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3 Application of 238U Mössbauer Spectroscopy to Heavy Fermion Superconductors

3 Application of 238U Mössbauer Spectroscopy to Heavy Fermion Superconductors

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7 STUDY OF EXOTIC URANIUM COMPOUNDS USING 238U MOSSBAUER

SPECTROSCOPY



128



TABLE 7.2 Characteristic Physical Properties in Uranium-Based Superconductors, UPd2Al3, URu2Si2,

and UPt3 [20,22–24]



Compound

UPd2Al3

URu2Si2

UPt3

Tx



max:



Neel Temperature (K)



Magnetic Moment (mB/U)



Tx max (K)



Tc (K)



14

17.5

6



0.85

0.03

0.03



$30

$50

$20



2

1.3

0.5



maximum temperature of magnetic susceptibility in magnetic easy axis.



heavy fermion compounds is caused by the magnetic degrees of freedom through the Kondo effect. The Kondo effect

makes the f electron hybridized with conduction electrons. Such behavior occurs not only in rare-earth compounds but

also in actinide compounds. In uranium intermetallics, several heavy fermion superconductors were discovered, such as

UPd2Al3, UNi2Al3, URu2Si2, and UPt3 [20–22,24]. The physical properties of UPd2Al3, URu2Si2, and UPt3 are shown in

Table 7.2. In these compounds, the superconductivity and antiferromagnetic ordering coexist at low temperature. The

results of the neutron scattering suggest the correlation between superconductivity and antiferromagnetic ordering in

these compounds [25–29]. The intensity of the magnetic reflection is reduced below the superconducting transition

temperature in UPd2Al3, UNi2Al3, URu2Si2, and UPt3. Since the heavy fermion behaviors in such superconductors are

produced by strong hybridization between 5f and conduction electrons through the Kondo effect, the investigation of the

magnetic properties with the microscopic probes are required. Unlike Ce compounds, M€

ossbauer spectroscopy is

available for the investigation of the local electronic states through the hyperfine interactions at uranium sites because of

the presence of several uranium M€

ossbauer transitions.

Characteristic temperatures associated with heavy fermion behaviors were investigated by both macroscopic and

microscopic measurements. On the viewpoint of the magnetic properties, the temperature dependence of the magnetic

susceptibility suggests the presence of the characteristic temperature for heavy fermion behaviors. This is a maximum of the

magnetic susceptibility at a certain temperature, called Tx max [20,22,30]. It has been believed that this behavior is correlated

with the Kondo effect. Below the temperature Tx max, sharp metamagnetic transitions were observed in UPd2Al3, URu2Si2,

and UPt3 [31–37]. This suggests that the maximum temperature in magnetic susceptibility is a typical energy scale to discuss

the heavy fermion behaviors in these compounds. On the other hand, Tx max seems to be a characteristic temperature in

uranium-based heavy fermion superconductors in the microscopic point of view. The electronic dynamics in these

compounds have been discussed by ligand site NMR [38–41]. NMR relaxation rate, especially T1, suggests that the

temperature around Tx max is a characteristic temperature. While the relaxation time is constant, the relaxation time is

proportionate to the inverse of temperature. It has been believed that the heavy fermion behavior is strongly connected

with an antiferromagnetic correlation. To discuss such correlation, the microscopic discussion at the on-site of the f

electron, say uranium site, not at the ligand sites is preferable. This is the one of the motivations in this work.

The target materials in the present work, UPd2Al3, URu2Si2, and UPt3, exhibit an antiferromagnetic ordering that can

coexist with their superconductivity, whether their orderings are a long-range or short-range one. UPd2Al3 exhibits an

antiferromagnetic ordering accompanied by a large magnetic moment of 0.85mB/U. In this compound, the magnetic

ordering is intrinsic, because experimental results by different magnetic measurements agree with each other. This means

that the transferred hyperfine field at 27 Al and 105 Pd nuclei as well as the magnetic reflection by neutron scattering was

observed [39,42–45]. However, the cases of URu2Si2 and UPt3 are different from that of UPd2Al3. In URu2Si2, the

