (**), Upton, NY 11973, U.S.A.

RBsumC. - Des mesures de magnttostriction et d'expansion thermique de CeAl, dans la phase et au voisinage de la phase antiferromagnetique (AF) ont etabli, en premier lieu, la fronti6re de la phase AF dans le diagramme H-T, en second lieu, la nature de la rtorientation des domaines AF et l'tvolution du paramhtre d'ordre AF dans un champ magnttique ainsi que les fluctuations au-dessus de T,, et, finalement, que l'tchange magnktique est ferromagnetique pour un champ magnetique eleve. Des mesures de diffusion intlastique de neutrons rtvklent une nouvelle particularitt a 17,5 meV qui n'a pas encore t t t expliquee.

Abstract. - Magnetostriction and thermal expansion measurements on CeAI, in and near the antiferromagnetic (AF) phase have established (1) the AF phase boundary in the H-T plane ; (2) the nature of the reorientation of the AF domains in field, the evolution of the AF order parameter in field and the nature of the AF fluctuations above T , ; and (3) that the magnetic exchange between Ce atoms is ferromagnetic in large fields. Inelastic neutron scattering measurements reveal a new and yet unexplained feature at 17.5 meV.

(*) Research supported in part by the Army Research Office

The compound CeA1, is an Anderson lattice system in the local moment regime, which appears to display

a competition between spin fluctuations and indirect ^100- magnetic exchange. In this paper we summarize the

results of an extensive study of the macroscopic

thermodynamic properties of CeAI, and present ^80- some preliminary results of an ongoing neutron

scattering study.

-

^60-

and ^theOffice of Naval ~eseaich.

-

(**) Research supported in part by the Basic Energy Sciences In a sufficiently large finite field, the A F polariza-

Division of the Department of Energy, under Contract No. EY-76- tion ^CeA12 reorients transverse the

C-02-0016. field [3]. This is manifested in single crystal dilitation

I I I I O'

/ /

/ -

/ / I / / / /

d

^-

I ,

;d

-

1. Macroscopic studies. ^-To facilitate discussion we present in figure 1 the phase diagram in the H-T v ;

plane of CeAl,. The line denoted by solid circles ^40- is the previously reported [I] antiferromagnetic (AF)

transition temperature TN(H) vs. field for a poly- ^\

crystalline sample. Since the high field critical field 20- - vv--

of the A F transition is anisotropic [2], this region, e.g., H

2

30 kOe, must be regarded as qualitative.

The TN(H) line is the only line in the figure which 2 3 4 5 T ( K )

represents a true phase transition. The other lines

mark changes in physical regimes as discussed Fig. 1. - Phase diagram of CeA1,. See text for explanation of

below. symbols and discussion of various features.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19795110

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C5-324 R. D. PARKS et al.

measurements (for polycrystalline results ( T = 2 K), see figure 3 of Ref. [4] as well as Ref. [3]) by the decrease in length in the (1 11) direction in increasing parallel field to a minimum value at H, and a subsequent increase. The field H, (denoted by the locus of solid triangles in figure 1) represents the field where the AF order is essentially completely transverse. In analogy with a continuous spin-flop transition, it is useful also to identify the maximum in the rate of spin reorientation with field. We have associated this maximum with the field HI where the maximum in field derivative of the length occurs (denoted by the locus of solid diamonds in figure 1). In contrast to strongly anisotropic systems, this spin-flopping is continuous in CeAl,, being reproducible in increasing and decreasing field.

We have also seen evidence [5] for transverse AF fluctuations for T > T,(H). Implicit in our inter- pretation of the magnetostriction results in this region is the conventional assumption that the local strain couples quadratically to the local magnetization. In the field region 5 kOe < H < 53 kOe and for T > 4 K, and in the absence of fluctuations, one would expect - a, (the longitudinal thermal expansion coefficient) to increase monotonically with the variable HIT. On the other hand AF fluctuations transverse to the field are expected to contribute a positive increment to a, which slows, stops and then reverses the - a, increase as T + T,(H) (see, e.g., figure 1 of Ref. [4]). Therefore, at a given field, - a, shows a peak at a temperature T, whose value is dictated by the strength of the AF fluctuations.

The values of T, in this field regime are represented as open circles in figure 1 and can be seen to track the shape of the phase boundary T,(H).

