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Proton spin-lattice relaxation in iron fluosilicate
Volume 47A, number 2
PHYSICS LETTERS
11 March 1974
PROTON SPIN-LATTICE RELAXATION IN IRON FLUOSILICATE S.M. SKJAEVELAND, I. SVARE Physics Department, Norwegian Institute of Technology, 7034 Trondheim, Norway
and D.P. TUNSTALL Physics Department, University of St. A ndrews, St. Andrews. Scotland Received 10 January 1974 Proton T 1 of FeSiF66H20 is proportional 2~iontoinexp(~/kfl this salt toatbeliquid D = (12.2 helium ± 1.0) temperatures, cm~usingwith E = ~0.54Dcmt — 3E. We find the crystal field splitting of the Fe
The paramagnetic properties of ferrous salts follow from the spin Hamiltonian I
I
I
[mS)
H = ~3H
2—S(S+ 1)73) +E(S~-.S~)
(I)
0gS+D(S
with S = 2 for Fe2~ions. If the crystal field splitting D is positive, the susceptibility x~goes to zero at low temperature T ~ D/k since the only populated state is then the nonmagnetic singlet 0). The electron moments must fluctuate to act as relaxation centers for the nuclear spins. Hence we expect the nuclear relaxation rate in such a salt to go to zero as
1000
-
~ C,~exp(-
~n!kT)
=
~
C~b~
.
100
-
(2)
Here we have assumed so low temperature (all Boltzmann factors b0 ~ 1) that transitions between the excited electron states in) can be neglected. The lowest excited states from (1) and the only ones to contribute to (2) have energies ~ D ±3E. Hence measurements of T1 is a way to determine the crystal field splitting. Our data in fig. 1 for proton relaxation in FeSiF6~6H2Oshow an exponential temperature dependence in the liquid helium range. These measurements were done with standard pulse methods at 16 MHz on single crystals aligned with H0 along the hexagonal z-axis. In this orientation the proton line [1] . 2~ions is not split by magnetic moments on the Fe Our data can be fitted forE = 01with = 11.0 [2] Dand D = cm 1 which agrees with D = 10.9 cm 10.4 cm’ [3] derived from susceptibility measurements. However, mm-wave show that E = to 1 [4] which is notESR negligible compared 0.54 cm
‘-
.
l/T 1
-
//
.
1
4 1 ~
/
0 1 Fig. 1. Proton T1 in FeSiF6’6H20 measured at 16MHz and liquid helium temperatures.
kT, and taking this into account we deriveD = (12.2 ±1.0)cm~,close to the ESR-found value D = 11.8 cm 1 [4] . The susceptibility above helium temperature is little influenced by the magnitude of E, hencewith we conclude D probably slightly increasingthat temperature in decreases FeSiF 6~6H2O. A variation of D with temperature is well known in NiSiF 6 ‘6H2O [51. This way of measuring level splittings of paramagnetic ions similarthe to that we used on copper acetate [6]is where splitting is caused by antiferro121
Volume 47A, number 2
PHYSICS LETTERS
Ii March 1974
magnetic coupling in CuO+ ion pairs. Jeffries and coworkers [7,8] have also demonstrated exp (—gf3H 0/kfl-dependent proton relaxation in Nd/La double nitrates when low temperatures and very high fields were usedvery to align the Nd3~spins.
The correlation time r can give information on the couplings in the electron spin system. Dipolar and
The magnitude of the proton relaxation give information about the fluctuation rate in the electron system. Dipolar interaction nucleus i --~ electron! gives a relaxation rate [9]
= (g2~2/2r~h)(l --3 cos2Oi~)+A k/h . (6) The interaction with other spins will broaden the levels of the pair to give a spin flip probability lIT ~ i’2 w2h/6~ . (7)
(l/T
Here ~w2 is the electron spin resonance second moment which in principle can be calculated with the formulas of McMillan and Opechowski [13], and which
1)q
f
x
2y~sin2O~ COS6~ r~
g
=
(S(0)5~~)exp(~_iwot)dt.
