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7Li NMR in the superconducting Li1+xTi2−xO4 spinel compounds
Physica C 157 (1989) 65-71 North-Holland, A m s t e r d a m
7Li NMR IN T H E SUPERCONDUCTING Lil +xTi2_xO4SPINEL C O M P O U N D S M. ITOH and Y. HASEGAWA Department of Physics, Faculty of Science, Chiba University, Yayoi-cho, Chiba 260, Japan
H. YASUOKA Institute for Solid State Physics, University of Tokyo, Roppongi. Minato-ku, Tokyo 106, Japan
Y. UEDA and K. KOSUGE Department of Chemistry, Faculty of Science, Kyoto University, Sakyo-ku, Kyoto 606, Japan Received 11 November 1988
Li t +xTi2 _xO4 (0 < x < 1/ 3 ) spinel compounds have two characteristic features: the metal-insulator transition near x ~ 0.16 and the superconducting transition at Tc ~ 13 K for x < 0.16. 7Li N M R experiments have been performed to investigate the microscopic properties of the electron spins in the metallic phase. The origin of the observed 7Li N M R in the normal state is discussed in connection with the crystallographic character. In the superconducting state the field penetration depth is estimated from the inhomogeneously broadened 7Li spin-echo field spectra. It is revealed that 7Li nuclear relaxation is governed by the Korringa process of conduction electrons at high temperatures and the process due to magnetic relaxation centers at low temperatures. The density of states at the Fermi level is discussed.
1. Introduction
Lil+xTi2_xO4 ( 0 < x ~ < l / 3 ) spinel compounds have two end members: the metallic LiTi204 which undergoes a superconducting transition at Tc ~ 13 K, and the insulating Li4/3Tis/304 [ 1 ]. The crystallographic feature in the spinel structure of the existence of the two sites occupied by the cations plays an important role as follows. In LiTi204 the Li and the Ti ions occupy the tetrahedral and the octahedral sites, respectively. In Li~ +xTi2_xO4 (x # 0), however, additional Li ions randomly substitute Ti ions on the octahedral sites. This partial occupation of the octahedral sites by the Li ions changes the electron number of the Ti ions. With increasing fraction of the Li ions on the octahedral sites the average charge increases from 3.5+ in LiTi204 to 4.0+ in L i 4 / 3 T i s / 3 0 4 . Hence the Ti:t2g conduction band is partially occupied in LiTi204 and is empty in Li4/3Tis/3Oa [ 2 ]. Thus it is expected that the metalinsulator transition occurs at the intermediate composition. Indeed the metal-insulator transition at a
critical concentration xc~0.1 was reported [ 1 ]. However, the origin of the metal-insulator transition remains unclear, although many experimental studies have been done in connection with the transition [ 1-7 ]. The metallic Lil +xTi2_xO4 undergoes a superconducting transition with the transition temperature Tc ~ 13 K which is almost independent of the composition [ 1,6]. The superconducting fraction determined from the ac magnetic susceptibility measurements reduces to zero at x ~ 0.16 which may be taken as the correct value of xc [ 6 ]. The occurrence of the local moments which complicates the superconducting properties and the metal-insulator transition has been pointed out from the magnetic and ESR measurements. Three types of the Ti 3+ local moments on the octahedral sites are considered from the ESR experiments [4 ]. Also a part of the magnetic susceptibility which obeys the Curie-Weiss law supports the presence of the local moments [ 1,4]. The remaining, almost temperature independent, magnetic susceptibility indicates the Pauli para-
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
66
M. Itoh et al. / ZLi NMR in L t+xTi 2_x04 spinel compounds
magnetism of the conduction electrons with the Stoner enhancement. From the specific heat experiments, LiTi204 is considered to be a d-band superconductor described by the BCS theory [3 ]. In order to investigate the microscopically magnetic properties of the electron spins in the metallic phase of the Li~+xTi2_xO4 spinel compounds, 7Li N M R experiments have been performed. We believe that the clarification of those in the metallic phase is important at first to understand the superconducting and the metal-insulator transitions. In this paper the origin of the observed 7Li N M R signals is discussed on the basis of the partial occupation of the Li ions on the octahedral sites, and from the 7Li N M R in the superconducting state the field penetration depth is estimated. Moreover, the process of the 7Li nuclear relaxation which yields the information of the low-lying excitation of the electron spins is discussed.
2. Experimental procedure Powdered samples used in the present experiment ( x ~ 0.125 ) were prepared by the solid state reaction of lithium carbonate (4N), titanium dioxide (4N) and titanium metal (3N) [ 8 ]. N M R experiments were performed by using a standard coherent pulsed spectrometer. Spin-echo spectra in the superconducting state were obtained by measuring spin-echo amplitude point by point of the external field. The nuclear spin-lattice relaxation time TI w a s measured by observing the recovery of spin-echo or free induction-decay amplitude after the saturation of the nuclear magnetization by a comb of rf pulses.
