Optical anisotropy of UNi2Si2

PHYSICA

Physica B 191 (1993) 263-273 North-Holland SDI: 0921-4526(93)E0106-Q

Optical anisotropy of UNi2Si 2 N . C a o , J . D . G a r r e t t a n d T. T i m u s k Department of Physics and Astronomy and Institute for Materials Research, McMaster University, Hamilton, Ont., Canada

Received 18 March 1993 The optical anisotropy of UNi2Si 2 has been systematically studied by reflectance spectroscopy in the range of 50 to 37 000 cm 1. A temperature-dependent absorption peak was found in the c-axis optical conductivity spectra centered at 280 cm -1 in the incommensurate longitudinal spin-density-wavephase (103 K < T < 130 K), which, we believe, arises from the opening up of a SDW pseudo-gap over a portion of the Fermi surface. A narrow absorption peak centered at zero frequency appears in both the c-axis and basal plane optical conductivity spectra at low temperatures. This peak results from the suppression in the scattering rate and the increase in the renormalization of the quasiparticle effective mass at low frequencies. Above the N6el temperature (Try), the optical conductivity decreases or saturates at low frequencies along the c-axis, while in the basal plane it develops a Drude-like absorption peak centered at to = 0.

1. Introduction N e u t r o n diffraction and transport measurem e n t s show that UNi2Si 2 has three different magnetically ordered phases at low temperatures [1] and its D C resistivity both in the basal plane and along the tetragonal (c) axis drops dramatically below the N r e l t e m p e r a t u r e (TN) [2]. In this paper, with use of reflectance spectroscopy, we investigate further the free carrier scattering mechanism of UNi2Si 2 above and below TN to d e t e r m i n e whether the magnetic ordering gives rise to absorption features in optical spectra. B o n n et al. [3] have previously studied the optical properties of the heavy fermion metal URu2Si 2 whose crystal structure is similar to that of UNi2Si 2. In their studies they found that the optical conductivity of URu2Si 2 increases monotonically with increasing frequency above the coherence t e m p e r a t u r e T c (=70 K), which, they believed, was characteristic of the scattering of conduction electrons by isolated magnetic imCorrespondence to: N. Cao, Department of Physics and Astronomy and Institute for Materials Research, McMaster University, Hamilton, Ont., Canada L8S 4MI.

purities. Below T c the optical conductivity of URu2Si 2 develops a narrow absorption p e a k centered at to = 0. This was interpreted in terms of a frequency dependent scattering rate and renormalization of the quasiparticle effective mass. Below the N r e l t e m p e r a t u r e Tr~ (=17.5 K) a t e m p e r a t u r e - d e p e n d e n t spin-density-wave gap was observed in the optical spectra of URu2Si 2. C o m p a r e d with URu2Si2, UNi2Si 2 has three different magnetically ordered phases instead of only one in URu2Si 2. The coherent state of UNi2Si 2 is in the same t e m p e r a t u r e range as the magnetically ordered states in contrast with the case of URu2Si 2 whereas the coherent and antiferromagnetic p h e n o m e n a occur in different t e m p e r a t u r e ranges. Lin et al. [1] have studied the crystal and magnetic structures of UNi2Si 2 by neutron diffraction. It was shown that it has a tetragonal ThCr2Si 2 crystal structure with a I 4 / m m m ( D 4~7) space group. Its magnetic structure is somewhat complicated. A b o v e 124 K UNi2Si 2 is in a paramagnetic (PM) state. A t 124 K it undergoes a second-order magnetic phase transition to an i n c o m m e n s u r a t e longitudinal spin-density-wave ( I L S D W ) phase with a t e m p e r a t u r e - d e p e n d e n t

