Terbium - H. Drulis, M. Drulis

POH -

2.1.3.8 Terbium

lb

1 ferro

c3

ferro helical para

0 219.6 .6 K 230.2 K 230.2 T-

Fig. 174. Ordered spin structures observed by neutron diffraction for Tb [63 K I].

14”

213 217 221 225 229 K 233

T-

Fig. 175. Helical turn angles as a function of temperature for Tb, showing the anomaly in the critical magnetic field at 223.1 K (open triangle) and w=20” [83 G I]. The broken line is an extrapolation of an approximately linear w vs. T relation in the temperature range 216K < T

<224K deduced from the neutron diffraction data (open circles) [67 D I]. Arrows indicate TN and Tc of [83 G I] while the other TN and Tc values are from work listed in [82 G I].

22”

21”

1 20”

3 19”

18”

17” I I I I I

-15 -12 -9 -6 -3 K 0

T-TN -

Fig. 176. Interlayer turn angle, w, for Tb as a function of T-T, at various pressures, determined from neutron diffraction. A value for (I/Q)dQ/dp of 20(2). low3 kbar-r

at T- TN = -4 K was estimated where Q is the modu- lation wavevector [68 U I].

Land&-Bijmstein

New Series IWlPdl

H. Drulis, M. Drulis

110 2.1.3.8 Tb: figures [Ref. p. 183

I

⁶

‘a 4

0 0.2 0.4 0.6 0.8 1.0 A-’ 1.2

sin 0/A -

Fig. 177. Magnetic form factor of Tb at 4.2 K vs. sin0/I..

The experimental points are determined by polarized (solid circles), or unpolarized (open circles), neutrons. The upper two lines are theoretical curves normalized to p=9.34ua and 9 pa respectively, while the lower one, extrapolated to8.18u,forsin0/i.=O,is thcrcsult ofatit to high-angle data only [67 S 11.

For Fig. 179, see next page.

0.8 I-LB

0.6

1 h 0.4

0.2

sin .9 /% -

Fig. 178. Magnetic form factor of Tb at room temperature. Fitting at high angles leads to a scale factor of 0.86 - the value of magnetic form factor renormalized to the full 4f magnetic moment of Tb at zero momentum transfer [70 B 11.

Gcm3 9 309

I I I I I

0 40 80 120 160 200 210 280 320 i 369

T--+

Fig. 180. Magnetization per gram, cr, vs. temperature for the b axis in Tb crystal in the temperature range from 1.4 to 360 K and magnetic field higher than 1 kOc. Plots of a* vs. Tat constant field extrapolated to a’=0 yield the ferromagnetic Curie temperature equal to 221(2) K [63 H 11.

H. Drulis, M. Drulis

Land&-Bbmstcin New Series 111,/19dl

Ref.

1831 2.1.3.8 Tb: figures 111

Fig. 179. Magnetization vs. magnetic field for the basal plane axes a and b, and for the hard-direction of magnetization (c axis) in Tb single crystal.

Within experimental error the basal- plane magnetization is almost iso- tropic. The saturation magnetic moment along the b axis corresponds to 9.34 @Tb [63 H I]. The saturation moment is higher than the maximum ionic moment of the Tb ground-state multiplet, guBJ = 9 pa. The difference is ascribed to a polarization of the con- duction electrons of 0.34 uu,/Tb.

I I I I I

_I 0 179.6

219.9 225.6 231.1 236.0 240.1 250.0

250

I 200 b

150

100

50 0 35 Gcm3

9 Hllc

-301

runI T=219.3K

A-Y ~231.3

0 2 4 6 8 IO 12 14 16 18 kOe

LandolGB6mstein

New Series 111/19dl

H. Drulis, M. Drulis

112 2.1.3.8 Tb:

figures

[Ref. p. 183

175 Gem!

9 150 125

I 100 b 75

25 n i

“ZiC

I I I \ I

215 220 225 230 ;

I- 5 K 2’4

Fig. 181. Magnetization per gram, CT, vs. temperature for the easy b direction in Tb crystal in the neighborhood of the N&l point. Applied magnetic fields are indicated.

The straight line shows the N&e! temperature extrapolated to zero field, yielding a value equal to 229(1)K [63 H 11.

180 Gcm3

9 160

H-

Fig. 182. Magnetization along the b axis of Tb as a function of the internal magnetic field for different temperatures, showing a licld-induced AFeF transition C83Gl-J.