3. Experimental results and discussion 3. I. 7Li N M R in the normal state In the normal state of all the samples, we have observed 7Li free induction-decay ( F I D ) signals with small Knight shift ( K < 0.005%) which was found to be almost independent of temperature. In fig. 1 the fractional change of the FID amplitude I ( x ) per unit mole of Li atoms is shown as a function of x. Here, we have determined I ( x ) by extrapolating the time
I 1
0
Lil,.~Ti2_xO,' 300 K
I 0.l
0.05
"""'+, 0.15
X Fig. 1. Composition dependence of the 7Li free induction-decay amplitude in Li~ +xTi2_~O4 at 300 K. The solid curve represents the calculated one on the basis of a model of the loss of the 7Li N M R due to the introduction of the Li ions to the octahedral sites (see the text). The dashed and the dotted curves are the ratio of the tetrahedral sites to the total Li sites and the superconducting volume fraction (see ref. [ 6 ] ), respectively.
spectrum of the 7Li FID signal to t = 0. The decrease of l ( x ) with increasing x means the increase of the Li sites that cannot contribute to the FID signal. As is mentioned in the introduction, Li ions substitute Ti ions on the octahedral sites in the x ~ 0 samples. Therefore we must determine what Li sites contribute to the observed 7Li N M R signal. The partial loss of the 7Li N M R signals with increasing x is not simply explained, although it is clear that the loss connects with the substitution of the Ti ions by the Li ions which may influence the electric properties of the neighboring Li ions. As references, we shall consider two curves shown in fig. 1. The dashed curve is the ratio of the tetrahedral sites to the total Li sites, and corresponds to the case of no observation of the signals from the Li nuclei on the octahedral sites. The dotted curve is the superconducting volume fraction f~(x) determined by the ac susceptibility [6]. The substitution of the Ti ions by the Li ions on the octahedral sites cuts the conducting path. In this case we see only the Li sites in the infinite conducting cluster which is responsible for the bulk superconductivity. Taking account of two cases mentioned above, we made up a model that the N M R signals from the Li nuclei on the tetrahedral sites nearest neighbor to the Li ions on the octahedral sites are wiped out as well as those on the octahedral sites. The result is shown by the solid curve in fig. 1. Qual-
M. Itoh et al. / 7Li NMR in L t+xTi e_x04 spinel compounds
itatively speaking, the solid curve agrees with the experimental results. Hence we may conclude that the observed signal comes from the Li nuclei on the tetrahedral sites far from the Li ions on the octahedral sites, although the physical reason of the loss of the signal is not clear. It should be noted that we observe Li NMR signals from the Li sites mentioned above in the finite conducting clusters as well as in the infinite cluster. Here we shall refer the chemical inhomogeneity of these spinel compounds. If there exists a spinodal decomposition into the Li-poor phases approaching LiTi204 and the Li-rich phases approaching Li4/3Tis/304 in Lil+xTiE_xO4 [6], the decrease of I ( x ) with increasing x should be explained by the composition dependence of the superconducting volume fraction. Hence we consider these metallic spinel compounds as the chemically homogeneous bulk superconductors. This is supported by the fact that the upper critical field shows the composition dependence [8 ]. 3.2. ZLi N M R in the superconducting state
In the superconducting state, we have observed 7Li spin-echo spectra with the inhomogeneous broadening due to the field penetration. Figure 2 shows the temperature dependence of the field-swept 7 L i spin-echo spectrum in LiTi204 taken at 13.00 MHz. With decreasing temperature below the superconducting transition temperature under the field Tc(H) ~ 11.5 K, the resonance field for the peak intensity shift is more negative, and the line width increases. LiTi204 is known to be a type II superconductor with the lower critical field Hd ~ 700 Oe and the upper critical field HoE~ 130 kOe [8]. Hence the present external field ~7.9 kOe is between H:, and HoE, where the quantum flux is known to form a triangular lattice. In the mixed state the maxima of the magnetic field occur at the center of the vortices, and the minima do at the center between the adjacent vortices [9 ]. Such local field distribution yields the asymmetric NMR spectrum as just observed in the present experiment. Also the observed field for the peak of the spectrum corresponds to the field at the saddle points of the local field. Figure 3 shows the temperature dependence of the 7 L i spin-echo spectrum in LiLoTTiL9304 taken at 13.00
67
K=0
Lil,xTiz-x O~.
/, ~
"~-.
I
.-
9.OK
ee-
•
.~'/I 1 ""-"~'~
Z80
"~.
I;
I
7.85 7.90 External Field (kOe)
4.2K "~"r-"
7.95
Fig. 2. Temperature dependence of the 7Li spin-echo spectrum in the superconducting state of LiTi204 taken at 13.00 MHz. The dashed line represents the field where the Knight shift is zero.
K=0'~ '~J/ 1IT'
O
-/
__,.
,
--?.
LIl,xTi 2-x04 X=0.07
°
~. ~..°
10.3 K • 9.OK
t~L
E
! , bJ
iJ' !/ ,/ ........
7.80
I
.....
•
~. ~
4.z K ......
I i I 7.85 7.90 External Field (kOe)
I 795
Fig. 3. Temperature dependence of the 7Li spin-echo spectrum in the superconducting state of LiLo7Til.gaO4 taken at 13.00 MHz. The dashed line represents the field where the Knight shift is zero.
68
M. Itoh et al. / ZLi NMR in L I +xTi2_ xO. spinel compounds
MHz. The behavior of the temperature dependence is similar to that in LiTi204 except the loss of the asymmetric pattern. The observed symmetric spectrum and smaller negative shift indicate deeper penetration of the magnetic field compared with LiTi204. In the intermediate field H~, << H<< H¢2, the second moment AH 2 of the NMR spectrum can be calculated on the basis of the vortex lattice as
I
i
Illll
i-~ 1(~'; -
--
),
•
iI
/
l)
where 00 = hc/2e is the flux quantum, ;Lthe field penetration depth and d the vortex lattice spacing [ 10 ]. The calculated values of 2 from the observed spectra at 4.2 K based on eq. ( 1 ) are plotted in fig. 4. One can easily see that 2 increases with increasing x.
