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Nuclear-spin-lattice relaxation of 51V in V-Fe Alloys
PHYSICS
volume 20, number 5
NUCLEAR-SPIN-LATTICE
15 March 1966
LETTERS
RELAXATION
OF
51V
IN V-Fe
ALLOYS*
D.O.VAN OSTENBURG and C.H.SOWERS Argonne National Laboratory,
Argonne,
Illinois
and
J. J. SPOKAS St. Procopius College, Lisle,
Illinois
Received 5 February 1966
The 61~ nuclear T1 has been measured up to V-40 at.8 Fe. The composition dependence of the relaxation rate closely resembles the term linear in temperature in the low temperature specific heat and shows a second peak near 34 at.% Fe.
The nuclear-spin-lattice relaxation time 2’1 is one of the important parameters with which to study the electronic structure of transition metals and their alloys as the relaxation rate (TIT)-1 is directly related to the character of the electron wave functions, density of electronic states, etc. Alloys were prepared by arc melting requisite amounts of electrolytic vanadium and Puron iron in an argon-helium atmosphere, heat treated for 168 hr and water quenched. All specimens were filed and some annealed for approximately 0.5 hr at 900°C. Tl’s of 51V nuclei in V-Fe alloys containing up to 40 at.% Fe were made at temperatures of 3000 and 77OK. Measurements were made at 12 Mc/sec by means of a phase coherent pulsed nmr spectrometer. Tl’s in samples containing less than 30 at.% Fe were made by a 1800, 90° sequence measuring the amplitude of the Bloch decay following the 90° pulse versus pulse spacing. Those of greater Fe content were studied via a 180°, 90° -30° sequence and the amplitude of the ensuing echo studied versus the spacing between the 180° and 90° -30° pulses. The data are shown in fig. 1 along with a plot of Y(-nd(EF)) term linear in Tin the low temperature specific heat [l]. The abscissa is in electron-atom ratio e/a (determined from the number of electrons outside the 3p shell). Measurements of Tl’s in V-Fe up to - 25 at. % Fe have been made by Masuda et al. [2] at 4.2oK and agree quite well with the current work although the on* Work performed under the auspices of the US Atomic Energy Commission.
-e-
77 ‘K
- 18
3J Il-
k-
-4 O.SOb 5.0
I 6.0
7.0
% Fig. 1. The 51V nuclear-spin-lattice relaxation time (2’1) and the low temperature specific heat coefficient &) as a function of electron : atom ratio (e/a).
set of magnetic moments at these temperatures precluded the measurements at higher Fe content, At 300°K the annealed samples consistently gave a relaxation rate - fi lower than the unannealed. The 38 and 40 at.% Fe specimens exhibited a distribution of Tl’s which is likely founded in variat,on in composition over the specimen. It is noted that at these iron concentrations the magnetic susceptibility is large and changing rapidly with composition [3]. The points on fig. 1 are weighted averages. 461
Volume
20, number
5
PHYSICS
In this system it is believed [4] that the predominant contribution to the relaxation rate is the orbital term. The s electrons are assumed to contribute approximately 0.04 (secoK)-l to the relaxation rate [4] and the sum of the two for a paramagnetic substance is (TlT)-l
= 6.04 (sec’K)-’ + +648E&
+ P2 ( Y-~);
$!j (EF) F(r),
where (re3)F is the average of the d-electron radii over the Fermi surface, tid(EF) is the ddensity of states at the Fermi surface, F(I) a function which depends upon the details of the d-wave functions and the rest of the quantities have their usual meaning. Obata [5] was the first to calculate this expression for the orbital relaxation rate for paramagnetic metals. In orbital relaxation the electrons interact with the nuclear spins without changing their own spins. Therefore, in ferromagnetic metals the orbital relaxation rate can be expressed as a sum of two terms each for a specific direction of electron spin. Using the calculation made by Moriya [6] the rate becomes -3 2 ) F x (~12’)~~ = 0.64 (sec’K)-’ + 316nB, p2(r
