Thulium

POH -

H. Drulis, M. Drub

2.1.3.12 Thulium

_--- 7

zb

ferri - magnetic FAD

a \ \ \ \ 4 I a / cz5

&

&

antiferro- magnetic sinusoidal variation CAM

K ! T-

1

^{7/z c}

poramagnetic P

5

Fig. 362. Ordered spin structures observed by neutron diffraction for Tm [62 K 1, 68 E I].

0.285

# 0.280 I 7 s

0.275

\ r, 0.270

0 10 20 30 40 50 K 60

T-

Fig. 363. Temperature dependence of the modulation wavevector, Q, parallel to the c axis of Tm determined from a neutron-diffraction investigation. The solid circles represent measurements taken with temperature decreas- ing and the open circles those taken with temperature increasing [70 B 31.

1.0 rJ-8 Tm 0.8

I I I I I I

0 0.2 ox 0.6 0.8 8-l 1.0

sin B/L -

Fig. 364. Magnetic form factor of Tm. The solid line is a theoretical curve normalized to the c axis ferromagnetic component, pe = 1 .O u,/Tm [70 B I]. Out-of-plane reflec- tions shown in the figure by open circles reflect the asphericity of the magnetic moment density distribution [69B4].

Land&Biimstein

New Series III/l9dl

H. Drulis, M. Drdis

176 2.1.3.12 Tm:

figures

[Ref.

p.

183

e Ps 7 6 i

5

$L 3 2 1 0

20 LO 60 80 kOe 1

H- Fig. 365. Magnetization of Tm at 4.2 K as a function of

internal magnetic field. The ferromagnetic arrangement

Fig. 366. Magnetization vs. internal magnetic field at fixed consisting of four layers of magnetic moments parallel to

temperature for the b axis Tm crystal. The b axis of the Tm the c axis followed by 3 antiparallel layers (so-called 4 up -

sample remains magnetically hard to at least 100kOe.

3 down structure) has a net magnetic moment of 1 pa

There is no remanent magnetic moment in the limit of which can be decoupled by a field of 28 kOe parallel to

zero applied field [69 R 11.

the c axis producing a ferromagnetic structure. The b axis is magnetically hard [69 R 11.

6[

Gem:

9

I b 3’

50 Gd jm

9 HII c 120.6/

0 20 LO 60 80 kOe 100 0 LO 80 120

H- 160 K 200

I- Fig. 367. Magnetization vs. internal magnetic lield for the

c axis Tm crystal in the paramagnetic region [69 R 11.

Fig. 368. Magnetization per gram as a function of tem- perature at several applied magnetic fields for the b axis Tm crystal. The sharp peak near 57K is the paramagnetic$antiferromagnetic phase transition [69 R 1-J.

60

Gcm3 Tm 9

_Hllb

50

H = 91.1 kOe

LO I \ I I

I

³⁰

b

H. Drulis, M. Drulis

Landok-Bbmstein New Series III/l9dl

Ref. p. 1831 2.1.3.12 Tm: figures 177

24 Gcm3

9 200

0 40 80 120 160 K 200 0 4 8 12 16405A/m20

l- H-

Fig. 369. Magnetization per gram as a function of tempera- ture at several applied magnetic fields for the c axis Tm crystal. The isotield magnetization for 13.5 and 25 kOe shows a characteristic peak at the NCel temperature of 56K. The crosses denote data extrapolated from iso- therms made from isofield data [69 R I].

Fig. 370. Easy-axis magnetizations in the FAD and CAM phases as a function of internal magnetic field in the c direction of Tm. The curves suggest that 35 K 5 T, $40 K [77 F 21.

3.5

*lo5 A/m 3.0

r,

5

44

0 10 20 30 40 50 K 60 0 IO 20 30 40 50 K 60

I-

Fig. 371. Easy axis magnetization M for internal magnetic fields of 8. lo5 and 12. lOsAm-’ in Tm for Tj TN. The

Fig. 372. Critical field H, along the c axis for the FAD+F transition vs. temperature in Tm. Experimental data:

solid lines are calculated for J(0.5 K, 1.15 K, 0, 0) and dashed-dotted line after [69 R I]; circles after [77 F2].

suitable CEF parameters, the dotted curve for J(0.5 K, Dashed line: calculated data for J(0.5 K, 1.15 K, 40) in the 1.15 K, -0.2K, 0.2K), and the dashed curve for J(0.5 K, CAM and FAD phases, and J(0) = 0.675 K in the F phase 1.15 K, -0.2K, -0.2 K), where J(J(O), J(Q), 5(3Q), J(5Q)) according to a mean field model, where J(J(O), J(Q), 5(3&), represents interplanar exchange parameters for wavevec- J(5Q)) represents interplanar exchange parameters for tors 0, Q, 3Q, and SQ, with Q=4x/7c representing the multiples of the modulation wavevector Q (cf. Fig. 371)

modulation wavevector [77 F 21. [77 F2].

3.5

,105

1 Tm P

30 .I05 A/m 25

/-

Land&-Bknstein

New Series III/l9dl

H. Drulis, M. Drulis

2.1.3.12 Tm: figures [Ref. p. 183

EC

7C

lx

I 5r:

7 N I[

3[

2[

1C

[ 50 100 150 200 250 K 3

I-

Fig. 373. Reciprocal differential magnetic volume suscep- tibilities (SI units) in the FAD, CAM and P phases. For T above TN applied magnetic fields varying from 4.10SAm-’ (SkOe) to 32.105Am-’ (40kOe) were used. Below TN the highest field applied was 19.10’ A m- ‘. For Ts 35 K only values for an applied field of 16.10’ A m-l are given. Above TN the suscepti- bilities are field-independent except for xc at 60 and 70K where the low-field values arc shown by the broken curve [77 F 23.