3.3. Temperature dependence of the nuclear relaxation rate 1/TI In order to investigate the dynamical properties of the electron spins, the 7Li nuclear spin-lattice relaxation time T~ has been measured in the temperature range from 4.2 to 300 K at 13.00 MHz. In LiTi204, 1/Tt has the temperature dependence as shown in fig. 5. Above about 20 K, 1/T, obeys the relation as (2)
which is shown by the solid line in fig. 5. Below about 20 K, 1/T~ departs from the above relation, and
600£
400( o~ v
Li~+xTi2-xOt. 4.2K 0.15 X
01.1
I
/ 1~:
I
I
0.15
Fig. 4. Composition dependence of the field penetration depth at 4.2 K in Li~ +xTi2_xO4 calculated from the observed 7Li spin-echo spectra.
i
i
I
i l l l l
I
.;/ /
/
Lil+NTiz-xOt' IX3=~IHz
I
,11 , , , l l
,
t I,,,,I
10
i
100 Temperature
(K)
t I1,,,I
1000
Fig. 5. Temperature dependence of the 7Li nuclear spin-lattice relaxation rate 1/T~ in LiTi204 taken at 13.00 MHz. The solid line is the best fit of data above 20 K to the relation 1/ ( T~T) = constant. The dashed curve represents the calculated one based on eq. (3).
gradually decreases with decreasing temperature. In the normal state the magnetic susceptibility due to the conduction electrons, which is almost independent of temperature, indicates Pauli paramagnetism of the conduction electrons [ 1,4]. Hence, the observed temperature dependence of 1IT, above about 20 K is considered to be determined by the Korringa process of the conduction electrons. The specific heat measurements established LiTi204 as a d-band superconductor described by the BCS theory [ 3 ]. In usual BCS superconductors, 1/ T~ is enhanced just below the superconducting transition temperature T¢ by a piling up of the density of states at the gap edges and the coherent factor, and obeys the relation as
1/TI ocexp(-d)/kBT)
06
L ~,111
I
/
(
I/(T,T)=(5.6+O.3)×lO-4(s-'K-~) ,
;/
ee
= {1 + ( 2 ~ . / d ) 2} -~/2q~o/()~2416~; 3 ) 00/(~2~
I
(T<
(3)
where the energy gap 2A=3.5kBT~ and kB is the Boltzmann constant [ 11 ]. Although the behaviour of the temperature dependence of 1/T~ under the field is modified, the low field has a relatively small effect onto 1/(Tl T). The dashed curve shows the temperature dependence of 1/T] calculated on the basis of eq. (3). The agreement between the calculated curve and the experimental results is not satisfactory. We believe that 1/T1 at low temperatures is determined by another process mentioned below. In Li, ÷xTi2_xO4 ( x ~ 0 ) we must note the form of the decay of the nuclear magnetization. The decay at
M. Itoh et al. I ZLi NMR in Lt+xTi2_xO4 spinel compounds Lil,xTiz..xO4 (x =0.07) 1.0
I
4.2 K
i
i
I
IIIII
I
69
I
I
I
I Illl
\
~
o~
I
I
Illll
I
• O00 • •
0.1
10-1
• •
'o
oooo ~° //
/i
,° •
21
I
//t
% °%
~E
0.0
I
260 K
//
/
//
42
t ~s4ec)
48
162
Fig. 6. The decay of the 7Li nuclear magnetization at 4.2 K (left) and 260 K (right) in Lim.ovTiL9304.
high and low temperatures is different as shown in fig. 6 where the data at 4.2 and 260 K in Lim.o7Til.930 4 are given. At 260 K the decay is expressed by a single exponential function, while that at 4.2 K is not. The change of the form of the decay of the nuclear magnetization mentioned above occurs at about 120 K. As is mentioned in the Introduction, the presence of the local moments in these ternary compounds is certain. If magnetic relaxation centers exist, the decay is expected to have multi-relaxation components. Assuming the interaction between the magnetic relaxation centers with the low concentration and the nucleus in concern is a dipole-like one, it is known that the long-time decay at sufficient time after a comb of the rf pulses can be expressed as {Mo - M ( t ) } / M o = e x p { - (t/Tl)'}
(4)
with n=0.5, where Mo and M(t) are the nuclear magnetizations in thermal equilibrium and at time t after the saturation of a comb of rf pulses, respectively [ 12 ]. It should be noted that the function of eq. (4) involves the decay expressed by a single-exponential function in the case of n = 1. Thus we apply eq. (4) to the observed decay. Figure 7 shows the temperature dependence of 1/TI determined by fitting the experimental results of the long-time decay to eq. (4) with T~ and n as parameters. 1/T1 decreases linearly with temperature from 300 K to about 120 K. Below about 120 K 1/T~ increases gradually with decreasing temperature. The changes of 1/T~ and the decay observed at about 120 K indicates that the relative importance of the two relaxation processes, the Korringa process and one due to the magnetic relaxation centers, changes at this
Lil,xTiz-x04
x=0.07 13 MHz
16
I
I
i I IIIII
1
I
I
IIIIII
I0 I0() Temperature (K)
I
I
I I Illll
I(3(3(}
Fig. 7. Temperature dependence of the 7Li nuclear spin-lattice relaxation rate I/T~ in Lil.o7Tit.9304 taken at 13.00 MHz. The dashed line is the best fit of the data above 170 K to the relation, 1/ ( T~T) = constant.
