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Study of the coercive force in ferromagnetic dysprosium metal by RF field enhancement
Jcurrtal of Magneti,am and Magnetic Materials 1 11976) 2 2 6 - 2 3 0 © North-Holland P~.ablishingCompany
S T U D Y OF THE COERCIVE FORCE IN FERROMAGNETIC DYSPROSKUM METAL ~ Y R F FIELD EN~ANCEMENI' * J. BARAK ** and Y. BERTH1ER Laberatoire de Spectrometric Physique af, Universite Scientifique et Medicale de Grenoble, B,P. 53, Centre de Tri! 38041 Grcn,3i~le-Cedex. France Received 2 .l!uly 1975 l'he RF field enhancement factor rl is calculated for the domains and domain walls of ferromagnetic D~ metal In the domains ~ ": 30. while in the walls it depends on "abe coercive force which limits the wall motion. The stud) of r/from spin echo signals of nuclei in the walls is used to determine this coercive force in powder of Dysprosium metal, 1,efore and after annealing.
I. Introduction
The origin of the NMR lines in ferromagnets which h.~:e mobile domain walls, was discussed by Butler [1 ] and the case of BrCr 3, including the enhancement of the linea, which originate in the center and the edges ~f ~he wide domain walls, was thoroughly examined ~ Cobb e~ M. [2]. In ferromagnetic rare earth metals a:Id alloys zhe magnelocrystailine aniso~ropy is often ot" the order of magnitude of the exchm:ge interaction. "[his results in very ~hkt domain walls [3-7] with an energy barrier wlhich limits the motion of all the walls ~.nd gives rise to an intrinsic coercive force. Furthermore, these walls may !be pqmed by imperfections like point defects [8] or dislocations. All this gives vise to a coerc:xe force H c. At the same time the screening of a small external field b) the motion of the walls is not efficient aad the RF field, used in NMR experiments, penetrates inio the domains, lit is thus interesting to compare be'....... ....... n ~he ,-,v t~t: ~mu ,-:..,_~ennancement _ , in the walls and in the d~mains in order to determine the origin ofthe NMR siglq~l of rare ear:h nuclei in ferromagnets and to find a r~ew mean to measure ,H. This is done in section 2
X~t:rk supported in part by OGRST, central n ° 71.7.28000. Present adress: Physics Department, UCSB, Santa Barbara, (~ 'dfor r aa 93106, I ,~'5~J;a~oirc associe au C.N.R.S.
and 3 for the Dysprosium metal. The experimental results are described in sec. 4. and corot ared in sec. 5 with the theory.
2. RF field enhancement in the domains
For the hexagonal structure of Dy metal with the easy axis in the x di, ection, the Hamiltonian of the system is [9]
i.j
i
-- ½ r~6 [(Jix + iJiy )6
+ (Jix--iJo,)6l +gjuBgi'H}
(i)
where ~i/is the exchange constant between spins J. and ¢/" ~2 gives the axial anisotropy in the c directien,/~6 represents thLesixfold anisotropy in the basat plane and v; is an external magnetic field standing i~ere for the RF fi,'.ld. For a small deviation of all the Sl,~ns from the x direction, described by the angle ¢ in the ba~al plane, and by the angle 0 out of the plane, equation (1) becomes for each of the parallel spins
J. Barak, Y. Berthier/Study o f the coercive force
~1 = _ K2 sin20 + K 6 cos6~ + C cos2# + la(Hx cosq~ +
Hy sin0 + H z sin0) + constant,
(2)
where C cos2¢ is added for the magnetoelastic energy [9], K~6 -= _ ~ j 6 , K2 -_ p~2J2 and U ---gJ~% is the 135,3+ local spin. Minimizing (2) with respect to ~ gives
(3)
=/.tHy/(36K~6 + 4C).
When applying an external alternating RF field//(co), ~band consequently the direction of the hyperfine field H n are modulated at the frequency w. This induces an
RF field OH n on the nuclei. The enhancement factor for this process is ~7), = P/-/n/(36K66 + 4C).
(4)
For K 6 = - 2 . 4 K/atom [10], C = 2 K/atom [9] , J = 15/2,g I = 4/3 a n d H n "" 6 MOe, this gives rTy = 30. There is no enhancement in the x direction, rtx = O. Similar calculations for 0, using K 2 = - 154 K [10], give 77z = 15.