0921-4526/93/$06.00 © 1993- Elsevier Science Publishers B.V. All rights reserved

264

N. Cao et al. / Optical anisotropy o f UNi2Si 2

wave vector Q = (0, 0, qz). As the temperature is lowered to 103K, a first-order magnetic phase transition takes place causing UNi2Si 2 to enter a simple body-centered antiferromagnetic (AM) state. The magnetic moment is aligned along the c-axis with a magnitude of (1.8 -+ 0.3)/zB. As the temperature is lowered further to 53 K, another first-order magnetic phase transition occurs and UNi2Si 2 enters a commensurate longitudinal spin-density-wave (CLSDW) phase with a wave vector Q = (0, 0, qz), where qz is 2. In addition, this phase shows a ferromagnetic component with a magnetic moment (m z = (1.0__0.3)/xB) that is also aligned along the c-axis. The DC resistivity of UNi2Si 2 with the current flowing along either the a- or c-axis was measured by Ning et al. [2]. Above 123 K the DC resistivity gradually increases along the a-axis, while showing a slight decrease along the c-axis. Below 123 K there is a dramatic decrease in the DC resistivity along both axes. The authors interpreted the sharp decrease in the DC resistivity along the c-axis as being due to a suppression in both the Kondo-like magnetic impurity scattering, where the conduction electron's spin flips, and the normal magnetic impurity scattering, where there are no spin-flips. Since Kondo-like scattering does not occur along the a-axis, only the suppression of the normal magnetic impurity scattering is responsible for the suppression in the resistivity in the basal plane. There also exist features which appear to be connected with the 103 K and 53 K magnetic phase transitions. At 103 K the slope of the DC resistivity becomes much steeper along the c-axis and shows a knee along the a-axis. At 47 K there is a local peak appearing in the c-axis DC resistivity curve. Ning et al. [4] also measured the magnetic susceptibility of UNi2Si 2 in a magnetic field of 1.6 T. When the field was applied parallel to the c-axis, the sample exhibited Curie-Weiss behavior above 130K. Below this temperature the magnetic phase transitions cause deviations from this behavior. The susceptibility shows a peak centered at 103K and ferromagnetic character for temperatures below 80 K. In contrast, when the field is applied perpendicular to the c-axis, a broad peak centered at 40 K is seen

and there is no indication of ferromagnetic behavior. In the present work, the results of the temperature-dependent reflectance measurements on UNizSi2, both in the basal plane and along the c-axis, are presented. We find that the scattering mechanism is quite different above and below TN and that a pseudo-gap opens up over a portion of the Fermi surface along the c-axis in the incommensurate longitudinal spindensity-wave (ILSDW) phase.

2. Experimental The two UNi2Si 2 samples used in these measurements were grown using the Czochralski technique. The details of the growth have been described elsewhere [2]. X-ray diffraction indicated that both samples were single crystals with lattice parameters a = 3 . 9 6 A and c = 9 . 5 1 A . Sample no. 1 was cut so as to exhibit its ac-face while sample no. 2 was cut to show the aa-face. The reflectance in the basal plane was measured for frequencies between 50 and 37 000 cm-l. Temperature dependent spectra for frequencies between 50 and 5000cm -1 were measured using a Michelson interferometer. In the frequency range of 3800-37 000 cm-~ a grating spectrometer was used at room temperature only. The reflectance spectra along the c-axis were only measured at low frequencies using the Michelson interferometer. In this case, wire grid polarizers were used to polarize the light along UNi2Si/s c-axis. For all measurements the absolute value of the reflectance was obtained by the in-situ evaporation of a metallic film onto the sample. Geometrical differences between the sample and reference mirror were taken into account by remeasuring the reflectance of the coated sample. The optical constants were obtained using a Kramers-Kronig analysis. This analysis requires high- and low-frequency extrapolations of the reflectance data. The Hagen-Rubens relation was used to extrapolate the reflectance to zero frequency. This is justified since the low-frequency extrapolated conductivity agrees with the

N. Cao et al. I Optical anisotropy o f UNi2Si2

DC conductivity. The room-temperature reflectance of UNi2Si 2 shows that there is an interband transition starting at ~30 000 cm -~. This interband transition is due to the Ni ions in UNi2Si 2. Thus, the reflectance of Ni [5] up to 250000cm -1 was used as the high-frequency extrapolation. Beyond this frequency free-electron behavior (R(to)oc to-4) was used to extrapolate the data.

3. Results

3. I. Optical properties of UNi2Si 2 in the basal plane The far-infrared reflectance of UNi:Si 2 in the basal plane for temperatures corresponding to each of the magnetic phases is shown in fig. 1. The inset shows the room-temperature reflectance up to 37 000 cm-1. Note that the reflectance decreases with increasing frequency up to ~30000cm -~ where it begins to turn up. An interband transition associated with the nickel ions in UNiESi 2 is responsible for this upturn [5].