temperature. In the former case, 1/ T~ is expressed as
1~Tin ocA2N(EF)2kBT,
(5)
where A is the coupling constant, and N(EF) the density of states at the Fermi level [ 13 ]. On the other hand, in the latter case, I/T~ is expressed as
1/ Tl ocA 2tle ,
(6)
where t~e is the correlation time of the magnetic relaxation centers [ 13 ]. From the analysis mentioned above it is clear that the nuclear relaxation at high temperatures is considered to be due to the conduction electrons, and that the relaxation at low temperatures is due to the magnetic relaxation centers. The gradual increase of 1/T~ with decreasing temperature below about 120 K is attributed to the temperature dependence of t~. The temperature dependences of 1/Tl in x = 0 , 0.07 and 0.125 samples are summarized in fig. 8. The tendency that 1/7"] at low temperatures increases with increasing x indicates the increase of the number of the relaxation center. In LiTi204 the relaxation rate at low temperatures is so small that it may be determined by the magnetic relaxation centers, not by the conduction electrons, even if the fraction of the magnetic center is small. On the other hand, at high temperatures it should be noted that the nuclear re-
70
M. Itoh et al. / ZLi NMR in L t+xTi 2_xO 4 spinel compounds I
I
I
lllll
I
0.125 + 0.07 o
I
I I llIH
I
I
l I llillJ
+
°%°°°2:,:f: 4"4"+ +-t-
A J
.l AA A
0.0
~
A
16:
1
Ul,xTi2-xOl. 13 MHz
I i lttlll
Fig. 8. Temperature relaxation rate l / T i LiH25Tit.sTsO4 ( + ) calculated one based
I
10
|
I I lilt[
i
I I I IIIIJ
100 Temperoture (K)
1000
dependence of the 7Li nuclear spin-lattice in LiTi204 ( ( A ) , Lit.o7TiL9304 (Q)) and taken at 13.00 MHz. The solid line is the on eq. (2).
laxation due to the conduction electrons is the same in three samples. Since we can easily see from eq. (5) that 1/ ( T~T) is a constant independent of temperature in the temperature region where 1/ T~ is due to the Korringa process, we have fitted the experimental data to the relation 1/ ( T~ T) = constant. The results are shown in fig. 9. The constant, which is linear to (AN(EF)}2, is almost independent of x. Since there is no drastic change of the lattice constant [ 1 ],
0
Lil,xTi2-x04 13 MHz
~2
it is considered that N(EF) is almost independent of the composition in the metallic Lij +xTi2_xO4 spinel compounds. This behavior of N(EF) is consistent with that determined from the electronic specific heat measurements [ 3 ]. As the fraction of the Li ions on the octahedral sites increases, the average charge of the Ti ions increases from 3.5 + in LiTi204 to 4.0+ in L i 4 / 3 T i s / 3 0 4. Then the conduction electron number deduces the Fermi level which lies in the Ti:t2g band in energy. Therefore, qualitatively speaking, this perturbation by the partial occupation of the Li ions on the octahedral sites seems to narrow the t2g band.
4. Conclusion 7Li N M R experimental have been performed to investigate the microscopic properties of the electron spins in the metallic LiTi204 spinel compounds. It has been found that the observed 7Li N M R signal may come from the Li nuclei on the tetrahedral sites far from the Li ions on the octahedral sites. The other signals from the Li nuclei on the octahedral sites and on the neighboring tetrahedral sites may be wiped out. In the superconducting state 7Li spin-echo spectra with the inhomogeneous broadening due to the field penetration have been observed. By calculating the second moments of the spectra we have estimated the penetration depth which increases with increasing x. Two processes have been identified as the 7Li nuclear spin-lattice relaxation rate 1/T1 in the metallic Li~ +xWi2_x04: the Korringa process at high temperatures and the process due to the magnetic relaxation centers at low temperatures. The density of states at the Fermi level deduced by the Korringa process of 1/Tt in the normal state is almost independent of the composition in the metallic phase.
References 0.05
X
0.I
0.15
Fig. 9. Composition dependence of the constant obtained by fitting the data of 1/ Ti in the temperature range where 1/ Tt is determined by the Korringa process to the relation 1/ ( T~ T) = constant.
[ 1 ] D.C. Johnston, J. Low Temp. Phys. 25 (1976) 145. [2] P.P. Edwards, R.G. Egdell, I. Fragala, J.B. Goodenough, M.R. Harrison, A.F. Orchard and E.G. Scott, J. Solid State Chem. 54 (1984) 127. [3] R.W. McCallum, D.C. Johnston, C.A. Luengo and M.B. Maple, J. Low Temp. Phys. 25 (1976) 177.
]14. ltoh et al. / 7Li N M R in L
[ 4 ].M.R. Harrison, P.P. Edwards and J.B. Goodenough, J. Solid State Chem. 54 (1984) 136. [5 ] M.R. Harrison, P.P. Edwards and J.B. Goodenough, J. Solid State Chem. 54 (1984) 426. [6] M.R. Harrison, P.P. Edwards and J.B. Goodenough, Philos. Mag. B 52 (1985) 679. [ 7 ] M. Watanabe, K. Kaneda, H. Takeda and N. Tsuda, J. Phys. Soc. Jpn. 53 (1984) 2437. [8] T. Tanaka, Y. Ueda, K. Kosuge, H. Yasuoka and M. Ishikawa, to be published in J. Solid State Chem.
l +x T i 2_ x O 4 spinel
compounds
71
[9] W. Fite II and A.G. Redfield, Phys. Rev. 15 (1966) 381. [10] P. Pincus, A.C. Gossard, V. Jaccarino and J.H. Wernick, Phys. Lett. 13 (1964) 2 I. [ l l ] D.E. MacLaughlin, Solid State Phys. 31 (1976) I. [ 12] M. Itoh, H. Yasuoka, A.R. King and V. Jaccarino, J. Phys. Soc. Jpn. 55 (1986) 964, and references therein. [13]A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961 ) pp. 358, 380.