macroscopic measurements such as the specific heat measurements and magnetic susceptibility suggest the presence of

the ordered magnetic moments. Particularly, the specific heat measurements suggest a magnetic ordering with large

ordered moments. On the other hand, very small ordered magnetic moments of about 0.03mB/U were observed by

neutron scattering. The disagreement among these experimental results leads to a need to discuss what the order

parameter in URu2Si2 is for a long time. Furthermore, no experimental evidence of any antiferromagnetic ordering was

found by specific heat, magnetic susceptibility, and NMR experiments [30,46,47], but antiferromagnetic ordering was

observed at 6 K by mSR, neutron scattering, and resonant X-ray diffraction experiments in UPt3 [25,26,48–50]. These

experimental disagreements in UPt3 suggest the time window dependence.

238

U M€

ossbauer spectra of several uranium heavy fermion superconductors, UPd2Al3, URu2Si2, and UPt3, were

measured at various temperatures [7,8,51]. Investigations of the hyperfine interactions at 238 U nuclei indicate the presence

of the magnetic hyperfine interaction in their paramagnetic states as well as their antiferromagnetic ordered states. The

observation of the magnetic hyperfine interactions in antiferromagnetic ordering is useful to discuss their antiferromagnetic





7.3 APPLICATION OF 238U MOSSBAUER

SPECTROSCOPY TO HEAVY FERMION SUPERCONDUCTORS



129



ground states, whose correlation with their superconductivity is suggested by neutron scattering [25–29]. In UPd2Al3 and

UPt3 cases, the observed hyperfine fields are consistent with the magnetic ordered moments reported previously

[25,43,44,49]. In URu2Si2 case, the hyperfine field obtained by the spectral analyses under the assumption of a pure magnetic

pattern is too large, compared with the value estimated from the observed ordered magnetic moment using the hyperfine

coupling constant mentioned in Section 7.2 [29,52,53]. On the other hand, the observation of the magnetic hyperfine

interactions in paramagnetic states is caused by that of the paramagnetic relaxation as previously reported in Np compounds

[54–56]. It is suggested that this is correlated with the formation of heavy fermion behaviors in these compounds, because of

the characteristic temperature of the observed hyperfine field in the paramagnetic state.

7.3.2 Magnetic Ordering and Paramagnetic Relaxation in Heavy Fermion Superconductors

ossbauer spectra of UPd2Al3 is shown in Fig. 7.6. The observed spectra are

Temperature dependence of 238 U M€

symmetric, indicating the absence of nuclear quadrupole interactions. Among the obtained spectra, the analyses using a

single Lorentz function were successful to reproduce the experimental data above 15 K, and those using a set of five

Lorentz functions with the same intensity were successful below 15 K. This reflects the spectral analyses of the whole

data in UPd2Al3 using a single Lorentz function. As shown in Fig. 7.7, the plots of the linewidth obtained by the single

Lorentz function analyses against temperature exhibit a line broadening below 15 K. Considering the Neel temperature,

TN, of UPd2Al3 as 14 K, the line broadening below 15 K is caused by the antiferromagnetic ordering at 14 K. In addition,

another line broadening is also observed around 30 K. This seems to be correlated with the maximum of the magnetic

susceptibility [20]. This is correlated with paramagnetic relaxation, discussed later.

To discuss the antiferromagnetic states, the spectra below 15 K were analyzed by the magnetic pattern of 238 U

M€

ossbauer spectra, which consists of five lines with same intensity and linewidth reflecting the E2 transition from I ¼ 2 to

I ¼ 0. The temperature dependence of the hyperfine field obtained by the spectral analyses is shown in Fig. 7.8. The

hyperfine field at 5.1 K is 140 Ỉ 10 T. Its temperature dependence is similar to that of the ordered magnetic moment

reported by the neutron scattering. It is evident that the observed hyperfine field is correlated with the antiferromagnetic

ordering in UPd2Al3. Since the ordered magnetic moment is 0.85mB/U, the hyperfine coupling constant in UPd2Al3 is

160 T/mB, agreed with that of UO2 and other uranium-based metallic compounds as mentioned above.



UPd2Al3



1.00

100 K

0.95

1.00

82 K



0.95

1.00



30 K

Relative transmission



0.90

1.00

20 K



0.95

1.00



10 K

0.90

1.00

5.1 K

0.90

–100



–50



0



50



Velocity (mm s–1)



100



FIGURE 7.6

238

€ ssbauer spectra of

U Mo

UPd2Al3 at selected

temperatures.



