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31P NMR studies of the ferromagnetic uranium compound U3P4
Journal of Magnetism and Magnetic Materials 52 (1985) 301-303 North-Holland, Amsterdam
301
31p N M R S T U D I E S O F T H E F E R R O M A G N E T I C S. T A K A G I ,
N. N I I T S U M A ,
T.SUZUKI
URANIUM COMPOUND
U 3 P4
a n d T. K A S U Y A
Group of Magnetism, Department of Physics, Faculty of Science, Tohoku University, Sendal 980, Japan
The NMR of 31p in the ferromagnet U3P4 has been investigated. The nuclear relaxation rate 1/T~ shows critical-like divergence with 1 / T I
1. Introduction
2. Experimental procedure
The magnetic and electronic properties of the uranium compound U3P4 with a cubic Th3P 4 type crystal structure have been of interest these past years. U3P4 shows metallic conductivity and orders ferromagnetically below 138 K. Earlier magnetization [1,2] and transport [3] measurements have shown that U3P4 exhibits an extremely large magnetocrystalline anisotropy in the ordered state with the easy axis of magnetization being in the [111] direction. From neutron diffraction studies [4], the magnetic structure was found to be an unusual, non-collinear, three-axial, canted structure, in which the magnetic moment on the U site tilts from the [111] direction by an angle of 13 ° to the local symmetry axis of the site (which is one of the three [100] directions according to the site). There have been many theoretical attempts to explain such a giant magnetocrystalline anisotropy and a non-collinear magnetic structure. One of these attempts is to introduce a strongly anisotropic p - f mixing effect, which was originally applied to explain a large magnetic anisotropy in CeSb and CeBi [5]. Based on the localized description of the U 5f electrons, this p - f mixing model, as applied to U3P4, has assumed both the U 5f 2 levels lying about 1 eV below the Fermi level and a strong mixing between 5f and valence-band p states, and has succeeded in explaining the characteristic magnetic properties of U 3 P4 semiquantitatively [6,7]. In order to clarify the magnetic properties of U3P4 from a microscopic viewpoint and to get better understanding of the magnetism in U3 P4, we have performed detailed 31p N M R measurements at temperatures from 4.2 to 800 K with particular emphasis on the temperature dependence of the nuclear longitudinal relaxation rate 1 / T 1 in the paramagnetic state.
The sample used in the present work was polycrystalline powders prepared by a solid state reaction of the constituent elements in an evacuated and sealed quartz tube. The powders were fine enough with particle sizes much smaller than the rf skin depth for the N M R measurements. The 31p N M R was observed by the spin-echo method with a phase-incoherent and a phasecoherent pulsed N M R spectrometers in the ferromagnetic and the paramagnetic states, respectively. T I was measured by observing the recovery of spin-echo amplitude after the saturation of nuclear spins by a comb of rf pulses.
0304-8853/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
3. Experimental results and discussion In the paramagnetic state, the measurement was made mostly at the resonance frequency of 21.5 MHz. The observed spectrum is almost symmetric. The Knight shift K shows approximately the Curie-Weiss (CW) behavior, although a deviation from the CW law is marked below about 180 K. This result is consistent with the recent observation [8] that the initial susceptibility shows a strong deviation from the higher temperature CW law below about 170 K with l/xcC [ ( T Tc)/Tc] Hg. The Knight shift K was found to be linear in the magnetic susceptibility X with a hyperfine coupling constant Ahf (defined as Ahr = Not~BdK/dx) of 27.1 k O e / ~ B. This value is to be compared with a value of 25.9 kOe//~ B obtained from the continuous wave measurement by Jones [9]. Fig. 1 shows the temperature dependences of both 1 / T 1 and T 1 in the paramagnetic state. T 1 was found to be independent of the resonance frequency from the
S. Takagi et aL / .Up NMR studies of the uranium compound U¢P4
302
measurements at 10.75 and 21.5 MHz at all temperatures. Above about 300 K, T] increases almost linearly with increasing temperature, and the best fit to the experimental data gives T,=3.69×10
5(s)+l.54x10-6(sK
])T.