For frequencies higher than 5000cm -1 these room-temperature data provide a good approximation of the reflectivity for all temperatures. With the use of this approximation and the extrapolations described earlier, the optical conductivity was calculated using the KramersKronig relations. The result (fig. 2) shows the development of an extremely narrow peak centered at to = 0 in the low-frequency region as the sample is cooled below the Nrel temperature (T~=124K). The small peak centered at 340 cm- ] in the 140 K data is not associated with the basal plane conductivity. It is a strong c-axis feature which appears in the basal plane's response due to a small leakage in the polarizer. Following the work of Webb and Sievers [6] we have used a generalized Drude theory to obtain the frequency-dependent scattering rate (F~(to)) and renormalization of the quasiparticle effective mass (k~(to)) of UNi2Si z. Since this theory is only valid for free carriers, the contributions from interband transitions and the highfrequency constant screening term (e=) must be subtracted from the total dielectric function. The

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700

700

Fig. 1. Reflectance of UNi2Si 2 in the basal plane as a function of frequency for temperatures corresponding to each of the four magnetic phases. The inset shows the roomtemperature reflectance in the basal plane for frequencies up to 37000cm -~.

Fig. 2. Temperature dependent optical conductivity of UNi2Si 2 in the basal plane as a function of frequency. The value of the D C conductivity of UNi2Si 2 in the basal plane at 140 K is labeled by a square on the left vertical axis (only the DC conductivity at 140 K can be labeled for the vertical-axis scale shown).

N. Cao et al. / Optical anisotropy of UNi2Si:

266

real and imaginary parts of the total dielectric function can be written as

1000

(1)

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=

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ez(to) = ~4"rr[o.fl(to) + o.~b(w)] ,

(2)

where the superscripts f and ib refer to the free carrier and interband transition components respectively. As a first approximation a Drude model is used to represent the response of the free carriers and Lorentz oscillators are used to describe the response of interband transitions. By fitting the optical conductivity, o's(to), one can obtain the parameters for the Lorentz oscillators, which are listed in table 1. Now, the real and imaginary parts of the dielectric function corresponding to the free carrier part, e~l(to) and trf~(to), can be determined by subtracting the contributions of the interband transitions and e~ (=4) from the total dielectric function obtained experimentally. They can then be used to calculate Fo(to) and h~(to).

600

E

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o..............

400 j, /

200

,¢ /

,

0~

' 100

i

' 200

I

300

i

' 400

i

' 500

I

660

700

Fig. 3. Frequency dependence of the scattering rate of UNiESi 2 in the basal plane at 40, 80, 110 and 140 K. Below the N6el temperature T s (= 124 K) the depressed scattering rate at low frequencies is a signature of heavy fermion behavior.

Figure 3 shows the scattering rate of UNi2Si 2 in the basal plane. It is essentially frequency independent above 300 cm-1 at all temperatures.

Table 1 The parameters used to fit the optical conductivity trl(to) of UNi2Si 2 in the basal plane, to o and 3% are the plasma frequency and scattering rate of the Drude part and toi, 3~ and cop~ are the center position, width and strength of the ith Lorentz oscillator. Mode (cm -1)

.o. .....