130





7 STUDY OF EXOTIC URANIUM COMPOUNDS USING 238U MOSSBAUER

SPECTROSCOPY



UPd2Al3

(a)



Tχ max



FWHM (mm s–1)



60



50



40



FIGURE 7.7

Temperature dependence of the

(a) spectral linewidth and (b)

integrated intensity in UPd2Al3

when the spectra are analyzed by

a single-line Lorentz function.

Solid curve is a theoretical one

calculated by the Debye model.

(Modified from Fig. 2 of Ref. 7

with permission of Springer.)



Area contribution (a.u.)



(b)



θD = 200 K



5.0



0.0

0 TN



50



100



150



Temperature (K)



Temperature dependence of the 238 U M€

ossbauer spectra in URu2Si2 is similar to that of UPd2Al3. The observed

spectra are all symmetric as shown in Fig. 7.9, indicating the absence of nuclear quadrupole interactions. Temperature

dependence of the linewidth obtained by the same spectral analyses using a single Lorentz function is similar to that in

UPd2Al3 as shown in Fig. 7.10. The line broadenings are observed below 15 K and around 50 K. The former agrees with

the antiferromagnetic ordering at 17.5 K reported originally. The latter agrees with the maximum temperature of the

magnetic susceptibility, which is correlated with paramagnetic relaxation, discussed later.

In terms of the antiferromagnetic ordering in URu2Si2, it has been discussed whether this is intrinsic or not for a long

time. Hereafter, the temperature of 17.5 K is called TO, not Neel temperature TN. The evident line broadening implies the

additional hyperfine interaction induced by an order of the electronic state. Judging from the observation of the magnetic

reflection due to an antiferromagnetic ordering, the observation of hyperfine fields is expected. When the spectra below

ossbauer spectra, the hyperfine field at 5.1 K is 90 Ỉ 20 T. This

TO were analyzed by the magnetic pattern of 238 U M€

corresponds to the ordered magnetic moment of 0.6mB/U estimated by the hyperfine coupling constant of 150 T/mB as

mentioned in Section 7.2, much larger than the ordered magnetic moment observed by neutron scattering [29,52,53]. On



UPd2Al3



FIGURE 7.8

Temperature dependence of the

hyperfine field at 238 U nuclei

el temperature of

below the Ne

UPd2Al3. Dotted curve is a guide

to the eye.



Hint (T)



200



100



0



TN

0



10

Temperature (K)



20





7.3 APPLICATION OF 238U MOSSBAUER

SPECTROSCOPY TO HEAVY FERMION SUPERCONDUCTORS



131



URu2Si2

1.00

150 K

0.95

1.00

100 K



0.95



Relative transmission



1.00

80 K

0.90

1.00

50 K

0.90

1.00

30 K



0.90

1.00



5.2 K

0.90

–100



–50



0



50



100



Velocity (mm s–1)



FIGURE 7.9

238

€ ssbauer spectra of

U Mo

URu2Si2 at selected

temperatures.



the other hand, the small ordered magnetic moment in UFe2, 0.01mB, is not successfully observed by 238 U M€

ossbauer

ossbauer spectroscopy is about 30 T. In

spectroscopy [2,57]. The lower limit of the hyperfine field observed by 238 U M€

this sense, the results in UFe2 are more reasonable than those in URu2Si2. In addition, considering the strong spin–orbit

coupling of 5f electrons in uranium atoms, the cancellation between the spin and orbital contribution of ordered magnetic

moments in UFe2 is probably not appropriate [58,59]. Therefore, this result at least suggests that the ordered state below

TO is not a conventional antiferromagnetic ordering.