(1)
On approaching T c from above, 1 / T 1 shows critical-like divergence, which can be well described as 1 / T 1 oz [(T - T c ) / T c ] -°'6s, as can be seen in fig. 2. Here, T c was determined to be 137.8 K from electrical resistivity measurement on a single crystal prepared from polycrystalline powders by the iodine vapour transport method. Although what the exponent of - 0 . 6 8 means is presently not clear, the observed divergent behavior may be considered as evidence of the development of short range magnetic ordering from well above Tc. It is also tempting to presume that this short range order effect has some relevance to the unusual stability of the canted spin structure under the external magnetic field in the ordered state [2,7]. Although T 1 seems to obey a single power law up to the highest temperature from fig. 2, it can also be interpreted as increasing almost linearly with temperature above about 300 K, as mentioned before. Because this latter interpretation leads to a quite natural explanation of the dynamical magnetic properties of the system, as will be discussed below, the power law behavior up to the highest temperature should be taken only as an appearance, and the "critical" region should be considered to persist at most up to 300 K. We must just note that both the critical-like divergence of I / T I at temperatures close to the magnetic ordering
TI -I (I03
SeC-I)
temperature and the T-linear dependence of T 1 at higher temperatures are also observed in other uranium phosphide systems, UP and U P 2 [10]. Since T 1 is determined by the fluctuation of the U 5f moments, it can be related to the correlation time ~'f of the U 5f moments through the transferred hyperfine interaction as
~
(2)
o : Z ° k B T N o ~ B "rf"
where YN is the nuclear gyromagnetic ratio of 3~p, z0 is the number of nearest neighbor U ions for a 31p nucleus, and Xio~ = (Y~qXq)/N0 is the local susceptibility. In deriving eq. (2), it has been assumed that the frequency spectrum of the fluctuation of the U 5f moments is of the Lorentzian, whose half width is independent of q, and that the transferred hyperfine interaction arises only from the nearest neighbor U ions. Evaluating Xio~ as given by N o p 2 f f l L 2 / 3 k B T (Peff being the effective moment deduced from the Curie constant in the uniform susceptibility), l / ' r f is obtained as a function of temperature. 1/~'f increases almost linearly with temperature above about 300 K, and eqs. (1) and (2) give I=2.68X10'2(s-')+l.12X1011(s
'K
1)T.
(3)
Tf
Generally, 1/~"r is considered to consist of two contributions, 1 / z e = 1/'rrf+ 1/~'f,, where 1/~-rr is due to the exchange interaction between 5f electrons, and 1/~'r~ is due to the scattering of the localized U 5f moments by conduction electrons. Because 1/'rff is temperature-
TI (I0-3Se¢) se c -I)
10 4
1o
<---
-,.. °
0.5
10 3
10 -I
1
10
(T-Tc)/T c
0
200
400
Temperature
600 (K)
O00
Fig. 1. The temperature dependences of the nuclear longitudinal relaxation rate I / T 1 of 31p in U3P4 (open circles) and its inverse (solid circles).
Fig. 2. The nuclear longitudinal relaxation rate I/T~ of 3]p in U3P4 as a function of the reduced temperature ( T - T c ) / T c in the form of double logarithmic plot. The solid line represents the best fit to the experimental data. The slope of the solid line gives the "critical" exponent of -0.68.
S. Takagi et aL / 31p NMR studies of the uranium compound U3P4
"C7~
-=-i ~-!
•
E;
•
<,
O O ..C,
•
g
.
65
.
.
.
.
70
,
~ott,
75
303
naturally in terms of the scattering of the localized U 5f moments by conduction electrons. This strongly suggests that U3P4 is a localized moment system and that a localized description of the 5f electrons is favorable in 153P4, although a strong mixing between 5f and valence band p states is considered to cause various anomalous magnetic properties of the system. The development of the short range magnetic ordering near Tc, evidence by the divergent behavior of 1 / T 1, seems to be related to the unusual stability of the canted spin structure under the external magnetic field in the ordered state.
Frequency (MHz)
Fig. 3. The spin-echo spectrum of 31p in U3P4 at 4.2 K under zero external field.
independent at T>> Tc, the constant term in eq. (3) may be ascribed to 1/~'ff. The T-linear term in eq. (3), on the other hand, is considered to arise from 1/Trc, which is known as the Korringa relaxation. In a simplified model, 1/"rtc is given as 1/'rfc = 4"rr/h[Jcrp(Ev)] 2 kBT, where Jet is the effective exchange interaction between conduction and 5f electrons, and p (EF) is the density of states of the conduction electrons at the Fermi level. From the coefficient of the T-linear term in eq. (3), [JcfP(Ev)[ is estimated to be 0.26. At 4.2 K in the ordered state, N M R signal was observed at around 70 MHz under zero external field, as shown in fig. 3. The observations of no enhancement of the signal and no decrease of the signal intensity under external field indicate that the signal comes mostly from domains. The observed spectrum is almost symmetric with a full width of half maximum of about 5 MHz. Although the origin of the width of the spectrum is not clear, the hyperfine field deduced from the centre of the spectrum almost agrees with that expected from the values of both the ferromagnetic moment (1.55~B) and A hr obtained in the paramagnetic state.