0 0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 kOe 1.0 0.8 kOe 1.0 H-

Fig. 182. Magnetization along the b axis of Tb as a function of the internal magnetic field for different temperatures, showing a licld-induced AFeF transition C83Gl-J.

0.8 2

” b 0.7 G

0.6 0.5 II

0 30 60 90 120 150 180 K 210

I-

Fig. 183. Reduced magnetization of Tb for a field of 18 kOc applied in the easy b direction. The broken curve represents the experimental results. The full curve is calculated including exchange and crystal licld terms [68 B 3-J.

H. Drulis, M. Drulis

Landok-BGmstein New Series 111/19dl

Ref.

1831 2.1.3.8 Tb: figures 113

0.90 I

0 0 IO IO 20 20 30 30 40 40 50 50 60 60 K 70 K 70 T-

Fig. 184. Relative spontaneous magnetization, m=

as/a, (0 K) of Tb as a function of temperature, calculated by [75 L l] with the spin wave energy gap at zero wavevector E&n = 20 K, together with the experimental results of [63 H l] shown as open circles.

IO2 I

kOe I I I I I

lb

I I

I.000 0.975 0.950 0.925 0.900 0.875 0.850 0.825 -m

Fig. 185. Critical magnetic field, H,, of Tb as a function of the relative spontaneous magnetization, m = a&, (0 K).

H, is the field along the hard planar axis required to switch the magnetization to this direction. The closed circles are the results obtained by [75 H 21, while the open symbols are the results of the measurements by [67 R 11.

The solid line represents the relation H,= 32.3m ".' kOe.

;I;

^{228 K} ²³⁰

T-

b* IO I z 0 13" 20

1 30 km3 9

0 30 60 90 120 K

T-

O Fig. 186. Temperature dependence of the critical magnetic Fig. 187. Temperature dependence of the difference be- field, H,, required to drive the helical phase into an tween the saturation magnetic moments at OK and at intermediate phase prior to becoming ferromagnetic for temperature, T, in Tb. The points are experimental values two Tb samples with Hlla and H/lb for both temperature from [63 H I]. The solid curve is a plot of relation increasing and decreasing through the helical phase. The T3j2 exp( - E&T) with E$k, = 20 K. The dashed curve samples were different in diameter [84 D I]. shows the T3j2 law.

Land&-Biimstein

New Series III/19dl

H. Drulis, M. Drulis

114 2.1.3.8 Tb: figures [Ref. p. 183

KKI Gcm3

300

b 200 I

100

0 Fig. 188. Temperature dependence of the magnetic moment in Tb at 18 kOe and of the reciprocal magnetic mass susceptibility along basal-plane and c axis directions. Basal-plane anisotropy prevents alignment of the moment along the a axis at 18 kOe below ~90 K [63 H 11.

300 500 700 900 1100 1300 K Ii-00 I-

Fig. 189. Temperature dependence of the reciprocal magnetic mass susceptibility, xr,, ofTb in the temperature range between 400 and 1450K. The Curie-Weiss law is obeyed up to 1450K with perr=9.62 us/Tb and 0=236 K [61 A I].

Fig. 190. (a) Reciprocal magnetic susceptibility per Tb atom for SC -0.561 at% Tb single crystal. The full curves are theoretical tits. The susceptibility measured at H = 1.35.10’ A/m has been corrected in the c direction below 9 K for the effects of ordering as illustrated in (b).

Parameters fitted to the susceptibility data are given in Table 3 [76 H 11.

4.0 406 A/m - PB

0 20 40 60 80 K '

a I-

0 1 8 12 16.105A/m20

b H-

H. Drulis, M. Drulis

Land&-Bhstein New Series 111119dl

Ref. p. 1831 2.1.3.8 Tb: figures 115

.10-21 Tb 1 I I I I I

60 100 140 180

. heating 0 o coolino

T-

Fig. 191. Variation of the initial susceptibility, xi, in SI units of Tb measured along the b axis with temperature.

xi represents the differential susceptibility deduced from xac for H = 0. Two high-temperature peaks are associated with magnetic phase transitions at &=217.7 and T,=228.5 K. The peak at 135 K originates from a very large magnetic viscosity [74 M 31.

208 212 216 220 226 228 K 2

T-

Fig. 192. Plot of the magnetic susceptibility, x (in arbi- trary units) vs. temperature around the Ntel and Curie temperatures of Tb at different pressures. The susceptibility is obtained for a magnetic field along the easy b axis [68 B 11.