T(K) 40

80

110

140

300

~ ~o

13 210 445

13 210 455

13 210 475

13 210 489

13 210 498

~1 ~rl

964 977 9471

905 1041 8395

791 859 7195

891 1492 12 360

769 1579 12 290

~2 3'2 ~r2

2035 3643 17 020

2766 4534 13 020

1466 2109 9678

4097 16000 64480

2461 9963 3984

~3 •3 ~P3

5130 16 120 58 920

4054 17 350 63 280

4739 16 960 62 410

5500 615 1913

3862 16300 66240

~4 ~4 ~r4

7377 1562 6153

7345 1384 5515

7381 1407 5117

7249 1200 4390

6761 2585 7542

N. Cao et al. / Optical anisotropy o f UNi2Siz

For the 140K data, that is above TN, it is essentially constant at all frequencies implying that the optical conductivity follows a simple Drude model. In contrast, the 40 K data show a drastic decrease in F~(to) for frequencies below 300cm -1. The 80K and 110 K data also show a decline in the scattering rate but the magnitude is reduced and the decline occurs at a lower frequency for the 110 K data. Figure 4 shows the frequency-dependent renormalization of the quasiparticle effective mass of UNi2Si 2 in the basal plane. From the figure it is evident that there is a mass enhancement at low frequencies once the sample is cooled below Try. For the 40 K data the frequency dependence begins at 400cm -~. Thus, there is a 100cm -1 frequency shift between the starting point of the strong frequency dependent behavior in F~(to) and that which is found in A,(to). A mass enhancement is also observed in the 80 K and 110 K data, but again the response is of reduced magnitude and is shifted to lower frequency for Aa(to) at 110 K. Even though the electron-phonon interaction can lead to a frequency dependent scattering rate [7,8], it is unlikely that this is occurring for the

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UNi2Si 2 compound since transport measurements indicate that only 14% of the DC resistivity along the a-axis comes from the phonon scattering contribution [9]. It is more likely that the frequency dependence of both Fa(to) and Aa(to) is due to heavy-fermion-like behavior in the basal plane, that is, the conduction electrons are scattered coherently from the magnetic ions below T N. Similar behavior to what is observed here has been seen in the mixed-valence compound CePd 3 [6] and in the heavy-fermion material URu2Si 2 [3]. In the case of URuESi2, Bonn et al. [3] found that a narrow absorption peak centered at to = 0 appears in the optical conductivity spectra at low frequencies below the coherence temperature, T c (=70 K) and an energy gap appears in the conductivity spectra below the N6el temperature, T~ (=17.5K). However, in the case of UNi2Si2, the N6el temperature is the same as the coherence temperature and we did not find the energy gap appearing in the conductivity spectra below T N (--124K). The characteristic energy for the UNi2Si 2 compound which separates the coherent scattering from the normal magnetic impurity scattering is 400cm -1 (=4.6kBTN) in the CLSDW and AM phases and 250 cm -1 (-2.9kBT~) in the ILSDW phase. It is the strong frequency dependence of F~(to) and Aa(to) which gives rise to the low DC resistivity and the narrow absorption peak in the optical conductivity spectra below the N6el temperature. Above T~, in the PM phase, Fa(to) and Aa(to) are nearly frequency independent which is the expected behavior for normal magnetic impurity" scattering.

3.2. Optical properties of UNieSi2 along the caxis

-16

16o 26o

46o 56o 6;o 7oo

Fig. 4. Frequency dependence of the rennrmalization of the quasiparticle effective mass of UNi2Si 2 in the basal plane at 40, 80, 110 and 140 K. The mass enhancement at low frequencies is characteristic of heavy ferminn behavior.

The far-infrared reflectance spectra of UNi2Si 2 for light polarized along the c-axis in the various magnetic phases are shown in fig. 5. Note that the reflectance at 40 K is significantly higher for frequencies below 350cm -1, but this trend is reversed at higher frequencies. Also note that there is a pronounced shoulder-like feature, which is indicated by two arrows in this figure,

N. Cao et al. 1 Optical anisotropy o f UNi2Si 2

268

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2800

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.............

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0.85 0

I

100

'

I

200

l

l

300

1

I

400

l

I

I

500

600

i

".

700

Fig. 5. Reflectance of UNi2Si a along the c-axis as a function of frequency for temperatures corresponding to each of the magnetic phases. T h e two arrows indicate the shoulder-like feature in the 115 K data.

exhibited by the 115K data for frequencies -1 between 225 and 335 cm Since the reflectance in the basal plane is similar to the c-axis reflectance near 5 000 cm -~, it was used to extrapolate the c-axis data in the Kramers-Kronig analysis. Other extrapolations were attempted, but they did not alter the results significantly. The resulting c-axis optical conductivity is shown in fig. 6. The 40 K data display a sharp peak centered at zero frequency and have the lowest conductivity at higher frequencies. The 100K data increase as the frequency is lowered below 150cm -1 and have a plateau region extending from 150 to 250cm -1. The -1 115 K data show a pronounced peak at 280 cm which is no longer present in the 135 K data. Also displayed on the figure are the values of the conductivity at to = 0 obtained from DC resistivity measurements. Note that there is good agreement between the two measurements. The absorption peak at 280 cm-1 is only found within the ILSDW phase. This suggests the existence of a SDW pseudo-gap. To study this