x { ndf(-%d +ndy(EF) } F(r)/K(U) where m& (EF) andndt !EF) are the d-density of states of down and up spin density respectively, K(u) = o2 + (1 -o)~ and c =ndl (EF)/2fid(EF)* The V-Fe alloy system is paramagnetic below - 20 at. % Fe. As the Fe content increases magnetic moments begin to appear around 22 at. 70 Fe [3] and ferromagnetic alignment begins to occur at low temperatures at compositions near 28 at.% Fe [7]. The striking feature of fig. 1 is that the composition dependence of the square root of the relaxation rate appears to be governed
*****
462
LETTERS
15 March
1966
strongly by the composition dependence of the d-density of electron states at the Fermi surface and not to changes in symmetry with composition which would change the relative weight of the I5 and I3 orbitals at the Fermi surface. As the temperature is lowered, above 25 at.% Fe (e/u = 5.75), the relaxation rate deviates from its Tl T= const. behavior. This may result from the separation of the spin up band relative to the spin down band as the onset of ferromagnetic alignment takes place. It is also possible that the moments contribute an additional relaxation path which increases the relaxation rate. The important observation of this study is that the relaxation data seem to show a peak near 34 at.% Fe (e/a = 6) in the d-density of states in the first long transition series. Low temperature specific heat measurements [l] also show a peak near this composition. Currently, the very broad lines, e.g., - 200 Oe at half maximum in the 30 at.% Fe sample at ‘77OK are under study using different pulse sequences and the method of echo amplitude versus magnetic field with the goal of separating the magnetic from the quadrupole interactions contributing to the line width.
References C.T.WeiandP.A.Beck, Phys. Rev. 1. C.H.Cheng, 120 (1960) 426. 2. Y. Masuda and K. Okamura, J. Phys . Sot . Japan 19 (1964) 1249. 3. D.J.Lam, D.O.VanOstenburg, M.V.Nevitt, H.D. Trapp andD.W.Pracht, Phys. Rev. 131 (1963) 1428. 4. D. 0. Van Ostenburg, J. J.Spokas and D. J. Lam, Phys. Rev. 139 (1965) A173. 5. Y.Obata, J. Phvs. Sot. Jaaan 18 09631 1020. J. Phys. Sot. Japan 19 ‘(1964) 681. 6. T.Moriya, and A. T. Aldred, J. Appl. Phys. 34 7. M.V.Nevitt (1963) 463.
volume 20, number 5
NUCLEAR-SPIN-LATTICE
15 March 1966
LETTERS
RELAXATION
OF
51V
IN V-Fe
ALLOYS*
D.O.VAN OSTENBURG and C.H.SOWERS Argonne National Laboratory,
Argonne,
Illinois
and
J. J. SPOKAS St. Procopius College, Lisle,
Illinois
Received 5 February 1966
The 61~ nuclear T1 has been measured up to V-40 at.8 Fe. The composition dependence of the relaxation rate closely resembles the term linear in temperature in the low temperature specific heat and shows a second peak near 34 at.% Fe.
The nuclear-spin-lattice relaxation time 2’1 is one of the important parameters with which to study the electronic structure of transition metals and their alloys as the relaxation rate (TIT)-1 is directly related to the character of the electron wave functions, density of electronic states, etc. Alloys were prepared by arc melting requisite amounts of electrolytic vanadium and Puron iron in an argon-helium atmosphere, heat treated for 168 hr and water quenched. All specimens were filed and some annealed for approximately 0.5 hr at 900°C. Tl’s of 51V nuclei in V-Fe alloys containing up to 40 at.% Fe were made at temperatures of 3000 and 77OK. Measurements were made at 12 Mc/sec by means of a phase coherent pulsed nmr spectrometer. Tl’s in samples containing less than 30 at.% Fe were made by a 1800, 90° sequence measuring the amplitude of the Bloch decay following the 90° pulse versus pulse spacing. Those of greater Fe content were studied via a 180°, 90° -30° sequence and the amplitude of the ensuing echo studied versus the spacing between the 180° and 90° -30° pulses. The data are shown in fig. 1 along with a plot of Y(-nd(EF)) term linear in Tin the low temperature specific heat [l]. The abscissa is in electron-atom ratio e/a (determined from the number of electrons outside the 3p shell). Measurements of Tl’s in V-Fe up to - 25 at. % Fe have been made by Masuda et al. [2] at 4.2oK and agree quite well with the current work although the on* Work performed under the auspices of the US Atomic Energy Commission.