3. RF field enhancement in the walls The simplest and most probable domain wall in Dysprosium metal is a 180 ° wall [5,11 ], perpendicular to the hexagonal c axis as represented in fig. 1. The spins at the wall edges are parallel or antiparallel to the x axis. Egami and Graham [5] calculated the structure and the energy of this wall. They found that the wall
/
/ I I
........ Fl<'-'I
/
/
/
/
/ / ,p / /
Y
Fig. 1. A row of spins showing the direction of spins in the 180 ° wall.
is n "" 7 atom with a period constant. For rium state, in energy of the
227
layers wide and the energy is periodic X = Co/2, where c o is the c axis httice a wall displacement z out of the equiliba direction perpendicular to this wall, the waft varies sinusoidaL~y
E I = Elo + AE sin2(21rZ/Co ),
(5)
where AE is the energy barrier and E ! is given for a row of spins in the wall like that in fig. 1. The magnetic mement of this row is/'/1 - (2/1r) r/p and lies alon~ the y axis. Under external field, the equiliibrium state is defined by the following equation (Pl X H)z = aEll5# = (~Et/6z)(dz/d~)
(6)
where (Pl x H)z is the z componeni of the extero.al torque. According to Egami and Giaham [5] for most nuclei in the wall we might take 2~r[(nCO) as the mean value of d~/dz, thus lattx = ~ 7r A E sin(41rz/c O)
(7)
for most parts of the wall (and a splitting of the line like in CrBr 3 [2] is not expected). Taking/-/c as the field needed to pass the higher torque point at z = r c0/8:/zH e = n A E / 2 , we obtain/-/x =/'/c sin(47rZ/Co)" For H x "¢ H e, z is small. Th:.- average departure of the spins from the directions for H = O, in an angle AO is found by multiplying this z value, by dq~/dz, rhe resulting enhancement is then 77x = Hn/(ZnH c).
(8)
Since H.. and H z induce , o torque which might move the wal~ r/,, and 77z in the walls are th,,i same as r/v and r/z in the "aomains. Egami and Graham [5] found that for Dy metal at OK, H c = 1 kOe. This value was confirmed experimentally for a single cry:aal, at high sweep rate, dH[dt > 10 40e/sec9[l 2 ] 1 0 (ehich is compatible with our RF field, dH/dt ~ Oe/se z)./-/c does not change much in the 0 - 10 K range. For this H_c (8) gives 77x = 500 and on average in the wails, o - 200. In a hypothetical Dy metaT domain wall with no coercive force, the enhancement would be much higher due to the high hyperfine field and narrow walls. 77 is then given by rl = d "Hn/DM " dc~/dz
(9)
where d is the domain width, with an average value of I/am [1 1 ] and DM is the demagnetization field, with an average value of 10 kOe, for the different particuie shapes in the powder. This leads to r/~" 106.
J. Barak, Y. Berthier/Study o f the coercive f o r ~
228
For such a high value of r/it is interesting to estimate how far the NMR frequencies are below the spin-wave fl equencies and to find if the NMR is decoupled from the normal modes of the electronic spins. The excited state ef the wall in which it oscillates parallel to itself ar.und the minimum energy plane is the k = 0 spin ~x~a~esmode of the walls. The energy of this mode was calculated by Winter [ l ? ] . He represents the stiffness of the wall by a term K (A¢) 2 ZaJ2v , where Jiy is the y direction spin component of the iith spin in a row of ~he w~all. In order to fred K' for the present case, (5) is ~witten for a small departure A~b of the angles of the spins fiom equilibrium
' ' '
' '"
I
'
i
'
i
"
A (N.A.S)
:tw=250
A
:tw:
o
(A.S.)
500
:t.=250
2
i"'~
I
.sec. nsec. nsec. ec.
"
i
1I " T I
L.-'~--~---~.__
/il
~ --'~*-~"
2p.Hc n2
El = Elo +
?T
(A~b)2.
(10)
This is taken as the above additional anisotropy term of the spins in the walls in Winter's model. For the row of spins V.J~z z,, -~ M2/2, thus K' = 4nM-Ic/(Trj2). The uniform mode energy is then given by [ 13]
tw0 = (81rK'btMs)l/2
= 4gfla B( 2Mtc Ms )1/2
= 4gfldSOlsHn/r~)l/2
(11)
For Dy metal, g j = 4/.~, " tl "" 7, I f c = 1 kOe and M s = 3 kOe. Tl~s gives v0 :- 50 GHz, a value 10 times smaller tharl the energy gap ,1 of the spin waves in the bulk, where .X = 24 K [9]. For reasonable values of mtI or C r/, v0 stays well above the NMR frequencies which are in the, range 300-2000 MHz in Dy metal [14], thus the D.C field susceptibility, considered in deriving (7) is relevant also for NMR frequencies.