2000

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1(30

' ' 400 ' ' 5 ~ 0 ' 600 ' ' 700 2OO ' ' .300

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Fig. 6. Optical conductivity of UNiESi 2 along the c-axis as a function of frequency. T h e values of the c-axis D C conductivity at 100, 115 and 135 K are labeled on the left vertical axis by a square, a triangle and a circle, respectively (the D C conductivity at 40 K is off scale). The top drawing shows the magnetic phase diagram of UNi2Si 2 showing the CLSDW, A M , I L S D W and PM phases.

phenomenon in more detail, we measured the c-axis reflectance at 105,115, 120 and 130 K. The resulting conductivity is shown in fig. 7. One can see that the peak position is temperature independent. However, the minimum position, at which the absorption begins, shifts towards lower frequency as temperature is increased. If a SDW pseudo-gap is formed over a portion of the Fermi surface, it is expected that it will soften for temperatures approaching TN. The temperature dependence of the minimum agrees with this expectation. The fact that the feature persists at 130 K, which is above the N6el temperature of 124K [1], may be due to sample-to-sample variation in T N. Ning et al. [4] measured the magnetic susceptibility of UNi/Si 2 for the sample used in this work and found deviations from Curie-Weiss behavior at 130 K for the magnetic field parallel to the c-axis. In any case, this absorption peak is no longer present at 135 K. The same fitting procedure that was used for

N. Cao et al. I Optical anisotropy o f UNi2Si2 5000

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(cm -1) Fig. 7. Optical conductivity of UNi2Si 2 along the c-axis as a function of frequency. The values of the DC conductivity of UNi2Si 2 at 105, 115, 120 and 130K are labeled on the left vertical axis by a square, a triangle, a circle and a cross, respectively. The absorption peak centered at 280cm -1 is interpreted as a SDW pseudo-gap opening up over a portion of the Fermi surface.

the basal plane results was also used to obtain Fc(tO) and k~(to) along the c-axis. The fitted parameters are listed in table 2 and the frequency dependence of F~(to) and kc(OJ) is given in figs. 8 and 9 respectively. At 40 K F~(to) is nearly frequency independent above 250cm -~. Below 250 cm -~ its value falls off sharply. At the same

-1)'5 0 '6 0 '700

Fig. 8. Frequency dependence of the scattering rate of UNi2Si 2 along the c-axis at 40, 85, 90, 115 and 300K. The depression of the scattering rate at low frequencies in the 40 and 85 K curves is an indication of heavy fermion behavior.

temperature, kc(to) increases sharply with decreasing frequency below 300 cm-~ and is essentially constant at higher frequencies. At 85 K, both F~(to) and kc(tO) are similar in shape to the 40 K data, but the magnitude weakens and the features move to lower frequency. At 90 and 115 K, instead of being depressed at low frequencies, the scattering rate increases as frequency is lowered from 300 to 200 cm- 1 and then plateaus at lower frequencies. As the scattering rate increases in this frequency range, At(to) develop a shallow valley-like feature between

Table 2 The parameters used to fit the optical conductivity ~l(to) of UNi2Si 2 along the c-axis, top and Yt) are the plasma frequency and scattering rate of the Drude part and tOo,Y and tOe are the center position, width and strength of a Lorentz oscillator. T (K)

to~ (cm -1)

3'0 (cm -1)

too (cm -1)

Y (cm -1)

O)p (cm -1)

40 85 90 115 300

11 490 12 930 13 570 13 770 14610

446 466 581 648 823

3747 3646 3949 3687 3860

15 200 14640 15 010 15 260 14 750

65 430 65 430 65 570 65 910 64770

270

N. Cao et al. / Optical anisotropy o f UNi2Si 2 ,

c-axis

,

,

,

l

,

because magnetic impurity scattering dominates at all frequencies.

,

40 K ................. 85 K . . . . . . . . . .

\

\

90 K . . . . . . .

\

115 K . . . . .

\

300 K

4. Discussion

~

',,..

1 -

-

~

=

-

~

_

.

z

.

~

.

-

-~z--.~

~.~=.=.-

- - .T...--

0

_

1 0

2 0

300

-1)

400

500

600

700

Fig. 9. Frequency dependence of the renormalization of the quasiparticle effective mass of UNiESi ~ along the c-axis at 40,85,90,115 and 300K. The mass enhancement at low frequencies for the 40 and 85 K curves is characteristic of heavy fermion behavior.