-e-
77 ‘K
- 18
3J Il-
k-
-4 O.SOb 5.0
I 6.0
7.0
% Fig. 1. The 51V nuclear-spin-lattice relaxation time (2’1) and the low temperature specific heat coefficient &) as a function of electron : atom ratio (e/a).
set of magnetic moments at these temperatures precluded the measurements at higher Fe content, At 300°K the annealed samples consistently gave a relaxation rate - fi lower than the unannealed. The 38 and 40 at.% Fe specimens exhibited a distribution of Tl’s which is likely founded in variat,on in composition over the specimen. It is noted that at these iron concentrations the magnetic susceptibility is large and changing rapidly with composition [3]. The points on fig. 1 are weighted averages. 461
Volume
20, number
5
PHYSICS
In this system it is believed [4] that the predominant contribution to the relaxation rate is the orbital term. The s electrons are assumed to contribute approximately 0.04 (secoK)-l to the relaxation rate [4] and the sum of the two for a paramagnetic substance is (TlT)-l
= 6.04 (sec’K)-’ + +648E&
+ P2 ( Y-~);
$!j (EF) F(r),
where (re3)F is the average of the d-electron radii over the Fermi surface, tid(EF) is the ddensity of states at the Fermi surface, F(I) a function which depends upon the details of the d-wave functions and the rest of the quantities have their usual meaning. Obata [5] was the first to calculate this expression for the orbital relaxation rate for paramagnetic metals. In orbital relaxation the electrons interact with the nuclear spins without changing their own spins. Therefore, in ferromagnetic metals the orbital relaxation rate can be expressed as a sum of two terms each for a specific direction of electron spin. Using the calculation made by Moriya [6] the rate becomes -3 2 ) F x (~12’)~~ = 0.64 (sec’K)-’ + 316nB, p2(r
x { ndf(-%d +ndy(EF) } F(r)/K(U) where m& (EF) andndt !EF) are the d-density of states of down and up spin density respectively, K(u) = o2 + (1 -o)~ and c =ndl (EF)/2fid(EF)* The V-Fe alloy system is paramagnetic below - 20 at. % Fe. As the Fe content increases magnetic moments begin to appear around 22 at. 70 Fe [3] and ferromagnetic alignment begins to occur at low temperatures at compositions near 28 at.% Fe [7]. The striking feature of fig. 1 is that the composition dependence of the square root of the relaxation rate appears to be governed
*****
462
LETTERS
15 March
1966
strongly by the composition dependence of the d-density of electron states at the Fermi surface and not to changes in symmetry with composition which would change the relative weight of the I5 and I3 orbitals at the Fermi surface. As the temperature is lowered, above 25 at.% Fe (e/u = 5.75), the relaxation rate deviates from its Tl T= const. behavior. This may result from the separation of the spin up band relative to the spin down band as the onset of ferromagnetic alignment takes place. It is also possible that the moments contribute an additional relaxation path which increases the relaxation rate. The important observation of this study is that the relaxation data seem to show a peak near 34 at.% Fe (e/a = 6) in the d-density of states in the first long transition series. Low temperature specific heat measurements [l] also show a peak near this composition. Currently, the very broad lines, e.g., - 200 Oe at half maximum in the 30 at.% Fe sample at ‘77OK are under study using different pulse sequences and the method of echo amplitude versus magnetic field with the goal of separating the magnetic from the quadrupole interactions contributing to the line width.
References C.T.WeiandP.A.Beck, Phys. Rev. 1. C.H.Cheng, 120 (1960) 426. 2. Y. Masuda and K. Okamura, J. Phys . Sot . Japan 19 (1964) 1249. 3. D.J.Lam, D.O.VanOstenburg, M.V.Nevitt, H.D. Trapp andD.W.Pracht, Phys. Rev. 131 (1963) 1428. 4. D. 0. Van Ostenburg, J. J.Spokas and D. J. Lam, Phys. Rev. 139 (1965) A173. 5. Y.Obata, J. Phvs. Sot. Jaaan 18 09631 1020. J. Phys. Sot. Japan 19 ‘(1964) 681. 6. T.Moriya, and A. T. Aldred, J. Appl. Phys. 34 7. M.V.Nevitt (1963) 463.