4. Experimental results The experiments were carried out on a powder sample of ~ 50/~m particles of 99.9% Dysprosium from LEICO ;,~,,o,~;~¢ l-~. 77was t-tCtClIIIIIICU ,~. . . . . . "-^'~ by l l l t : U 3 U l i l l ~ tile aniplitude of the spin echo of 163Dy as a function of the RF field H l . This determination has been done for two values of zhe pulse width t w in a sequence (tw,l",2tw...). The value of H~ is calculated from the RF power, the measured Q of the sample loaded cavity and from the geometry of the cavity. The measurements were made witl~, sample, once after grinding, and then after annealing it in vacuum during 60 hours a[ 550 ° C. The . . . . . . . . . . . . . . . .
0 L--.--.~--L--...~~___I_ 0
1
2 RF
field
3
4
(Oe)
Fig. 2. Echo amplitude of t63Dy in Dy metal (11{,3 MHz '.ine) at 1.4 K, versus RF field for two values of t w, in tlhe non annealed sample (NAS) and in the annealed sample (AS).
results at 1.4 K for the 1163 MHz line are given in fig. 2. These are typical spin echo results in domain walls of ferromagnets, with dis;ribution ol the values of 77 [15] The maximum enhancement value is calculated using 1633, r/H i t w = 1, for the top amplitude point. With 1633, = 160 Hz/Oe, 77 is found to be 2.5 x 103 for the non annealed sample and 2 x 104 for the annealed one. The high r~ values confirm that the origin of the NMR signal is in the domain walls. Since the NMR linewidth (~ 3MHz) is of the order of 1/t w, the shorter the t w and the higher the HI, the more nuclei participate in the echo and its amplitude is higher as demonstrated. The value of r/is not sensitive to temperature between 1.4 K and 20 K, but application and then removal of an external magnetic field H 0 = 30 kOe, on a non annealed sample raises the value of rl. The amplil:ude of the echo as a function of external field H 0 is given in fig. 3. It shows a reduction in the number of walls when H 0 increases. This effect is typical for NMR from nuclei in domain walls and confirms the origin of the signal in our two samples.
J. Bamk. Y. Berthier/Study o f the coercive .force
'
I
'
D y 163 in
I
'
I
Dy metal
9(
, U uJ
,
0
I 10
i
l
20 External Field (kOe)
,
I
30
Fig. 3. External field dependence of the echo amplitude of t63Dy in Dy metal (1163 MHz line) at 1.4 K in the non annealed sample.
5. D i s c u s s i o n
Since the spin echo signals originate in the domain walls, we would like to calculate the coercive force which corresponds to the measured 77. By (8), with n -~ 7, we get H c = 200 Oe (r/= 2.5 x 10~) and H c = 20 Oe (77 -- 2 x 104) in the nonannealed and annealed samples respectively. The change of H c is attributed to pinning by imperfections which are partly removed by the annealing. The similar though smaller effect obtained by application of high external magnetic field (H 0 >>Hc) on a non annealed sample is also attributed to the removing of the walls from the trapping area of dislocations. H c in the annealed sample (20 Oe) is much lower than the 1 kOe value of Egami and Graham (which gives r/= 500, see sec. 3). It seems, thus, that the walls in the pure crystal are more mobile than thought before, perhaps due to the action of the non-flat displacements, suggested by Van der Brock and Lyistra . . . . . . . rt'+l. A, In this motion, only a strip of the wall moves with a much lower energy barrier, r/is then greater, but fewer nuclei are affected. The highH c measured by Egami [12] may results from imperfections. So,~e mechanisms 0y whlLch the imperfections may highly influence the energy of narrow domain walls were recently reported. Craik and Hill [16] have shown that a small weakening of the magnetocrystalline anilso-
229
tropy or the exchange coupling, between two neighbouring layers of spins in the walls, can result in very steep energy gradients which pin the walr..s and give ri~ to high coercive force. Since both the anisotropy and the exchange interactions are sensitive to lattice imper. fections, this might be the process by which the dislocations trap the narrow domain walls. An othew mechanism, by which the existence of point defects may result in high H c is proposed by KronmuUer and hilzinger [81. Preliminary experiments with Dy nuclei in annealed ferromagnetic DyAI 2 powder show r/values much lower than in Dy metal. The measured r~ -~ 700 indicates high nH c. We find n H c = 5 x 103 Oe in this sample compated to nH c = 175 Oe in annealed Dy metal. Similarly one might estimate the value of r/using the known/-/c and estimated n. In DY3AI2, n = 1 and H c -~ 25 kOe at liquid helium temperature [3]. From (8), r/= 140 and long high power pulses are needed in order to obtain a spin echo signal. Since for equal total area of walls and good pulses conditions, the signal will be propostional to r?n or, from (8), to 1/H c, the amplitude of the echo in these materials is expected to be very weak.