21 0

Landolt-Biimstein

New Series 111/19dl

H. Drulis, M. Drulis

116 2.1.3.8 Tb: figures [Ref. p. 183

:10 215 220 225 230

I I

215 215 220 220 225 225 230 230 235 235 K 260 K 260 I-

I-

235 240 K 2L5 Fig. 193. Temperature dependence of the ac magnetic susceptibility, I., (v= lOkHz), of polycrystalline Tb for various magnetic fields [SS D 11.

Fig. 194. Preliminary H- T phase diagram for Tb. Solid circles: data from electrical rcsistivity, open circles: data from ac magnetic susceptibility measurements taken from Fig. 193. P: paramagnetic, H: helicoidal AF phase, F:

ferromagnetic phase, X: intermediate phase [85 D 11.

4 5 5 6 6 I I 8 me\/ 9 8 me\/ 9 f-

Fig. 195. Neutron groups obtained in Tb at 90 K when a magnetic field of 1OkOe is applied along a b axis perpendicular to the scattering plane. The scattering vector of the neutrons is the sum of the reciprocal lattice vector (l,l,O) and the wavevector q along the c axis (q=0.6i%- ‘). The two peaks observed are due to the optical magnon mode (MO) and the transverse optical phonon mode polarized perpendicular to the magnctiza- tion (TO,) at q=0.5k1 [75J 11.

H. Drulis, M. Drulis

Land&-Btimsfein New Series II1/19dl

Ref. p. 1831 2.1.3.8 Tb: figures

--- f e

r E - -3 .L

72 --- .- .-

N m CD m -3

E -3 Land&Biirnstein New Series 111/19dl

H. Drulis, M. Drulis

2.1.3.8 Tb: figures [Ref. p. 183

r

1.53 me\’ lb

qllc 1.25

I 1.00 --

\ F z z 0.75 D

lb I

I=L.2K a - direclion I

b -direction c-dir 'PC

l I(O)-/(g) 0 /'(II)-I'(91

a1/'(0)1*-1/'(9)1~

I

I/

tion

Fig. 197. Fourier-transformed exchange parameters, J”‘(0)-J(‘l(q), for intrasublattice (J) and intersublattice (J’) exchange interaction at 4.2K, deduced from the magnon dispersion relations of Tb along all the symmetry lines in the zone. IJ’(0)12 - 1J’(q)12 for the b direction is given as well [66 M 11.

U.6 0.8

1.2 r Fig. 198. Exchange parameter J(O)-J(q), for q along the c direction, scaled by the relative magnetization, nr = u/a (0 K), at different temperatures in the ferromagnetic phase of Tb derived from inelastic neutron scattering measurements [72 M 11.

K 2(

Tb H --$k

u

25 50 75 100 125 K 150

I-

Fig. 199. Magnon energy gap at zero wavevector as a function of temperature in Tb: the experimental results from neutron scattering are shown as open circles, and those from infrared resonance are shown as full circles; the line is a theoretical curve. The deduced value of the gap at low temperatures is equal to 21 K. The gap decreases with temperature and is zero at the ferromagnetic- helimagnetic transition [72 M 11.

H. Drulis, M. Drulis

Land&BGmstcin New Series III119dl

Ref. p. 1831 2.1.3.8 Tb: figures 119

5.5 meV*

5.0

I 3.5 3.0

* 2.5

0 ¹ 2 3 4 T 5

lJoH----

Fig. 200. Magnon energy gap squared for various temperatures as a function of the internal magnetic field in the easy (solid symbols) and hard (open symbols) direction [75H 23. The solid lines represent fits obtained using eight anisotropy parameters: the crystal field parameters, B$, B$ B$ and Bg, two magnetostriction constants, and two additional anisotropy parameters with axial and six- fold symmetry, respectively [75 R 11.

I 6

^ I I I ” L.02

d 4

200 250 K 300

50 100 150

a T-

0.10 0.10 meV meV 0.08 0.08

0.06 0.06

I 0.04 I 0.04 5 5

0.02 0.02

0 P P - - P P Y Y i i

P -a02 P

-a02 1 1

0 2.5 2.5 5.0 5.0 1.5 1.5 10.0 10.0 12.5 12.5 4 4 15.0 15.0 R-

R-

Fig. 201. Spatial dependence of the exchange parameter between ions on the same sublattice in Tb at 4.2K [68 H I].