4. Conclusion
We have shown that the observed T-linear increase of T~ at higher temperatures can be interpreted quite
This work was supported in part by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture. The nuclear relaxation measurements were performed at Institute for Solid State Physics, University of Tokyo. One of the authors (S.T.) would like to acknowledge Prof. H. Yasuoka at ISSP for valuable discussions and continuous encouragement.
References
[1] C.F. Buhrer, J. Phys. Chem. Solids 30 (1969) 1273. [2] K.P. Belov, Z. Genke, A.S. Dmitrievskii, R.Z. Levitin and W. Trzebiatowski, Zh. Eksp. Teor. Fiz. 64 (1973) 1351. [3] Z. Henkie, Physica 102B (1980) 329. [4] P. Burlet, J. Rossat-Mignod, R. Tro6 and Z. Henkie, Solid State Commun. 39 (1981) 745. [5] K. Takegahara, H. Takahashi, A. Yanase and T. Kasuya, J. Phys. C14 (1981) 737. [6] K. Takegahara, A. Yanase and T. Kasuya, in: Crystalline Electric Fields and f Electron Magnetism, eds. R.P. Guertin, W. Suski and Z. Zolnierek (Plenum, New York, 1982) p. 533. [7] T. Suzuki, S. Takagi, N. Niitsuma, K. Takegahara, T. Kasuya, A. Yanase, T. Sakakibara, M. Date, P.J. Markowski and Z. Henkie, in: Proc. Intern. Symp. on High Field Magnetism, ed. M. Date (North-Holland, Amsterdam, 1983) p. 183. [8] R. Tro6 and A.T. Aldred, Z. Phys. B53 (1983) 295. [9] E.D. Jones, Phys. Lett. 25A (1967) 111. [10] S. Takagi, N. Niitsuma and T. Kasuya, in preparation.
301
31p N M R S T U D I E S O F T H E F E R R O M A G N E T I C S. T A K A G I ,
N. N I I T S U M A ,
T.SUZUKI
URANIUM COMPOUND
U 3 P4
a n d T. K A S U Y A
Group of Magnetism, Department of Physics, Faculty of Science, Tohoku University, Sendal 980, Japan
The NMR of 31p in the ferromagnet U3P4 has been investigated. The nuclear relaxation rate 1/T~ shows critical-like divergence with 1 / T I
1. Introduction
2. Experimental procedure
The magnetic and electronic properties of the uranium compound U3P4 with a cubic Th3P 4 type crystal structure have been of interest these past years. U3P4 shows metallic conductivity and orders ferromagnetically below 138 K. Earlier magnetization [1,2] and transport [3] measurements have shown that U3P4 exhibits an extremely large magnetocrystalline anisotropy in the ordered state with the easy axis of magnetization being in the [111] direction. From neutron diffraction studies [4], the magnetic structure was found to be an unusual, non-collinear, three-axial, canted structure, in which the magnetic moment on the U site tilts from the [111] direction by an angle of 13 ° to the local symmetry axis of the site (which is one of the three [100] directions according to the site). There have been many theoretical attempts to explain such a giant magnetocrystalline anisotropy and a non-collinear magnetic structure. One of these attempts is to introduce a strongly anisotropic p - f mixing effect, which was originally applied to explain a large magnetic anisotropy in CeSb and CeBi [5]. Based on the localized description of the U 5f electrons, this p - f mixing model, as applied to U3P4, has assumed both the U 5f 2 levels lying about 1 eV below the Fermi level and a strong mixing between 5f and valence-band p states, and has succeeded in explaining the characteristic magnetic properties of U 3 P4 semiquantitatively [6,7]. In order to clarify the magnetic properties of U3P4 from a microscopic viewpoint and to get better understanding of the magnetism in U3 P4, we have performed detailed 31p N M R measurements at temperatures from 4.2 to 800 K with particular emphasis on the temperature dependence of the nuclear longitudinal relaxation rate 1 / T 1 in the paramagnetic state.