6. Conclusion The RF field enhancement factor was calculated tbr the domains and the domain walls ill Dy metal and compared with the enhancement measured by NMR spin echo signals. The NMR is shown to come from thc wafts where the enhancement depends on the mubility of the walls. Thus the measurement of the enhancement factor gives a useful intormation on the coercive force which limits the motion of these walls. We would like to thank Dr. P. Averbuch and Dr. B Barbara for helpfull remarks. We are also grateful to Mr. R. Gamond for his skilful technical aid.
References [1] M.A. Butler, J. Phys. Soc. Japan 34 (1973) 1419. [2] C.H. Cobb, V. Jaccarino, M.A. Butler, J.P. Remeika and tt. Yasuoka, Phys. Rev. B7 (1973) 307. [3] B. Barbara, C. Becle, R. Lemaire and D. Paccard, J. de Phys. 32 (1971) C1 299. [4] J.J. van der Broek and H. Zyl~tra, IEEE. Trans. On Magn.. Mag. 7 (197l) 226.
230
l,Sl I'TI
191 llOl
r, Barak, Y. Berthier/Study of the coercilTe force "I', l~lmi an,,l C.D. Graham Jr., J. Appl. Phys. 42 (1971) 1299, lt,R. Hiizinger and H. Kronmuller, Phys, Sta. Sol. ~b~ 54 (1972) 593 and Phy~ Stat, Sol, (b) 59 (1971) 71, R, l,'riedberg and D,I, Paul, Phys, Rev. Lett, 34 (1975) 1234:aml Phys, Rev, Lett, 34 (1975) 1415, H, Kronmuller and H,R, Hilzinger, Int. J. Magnetism 5 {1973) 27, B.R. Cooper, Solid Slate Phys. 21 (1968) 393. J..l,Rhy~c and A.E. Clark, 3. Appl. Phys, 38 (1967) 1379; and J.L Feron, Thesis Url,versity of Grenoble ~1969).
[11] C.P. Helring and J.P. Jakubovics, J. Phys. F: Met.tl Phys. 3 (1973) 157. [12] T, Egami, American Inst. of Phys., Proceed. of the 17th Conf. on magnetism and magnetic materials (1971). [13] J:M. Winter, Phys. Rev. 124 (1961) 451. [14] N, Sand and S. Kobayashi, J. Itoh, Prog. Theor. Phys. Suppl. 46 (1970) 84. [15] M,B. S1ern, Phys. Rev. 162 (1967) 496. [16] D.J. Craik and E. Hill, Phys. Lett. 48A (1974) 157; and private communication.
S T U D Y OF THE COERCIVE FORCE IN FERROMAGNETIC DYSPROSKUM METAL ~ Y R F FIELD EN~ANCEMENI' * J. BARAK ** and Y. BERTH1ER Laberatoire de Spectrometric Physique af, Universite Scientifique et Medicale de Grenoble, B,P. 53, Centre de Tri! 38041 Grcn,3i~le-Cedex. France Received 2 .l!uly 1975 l'he RF field enhancement factor rl is calculated for the domains and domain walls of ferromagnetic D~ metal In the domains ~ ": 30. while in the walls it depends on "abe coercive force which limits the wall motion. The stud) of r/from spin echo signals of nuclei in the walls is used to determine this coercive force in powder of Dysprosium metal, 1,efore and after annealing.