(a)



URu2Si2

60



FWHM (mm s–1)



Tχ max



50



40



Area contribution (a.u.)



(b)



FIGURE 7.10



θD = 225 K



5.0



0.0

0 TO



50



100



150



Temperature (K)



200



Temperature dependence of the

(a) spectral linewidth and (b)

integrated intensity in URu2Si2

when the spectra are analyzed by

a single-line Lorentz function.

Solid curve is a theoretical one

calculated by the Debye model.

(Modified from Fig. 4 of Ref. 7

with permission of Springer.)





7 STUDY OF EXOTIC URANIUM COMPOUNDS USING 238U MOSSBAUER

SPECTROSCOPY



132



UPt3

1.00

60 K



0.95

1.00



30 K



Relative transmission



0.95

1.00



20 K



0.95

1.00

0.95



10 K



1.00

5.5 K



0.95

1.00



2.8 K



0.95



FIGURE 7.11

238

€ ssbauer spectra of UPt3 at

U Mo

selected temperatures.



–100



–50



0



50



100



Velocity (mm s–1)



238



U M€

ossbauer spectra of UPt3 differ from those of UPd2Al3 and URu2Si2, as shown in Fig. 7.11. The asymmetry of

the spectra indicates the presence of a nuclear quadrupole interaction. More clear temperature dependence is observed

in UPt3 than in UPd2Al3 and URu2Si2. Since UPt3 exhibits only superconductivity at low temperature and undergoes no

structural transition in any reports, it is difficult to explain the observed temperature dependence of the spectra only by

the change of the nuclear quadrupole interaction. Considering the difficulty of the observation of isomer shifts in 238 U

M€

ossbauer spectroscopy, a possible factor of the temperature dependence is hyperfine field at 238 U nuclei due to

paramagnetic relaxation as discussed in UPd2Al3 and URu2Si2 cases. The details of the paramagnetic relaxation in UPt3

will be discussed with those in UPd2Ald3 and URu2Si2. In UPt3, on the other hand, the spectra were measured up to 2.8 K.

Low-temperature experiments using many techniques suggested the time-dependent antiferromagnetic ordering. 238 U

M€

ossbauer spectra do not show any temperature dependence at 6 K, a Neel temperature determined by neutron

scattering [25,26,50]. The present result agrees with the other experiments. The ordered magnetic moment in UPt3 is

determined as 0.02mB/U by neutron scattering. Using the hyperfine coupling constant of 150 T/mB in uranium

ossbauer spectroscopy.

intermetallics, the expecting hyperfine field is 4.5 T, that is, too small to be observed by 238 U M€

The absence of the hyperfine field in the measurement at 2.8 K also indicates that PuO2 is still nonmagnetic within the

experimental error. This agrees with the results of paramagnetic superconductors U6Fe and UBe13 at low temperature

(S. Tsutsui, et al., unpublished).

The observation of the hyperfine field in paramagnetic state is certainly unusual in conventional magnetic materials,

ossbauer

but the correlation between the temperature dependences of the linewidth and integrated intensity in 238 U M€

spectra of UPd2Al3 and URu2Si2 implies the presence of the hyperfine field even in the paramagnetic state. Generally, the

line shape of the M€

ossbauer resonant absorption is given as

Z

pvị ẳ BG ỵ

S E ị ẳ



ỵ1

1



SE vịexpẵsEịdE;



f S GS

1

;

2p E E0 ị2 ỵ GS =2ị2



s E ị ẳ



teff GA =2ị2

E E 0 ị2 ỵ GA =2Þ2



:



(7.1)

(7.2)



(7.3)





7.3 APPLICATION OF 238U MOSSBAUER

SPECTROSCOPY TO HEAVY FERMION SUPERCONDUCTORS



133



Equation (7.2) gives the distribution of the g-ray emitted by source and Eq. (7.3) the cross section of the absorber, the

sample in the present case. BG means the background of the spectra, fS is the recoil-free fraction of source, GS the

linewidth of the source, E0 the resonant energy, teff the effective thickness in absorber, and GA the linewidth of the

absorber. The effective thickness of the absorber is given as teff ¼ f A nA aA s 0 tA , where fA is the recoil-free fraction of

absorber, nA the number of the probe atoms per unit volume, aA the fractional abundance of the probe isotope, s 0 the

cross section of the M€

ossbauer effect in the probe isotope, and tA the thickness of the absorber. When the sample

thickness is small enough, the line broadening of the resonant lines is approximately proportionate to the effective

thickness of the sample. Temperature-dependent factor in the effective thickness is the recoil-free fraction of the sample.