7Li NMR IN T H E SUPERCONDUCTING Lil +xTi2_xO4SPINEL C O M P O U N D S M. ITOH and Y. HASEGAWA Department of Physics, Faculty of Science, Chiba University, Yayoi-cho, Chiba 260, Japan
H. YASUOKA Institute for Solid State Physics, University of Tokyo, Roppongi. Minato-ku, Tokyo 106, Japan
Y. UEDA and K. KOSUGE Department of Chemistry, Faculty of Science, Kyoto University, Sakyo-ku, Kyoto 606, Japan Received 11 November 1988
Li t +xTi2 _xO4 (0 < x < 1/ 3 ) spinel compounds have two characteristic features: the metal-insulator transition near x ~ 0.16 and the superconducting transition at Tc ~ 13 K for x < 0.16. 7Li N M R experiments have been performed to investigate the microscopic properties of the electron spins in the metallic phase. The origin of the observed 7Li N M R in the normal state is discussed in connection with the crystallographic character. In the superconducting state the field penetration depth is estimated from the inhomogeneously broadened 7Li spin-echo field spectra. It is revealed that 7Li nuclear relaxation is governed by the Korringa process of conduction electrons at high temperatures and the process due to magnetic relaxation centers at low temperatures. The density of states at the Fermi level is discussed.
1. Introduction
Lil+xTi2_xO4 ( 0 < x ~ < l / 3 ) spinel compounds have two end members: the metallic LiTi204 which undergoes a superconducting transition at Tc ~ 13 K, and the insulating Li4/3Tis/304 [ 1 ]. The crystallographic feature in the spinel structure of the existence of the two sites occupied by the cations plays an important role as follows. In LiTi204 the Li and the Ti ions occupy the tetrahedral and the octahedral sites, respectively. In Li~ +xTi2_xO4 (x # 0), however, additional Li ions randomly substitute Ti ions on the octahedral sites. This partial occupation of the octahedral sites by the Li ions changes the electron number of the Ti ions. With increasing fraction of the Li ions on the octahedral sites the average charge increases from 3.5+ in LiTi204 to 4.0+ in L i 4 / 3 T i s / 3 0 4 . Hence the Ti:t2g conduction band is partially occupied in LiTi204 and is empty in Li4/3Tis/3Oa [ 2 ]. Thus it is expected that the metalinsulator transition occurs at the intermediate composition. Indeed the metal-insulator transition at a
critical concentration xc~0.1 was reported [ 1 ]. However, the origin of the metal-insulator transition remains unclear, although many experimental studies have been done in connection with the transition [ 1-7 ]. The metallic Lil +xTi2_xO4 undergoes a superconducting transition with the transition temperature Tc ~ 13 K which is almost independent of the composition [ 1,6]. The superconducting fraction determined from the ac magnetic susceptibility measurements reduces to zero at x ~ 0.16 which may be taken as the correct value of xc [ 6 ]. The occurrence of the local moments which complicates the superconducting properties and the metal-insulator transition has been pointed out from the magnetic and ESR measurements. Three types of the Ti 3+ local moments on the octahedral sites are considered from the ESR experiments [4 ]. Also a part of the magnetic susceptibility which obeys the Curie-Weiss law supports the presence of the local moments [ 1,4]. The remaining, almost temperature independent, magnetic susceptibility indicates the Pauli para-
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
66
M. Itoh et al. / ZLi NMR in L t+xTi 2_x04 spinel compounds
magnetism of the conduction electrons with the Stoner enhancement. From the specific heat experiments, LiTi204 is considered to be a d-band superconductor described by the BCS theory [3 ]. In order to investigate the microscopically magnetic properties of the electron spins in the metallic phase of the Li~+xTi2_xO4 spinel compounds, 7Li N M R experiments have been performed. We believe that the clarification of those in the metallic phase is important at first to understand the superconducting and the metal-insulator transitions. In this paper the origin of the observed 7Li N M R signals is discussed on the basis of the partial occupation of the Li ions on the octahedral sites, and from the 7Li N M R in the superconducting state the field penetration depth is estimated. Moreover, the process of the 7Li nuclear relaxation which yields the information of the low-lying excitation of the electron spins is discussed.
2. Experimental procedure Powdered samples used in the present experiment ( x ~ 0.125 ) were prepared by the solid state reaction of lithium carbonate (4N), titanium dioxide (4N) and titanium metal (3N) [ 8 ]. N M R experiments were performed by using a standard coherent pulsed spectrometer. Spin-echo spectra in the superconducting state were obtained by measuring spin-echo amplitude point by point of the external field. The nuclear spin-lattice relaxation time TI w a s measured by observing the recovery of spin-echo or free induction-decay amplitude after the saturation of the nuclear magnetization by a comb of rf pulses.