I. Introduction
The origin of the NMR lines in ferromagnets which h.~:e mobile domain walls, was discussed by Butler [1 ] and the case of BrCr 3, including the enhancement of the linea, which originate in the center and the edges ~f ~he wide domain walls, was thoroughly examined ~ Cobb e~ M. [2]. In ferromagnetic rare earth metals a:Id alloys zhe magnelocrystailine aniso~ropy is often ot" the order of magnitude of the exchm:ge interaction. "[his results in very ~hkt domain walls [3-7] with an energy barrier wlhich limits the motion of all the walls ~.nd gives rise to an intrinsic coercive force. Furthermore, these walls may !be pqmed by imperfections like point defects [8] or dislocations. All this gives vise to a coerc:xe force H c. At the same time the screening of a small external field b) the motion of the walls is not efficient aad the RF field, used in NMR experiments, penetrates inio the domains, lit is thus interesting to compare be'....... ....... n ~he ,-,v t~t: ~mu ,-:..,_~ennancement _ , in the walls and in the d~mains in order to determine the origin ofthe NMR siglq~l of rare ear:h nuclei in ferromagnets and to find a r~ew mean to measure ,H. This is done in section 2
X~t:rk supported in part by OGRST, central n ° 71.7.28000. Present adress: Physics Department, UCSB, Santa Barbara, (~ 'dfor r aa 93106, I ,~'5~J;a~oirc associe au C.N.R.S.
and 3 for the Dysprosium metal. The experimental results are described in sec. 4. and corot ared in sec. 5 with the theory.
2. RF field enhancement in the domains
For the hexagonal structure of Dy metal with the easy axis in the x di, ection, the Hamiltonian of the system is [9]
i.j
i
-- ½ r~6 [(Jix + iJiy )6
+ (Jix--iJo,)6l +gjuBgi'H}
(i)
where ~i/is the exchange constant between spins J. and ¢/" ~2 gives the axial anisotropy in the c directien,/~6 represents thLesixfold anisotropy in the basat plane and v; is an external magnetic field standing i~ere for the RF fi,'.ld. For a small deviation of all the Sl,~ns from the x direction, described by the angle ¢ in the ba~al plane, and by the angle 0 out of the plane, equation (1) becomes for each of the parallel spins
J. Barak, Y. Berthier/Study o f the coercive force
~1 = _ K2 sin20 + K 6 cos6~ + C cos2# + la(Hx cosq~ +
Hy sin0 + H z sin0) + constant,
(2)
where C cos2¢ is added for the magnetoelastic energy [9], K~6 -= _ ~ j 6 , K2 -_ p~2J2 and U ---gJ~% is the 135,3+ local spin. Minimizing (2) with respect to ~ gives
(3)
=/.tHy/(36K~6 + 4C).
When applying an external alternating RF field//(co), ~band consequently the direction of the hyperfine field H n are modulated at the frequency w. This induces an
RF field OH n on the nuclei. The enhancement factor for this process is ~7), = P/-/n/(36K66 + 4C).
(4)
For K 6 = - 2 . 4 K/atom [10], C = 2 K/atom [9] , J = 15/2,g I = 4/3 a n d H n "" 6 MOe, this gives rTy = 30. There is no enhancement in the x direction, rtx = O. Similar calculations for 0, using K 2 = - 154 K [10], give 77z = 15.
3. RF field enhancement in the walls The simplest and most probable domain wall in Dysprosium metal is a 180 ° wall [5,11 ], perpendicular to the hexagonal c axis as represented in fig. 1. The spins at the wall edges are parallel or antiparallel to the x axis. Egami and Graham [5] calculated the structure and the energy of this wall. They found that the wall
/
/ I I
........ Fl<'-'I
/
/
/
/
/ / ,p / /
Y
Fig. 1. A row of spins showing the direction of spins in the 180 ° wall.
is n "" 7 atom with a period constant. For rium state, in energy of the
227
layers wide and the energy is periodic X = Co/2, where c o is the c axis httice a wall displacement z out of the equiliba direction perpendicular to this wall, the waft varies sinusoidaL~y
E I = Elo + AE sin2(21rZ/Co ),
(5)
where AE is the energy barrier and E ! is given for a row of spins in the wall like that in fig. 1. The magnetic mement of this row is/'/1 - (2/1r) r/p and lies alon~ the y axis. Under external field, the equiliibrium state is defined by the following equation (Pl X H)z = aEll5# = (~Et/6z)(dz/d~)
(6)
where (Pl x H)z is the z componeni of the extero.al torque. According to Egami and Giaham [5] for most nuclei in the wall we might take 2~r[(nCO) as the mean value of d~/dz, thus lattx = ~ 7r A E sin(41rz/c O)
(7)
for most parts of the wall (and a splitting of the line like in CrBr 3 [2] is not expected). Taking/-/c as the field needed to pass the higher torque point at z = r c0/8:/zH e = n A E / 2 , we obtain/-/x =/'/c sin(47rZ/Co)" For H x "¢ H e, z is small. Th:.- average departure of the spins from the directions for H = O, in an angle AO is found by multiplying this z value, by dq~/dz, rhe resulting enhancement is then 77x = Hn/(ZnH c).