78; . . 1.05 1.10 1.15

b ^{T/T, -}

Fig. 202. (a) Magnetocaloric effects as a function of temperature for various magnetic fields applied along the b axis of a Tb single crystal. (b) shows the specific heat of terbium in zero magnetic field and in p,H=6.02T [85Nl].

Land&-BBmstein New Series IWl9dl

H. Drulis, M. Drulis

120 2.1.3.8 Tb: figures [Ref. p. 183

228 230 K 2 Fig. 203. Specific heat measurcmcnts for Tb single crystal.

A value for the latent heat of 13.6(6) Jmol-’ at T,

=221.45(3) K was obtained. The peak at TN=229 K is associated with an antifcrromagnetic$paramagnetic phase transition [83 J 11.

12 mJ mol K2

I 8

2 4

J cl,

0 4 8 12 16 K2 20

8 J

mol K

Fig. 205. Specific heat of Tb metals vs. temperature:

full circles [68A 11, triangles [62Ll], open circles * [64 K 23. The theoretical curve is a plot with n’=0.1495 K and P=O.O16K (cf. Table 5) as determined by NMR of ⁶ ls9Tb [67K2]. The arrow indicates the tempcraturc

below which the nuclear specific heat constitutes more 4.10-’

. ^ - ^ - .

Fig. 204. Total specific heat of Tb, C,, as a function of temperature and (C-&)/T vs. T2, where C, is the nuclear specific heat contribution [74 H 11.

than YY% of the total specific heat. 2w 4 6 8 10.’ 2 c 6 K 1

I-

H. Drulis, M. Drulis

Iandolt-BBmstein New Series III/19dl

Ref. p. 1831 2.1.3.8 Tb: figures 121 T-

6 8 10 15K20

I I I I I

1

227 229 231 233 235 K 2 3;

1,

T-

Fig. 206. Magnetic contribution to the specific heat, Cmag, and temperature derivative of the electrical resistance, dR/dT, relative to the respective maximum values, as a function of temperature near TN for a Tb sample with the ratio ~(300 K)/~(4.2 K)=25 [84A 11.

I.2

- -

-125 II

Tb DY Ho El. Tm

- 2000 - 1000 - mJ

mol K - 400 -200 I

g - ‘8oY - 60 - 40

-1

²⁰

I , , I I

4 6 8 IO 20 K LO

T-

Fig. 207. Spin wave contribution to the specific heat of Tb plotted as Cmag vs. T on logarithmic scales (bottom and right-hand side) and C,,$T3/’ vs. T on logarithmic (left-hand side) and l/T (top) scale. The straight lines correspond to the relations (I) Cmag

= 36 T312 exp( -23.5/T) mJ/mol K and (4 Gag

=0.031 T3.5 mJ/molK with T in K. The full circles correspond to a run where the specimen was cooled to only 15 K before this run was started. The value deduced of the spin wave gap is 23.5K, in agreement with experimental values deduced from magnetization curves [66Ll].

Fig. 208. Contribution of the exchange anisotropy and of the single-ion anisotropy to the total anisotropy in Tb, Dy, Ho, Er, and Tm. Experimental values of (0, - 0 t,) (0 “C) are taken from [72A I] (solid circles) and [69A I] (full triangles). The open circles represent the experimental values of the single-ion anisotropy determined from measurements of single crystals of dilute alloys of the respective rare earth elements in Gd [71 T I].

The open triangle indicates the theoretical value of the single-ion anisotropy calculated by [74 B 11.

Landolt-Bbstein

New Series III/19dl

H. Drdis, M. Drulis

122 2.1.3.8 Tb: figures [Ref. p. 183

125 125 x x Tb Tb 100 100

1 ,” “,:i:J 167Rll - c 168821

L 0" I I

25 25

0 0 50 100 150 200 K 250

10.0 10.0 K K lb lb 1.5 1.5 I I

s s 5.0 5.0 > >

Fig. 210. Comparison between existing data for the basal- plane anisotropy coefficient, Kg(T), in Tb. [67 R 11: strain measurcmcnts.

2.5 2.5

Fig. 209. Experimental points and theoretical plot of the anisotropy constants, K, (a) and K, (b), vs. temperature in Tb. In (a) the circles connected by the dashed line. give the experimental data, while the full line gives the theoretical curve 5.65. 108~9i2[.Yip ‘(m)] erg/cm3, where rn is the relative magnetization determined from magnetization mcasuremcnts [69 F 11.