3. Experimental results and discussion 3. I. 7Li N M R in the normal state In the normal state of all the samples, we have observed 7Li free induction-decay ( F I D ) signals with small Knight shift ( K < 0.005%) which was found to be almost independent of temperature. In fig. 1 the fractional change of the FID amplitude I ( x ) per unit mole of Li atoms is shown as a function of x. Here, we have determined I ( x ) by extrapolating the time
I 1
0
Lil,.~Ti2_xO,' 300 K
I 0.l
0.05
"""'+, 0.15
X Fig. 1. Composition dependence of the 7Li free induction-decay amplitude in Li~ +xTi2_~O4 at 300 K. The solid curve represents the calculated one on the basis of a model of the loss of the 7Li N M R due to the introduction of the Li ions to the octahedral sites (see the text). The dashed and the dotted curves are the ratio of the tetrahedral sites to the total Li sites and the superconducting volume fraction (see ref. [ 6 ] ), respectively.
spectrum of the 7Li FID signal to t = 0. The decrease of l ( x ) with increasing x means the increase of the Li sites that cannot contribute to the FID signal. As is mentioned in the introduction, Li ions substitute Ti ions on the octahedral sites in the x ~ 0 samples. Therefore we must determine what Li sites contribute to the observed 7Li N M R signal. The partial loss of the 7Li N M R signals with increasing x is not simply explained, although it is clear that the loss connects with the substitution of the Ti ions by the Li ions which may influence the electric properties of the neighboring Li ions. As references, we shall consider two curves shown in fig. 1. The dashed curve is the ratio of the tetrahedral sites to the total Li sites, and corresponds to the case of no observation of the signals from the Li nuclei on the octahedral sites. The dotted curve is the superconducting volume fraction f~(x) determined by the ac susceptibility [6]. The substitution of the Ti ions by the Li ions on the octahedral sites cuts the conducting path. In this case we see only the Li sites in the infinite conducting cluster which is responsible for the bulk superconductivity. Taking account of two cases mentioned above, we made up a model that the N M R signals from the Li nuclei on the tetrahedral sites nearest neighbor to the Li ions on the octahedral sites are wiped out as well as those on the octahedral sites. The result is shown by the solid curve in fig. 1. Qual-
M. Itoh et al. / 7Li NMR in L t+xTi e_x04 spinel compounds
itatively speaking, the solid curve agrees with the experimental results. Hence we may conclude that the observed signal comes from the Li nuclei on the tetrahedral sites far from the Li ions on the octahedral sites, although the physical reason of the loss of the signal is not clear. It should be noted that we observe Li NMR signals from the Li sites mentioned above in the finite conducting clusters as well as in the infinite cluster. Here we shall refer the chemical inhomogeneity of these spinel compounds. If there exists a spinodal decomposition into the Li-poor phases approaching LiTi204 and the Li-rich phases approaching Li4/3Tis/304 in Lil+xTiE_xO4 [6], the decrease of I ( x ) with increasing x should be explained by the composition dependence of the superconducting volume fraction. Hence we consider these metallic spinel compounds as the chemically homogeneous bulk superconductors. This is supported by the fact that the upper critical field shows the composition dependence [8 ]. 3.2. ZLi N M R in the superconducting state
In the superconducting state, we have observed 7Li spin-echo spectra with the inhomogeneous broadening due to the field penetration. Figure 2 shows the temperature dependence of the field-swept 7 L i spin-echo spectrum in LiTi204 taken at 13.00 MHz. With decreasing temperature below the superconducting transition temperature under the field Tc(H) ~ 11.5 K, the resonance field for the peak intensity shift is more negative, and the line width increases. LiTi204 is known to be a type II superconductor with the lower critical field Hd ~ 700 Oe and the upper critical field HoE~ 130 kOe [8]. Hence the present external field ~7.9 kOe is between H:, and HoE, where the quantum flux is known to form a triangular lattice. In the mixed state the maxima of the magnetic field occur at the center of the vortices, and the minima do at the center between the adjacent vortices [9 ]. Such local field distribution yields the asymmetric NMR spectrum as just observed in the present experiment. Also the observed field for the peak of the spectrum corresponds to the field at the saddle points of the local field. Figure 3 shows the temperature dependence of the 7 L i spin-echo spectrum in LiLoTTiL9304 taken at 13.00
67
K=0
Lil,xTiz-x O~.
/, ~
"~-.
I
.-
9.OK
ee-
•
.~'/I 1 ""-"~'~
Z80
"~.
I;
I
7.85 7.90 External Field (kOe)
4.2K "~"r-"
7.95
Fig. 2. Temperature dependence of the 7Li spin-echo spectrum in the superconducting state of LiTi204 taken at 13.00 MHz. The dashed line represents the field where the Knight shift is zero.
K=0'~ '~J/ 1IT'
O
-/
__,.
,
--?.
LIl,xTi 2-x04 X=0.07
°
~. ~..°
10.3 K • 9.OK
t~L
E
! , bJ
iJ' !/ ,/ ........
7.80
I
.....
•
~. ~
4.z K ......
I i I 7.85 7.90 External Field (kOe)
I 795
Fig. 3. Temperature dependence of the 7Li spin-echo spectrum in the superconducting state of LiLo7Til.gaO4 taken at 13.00 MHz. The dashed line represents the field where the Knight shift is zero.
68
M. Itoh et al. / ZLi NMR in L I +xTi2_ xO. spinel compounds
MHz. The behavior of the temperature dependence is similar to that in LiTi204 except the loss of the asymmetric pattern. The observed symmetric spectrum and smaller negative shift indicate deeper penetration of the magnetic field compared with LiTi204. In the intermediate field H~, << H<< H¢2, the second moment AH 2 of the NMR spectrum can be calculated on the basis of the vortex lattice as
I
i
Illll
i-~ 1(~'; -
--
),
•
iI
/
l)
where 00 = hc/2e is the flux quantum, ;Lthe field penetration depth and d the vortex lattice spacing [ 10 ]. The calculated values of 2 from the observed spectra at 4.2 K based on eq. ( 1 ) are plotted in fig. 4. One can easily see that 2 increases with increasing x.