We interpret [5] the precipitous drop in temperature of the - a, peaks below 5 kOe as due to a nonlinear crossover from transverse to isotropic AF fluctuations, analagous to the crossover in the sponta- neous AF polarization for T < T,. In fields above 55 kOe the AF phase is suppressed and the - a, curves exhibit Schottky-like peaks at a temperature proportional to the Zeeman energy 151. This follows by virtue of the quadratic coupling of length to local magnetization M, which implies a,

-

^d⁽^{M 2}^)/dT.

The Zeeman splitting one calculates corresponding to the three highest field points in figure 1 is too large for even the full T, moment [5]. Moreover, the three high field points for the peak in - a, (i.e., H = 65, 77.5, 109 kOe) extrapolate to a finite temperature, H = 0 intercept. We interpret these results as being caused by (high field) ferromagnetic interactions which increase the internal effective field. The quantitative sorting out of magnetic interaction, crystal electric field (CEF), and moment reduction effects in high field is made difficult by the comparable magnitudes of the three effects.

2. Neutron scattering studies. - We are accurently carrying out elastic and inelastic neutron scattering studies of single crystal CeAl, using a triple axis spectrometer. The elastic scattering results confirm the structure found by Barbara et al. [6] using powder- ed samples ; and the field dependence for the magnetic Bragg scattering shows a phase diagram T,(H) similar to that in figure 1. In figure 2 we show an inelastic spectrum taken at T = 2 K which shows a quasielastic line centered at zero energy transfer and two inelastic lines at

9.0

+

0.5 meV and 17.5

+

^{1.5 meV}

The line widths of these two excitations are larger than the instrumental resolution and increase strongly at higher temperatures.

0 5 10 15 2 0 2 5 30

ENERGY ( m e V )

Fig. 2. - Neutron scattering intensity versus energy transfer taken at Q = (512, 312, 112) in CeA1,.

The observed position and temperature depen- dence of the energy width for the 9 meV T, + T, CEF excitation are in qualitative agreement with the time of flight measurements of Lowenhaupt and Ste- glich (LS) [7]. However, the inelastic excitation which we observe at 17.5

+

1.5 meV has not previously been reported, although LS reported without comment excess absorption in this energy region. A number of explanations for this peak could be entertained ; e.g., phonon scattering or a Jahn-Teller (JT) distortion which splits the T, level. Preliminary investi- gation of phonon dispersion curves shows higher energy structure but no structure at 17.5 meV. In addition, the observed 4f form factor behavior of the excitation argues against this explanation. The form factor dependence would be consistent with a JT splitting of the T, level ; however, no such evidence for a distortion above the ordering temperature has ever been presented for any of the rare earth dia- lurninides. The most exciting explanation, which

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GROUND STATE PROPERTIES AND ENERGY PARAMETERS OF THE ANDERSON LATTICE SYSTEM, CeAI, C5-325

we are critically pursuing is that the 17.5 meV excita- behaviour in La,-,Ce& systems yields E

-

^{45 meV}

tion could be an excitation directly from the T , level (or 500 K), which, within the exponential uncertainty to the Fermi energy E,. An independent estimate of of the calculation, is consistent with the 17.5 meV this excitation energy E based upon observed Kondo feature in figure 2.

References

[l] ZORIC, I., MARKOVICS, J., KUPFERBERG, L., CROFT, M. and [5] CROFT, M. C., ZORIC, I. and PARKS, R. D., Phys. Rev. B 18 PARKS, R., Valence Instabilities and Related Narrow (1978) 5065.

Band Phenomena, edited by R. D. Parks (Plenum, New [6] BARBARA, B., BOUCHERLE, J. X., BUEVOZ, J. L., ROSSIGNOL, York) 1977 p. 479. M. F. and SCHWEIZER, J., Solid State Cowtmun. 24 (1977) [2] BARBARA, B., ROSSIGNOL, M. F., PURWINS, H. G. and WALKER, 481.

W. E., Solid State Commun. 17 (1975) 1525. [7] LOEWENHAUPT, M. and STEGLICH, F., Physica 86-88B (1977) [3] CROFT, M. C., ZORIC, I. and PARKS, R. D., Phys. Rev. B 18 187.

(1978) 345.

[4] CROFT, M., ZORIC, I., MARKOVICS, J. and PARKS, R., Ref. [I], p. 475.