0 250 500 750 1000 1250 K 1:

I-

Fig. 375. Reciprocal magnetic susceptibility, l/x*, as a function of temperature of Tm for high temperatures between 200...1500 K [6OA 11. The symbols represent data for different samples.

0 60 80 120 160 200 K 210

I-

Fig. 374. Plot of the inverse magnetic susceptibility, l/X*, as a function of temperature for the c and b axes of Tm crystals, giving paramagnetic Curie temperatures, Ob = - 17 K and 0,=41 K, respectively [69 R 1-J. The dashed line shows polycrystalline data [58 R 1-J.

50 A- mol K

10

I 30 2

20

10

0 100 200 300 K

I-

Fig. 376. Heat capacity of Tm from 15 to 360K. Apart from the h-type anomaly near 55K, which is asso- ciated with magnetic ordering, there are anomalous changes in the slope of the heat capacity near 88,162 and 180K. The results in the temperature range from 14 to 21 K support a T3-dependence of the magnetic specific heat as predicted by spin-wave theory for an anti- ferromagnet [61 J 11.

H. Drulis, M. Drulis

Landoll-BBmstein New Series 111/19dI

Ref.

p.

1831 2.1.3.12 Tm: figures 179

1 2 4 6 810 20 K 40

T-

Fig. 377. Magnetic specific heat of Tm metal 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 line corresponds to the relation Cmag =8.3 T2.3 mJ/mol K with T in K [66 L I].

60

@cm

1 40

Qr 20

I 60

II 50 100 150 200 250 K 300

T-

Fig. 380. Temperature dependence of the electrical resis- tivity, e, for the a, b, and c axes of a Tm single crystal between 1.3 and 300 K. Arrows show TN, and the dashed lines are calculated. The resistivity along the a and b axes do not exhibit any anomaly at 38 K where Tm becomes ferromagnetic [68 E 11.

J”

mol K 2

IO-'

10-2 2 I 6 8 10“ 2 c 6 Kl

Fig. 378. Specific heat of Tm vs. temperature. The arrow indicates the temperature below which C - C, = (17.9 T

+ 2.84 T3) mJ/mol K, with T in K, is smaller than 1% of C. C, is the nuclear contribution to C. The solid curve represents the optimum fit a’= -0.1072 K (cf. Table 5), the Schottky curve expected for the two-level energy scheme of 16’Trn being scaled by the factor 0.950 [69 H I].

0.99710>+0.055 1+6:

+0.0551-6:

0.9101~2>+0.4151T4:

0.7071+3>+0.7071-3:

0.9741+-5>-0.2281s1:

0.9101~4>-0.4151s2:

0.7071+3>-0.7071-3.

0.707 I + 6> - 0.707 I - 6’

0.7051+6>+0.7051-6 -0.0781 0

Tm

HII c

2d

I I I

100 K

50

0

.50 I -s"

2

400

150

200

0 40 80 .103 A/m 160

Fig. 379. Energy levels for Tm3 ‘iahexagonal crystal field calculated from axial anisotropy measurements. Bi

=-l.OK, B~=l.l.10-3K, Bz=-7.6.10-‘K and Bz

= 7.3 . 10e4 K were used. An effective field is applied in the c direction [77 F 2-J.

Land&Bhstein

New Series 111/19dl

H. Drulis, M. Drulis

180 2.1.3.13 Yb: figures [Ref. p. 183 2.1.3.13 Ytterbium

3 .lrt - mol cm3

1

H=14.24 kOe I

0 100 200 300 K 400

T---c

Fig. 382. Plot of l/(x-x,,) vs. temperature for the same Yb samples shown in Fig. 381. x0 is the background susceptibility obtained by plotting x vs. l/T and assum- ing temperature independence. f is the fraction of Yb3+

in metal, while the arrows indicate the onset of the phase transition to the diamagnetic state [70 B 23.

0 100 200 300 K 400

l----c

Fig. 381. Magnetic susceptibility vs. temperature of hcp 7 Yb: (open circles) as condensed at 450°C (solid circles) annealed at 680 “C; and of fee Yb obtained from diamag-

$ netic hcp Yb by plastic deformation. The magnetic 6 transition at about 270...290K from paramagnetic to the diamagnetic state is associated with the fcc+hcp 5 phase transformation. The numbers f-8 indicate the sequence of the measurements [70 B 23.

I 4 g 3

1

0 3 6 9 12 kOe

H-

Fig. 383. Magnetization vs. magnetic field for hcp Yb at 1.405 K. The solid line represents a Brillouin function calculation for I-, ground state and O.l15at% Yb3+. The broken lines show calculated initial slopes of the mag- netization curve for the various ground states which are possible in a crystal field of octahedral symmetry, based on the assumption that the atomic fraction of Yb3+

retains its high-temperature value of 0.58 at% [70 B 21.

H. Drulis, M. Drulis

LandolbB6mstcin New Series 111/19dl

Ref. p. 1831 2.1.3.14 Lu: figures 181

50 mJ mol K2

45

I 30 )- 25

\ c?

20

0 5 IO 15 20 25 K2 30

T2-

Fig. 384. Specific heat CJT vs. TZ for hcp Yb as- condensed (open circles), and annealed (solid circles), and for fee Yb (obtained by plastic deformation of hcp Yb) at zero magnetic field (open triangles) and 106 kOe (solid triangles) [70B 21. The dashed line represents data of [63 L I].