(3)
--
exchange coupling would flips between 5k withgive frequency [1 2] unperturbed spins S~and
ideally goes to zero at low temperature. However, the line width will in practice stay finite because of the
The autocorrelation function ~S~(0)S~(t)) of the ion is determined by the transition probabilities between the ground state [0) and the two mixed states
unavoidable spread 5~in crystalline field splitting between neighbours due to strains and imperfections in the lattice. Knowledge of 5~would allow an esti-
1±)= (sinai ~ 1) ±cosn~ ±1)) due to interaction with other ions or the lattice. The effective moments of
mate from i of the exchange coupling A in FeSiF 6 6H~O. diamagnetically crystals T becomes andInwill eventually be diluted determined by the electronlonger
the states 2+(g ±) with energies = 2]12 ~depend upon the degree D [(3E) given2~3H0) of ± mixing by tan2n = 6E/2g 2~H0[10]. The matrix elements for both transitions are equal, we assume that the excited levels have equal widths, and since spin flips up occur with probabilities b~ times the probability W for the autocorrelation function in down the lowtransitions, temperature lin~itis
2cs—sin2ct)2(b~+b )exp(-- Wt). (4)
spin-lattice relaxation. In this case also we expect exponential temperature dependence of the proton relaxation, and its magnitude will depend upon proton spin diffusion. It is interesting 2~ions to note against that there will he no barrier around the Fe the spin diffusion as long as W 0T ~ I. References
(S(0)S(t)) = (cos Hence
(l/T 1)q
=
2O~cos2O~(cos2cssin2~)2 r~~+b_)
22) g ]3yj- sin
--
r~
(l+w2T2) 0
which for constant correlation time excited states gives (I IT
T =
1/Win the
1) (b.~.+b) as expected. Note that the relaxation rate depends strongly upon the magnitude of (g2j3H0/E) through the n term, and I /T1 is proportional to H~for small fields. In FeSIF6’6H202+ theion, protons r~= 2.7 A away and 0 are . is 38°or 69°when from the nearest Fe H 2O~,g~= 2.00. [11] . Using cos E 0= lIz 0.54 cm~ [4] the , H average sin~O~ 0 = 3760 gauss and neglecting relaxation transitions caused by more distant ions. our relaxation data giver 2.2 X l0~0s assuming ~ I. 122
[1] 12] [3] [4]
DB. Utton, J. Phys. C., Solid St. Phys. 4 (1971) 117. D. Palumbo, Nuovo Cim. 8 (1958) 271. T. Ohtsuka. J. Phys. Soc. Japan 14 (1959) 1245. R.S. Robins and H.R. Fetterman, Bull. Am. Phys. Soc. 16(1971)522. [5] R.P. Penrose and KWH. Stevens, Proc. Phys. Soc. 63A (1950) 29.
16] 1. Svare and D.P. Tunstall. Phys. Lett. 35A (1971)123. [7] Ti. Schmugge and C.D. Jeffries, Phys. Rev. 1 38A (1965) 1785. [81 CD. Jeffries (1968) 499. and T.E. Gunther, J. AppI. Phys. 39 [9] A. A. Abragam Abragam, and Nuclear magnetism (Oxford 1961) p. 380. [101 B. Bleaney, Electron paramagnetic resonance of transition ions (Oxford 1970) p.210. [11] W.C. Hamilton, Acta Cryst. 15 (1962) 353. 1121 A. Abragam, Nuclear magnetism (Oxford 1961) p. 137. 1131 M. McMillan and W. Opechowski, Can. J Phys. 38 (1960) 1168.
PHYSICS LETTERS
11 March 1974
PROTON SPIN-LATTICE RELAXATION IN IRON FLUOSILICATE S.M. SKJAEVELAND, I. SVARE Physics Department, Norwegian Institute of Technology, 7034 Trondheim, Norway
and D.P. TUNSTALL Physics Department, University of St. A ndrews, St. Andrews. Scotland Received 10 January 1974 Proton T 1 of FeSiF66H20 is proportional 2~iontoinexp(~/kfl this salt toatbeliquid D = (12.2 helium ± 1.0) temperatures, cm~usingwith E = ~0.54Dcmt — 3E. We find the crystal field splitting of the Fe
The paramagnetic properties of ferrous salts follow from the spin Hamiltonian I
I
I
[mS)
H = ~3H
2—S(S+ 1)73) +E(S~-.S~)
(I)
0gS+D(S
with S = 2 for Fe2~ions. If the crystal field splitting D is positive, the susceptibility x~goes to zero at low temperature T ~ D/k since the only populated state is then the nonmagnetic singlet 0). The electron moments must fluctuate to act as relaxation centers for the nuclear spins. Hence we expect the nuclear relaxation rate in such a salt to go to zero as
1000
-
~ C,~exp(-
~n!kT)
=
~
C~b~
.
100
-
(2)
Here we have assumed so low temperature (all Boltzmann factors b0 ~ 1) that transitions between the excited electron states in) can be neglected. The lowest excited states from (1) and the only ones to contribute to (2) have energies ~ D ±3E. Hence measurements of T1 is a way to determine the crystal field splitting. Our data in fig. 1 for proton relaxation in FeSiF6~6H2Oshow an exponential temperature dependence in the liquid helium range. These measurements were done with standard pulse methods at 16 MHz on single crystals aligned with H0 along the hexagonal z-axis. In this orientation the proton line [1] . 2~ions is not split by magnetic moments on the Fe Our data can be fitted forE = 01with = 11.0 [2] Dand D = cm 1 which agrees with D = 10.9 cm 10.4 cm’ [3] derived from susceptibility measurements. However, mm-wave show that E = to 1 [4] which is notESR negligible compared 0.54 cm
‘-
.
l/T 1
-
//
.