(8)
Since H.. and H z induce , o torque which might move the wal~ r/,, and 77z in the walls are th,,i same as r/v and r/z in the "aomains. Egami and Graham [5] found that for Dy metal at OK, H c = 1 kOe. This value was confirmed experimentally for a single cry:aal, at high sweep rate, dH[dt > 10 40e/sec9[l 2 ] 1 0 (ehich is compatible with our RF field, dH/dt ~ Oe/se z)./-/c does not change much in the 0 - 10 K range. For this H_c (8) gives 77x = 500 and on average in the wails, o - 200. In a hypothetical Dy metaT domain wall with no coercive force, the enhancement would be much higher due to the high hyperfine field and narrow walls. 77 is then given by rl = d "Hn/DM " dc~/dz
(9)
where d is the domain width, with an average value of I/am [1 1 ] and DM is the demagnetization field, with an average value of 10 kOe, for the different particuie shapes in the powder. This leads to r/~" 106.
J. Barak, Y. Berthier/Study o f the coercive f o r ~
228
For such a high value of r/it is interesting to estimate how far the NMR frequencies are below the spin-wave fl equencies and to find if the NMR is decoupled from the normal modes of the electronic spins. The excited state ef the wall in which it oscillates parallel to itself ar.und the minimum energy plane is the k = 0 spin ~x~a~esmode of the walls. The energy of this mode was calculated by Winter [ l ? ] . He represents the stiffness of the wall by a term K (A¢) 2 ZaJ2v , where Jiy is the y direction spin component of the iith spin in a row of ~he w~all. In order to fred K' for the present case, (5) is ~witten for a small departure A~b of the angles of the spins fiom equilibrium
' ' '
' '"
I
'
i
'
i
"
A (N.A.S)
:tw=250
A
:tw:
o
(A.S.)
500
:t.=250
2
i"'~
I
.sec. nsec. nsec. ec.
"
i
1I " T I
L.-'~--~---~.__
/il
~ --'~*-~"
2p.Hc n2
El = Elo +
?T
(A~b)2.
(10)
This is taken as the above additional anisotropy term of the spins in the walls in Winter's model. For the row of spins V.J~z z,, -~ M2/2, thus K' = 4nM-Ic/(Trj2). The uniform mode energy is then given by [ 13]
tw0 = (81rK'btMs)l/2
= 4gfla B( 2Mtc Ms )1/2
= 4gfldSOlsHn/r~)l/2
(11)
For Dy metal, g j = 4/.~, " tl "" 7, I f c = 1 kOe and M s = 3 kOe. Tl~s gives v0 :- 50 GHz, a value 10 times smaller tharl the energy gap ,1 of the spin waves in the bulk, where .X = 24 K [9]. For reasonable values of mtI or C r/, v0 stays well above the NMR frequencies which are in the, range 300-2000 MHz in Dy metal [14], thus the D.C field susceptibility, considered in deriving (7) is relevant also for NMR frequencies.
4. Experimental results The experiments were carried out on a powder sample of ~ 50/~m particles of 99.9% Dysprosium from LEICO ;,~,,o,~;~¢ l-~. 77was t-tCtClIIIIIICU ,~. . . . . . "-^'~ by l l l t : U 3 U l i l l ~ tile aniplitude of the spin echo of 163Dy as a function of the RF field H l . This determination has been done for two values of zhe pulse width t w in a sequence (tw,l",2tw...). The value of H~ is calculated from the RF power, the measured Q of the sample loaded cavity and from the geometry of the cavity. The measurements were made witl~, sample, once after grinding, and then after annealing it in vacuum during 60 hours a[ 550 ° C. The . . . . . . . . . . . . . . . .