125 and 325 cm -1. At 300K the scattering rate and the renormalization of the quasiparticle effective mass only show a weak frequency dependence. The depression in F~(to) and the increase in At(to) in the low-frequency range that develops in the CLSDW phase is an indication of heavyfermion-.like behavior. This strong frequency dependence causes both the low DC resistivity and the narrow absorption peak centered at to = 0 in the optical conductivity. As the temperature is increased to 85 K and the material enters into the AM phase, this heavy-fermion-like behavior persists. At 90 K it disappears. The energy which separates the heavy fermion behavior from both types of magnetic impurity scattering (i.e. with and without spin-flips), which dominate at higher frequencies, is 300 cm -1 (=3.5k BTN) a t 40 K and 250cm -~ (=2.9kBTN) at 85K. The form of the frequency-dependent scattering rate observed in the AM phase above 90 K and in the ILSDW phase has also been seen in URu2Si 2 [3] and was attributed to the scattering of conduction electrons by isolated magnetic ions. In the PM phase both F~(to) and Ac(to) are frequency independent

Above 124KUNi2Si 2 is in a paramagnetic phase. The DC resistivity measurements show that the scattering mechanisms along the a- and c-axis in this phase are different because there is no Kondo-like magnetic impurity scattering in the basal plane. This fundamental difference also manifests itself in the optical conductivity. Figure 10 shows a comparison of the a- and c-axis conductivity. In the basal plane a Drude-like peak develops at low frequencies, while the c.

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s

,

,

=

i

t

=

t

t

J

,

i

i

I

J

~ 7000

500C

300C

200

400

600

Fig. 10. (a) Optical conductivity of UNi2Si 2 as a function of frequency along the c-axis (dashed line) at 135 K and in the basal plane (solid line) at 140 K. (b) Optical conductivity of UNi2Si 2 along the c-axis (dashed line) and in the basal plane (solid line) at 300 K. The corresponding DC conductivities obtained from transport measurements are plotted for the c-axis (triangles) and the basal-plane (squares) results. The anisotropy of the conductivity between the basal plane and c-axis is due to the different scattering mechanisms (see details in the text).

N. Cao et al. / Optical anisotropy o f UNi2Si2

axis conductivity saturates and may even decrease slightly as frequency is lowered. In the basal plane, the heavy-fermion-like behavior appears in the CLSDW, AM and ILSDW phases. Along the c-axis it only appears in the CLSDW phase and in part of the AM phase (below 85 K). Thus, the heavy-fermionlike interaction along the c-axis between the conduction electrons of Ni and the 5f electrons of U must be suppressed in part of the AM phase (above 90 K) and in the ILSDW phase. The fact that the DC susceptibility measurements with the magnetic field parallel to the c-axis [4] show a ferromagnetic component below 80 K in both the AM and CLSDW phases indicates that this component may be connected with the development of the heavy-fermion-like behavior. Even in the basal plane this heavyfermion-like behavior is temperature dependent in the different magnetically ordered phases. The magnitude of the behavior becomes weaker with increasing temperature and in the ILSDW phase the energy which separates the heavy-fermionlike behavior from the normal magnetic impurity scattering shifts to a lower frequency. In the case of UNi2Si 2, a SDW pseudo-gap is formed in the energy spectrum of electrons at the surfaces of k z = ---½It21, which intersects the Fermi surface, in reciprocal space. Here Q is the wave vector of SDW in the ILSDW phase and points in the direction of the tetragonal (c) axis. A periodic magnetic potential whose period is along the c-axis in real space causes the mixing of magnetic wave functions near the Fermi surface and the splitting of bands where they cross. The strongest gap feature is expected to show up when the incident beam is polarized in the direction of Q. This is because the SDW pseudo-gap opens on pieces of the Fermi surface whose velocity vectors are predominantly along Q. This can be seen from the results of the DC resistivity measurements [2]: the DC resistivity is higher for the measuring current I parallel to Q compared with the case of I perpendicular to Q. A SDW gap was found in Cr by optical reflectance measurements [10]. It appears as an absorption peak in the optical conductivity near 1000 cm -~ for temperatures below TN = 312 K.