3.3. Temperature dependence of the nuclear relaxation rate 1/TI In order to investigate the dynamical properties of the electron spins, the 7Li nuclear spin-lattice relaxation time T~ has been measured in the temperature range from 4.2 to 300 K at 13.00 MHz. In LiTi204, 1/Tt has the temperature dependence as shown in fig. 5. Above about 20 K, 1/T, obeys the relation as (2)
which is shown by the solid line in fig. 5. Below about 20 K, 1/T~ departs from the above relation, and
600£
400( o~ v
Li~+xTi2-xOt. 4.2K 0.15 X
01.1
I
/ 1~:
I
I
0.15
Fig. 4. Composition dependence of the field penetration depth at 4.2 K in Li~ +xTi2_xO4 calculated from the observed 7Li spin-echo spectra.
i
i
I
i l l l l
I
.;/ /
/
Lil+NTiz-xOt' IX3=~IHz
I
,11 , , , l l
,
t I,,,,I
10
i
100 Temperature
(K)
t I1,,,I
1000
Fig. 5. Temperature dependence of the 7Li nuclear spin-lattice relaxation rate 1/T~ in LiTi204 taken at 13.00 MHz. The solid line is the best fit of data above 20 K to the relation 1/ ( T~T) = constant. The dashed curve represents the calculated one based on eq. (3).
gradually decreases with decreasing temperature. In the normal state the magnetic susceptibility due to the conduction electrons, which is almost independent of temperature, indicates Pauli paramagnetism of the conduction electrons [ 1,4]. Hence, the observed temperature dependence of 1IT, above about 20 K is considered to be determined by the Korringa process of the conduction electrons. The specific heat measurements established LiTi204 as a d-band superconductor described by the BCS theory [ 3 ]. In usual BCS superconductors, 1/ T~ is enhanced just below the superconducting transition temperature T¢ by a piling up of the density of states at the gap edges and the coherent factor, and obeys the relation as
1/TI ocexp(-d)/kBT)
06
L ~,111
I
/
(
I/(T,T)=(5.6+O.3)×lO-4(s-'K-~) ,
;/
ee
= {1 + ( 2 ~ . / d ) 2} -~/2q~o/()~2416~; 3 ) 00/(~2~
I
(T<
(3)
where the energy gap 2A=3.5kBT~ and kB is the Boltzmann constant [ 11 ]. Although the behaviour of the temperature dependence of 1/T~ under the field is modified, the low field has a relatively small effect onto 1/(Tl T). The dashed curve shows the temperature dependence of 1/T] calculated on the basis of eq. (3). The agreement between the calculated curve and the experimental results is not satisfactory. We believe that 1/T1 at low temperatures is determined by another process mentioned below. In Li, ÷xTi2_xO4 ( x ~ 0 ) we must note the form of the decay of the nuclear magnetization. The decay at
M. Itoh et al. I ZLi NMR in Lt+xTi2_xO4 spinel compounds Lil,xTiz..xO4 (x =0.07) 1.0
I
4.2 K
i
i
I
IIIII
I
69
I
I
I
I Illl
\
~
o~
I
I
Illll
I
• O00 • •
0.1
10-1
• •
'o
oooo ~° //
/i
,° •
21
I
//t
% °%
~E
0.0
I
260 K
//
/
//
42
t ~s4ec)
48
162
Fig. 6. The decay of the 7Li nuclear magnetization at 4.2 K (left) and 260 K (right) in Lim.ovTiL9304.
high and low temperatures is different as shown in fig. 6 where the data at 4.2 and 260 K in Lim.o7Til.930 4 are given. At 260 K the decay is expressed by a single exponential function, while that at 4.2 K is not. The change of the form of the decay of the nuclear magnetization mentioned above occurs at about 120 K. As is mentioned in the Introduction, the presence of the local moments in these ternary compounds is certain. If magnetic relaxation centers exist, the decay is expected to have multi-relaxation components. Assuming the interaction between the magnetic relaxation centers with the low concentration and the nucleus in concern is a dipole-like one, it is known that the long-time decay at sufficient time after a comb of the rf pulses can be expressed as {Mo - M ( t ) } / M o = e x p { - (t/Tl)'}
(4)
with n=0.5, where Mo and M(t) are the nuclear magnetizations in thermal equilibrium and at time t after the saturation of a comb of rf pulses, respectively [ 12 ]. It should be noted that the function of eq. (4) involves the decay expressed by a single-exponential function in the case of n = 1. Thus we apply eq. (4) to the observed decay. Figure 7 shows the temperature dependence of 1/TI determined by fitting the experimental results of the long-time decay to eq. (4) with T~ and n as parameters. 1/T1 decreases linearly with temperature from 300 K to about 120 K. Below about 120 K 1/T~ increases gradually with decreasing temperature. The changes of 1/T~ and the decay observed at about 120 K indicates that the relative importance of the two relaxation processes, the Korringa process and one due to the magnetic relaxation centers, changes at this
Lil,xTiz-x04
x=0.07 13 MHz
16
I
I
i I IIIII
1
I
I
IIIIII
I0 I0() Temperature (K)
I
I
I I Illll
I(3(3(}
Fig. 7. Temperature dependence of the 7Li nuclear spin-lattice relaxation rate I/T~ in Lil.o7Tit.9304 taken at 13.00 MHz. The dashed line is the best fit of the data above 170 K to the relation, 1/ ( T~T) = constant.