1
4 1 ~
/
0 1 Fig. 1. Proton T1 in FeSiF6’6H20 measured at 16MHz and liquid helium temperatures.
kT, and taking this into account we deriveD = (12.2 ±1.0)cm~,close to the ESR-found value D = 11.8 cm 1 [4] . The susceptibility above helium temperature is little influenced by the magnitude of E, hencewith we conclude D probably slightly increasingthat temperature in decreases FeSiF 6~6H2O. A variation of D with temperature is well known in NiSiF 6 ‘6H2O [51. This way of measuring level splittings of paramagnetic ions similarthe to that we used on copper acetate [6]is where splitting is caused by antiferro121
Volume 47A, number 2
PHYSICS LETTERS
Ii March 1974
magnetic coupling in CuO+ ion pairs. Jeffries and coworkers [7,8] have also demonstrated exp (—gf3H 0/kfl-dependent proton relaxation in Nd/La double nitrates when low temperatures and very high fields were usedvery to align the Nd3~spins.
The correlation time r can give information on the couplings in the electron spin system. Dipolar and
The magnitude of the proton relaxation give information about the fluctuation rate in the electron system. Dipolar interaction nucleus i --~ electron! gives a relaxation rate [9]
= (g2~2/2r~h)(l --3 cos2Oi~)+A k/h . (6) The interaction with other spins will broaden the levels of the pair to give a spin flip probability lIT ~ i’2 w2h/6~ . (7)
(l/T
Here ~w2 is the electron spin resonance second moment which in principle can be calculated with the formulas of McMillan and Opechowski [13], and which
1)q
f
x
2y~sin2O~ COS6~ r~
g
=
(S(0)5~~)exp(~_iwot)dt.
(3)
--
exchange coupling would flips between 5k withgive frequency [1 2] unperturbed spins S~and
ideally goes to zero at low temperature. However, the line width will in practice stay finite because of the
The autocorrelation function ~S~(0)S~(t)) of the ion is determined by the transition probabilities between the ground state [0) and the two mixed states
unavoidable spread 5~in crystalline field splitting between neighbours due to strains and imperfections in the lattice. Knowledge of 5~would allow an esti-
1±)= (sinai ~ 1) ±cosn~ ±1)) due to interaction with other ions or the lattice. The effective moments of
mate from i of the exchange coupling A in FeSiF 6 6H~O. diamagnetically crystals T becomes andInwill eventually be diluted determined by the electronlonger
the states 2+(g ±) with energies = 2]12 ~depend upon the degree D [(3E) given2~3H0) of ± mixing by tan2n = 6E/2g 2~H0[10]. The matrix elements for both transitions are equal, we assume that the excited levels have equal widths, and since spin flips up occur with probabilities b~ times the probability W for the autocorrelation function in down the lowtransitions, temperature lin~itis
2cs—sin2ct)2(b~+b )exp(-- Wt). (4)
spin-lattice relaxation. In this case also we expect exponential temperature dependence of the proton relaxation, and its magnitude will depend upon proton spin diffusion. It is interesting 2~ions to note against that there will he no barrier around the Fe the spin diffusion as long as W 0T ~ I. References
(S(0)S(t)) = (cos Hence
(l/T 1)q
=
2O~cos2O~(cos2cssin2~)2 r~~+b_)
22) g ]3yj- sin
--
r~
(l+w2T2) 0
which for constant correlation time excited states gives (I IT
T =
1/Win the
1) (b.~.+b) as expected. Note that the relaxation rate depends strongly upon the magnitude of (g2j3H0/E) through the n term, and I /T1 is proportional to H~for small fields. In FeSIF6’6H202+ theion, protons r~= 2.7 A away and 0 are . is 38°or 69°when from the nearest Fe H 2O~,g~= 2.00. [11] . Using cos E 0= lIz 0.54 cm~ [4] the , H average sin~O~ 0 = 3760 gauss and neglecting relaxation transitions caused by more distant ions. our relaxation data giver 2.2 X l0~0s assuming ~ I. 122
[1] 12] [3] [4]
DB. Utton, J. Phys. C., Solid St. Phys. 4 (1971) 117. D. Palumbo, Nuovo Cim. 8 (1958) 271. T. Ohtsuka. J. Phys. Soc. Japan 14 (1959) 1245. R.S. Robins and H.R. Fetterman, Bull. Am. Phys. Soc. 16(1971)522. [5] R.P. Penrose and KWH. Stevens, Proc. Phys. Soc. 63A (1950) 29.
16] 1. Svare and D.P. Tunstall. Phys. Lett. 35A (1971)123. [7] Ti. Schmugge and C.D. Jeffries, Phys. Rev. 1 38A (1965) 1785. [81 CD. Jeffries (1968) 499. and T.E. Gunther, J. AppI. Phys. 39 [9] A. A. Abragam Abragam, and Nuclear magnetism (Oxford 1961) p. 380. [101 B. Bleaney, Electron paramagnetic resonance of transition ions (Oxford 1970) p.210. [11] W.C. Hamilton, Acta Cryst. 15 (1962) 353. 1121 A. Abragam, Nuclear magnetism (Oxford 1961) p. 137. 1131 M. McMillan and W. Opechowski, Can. J Phys. 38 (1960) 1168.