The sample used in the present work was polycrystalline powders prepared by a solid state reaction of the constituent elements in an evacuated and sealed quartz tube. The powders were fine enough with particle sizes much smaller than the rf skin depth for the N M R measurements. The 31p N M R was observed by the spin-echo method with a phase-incoherent and a phasecoherent pulsed N M R spectrometers in the ferromagnetic and the paramagnetic states, respectively. T I was measured by observing the recovery of spin-echo amplitude after the saturation of nuclear spins by a comb of rf pulses.
0304-8853/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
3. Experimental results and discussion In the paramagnetic state, the measurement was made mostly at the resonance frequency of 21.5 MHz. The observed spectrum is almost symmetric. The Knight shift K shows approximately the Curie-Weiss (CW) behavior, although a deviation from the CW law is marked below about 180 K. This result is consistent with the recent observation [8] that the initial susceptibility shows a strong deviation from the higher temperature CW law below about 170 K with l/xcC [ ( T Tc)/Tc] Hg. The Knight shift K was found to be linear in the magnetic susceptibility X with a hyperfine coupling constant Ahf (defined as Ahr = Not~BdK/dx) of 27.1 k O e / ~ B. This value is to be compared with a value of 25.9 kOe//~ B obtained from the continuous wave measurement by Jones [9]. Fig. 1 shows the temperature dependences of both 1 / T 1 and T 1 in the paramagnetic state. T 1 was found to be independent of the resonance frequency from the
S. Takagi et aL / .Up NMR studies of the uranium compound U¢P4
302
measurements at 10.75 and 21.5 MHz at all temperatures. Above about 300 K, T] increases almost linearly with increasing temperature, and the best fit to the experimental data gives T,=3.69×10
5(s)+l.54x10-6(sK
])T.
(1)
On approaching T c from above, 1 / T 1 shows critical-like divergence, which can be well described as 1 / T 1 oz [(T - T c ) / T c ] -°'6s, as can be seen in fig. 2. Here, T c was determined to be 137.8 K from electrical resistivity measurement on a single crystal prepared from polycrystalline powders by the iodine vapour transport method. Although what the exponent of - 0 . 6 8 means is presently not clear, the observed divergent behavior may be considered as evidence of the development of short range magnetic ordering from well above Tc. It is also tempting to presume that this short range order effect has some relevance to the unusual stability of the canted spin structure under the external magnetic field in the ordered state [2,7]. Although T 1 seems to obey a single power law up to the highest temperature from fig. 2, it can also be interpreted as increasing almost linearly with temperature above about 300 K, as mentioned before. Because this latter interpretation leads to a quite natural explanation of the dynamical magnetic properties of the system, as will be discussed below, the power law behavior up to the highest temperature should be taken only as an appearance, and the "critical" region should be considered to persist at most up to 300 K. We must just note that both the critical-like divergence of I / T I at temperatures close to the magnetic ordering
TI -I (I03
SeC-I)
temperature and the T-linear dependence of T 1 at higher temperatures are also observed in other uranium phosphide systems, UP and U P 2 [10]. Since T 1 is determined by the fluctuation of the U 5f moments, it can be related to the correlation time ~'f of the U 5f moments through the transferred hyperfine interaction as
~
(2)
o : Z ° k B T N o ~ B "rf"
where YN is the nuclear gyromagnetic ratio of 3~p, z0 is the number of nearest neighbor U ions for a 31p nucleus, and Xio~ = (Y~qXq)/N0 is the local susceptibility. In deriving eq. (2), it has been assumed that the frequency spectrum of the fluctuation of the U 5f moments is of the Lorentzian, whose half width is independent of q, and that the transferred hyperfine interaction arises only from the nearest neighbor U ions. Evaluating Xio~ as given by N o p 2 f f l L 2 / 3 k B T (Peff being the effective moment deduced from the Curie constant in the uniform susceptibility), l / ' r f is obtained as a function of temperature. 1/~'f increases almost linearly with temperature above about 300 K, and eqs. (1) and (2) give I=2.68X10'2(s-')+l.12X1011(s
'K
1)T.