Unless hyperfine fields or nuclear quadrupole interactions are observed at the probe nuclei, the linewidth is correlated

only with the recoil-free fraction of the sample. The recoil-free fraction is proportionate to the integrated intensity of the

spectra. The linewidth and integrated intensity in M€

ossbauer spectra exhibit similar temperature dependence. However,

the temperature dependence of the linewidth in the paramagnetic states of UPd2Al3 and URu2Si2 is not correlated with

that of the integrated intensity. The temperature dependence of the integrated intensity is fitted by the curves calculated

by the Debye model. This means that a monotonous increase of the linewidth is expected with a decrease in temperature

if temperature-dependent hyperfine interactions are absent.

Considering the symmetric spectra in both UPd2Al3 and URu2Si2, the maxima of the observed linewidth are

correlated with the observation of paramagnetic relaxation due to fluctuation of uranium magnetic moments. Why does

the linewidth exhibit a maximum around Tx max in UPd2Al3 and URu2Si2? The observed line broadening shows the

temperature dependence of the fluctuation and magnitude of the uranium magnetic moments, which is correlated with

Kondo-effect-like behaviors in f electron systems. In many uranium intermetallics, the magnetic susceptibility obeys the

Curie–Weiss relation at a higher temperature [60], and it has been believed that the magnitude of the magnetic moment

is reduced by Kondo effect below a characteristic temperature, that is the Kondo temperature in many of rare-earth

intermetallics. Although the magnetic moments fluctuate above magnetic ordered temperatures, the fluctuation

frequencies decrease with a decrease in temperature. Therefore, the paramagnetic relaxation is observed by

238

U M€

ossbauer spectroscopy, when the fluctuation frequency of the magnetic moments matches the time window

ossbauer effect. This means that the temperature dependence of the linewidth in the paramagnetic states of

of the 238 U M€

UPd2Al3 and URu2Si2 is qualitatively interpreted as slowing down the fluctuation frequency of the magnetic moments

above Tx max and reducing the magnitude of the magnetic moments below Tx max. However, the estimate of the magnitude

and fluctuation frequency of the magnetic moment is not easy, because the product of the fluctuation frequency and

hyperfine field due to the magnetic moments satisfies the condition of the uncertainty principle as mentioned in

Refs 61,62. Although the spectra of UPt3 exhibit different temperature dependence from those of UPd2Al3 and URu2Si2,

the observed temperature dependence is interpreted in a similar way. One of the factors in the differences is the

presence of the nuclear quadrupole interactions. This makes the temperature dependence of the spectra more

complicated. The common feature in the temperature dependence of the spectra among UPd2Al3, URu2Si2, and

UPt3 is the fact that each Tx max is close to a critical temperature in the temperature dependence. Since the magnetization

by high magnetic field suggests that the temperature Tx max is a characteristic temperature in the heavy fermion behavior

[31–37], the observation of the paramagnetic relaxation in these compounds is correlated with the heavy fermion

behavior. Considering the sensitivity of the magnetic moments and time window in neutron scattering, the signals

correlated with the paramagnetic relaxation could be observed by neutron scattering. No reports of such observations

are probably correlated with the correlation length in magnetic interactions, because M€

ossbauer spectroscopy is more

sensitive to short-range orderings.