0 0 0 0 40 40 80 80 120 120 160 K 200 160 K 200

I- I-

Fig. 209. Experimental points and theoretical plot of the anisotropy constants, K, (a) and K, (b), vs. temperature in Tb. In (a) the circles connected by the dashed line give the experimental data, while the full line gives the theoretical curve 5.65. 108~9i2[.Yip ‘(m)] erg/cm3, where rn is the relative magnetization determined from magnetization mcasuremcnts [69 F 11.

5.5

.t 5.3

“E r, 5.1 2

z 4.9

47 0 0.1 0.2 0.3 0.4 0.5 0.6 a -log i,,,,&-“(m)) -

5.5, I I

j ^5.3

“E 2 5.1 2

E 4.9 4.11

0 0.1 0.2 0.3 0.4 0.5 0.6 0.1

b -log [ f5,2(be’(m)) i9,2kf’(m))] -

Fig. 211. Comparison of Kg(T) with theoretical predic- tions of the temperature dependence of the anisotropy of (a) single-ion and (b) magnetoelastic origin. m is the relative magnetization. The much better tit to the single- ion crystal field theory suggests that the anisotropy is of magnetocrystalline origin [77 B 11.

H. Drulis, M. Drulis

Landolt-B6mstein New Series III/l9dl

Ref. p. 1831 2.1.3.8 Tb: figures 123

5.12 A

I 5.71 c,

5.70

5.69 6.27 w

I 6.26 -4

6.25

6.24 3.61 8, I 3.60 D

3.59

3.58

0 50 100 150 200 250 K 300

T-

Fig. 212. a, b, c axis lattice parameters as a function of temperature for Tb from X-ray studies [63 D 41.

.10-: 3.6 3.2 2.8 2.4 2.0

I 1.6 : G 1.2

0.8 06

0 -0.4 -0.8

0.8 40-J

0 -0.8 -1.6

4.0 2

WI-h.8

- 5.6 - 6.4

0 50 100 150 200 250 300 K 350

a T-

I

^-0.65^-0.70

: z-o.75

-0.80 -0.85

216 217 218 219 220 221 222 K 223

b T-

Fig. 213. a, b, c axis linear strains in Tb as a function of temperature. Data are shown for both zero magnetic field and a 30 kOe saturating field applied along the b axes. G is the gauge direction. The orthorhombic distortion at Tc is barely discernible as shown in (b) due to the small magnetic moment and energy difference between ferromagnetic and antiferromagnetic state [65 R 31.

Land&Bihstein

New Series III/i9dl

H. Drulis, M. Drulis

124 2.1.3.8 Tb: figures [Ref. p. 183

2.10 10

I 10

-d

‘b I

7 ‘\

\ \ \ I

B

1 2 4 6 8 lo-' 2 4 6 ll lo-'

c-m

Fig. 214. Shear maenctostriction paramctcr of Tb as a function of the rela&e magnetization. Closed circles and open circles denote the results dcduccd by [75 J 1] and [65 D 11, respcctivcly. Solid lint: 1.‘=9.25. toe3 n~l.‘~, and dashed line: I.‘= 15.0. 10e3 f~,2(Y-‘(n~)), where nl is the relative magnetization

I I I

0 50 100 150 200 250 K 300

Fig. 217. Temperature dependence of the experimental forced magnetostriction coefficients of Tb along the a, b, and c axis for H parallel to the b axis. The expcrimcntal points at a given temperature arc given by the slopes in the high-field region of the magnetostriction vs. applied magnetic held curves. When the temperature increases, the forced magnetostriction increases in absolute value and it is necessary to have a higher field to obtain the saturation of the magnetostriction vs. field curve [65 R 33.

I I I I

0 50 100 150 200 250 300 K 3 I-

Fig. 215. Magnetostriction constants for Tb as a function of temperature. The theoretical single-ion dependence is shown for the y-mode constants. nl is the relative magncti- zation. G and D arc, respectivcly,combinations of c and a axes u-mode constants: G=%;~0-I.;.2/3 and D=LT.’

-rl:,2/3 [65 R 3-J.