temperature. In the former case, 1/ T~ is expressed as
1~Tin ocA2N(EF)2kBT,
(5)
where A is the coupling constant, and N(EF) the density of states at the Fermi level [ 13 ]. On the other hand, in the latter case, I/T~ is expressed as
1/ Tl ocA 2tle ,
(6)
where t~e is the correlation time of the magnetic relaxation centers [ 13 ]. From the analysis mentioned above it is clear that the nuclear relaxation at high temperatures is considered to be due to the conduction electrons, and that the relaxation at low temperatures is due to the magnetic relaxation centers. The gradual increase of 1/T~ with decreasing temperature below about 120 K is attributed to the temperature dependence of t~. The temperature dependences of 1/Tl in x = 0 , 0.07 and 0.125 samples are summarized in fig. 8. The tendency that 1/7"] at low temperatures increases with increasing x indicates the increase of the number of the relaxation center. In LiTi204 the relaxation rate at low temperatures is so small that it may be determined by the magnetic relaxation centers, not by the conduction electrons, even if the fraction of the magnetic center is small. On the other hand, at high temperatures it should be noted that the nuclear re-
70
M. Itoh et al. / ZLi NMR in L t+xTi 2_xO 4 spinel compounds I
I
I
lllll
I
0.125 + 0.07 o
I
I I llIH
I
I
l I llillJ
+
°%°°°2:,:f: 4"4"+ +-t-
A J
.l AA A
0.0
~
A
16:
1
Ul,xTi2-xOl. 13 MHz
I i lttlll
Fig. 8. Temperature relaxation rate l / T i LiH25Tit.sTsO4 ( + ) calculated one based
I
10
|
I I lilt[
i
I I I IIIIJ
100 Temperoture (K)
1000
dependence of the 7Li nuclear spin-lattice in LiTi204 ( ( A ) , Lit.o7TiL9304 (Q)) and taken at 13.00 MHz. The solid line is the on eq. (2).
laxation due to the conduction electrons is the same in three samples. Since we can easily see from eq. (5) that 1/ ( T~T) is a constant independent of temperature in the temperature region where 1/ T~ is due to the Korringa process, we have fitted the experimental data to the relation 1/ ( T~ T) = constant. The results are shown in fig. 9. The constant, which is linear to (AN(EF)}2, is almost independent of x. Since there is no drastic change of the lattice constant [ 1 ],
0
Lil,xTi2-x04 13 MHz
~2
it is considered that N(EF) is almost independent of the composition in the metallic Lij +xTi2_xO4 spinel compounds. This behavior of N(EF) is consistent with that determined from the electronic specific heat measurements [ 3 ]. As the fraction of the Li ions on the octahedral sites increases, the average charge of the Ti ions increases from 3.5 + in LiTi204 to 4.0+ in L i 4 / 3 T i s / 3 0 4. Then the conduction electron number deduces the Fermi level which lies in the Ti:t2g band in energy. Therefore, qualitatively speaking, this perturbation by the partial occupation of the Li ions on the octahedral sites seems to narrow the t2g band.
4. Conclusion 7Li N M R experimental have been performed to investigate the microscopic properties of the electron spins in the metallic LiTi204 spinel compounds. It has been found that the observed 7Li N M R signal may come from the Li nuclei on the tetrahedral sites far from the Li ions on the octahedral sites. The other signals from the Li nuclei on the octahedral sites and on the neighboring tetrahedral sites may be wiped out. In the superconducting state 7Li spin-echo spectra with the inhomogeneous broadening due to the field penetration have been observed. By calculating the second moments of the spectra we have estimated the penetration depth which increases with increasing x. Two processes have been identified as the 7Li nuclear spin-lattice relaxation rate 1/T1 in the metallic Li~ +xWi2_x04: the Korringa process at high temperatures and the process due to the magnetic relaxation centers at low temperatures. The density of states at the Fermi level deduced by the Korringa process of 1/Tt in the normal state is almost independent of the composition in the metallic phase.
References 0.05
X
0.I
0.15
Fig. 9. Composition dependence of the constant obtained by fitting the data of 1/ Ti in the temperature range where 1/ Tt is determined by the Korringa process to the relation 1/ ( T~ T) = constant.
[ 1 ] D.C. Johnston, J. Low Temp. Phys. 25 (1976) 145. [2] P.P. Edwards, R.G. Egdell, I. Fragala, J.B. Goodenough, M.R. Harrison, A.F. Orchard and E.G. Scott, J. Solid State Chem. 54 (1984) 127. [3] R.W. McCallum, D.C. Johnston, C.A. Luengo and M.B. Maple, J. Low Temp. Phys. 25 (1976) 177.
]14. ltoh et al. / 7Li N M R in L
[ 4 ].M.R. Harrison, P.P. Edwards and J.B. Goodenough, J. Solid State Chem. 54 (1984) 136. [5 ] M.R. Harrison, P.P. Edwards and J.B. Goodenough, J. Solid State Chem. 54 (1984) 426. [6] M.R. Harrison, P.P. Edwards and J.B. Goodenough, Philos. Mag. B 52 (1985) 679. [ 7 ] M. Watanabe, K. Kaneda, H. Takeda and N. Tsuda, J. Phys. Soc. Jpn. 53 (1984) 2437. [8] T. Tanaka, Y. Ueda, K. Kosuge, H. Yasuoka and M. Ishikawa, to be published in J. Solid State Chem.
l +x T i 2_ x O 4 spinel
compounds
71
[9] W. Fite II and A.G. Redfield, Phys. Rev. 15 (1966) 381. [10] P. Pincus, A.C. Gossard, V. Jaccarino and J.H. Wernick, Phys. Lett. 13 (1964) 2 I. [ l l ] D.E. MacLaughlin, Solid State Phys. 31 (1976) I. [ 12] M. Itoh, H. Yasuoka, A.R. King and V. Jaccarino, J. Phys. Soc. Jpn. 55 (1986) 964, and references therein. [13]A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961 ) pp. 358, 380.