€ ssbauer Spectroscopy of Uranium-Based Heavy Fermion Superconductors

7.3.3 Summary of 238 U Mo

238



U M€

ossbauer spectroscopy was applied to heavy fermion superconductors of UPd2Al3, URu2Si2, and UPt3. A common

feature in these compounds is the observation of paramagnetic relaxation. However, the observation of the hyperfine

field in their antiferromagnetic ordered states is different among them. The conclusions of the application of the 238 U

M€

ossbauer spectroscopy to the heavy fermion superconductors are as follows:

(1) The hyperfine field due to the antiferromagnetic ordering was observed only in UPd2Al3. The observed

hyperfine field agrees with the ordered magnetic moment determined by neutron scattering, where

the hyperfine coupling constant has the same value as in the other uranium intermetallics. On the other

hand, the hyperfine field was not observed in UPt3. This is caused by small ordered magnetic moment detected

ossbauer spectroscopy. This also agrees with the results of the previous neutron scattering. However,

by 238 U M€





7 STUDY OF EXOTIC URANIUM COMPOUNDS USING 238U MOSSBAUER

SPECTROSCOPY



134



the results of URu2Si2 differ from those of UPd2Al3 and UPt3. The spectra below the transition temperature of

17.5 K, which is thought as the Neel temperature previously, suggest the presence of the hyperfine field, but the

magnitude of the hyperfine field is too large, which is estimated by the neutron scattering results and the

hyperfine coupling constants in the other uranium intermetallics. This problem has not been resolved yet.

(2) The temperature dependence of the spectra is different among UPd2Al3, URu2Si2, and UPt3. In UPd2Al3 and

URu2Si2, the paramagnetic relaxation was observed as additional line broadening without nuclear quadrupole

interactions within the experimental error. The linewidth in their paramagnetic states has a maximum around

the temperature where the magnetic susceptibility shows a maximum. In UPt3, on the other hand, the spectra

contain nuclear quadrupole interaction. Since the temperature region where peculiar temperature dependence

of linewidth agrees with the temperature where the magnetic susceptibility exhibits a maximum in each

compound, the observation of the paramagnetic relaxation is correlated with the heavy fermion behavior. The

paramagnetic relaxation is observed as temperature dependence of the spectral shape as well as line broadening.



7.4 APPLICATION TO TWO-DIMENSIONAL (2D) FERMI SURFACE SYSTEM OF

URANIUM DIPNICTIDES

7.4.1 Introduction of Uranium Dipnictides

Orbital degrees of freedom are one of the important parameters to discuss the ordered ground states in materials.

Orbital occupancy reflects electric field gradient (EFG) at nuclei. Then, M€

ossbauer spectroscopy can detect orbital

occupancy of electrons, especially d or f electron cases. Electronic orbits in f electrons are usually called electronic

quadrupole moments. Electronic quadrupole moments directly interact with nuclear quadrupole moments, which are

ossbauer transition is

observed as nuclear quadrupole interactions. Since the nuclear quadrupole moment in the 238 U M€

relatively large, 3.1 barn, the nuclear quadrupole interaction is relatively easy to detect as asymmetry of spectra even

when hyperfine fields are observed.

Uranium dipnictides are an attractive series of uranium compounds. Their crystal structure has tetragonal symmetry

with a long c-axis [63]. Although the crystal structure of UP2 is different from the other uranium dipnictides, the local

structure around the uranium atoms is nearly the same in these compounds. Table 7.3 shows the list of the physical

properties in uranium dipnictides. These compounds exhibit an antiferromagnetic ordering at a temperature above

150 K. The magnetic structure was determined by neutron scattering. The ordered magnetic moments are aligned along

the c-axis. While the magnetic sequence in UBi2 is an ("#) one, those in the others are an ("##") one [64–66]. This

indicates that the magnetic Brillouin zones in the uranium dipnictides are reduced by their antiferromagnetic ordering.

The Fermi surface structures obtained by the de Haas–van Alphen effect measurements suggest that the electronic

structures in their ground states are correlated with their magnetic sequence [67]. Two-dimensional Fermi surfaces were

found by the de Haas–van Alphen effect. The Fermi surfaces in UBi2 consist of one spherical surface and one cylindrical

one; those in the others consist of cylindrical ones. It is believed that the differences of the Fermi surface between UBi2

and the others are formed by the magnetic sequences. Considering the correlation between the shape of the Fermi

surfaces and the magnetic sequences in the uranium dipnictides, the correlation between the electronic structures and

the magnetic sequences was expected.