Tb ’ I i

--- 0 50 100 150 200 250 300 K 3 0

T-

Fig. 216. Experimental values and theoretical plots of the magnetostriction constants A and C ofTb determined at 30kOe applied field. Data obtained from a axis (full circles), or b axis (open circles), strain vs. field-angle curves are shown. The solid lines represent theoretical expressions for the temperature dependence of the con- stantsgiven, respectively, by C=4.35. 10-3~~,2[P’-1(m)]

and A=2.14. 10-3~a,2[Y4-‘(nr)], where m is the relative magnetization [65 R 33.

H. Drulis, M. Drulis

Iandolt-BBmstein New Series III/19dl

Ref. p. 1831 2.1.3.8 Tb: figures 125

.I063 Tb

0 50 50 100 100 150 150 200 K 250 200 K 250 T-

T-

Fig. 218. Spontaneous magnetization E,, along the c axis Fig. 218. Spontaneous magnetization E,, along the c axis of Tb. The full line represents the experimental data of Tb. The full line represents the experimental data obtained from [65 R 31 after correction for the thermal obtained from [65 R 31 after correction for the thermal dilatation of an equivalent nonmagnetic lattice. The dilatation of an equivalent nonmagnetic lattice. The dashed line is the theoretical determination of [71 B I].

dashed line is the theoretical determination of [71 B I].

!

210 215 220 225 230 235 2&O 245K 250

a T-

!

b axis 1

0 , I I I

227 228 229 230 231 K 232

b T-

Fig. 219. (a) Differential expansivity of Tb relative to the Be-Cu cell from 210 K to 250 K. The left-hand scale is for the b axis and the right-hand scale for the c axis. (b) shows details of the b axis data near TN after the subtraction of 1.5. 10m5 K-l from the slope for clarity of presentation.

The Ntel transition proceeds smoothly as a second-order phase transition without any abrupt change in length [83 T 11.

120 120 p&m p&m 100 100

t t

80 80

60 60 Q- Q-

40 40

20 20

0 0 a a

112.5 112.5 pS2cm pS2cm 110.0 110.0

I I 107.5 107.5 pp105.0 pp105.0

102.5 102.5 100.0 100.0

50 100 100 150 150 200 200 250 250 300 300 K K : : 0

200 210 220 230 210 K 250

b ^T-

Fig. 220. Temperature dependence of the electrical resistivity, Q, ofTb polycrystals showing (a) a change of slope at 229K and (b) a slight anomaly with a small change of slope at 219 K [6OC 21.

Land&-BBmstein

New Series III/l9dl

H. Drulis, M. Drulis

126 2.1.3.8 Tb: figures [Ref. p. 183

140

p&m lb I

120)’

0 50 100 150 200 250 K 300

&km 115

I

¹¹⁰

cb 105

100

2 I 210 220 230 260 K 250

T-

Fig. 221. Temperature depcndcncc of the electrical resis- Fig. 222. Temperature dependence of the electrical resistivity of Tb single crystals along the a and c axes in the tivity of Tb single crystals along the a and c axes in the temperature ran_pe between 4 to 3CQK. The residual vicinity of the phase transition temperatures [69 N 11.

resistivity is subtracted [69 N 11.

6.15 6.10

* 1,775

1.725

5 tl I

2.LOO 2.375

2.350

1.650 1 I I I I

0 20 40 60 kOe 80

H-

Fig. 223. Variation of the transverse magnctoresistance as a function of the applied magnetic field for a Tb crystal with J\(b and H((a up to 80kOe [77S 11.

H. Drulis, M. Drulis

Land&BBmstein Ne\v Series 111~19dI

Ref.

1831 2.1.3.8 Tb: figures 127

GPa Tb

161 I

0 50 100 150 200 250 K 300

T-

Fig. 224. Comparison of the temperature dependence of

c44, Cl23 and ci3 for Tb as determined by (solid line)

[72 S I] and (dashed line) [74P I].

cm3

1 0.5 0.4 0.10

G I

0.3 -s” \

0.2 0.05

01 IO

215.0 217.5 220.0 222.5 225.0 227.5 K 230.0 T-.-w

Fig. 226. Temperature dependence of the driving energy, E,, for ferromagnetic alignment in Tb. The full line represents the experimental values, while the dashed line represents the theoretical values [69 F 21.

0 50 100 150 200 250 K 300

T-

Fig. 225. Temperature dependence of cr I and cS3 for Tb as determined by (solid line) [72S l] and (dashed line) [74P 11.

