Spin Fluctuations in the Antiferromagnetic Heavy-Fermion System U2Znt7

Inelastic neutron scattering from the antiferromagnetic (TN =9. 7 K) heavy-fermion system U2zn/7 reveals magnetic fluctuations which are highly localized in reciprocal space and broad in frequency. At higher energies, the fluctuations persist almost unchanged up to temperatures well above TN. Analysis of the neutron and bulk susceptibility data in terms of Kondo-type single-ion response functions modified by Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between ions indicates that it is the temperature dependence — anticipated theoretically — of the eflective RKKY coupling which drives the magnetic phase transition in U2znl 7.

U2Zn~7 is an antiferromagnet with many remarkable properties. ' For temperatures well below its Neel temperature (TN=9. 7 K), the magnetic specific heat consists of a large linear term, yT (y =200 mJ/mole It ), ' generally associated with paramagnetic heavy-fermion systems, and a cubic contribution, aT, characteristic of antiferromagnetic spin waves. The latter is unusual in that the typical spin-wave energy associated with a is 120 K, which exceeds TN by more than an order of magnitude. Neutron diA'raction shows that the ordered moment (0.8pa) is considerably less than the paramagnetic moment [(2.2-3.3)pa] deduced from high-T susceptibility data. ' Nonetheless, the magnetic structure is exceedingly simple: The magnetic unit cell, which contains two oppositely polarized U ions, is identical to the nuclear unit cell.
To observe the magnetic excitations which give rise to the anomalous properties of U2Zn~7, we have performed an inelastic-neutron-scattering study. The principal result is that in the ordered state, the magnetic fluctuations, while very broad in energy, are sharply localized in reciprocal space. The fluctuations persist to temperatures above TN, and finally disappear for T & 18 K, where the maxima in the bulk susceptibility, resistivity, and Hall coe%cient occur. ' Our crystal of U2Sn~7 was found in a melt produced at 1050 C from the appropriate amounts of U and Zn. Its approximate dimensions are 5&7&8 mm . We attached the crystal to the cold finger of a pumped He cryostat, which in turn was mounted on the triple-axis spectrometer TAS-6 at Ris@ National Laboratory. The horizontal scattering plane of the spectrometer coincided with the (/t 0/) zone of the rhombohedral (space group R3m) crystal; throughout this Letter, we use hexagonal indices, with a* =4'/J3a =0.811 A ' and c* =2m/c =0.479 ', to label points in reciprocal space. Our sample displays macroscopic sixfold symmetry, which implies that it consists of twins related to each other by reflection through the (001) plane.
Pyrolytic graphite crystals, set for their (002) reflections, were the monochromating and analyzing elements of our spectrometer, operated with the final energy fixed at 7.5 meV. The energy resolution, as measured for incoherent elastic scattering, was 0.4 meV, full width at half maximum. Because the source of the neutrons was the Riso National Laboratory H2 moderator, higherorder contamination of the signal was sufticiently small to make the use of a filter superfluous.
We consider first the magnetic fluctuations in the ordered state. Figure 1 shows the scattered intensity, S(g, cu), probed in a series of constant-energy scans for momentum transfers g =(h, 0, 3h); note that there is a magnetic Bragg peak at Qo =(1,0,2), where h = l. such scans would each contain two maxima, at h =1~q , derived from spin waves propagating in opposite directions. When q is small, cq =co where c is the spin-wave velocity, typically of order kBTNa/( J3h). Furthermore, S(Q, cu) essentially vanishes for hcu) kaTN. From Fig.   1 it is apparent that U2Zni7 is unusual.
The surface above the h-cu plane defined by 5(Q, ru) contains only a single ridge parallel to the co axis, instead of two ridgesdue to propagating spin~avesconverging at the Bragg point, Qp, with h = I and cu=0. In addition to being sharply peaked at Qp for hcu (3 meV, S(Q, cu) is appreciably above background for the highest energy (4 meV =4 8kaTN) at . which measurements were performed. Data similar to those in Fig. 1 have been obtained at much larger energy transfers (hcu ) 10 meV) for both UN and Cr. As is known from studies of Cr and its Mn alloys, the finite instrumental resolution can merge the two spinwave peaks (observed in constant h cu scans) at q =~r u/c into a single peak at Qp. Nonetheless, attempts to fit the data in Fig. 1  (2) the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling, also due to interactions with the conduction electrons, between f-like moments at diAerent lattice sites.
From extensive experimental and theoretical work, '' it where k; and kf represent the wave vectors of the incident and scattered neutrons, yp =(0.073 b)/pa, and f(Q) is the form factor of the magnetic electrons. We assume that the only appreciable RKKY coupling, Jo, is isotropic and acts between nearest neighbors on different sublattices. The corresponding expression for the imaginary part of X(g, rp) is then are temperature independent.
However, the evolution of AI is not so surprising when we consider that for heavyelectron systems, AI is inversely proportional to the density n(e F) of quasiparticle states at the Fermi level, ' and that spin-density-wave transitions in metals generally reduce n (e F). Indeed, the specific-heat measurements indicate that n(eF) is -2.5 times smaller in the ordered phase of U2Zn]7, in agreement with the increase in the parameter 6I extracted from our data.
In summary, we have performed elasticand inelasticneutron-scattering measurements on the heavy-electron antiferromagnet U2Zn]7. The order parameter develops in the manner expected for short-range-coupled x-J magnets.
The magnetic fluctuations both above and To study the temperature dependence of Zo, I, and Jo, we have performed two sets of fits, the first with the three parameters unconstrained and the second with the extrapolated Z(q =0, cd=0) held equal to the temperature-dependent bulk susceptibility' scaled to match the neutron result at 2 K. The two procedures yield the same qualitative results. Figure 3 displays the temperature dependence of Xo, Jo, and 6 I obtained in the second series of fits. At all T, the system nearly satisfies the instability condition, 1 =Xp~J'(gp) I, which is associated with the onset of magnetic order. Not surprisingly, Another feature of Fig. 3 is that the characteristic energy AI for the single-ion fluctuations increases greatly as T passes through TN. Thus, U2Zn~7 is not analogous to typical singlet ground-state systems, where the (crystal-field) parameters specifying single-ion dynamics