TABLE 7.3 Characteristic Physical Properties in Uranium Dipnictides [63,66]

Lattice Parameters

Position Parameters

Compound

UP2

UAs2

USb2

UBi2



Neel Temperature (K)



Magnetic Moment (mB/U)



c/a



u



v



204

274

203

181



2.0

1.61

1.88

2.1



2.04

2.06

2.05

2.00



0.280

0.280

0.280

0.280



0.635

0.635

0.635

0.643



7.4 APPLICATION TO TWO-DIMENSIONAL (2D) FERMI SURFACE SYSTEM OF URANIUM DIPNICTIDES



135



In 238 U M€

ossbauer spectroscopy, isomer shift, which is one of the important parameters to discuss the hybridization

between 5f electrons at uranium atoms and electrons at the other atoms, is difficult to observe as mentioned above.

However, hyperfine coupling constant at 238 U nuclei is a complementary parameter to discuss the hybridization at the

uranium site. Typical coupling constants in uranium-based intermetallics are about 150 T/mB, to our best knowledge.

When coupling constants smaller than 150 T/mB are obtained in some compounds, it can be concluded that the nature of

the 5f electrons in them is more delocalized than that in typical uranium-based intermetallics because of the expansion of

the wave functions of 5f electrons.

7.4.2 Hyperfine Interactions Correlated with the Magnetic Structures in Uranium Dipnictides

238



U M€

ossbauer spectra previously reported in magnetically ordered compounds such as UO2, UGe2, and UPd2Al3

[2,3,6,7] are a pure magnetic pattern. In some of them, absence of the nuclear quadrupole interaction is caused by the

ossbauer spectra of uranium dipnictides differ from the

same reason as in UO2 as mentioned in Section 7.2. The 238 U M€

spectra of UO2 and UPd2Al3 as shown in Fig. 7.12 [11]. The spectra in uranium dipnictides are asymmetric except for UBi2

where the spectrum is symmetric. Since the spectral asymmetry is caused only by the presence of the nuclear quadrupole

ossbauer spectroscopy, the observation of the asymmetric spectra in UP2, UAs2, and

interaction in the case of 238 U M€

USb2 indicates the coexistence of magnetic dipole and electronic quadrupole interactions at the 238 U nuclei. On the other

hand, the interpretation of the spectrum of UBi2 is the observation of pure hyperfine field or pure nuclear quadrupole

interaction with the asymmetry parameter of h ¼ 1. Considering the Neel temperature of 181 K and the large ordered

magnetic moment of 2.1mB at the uranium site in UBi2 as shown in Table 7.3, the latter case was ruled out. The measured

temperatures in all the samples are 5.1 K, much lower than their Neel temperature. The spectra shown in Fig. 7.12 were

measured in the antiferromagnetic states, because all the uranium dipnictides exhibit an antiferromagnetic ordering at

about 200 K. Why is the spectrum of UBi2 different from those of the other dipnictides, although their crystal structure is

the same or similar among uranium dipnictides? One of possible reasons is the different magnetic sequence in UBi2. The

magnetic unit cell volume in UBi2 is a double of the unit cell in its crystal structure, while that in the other uranium

dipnictides is a quadruple of the unit cell. On the other hand, the two-dimensional Fermi surface formed by a flat magnetic

Brillouin zone was observed by de Haas–van Alphen measurements [68–71]. This is one of the evidence that the

electronic state of the ground state is correlated with the magnetic sequence (structure) in uranium dipnictides.

Therefore, the obtained M€

ossbauer spectra indicate the ground state of the electronic structure strongly connected with

magnetic sequences in these compounds.



1.00



UP2

0.95



Relative transmission



1.00



UAs2



0.95



1.00



USb2



0.95



1.00



UBi2



0.96

–100



–50



0



50



Velocity (mm s–1)



100



FIGURE 7.12

238

€ ssbauer spectra of

U Mo

uranium dipnictides at 5.1 K.



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