(3)
Tf
Generally, 1/~"r is considered to consist of two contributions, 1 / z e = 1/'rrf+ 1/~'f,, where 1/~-rr is due to the exchange interaction between 5f electrons, and 1/~'r~ is due to the scattering of the localized U 5f moments by conduction electrons. Because 1/'rff is temperature-
TI (I0-3Se¢) se c -I)
10 4
1o
<---
-,.. °
0.5
10 3
10 -I
1
10
(T-Tc)/T c
0
200
400
Temperature
600 (K)
O00
Fig. 1. The temperature dependences of the nuclear longitudinal relaxation rate I / T 1 of 31p in U3P4 (open circles) and its inverse (solid circles).
Fig. 2. The nuclear longitudinal relaxation rate I/T~ of 3]p in U3P4 as a function of the reduced temperature ( T - T c ) / T c in the form of double logarithmic plot. The solid line represents the best fit to the experimental data. The slope of the solid line gives the "critical" exponent of -0.68.
S. Takagi et aL / 31p NMR studies of the uranium compound U3P4
"C7~
-=-i ~-!
•
E;
•
<,
O O ..C,
•
g
.
65
.
.
.
.
70
,
~ott,
75
303
naturally in terms of the scattering of the localized U 5f moments by conduction electrons. This strongly suggests that U3P4 is a localized moment system and that a localized description of the 5f electrons is favorable in 153P4, although a strong mixing between 5f and valence band p states is considered to cause various anomalous magnetic properties of the system. The development of the short range magnetic ordering near Tc, evidence by the divergent behavior of 1 / T 1, seems to be related to the unusual stability of the canted spin structure under the external magnetic field in the ordered state.
Frequency (MHz)
Fig. 3. The spin-echo spectrum of 31p in U3P4 at 4.2 K under zero external field.
independent at T>> Tc, the constant term in eq. (3) may be ascribed to 1/~'ff. The T-linear term in eq. (3), on the other hand, is considered to arise from 1/Trc, which is known as the Korringa relaxation. In a simplified model, 1/"rtc is given as 1/'rfc = 4"rr/h[Jcrp(Ev)] 2 kBT, where Jet is the effective exchange interaction between conduction and 5f electrons, and p (EF) is the density of states of the conduction electrons at the Fermi level. From the coefficient of the T-linear term in eq. (3), [JcfP(Ev)[ is estimated to be 0.26. At 4.2 K in the ordered state, N M R signal was observed at around 70 MHz under zero external field, as shown in fig. 3. The observations of no enhancement of the signal and no decrease of the signal intensity under external field indicate that the signal comes mostly from domains. The observed spectrum is almost symmetric with a full width of half maximum of about 5 MHz. Although the origin of the width of the spectrum is not clear, the hyperfine field deduced from the centre of the spectrum almost agrees with that expected from the values of both the ferromagnetic moment (1.55~B) and A hr obtained in the paramagnetic state.
4. Conclusion
We have shown that the observed T-linear increase of T~ at higher temperatures can be interpreted quite
This work was supported in part by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture. The nuclear relaxation measurements were performed at Institute for Solid State Physics, University of Tokyo. One of the authors (S.T.) would like to acknowledge Prof. H. Yasuoka at ISSP for valuable discussions and continuous encouragement.
References
[1] C.F. Buhrer, J. Phys. Chem. Solids 30 (1969) 1273. [2] K.P. Belov, Z. Genke, A.S. Dmitrievskii, R.Z. Levitin and W. Trzebiatowski, Zh. Eksp. Teor. Fiz. 64 (1973) 1351. [3] Z. Henkie, Physica 102B (1980) 329. [4] P. Burlet, J. Rossat-Mignod, R. Tro6 and Z. Henkie, Solid State Commun. 39 (1981) 745. [5] K. Takegahara, H. Takahashi, A. Yanase and T. Kasuya, J. Phys. C14 (1981) 737. [6] K. Takegahara, A. Yanase and T. Kasuya, in: Crystalline Electric Fields and f Electron Magnetism, eds. R.P. Guertin, W. Suski and Z. Zolnierek (Plenum, New York, 1982) p. 533. [7] T. Suzuki, S. Takagi, N. Niitsuma, K. Takegahara, T. Kasuya, A. Yanase, T. Sakakibara, M. Date, P.J. Markowski and Z. Henkie, in: Proc. Intern. Symp. on High Field Magnetism, ed. M. Date (North-Holland, Amsterdam, 1983) p. 183. [8] R. Tro6 and A.T. Aldred, Z. Phys. B53 (1983) 295. [9] E.D. Jones, Phys. Lett. 25A (1967) 111. [10] S. Takagi, N. Niitsuma and T. Kasuya, in preparation.