121 I I” 1

I 9 s

” I I I I I I I

u70

I I I , I I

100 130 160 190 220 K 250

T-

Fig. 227. Temperature dependence of the FMR field in Tb at 24 GHz. Triangles with the vertex pointing up or down represent data taken while increasing or decreasing the applied magnetic field Ejdc with time, respectively. The full triangles correspond to the situation where Hdc lies 1” off the a (hard) axis and the open triangles to that where Hdc is along the b (easy) axis. The curves (1) and (2) are obtained by the calculation of [71 V 1, 72V I] within the free- lattice model for Hdc parallel to a axis. Curve 3 corresponds to the paramagnetic resonance [71 H 2).

Land&Bknstein

New Series IIIjl9dl

H. Drub, M. Drulis

128 2.1.3.8 Tb: figures [Ref. p. 183

24 kOe 20

I 16

aI7 12

0 160 160 180 200 220 240 260 280 K :

l- Fig 229. Temperature dependence of the FMR field in Tb at 100 GHz with the field applied along a hard planar axis.

Resonance absorption at low fields and low temperatures T< Tc is associated with the effects of domain rotation.

The temperature-independent line at ~19kOe at tern- l6 peratures higher than room temperature is unidentified [67S2].

I Fie. 228. Temoerature deoendence of the FMR field in Tb b c 8 at 98.2 GHz with the dc held applied along a hard planar axis. The open circles represent the experimental points, while the solid circles represent absorption maxima believed to be associated with the onset of magnetostriction. The curves (I) and (2) are theoretical curves: (I) is the frozen-lattice plot with P,S* = 19OK/Tb, P$S6

=- 0.28 K/Tb and D’= 1.49 K/Tb. The curve (2) is the best tit of a frozen-lattice model to experiment with P$

=108K/Tb and Dy=1.7K/Tb [69Wl].

100 120 140 160 180 200 220 K ; l-

4 kOe kOe

1 1 3 3

'd2 'd2 1 1

ioo

125 150 175 200 225 K

Fig. 230. Temperature dependence of the absorption Fig. 231. Critical ultrasonic attenuation in the vicinity of linewidth of FMR for Tb with the dc field along a hard TN and Tc for Tb. Solid symbols are data from longi- planar axis; the experimental points are obtained at 9.44 tudinal sound propagation and open symbols are for

and 35.3 GHz [67 B 11. shear wave propagation [69P 11.

s

15.0

12.5 I II I

IL I IO.0

2.5

FlO I I I I I

215 220 225 230 235 K ;

!40

H. Drulis, M. Druiis

Landok-Bbmstein New Series III119dl

Ref.

1831 2.1.3.9 Dy: figures 129 2.1.3.9 Dysprosium

fur0

GJ

_helical _par0

88.3 K 176

T-

Fig. 232. Ordered spin structures observed by neutron diffraction for Dy [61 W 21.

.lcl~

IDY

I

²⁰

.= 1 2 @J z 15 .- Y a 10 8

5 a

176.0 176.3 176.6 176.9 177.2 177.5 K 17 T-

Fig. 233. High-resolution neutron diffraction investiga- tion in Dy. Temperature dependence of the (002)) peak intensity for two independent runs showing that the observed magnetic scattering is continuous through TV No evidence for a first-order transition at TN theoretical expected [85 B 21.

Land&-Biimstein

New Series 111119dl

H. Drulis, M. Drulis

2.1.3.9 Dy: figures [Ref. p. 183

3.25 - .lO~ Dy A/m Hllo

- a- - b

2.25

1.25

0.50

I i 1-

0.25

t 1 =lL0.5K

m 145.0

n 150.0

0 160.0

P 16L.5

9 170.0

r 172.5

s 173.6

t 176.0

u 177.0 K

0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 .106A/m :

H-

Fig. 234. Isothermal magnetization curves of Dy in the temperature range between 4.5 and 177 K. H denotes the internal magnetic field, which lies parallel to one of the easy u directions. H, and H, denote the critical fields for transitions from the helical phase to the fan-like phase and from the fan-like phase to the ferromagnetic phase, respectively [78 H 21.

0 25 50 75 100 125 kOe 150

H-

Fig. 235. Magnetization of a Dy single crystal at 4.2K relative to the easy-axis saturation magnetization as a function ofmagnetic field applied in the hard cdirection of magnetization [68 R 2).

H. Drulis, M. Drulis

Landok-BBmstein New Series 111/19dl

Dalam dokumen H. Drulis, M. Drulis (Halaman 110-166)