271

In a review paper, Fawcett [11] suggested that there may be a connection between the temperature dependence of the intensity of the elastic neutron scattering peaks, which gives the temperature dependence of the amplitude of the SDW and the size of the SDW gap determined by spectroscopic methods. The comparison of this optical data to the neutron diffraction work [1], shown in fig. 11, indicates that this is also the case for UNi2Si 2. The figure shows the temperature dependence of the frequency of the absorption threshold in the optical conductivity along the c-axis as well as the integrated intensity of the (1, 0, 0.256) magnetic Bragg peak. Both curves have a similar temperature dependence. Associated with the antiferromagnetic transition in Cr is an anomaly in the DC resistivity occurring at the N6el temperature [12]. There is no such feature in the DC resistivity measurements on UNi2Si 2 with the current flowing along the c-axis. However, the slope of the DC resistivity versus temperature curve [9] displayed in fig. 12 does become steeper at 103 K. At 100 K the slope changes again giving rise to a gentle decrease in the resistivity as temperature is

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272

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similar to that of the integrated intensity of the (1, 0, 0.256) magnetic Bragg peak. This indicates that the SDW pseudo-gap decreases in magnitude and moves to lower energies as the amplitude of the ILSDW decreases with increasing temperature. The optical conductivity above 130 K shows a distinct difference between the a- and c-axis. In the basal plane the optical conductivity develops a Drude-like peak centered at to = 0 which is caused by the normal magnetic impurity scattering. Both Kondo-like magnetic impurity scattering and normal magnetic impurity scattering give rise to a c-axis conductivity which nearly saturates at low frequencies. Heavy-fermion-like behavior appears in the C L S D W phase and in the A M phase below 85 K along the c-axis and also appears in the CLSDW, A M and ILSDW phases in the basal plane. This is indicated by a suppression in the scattering rate and an increase in the renormalization of the quasiparticle effective mass at low frequencies, which gives rise to a low D C resistivity and a narrow absorption peak centered at t o - - 0 in the optical conductivity spectra.

Acknowledgements

We would like to thank Drs. M.F. Collins, J.P. Carbotte, C. Kallin, B.D. Gaulin and D. Bonn for valuable discussions and R.A. Duncan, D. Crandles, M. Reedyk, R. Hughes, C. Homes, X.C. Wu and A. McConnell for their appreciated help. This work was supported by the Natural Science and Engineering Research Council of Canada.

5. Conclusions References

The optical conductivity of UNi2Si 2 is quite anisotropic between the basal plane and the caxis. An absorption peak was found in the optical conductivity spectra at 280 c m - 1 in the I L S D W phase along the c-axis. It was interpreted in terms of a SDW pseudo-gap. The temperature dependence of this pseudo-gap is

[1] H. Lin, L. Rebelsky, M.F. Collins, J.D. Garrett and W.J.L. Buyers, Phys. Rev. B 43 (1991) 13232. [2] Y.B. Ning, J.D. Garrett and W.R. Datars, Phys. Rev. B 42 (1990) 8780. [3] D.A. Bonn, J.D. Garrett and T. Timusk, Phys. Rev. Lett. 61 (1988) 1305. [4] Y.B. Ning, V.V. Gridin, C.V. Stager, W.R. Datars, A.

N. Cao et al. / Optical anisotropy o f UNi2Si e

LeR. Dawson and D.H. Ryan, J. Phys.: Condens. Matter 3 (1991) 4399. [5] R.C. Vehse and E.T. Arakawa, Phys. Rev. 180 (1969) 695. [6] B.C. Webb and A.J. Sievers, Phys. Rev. Lett. 57 (1986) 1951. [7] A.B. Pippard, in: Optical Properties and Electronic Structure of Metals and Alloys, ed. F. Abel,s (NorthHolland, Amsterdam, 1966) p. 623; A.J. Leggett, Ann. Phys. (N.Y.) 46 (1968) 76.

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[8] P.B. Allen, Phys. Rev. B 3 (1971) 305. [9] Y.B. Ning, PhD Thesis, McMaster University, Hamilton, Ont. (1991). [10] A.S. Barker Jr., B.I. Halperin and T.M. Rice, Phys. Rev. Lett. 20 (1968) 384. [11] E. Fawcett, Rev. Mod. Phys. 60 (1988) 209. [12] A.S. Barker Jr. and J.A. Ditzenberger, Phys. Rev. B 1 (1970) 4378.