0 L--.--.~--L--...~~___I_ 0
1
2 RF
field
3
4
(Oe)
Fig. 2. Echo amplitude of t63Dy in Dy metal (11{,3 MHz '.ine) at 1.4 K, versus RF field for two values of t w, in tlhe non annealed sample (NAS) and in the annealed sample (AS).
results at 1.4 K for the 1163 MHz line are given in fig. 2. These are typical spin echo results in domain walls of ferromagnets, with dis;ribution ol the values of 77 [15] The maximum enhancement value is calculated using 1633, r/H i t w = 1, for the top amplitude point. With 1633, = 160 Hz/Oe, 77 is found to be 2.5 x 103 for the non annealed sample and 2 x 104 for the annealed one. The high r~ values confirm that the origin of the NMR signal is in the domain walls. Since the NMR linewidth (~ 3MHz) is of the order of 1/t w, the shorter the t w and the higher the HI, the more nuclei participate in the echo and its amplitude is higher as demonstrated. The value of r/is not sensitive to temperature between 1.4 K and 20 K, but application and then removal of an external magnetic field H 0 = 30 kOe, on a non annealed sample raises the value of rl. The amplil:ude of the echo as a function of external field H 0 is given in fig. 3. It shows a reduction in the number of walls when H 0 increases. This effect is typical for NMR from nuclei in domain walls and confirms the origin of the signal in our two samples.
J. Bamk. Y. Berthier/Study o f the coercive .force
'
I
'
D y 163 in
I
'
I
Dy metal
9(
, U uJ
,
0
I 10
i
l
20 External Field (kOe)
,
I
30
Fig. 3. External field dependence of the echo amplitude of t63Dy in Dy metal (1163 MHz line) at 1.4 K in the non annealed sample.
5. D i s c u s s i o n
Since the spin echo signals originate in the domain walls, we would like to calculate the coercive force which corresponds to the measured 77. By (8), with n -~ 7, we get H c = 200 Oe (r/= 2.5 x 10~) and H c = 20 Oe (77 -- 2 x 104) in the nonannealed and annealed samples respectively. The change of H c is attributed to pinning by imperfections which are partly removed by the annealing. The similar though smaller effect obtained by application of high external magnetic field (H 0 >>Hc) on a non annealed sample is also attributed to the removing of the walls from the trapping area of dislocations. H c in the annealed sample (20 Oe) is much lower than the 1 kOe value of Egami and Graham (which gives r/= 500, see sec. 3). It seems, thus, that the walls in the pure crystal are more mobile than thought before, perhaps due to the action of the non-flat displacements, suggested by Van der Brock and Lyistra . . . . . . . rt'+l. A, In this motion, only a strip of the wall moves with a much lower energy barrier, r/is then greater, but fewer nuclei are affected. The highH c measured by Egami [12] may results from imperfections. So,~e mechanisms 0y whlLch the imperfections may highly influence the energy of narrow domain walls were recently reported. Craik and Hill [16] have shown that a small weakening of the magnetocrystalline anilso-
229
tropy or the exchange coupling, between two neighbouring layers of spins in the walls, can result in very steep energy gradients which pin the walr..s and give ri~ to high coercive force. Since both the anisotropy and the exchange interactions are sensitive to lattice imper. fections, this might be the process by which the dislocations trap the narrow domain walls. An othew mechanism, by which the existence of point defects may result in high H c is proposed by KronmuUer and hilzinger [81. Preliminary experiments with Dy nuclei in annealed ferromagnetic DyAI 2 powder show r/values much lower than in Dy metal. The measured r~ -~ 700 indicates high nH c. We find n H c = 5 x 103 Oe in this sample compated to nH c = 175 Oe in annealed Dy metal. Similarly one might estimate the value of r/using the known/-/c and estimated n. In DY3AI2, n = 1 and H c -~ 25 kOe at liquid helium temperature [3]. From (8), r/= 140 and long high power pulses are needed in order to obtain a spin echo signal. Since for equal total area of walls and good pulses conditions, the signal will be propostional to r?n or, from (8), to 1/H c, the amplitude of the echo in these materials is expected to be very weak.
6. Conclusion The RF field enhancement factor was calculated tbr the domains and the domain walls ill Dy metal and compared with the enhancement measured by NMR spin echo signals. The NMR is shown to come from thc wafts where the enhancement depends on the mubility of the walls. Thus the measurement of the enhancement factor gives a useful intormation on the coercive force which limits the motion of these walls. We would like to thank Dr. P. Averbuch and Dr. B Barbara for helpfull remarks. We are also grateful to Mr. R. Gamond for his skilful technical aid.
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l,Sl I'TI
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