Collaborators: R. Grössinger D. Triyono H. Sassik J. Fidler H. Michor G. Badurek G. Wiesinger J.P. Sinnecker M. Knobel J.H. Espina J.

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2 Collaborators: R. Grössinger D. Triyono H. Sassik J. Fidler H. Michor G. Badurek G. Wiesinger J.P. Sinnecker M. Knobel J.H. Espina J. Eckert

3 Magnetisation (emu/g) pulsed field static field 175 K Coercive Field (T)

4 dh/dt [(GA/m)/s)] 2 Cu 1.5 Cu 2. SmCo 5-x Cu x Cu Cu 3. Cu 2. as-cast Cu 2.5 as-cast dh dh = dt dt e H S c v,4,8 1,2 1,6 H c [MA/m] (dh/dt)/(dh 1 /dt) Cu 2.5,,2,4,6,8 SmCo 5-x Cu x Cu 1.5 Cu 2. Cu 2.5 Cu 3. Cu 2. as-cast Cu 2.5 as-cast 1,,1,2,3,4 H c [MA/m] S v = H c1 dh ln dh H 1 21 c2 dt dt = ln H dh dh 1 c 21 dt dt ;

5 H c [MA/m] H c [MA/m] as-cast VSM 1.6 (b) SmCo 5-x Cu x (VSM) (Pulse) as-cast (Pulse) Composition x (a) as-cast S v [MA/m],2,15,1,5 x = 3 Sv (pulse) Svac (pulse) SvVSM (VSM) as-cast (VSM),,2,3,4,5,6,7,8 H c [MA/m]

6 K 15 K 214 K 255 K 35 K 4 K x = 2.5 For very narrow domain walls: 8πAKN 1 H c = ktm ln t τ. s 1/Hc (m/ma) K 14 K 2 K 35 K 45 K 5 K x = 2. A is the exchange energy N is the density of defects relaxation time t: t = τ exp(e/kt), ln t (s) E is the energy barrier; τ depends on the exact nature of the magnetizing reversal process and lies between 1-12 and s

7 Coecive field (MA/m) H c (MA/m) x = x = 2 x = T (K) 163 MA/m.s 28.4 MA/m.s.69 MA/m.s H 8πAKN 1 c = ktm ln t τ. s 2.. x = Temperature (K)

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9 Melt-spun Nd 6 Fe 3 Al 1,1 Nd 6 Fe 3 Al 1 ribbon (as-cast) 12,2 Nd 6 Fe 3 Al 1 ribbon (as-cast) 24 Polarization (T),5, -,5 296 K 6-6 Magnetization (emu/g) Polarization (T),1, -,1 2 K Magnetization (emu/g) -,1.5 T/s 17 T/s -12 -,2.5 T/s 17 T/s -24-1, -,5,,5 1, µ H (T) µ H (T)

10 Bulk Nd 6 Fe 2 Co 1 Al 1 Polarization (T),1, -,1 296 K Nd 6 Fe 2 Co 1 Al 1 bulk ( at 773 C) 2 K.5 T/s 17 T/s Magnetization (emu/g) µ H (T)

11 3 Nd 6 Fe 3 Al 1 as-cast at 63 K χ (1-4 m 3 /kg) 2 1 χ (1-6 m 3 /kg) 6, 5, Temperature (K) T P T P Temperature (K) 3 bulk (as-cast) bulk ( at 773 K) ribbon (as-cast) Nd 6 Fe 2 Co 1 Al 1 χ (1-4 m 3 /kg) 2 1,4,2 T P, Temperature (K)

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13 ,8 Polarization (T),4, -,4 -,8 Nd 6 Fe 3 Al 1 ribbon (as-cast) 296 K, µ H =, µ H = -,48 T, µ H = -,54 T, µ H = -,8 T Linear fits ln t (ln s),8 Polarization (T),4, -,4 as-cast, T = 297 K; µ H = -.37 T, T = 2 K; µ H = -1.3 T at 773 K, T = 297 K; µ H = -,39 T, T = 2 K; µ H = -1,3 T Linear fits Nd 6 Fe 2 Co 1 Al 1 bulk ln t (ln s)

14 If a steady reverse field is applied to a ferromagnet, after saturation the polarization (J = µ M) continues to decrease with time, t, after the reversal: J = const + S ln t, where S is the magnetic viscosity coefficient. In the absence of any diffusion effects, this decline with time must be due to the thermal activation of domains, or domain walls, over free energy barriers. Street and Wooley: S = de k T χ B irr dh, where E is the activation energy for an energy barrier H and χ irr = ( M / H ) at the field where S is measured.

15 S v = S( 1 Nχ ) / χ where N is the demagnetization factor of the material and χ rev is the reversible susceptibility. Generally Nχ rev << 1, then: J = const rev S + v ln t χ i irr, S v = k B T / de dh

16 S ν is related to the so-called activation volume v (volume within which the magnetization is reversed by one individual activation process): S v = According to Givord et al. [7], in Nd-Fe-B magnets, v is related to domain wall width, δ, as follows: v/δ³ =constant k M B T s v

17 Table1. Values of the irreversible susceptibility, the activation volume, and the viscosity parameters obtained from different methods. T (K) S v (T) S v,p (T) S v,j (T) v H x (T) χ irr (at H c1 ) (at H x ) (1-24 m 3 ) Nd 6 Fe 3 Al 1 as-cast Nd 6 Fe 3 Al 1 as-cast Nd 6 Fe 3 Al 1 as-cast Nd 6 Fe 3 Al 1 as-cast Nd 6 Fe 2 Co 1 Al 1 as-cast Nd 6 Fe 2 Co 1 Al 1 as-cast Nd 6 Fe 2 Co 1 Al Nd 6 Fe 2 Co 1 Al

18 µ H c (T) (a) Nd 6 Fe 3 Al 1 (ribbon) as-cast (b) Nd 6 Fe 2 Co 1 Al 1 bulk (as-cast) bulk () ribbon (as-cast) Magnetization (Am²/kg) (b) bulk (as-cast) 6 Nd 6 Fe 2 Co 1 Al 1 (a) ribbon (as-cast) 296 K 29 K 25 K 5 K 75 K 5 K K Temperature (K) K 1 2 Field µ H (T)

19 H c = H ln H 4 τ τ bf k B 2/3 T 2/3 (µ H c ) 1/2 (T) 1/2 1,5 1, as-cast model Nd 6 Fe 2 Co 1 Al 1 (bulk), Temperature 2/3 (K) 2/3 R. Sato Turtelli, D. Triyono, R. Grössinger, H. Michor, J.H. Espina, J.P. Sinnecker, H. Sassik, J. Eckert, G. Kumar, Z.G. Sun, G.J. Fan, Coercivity Mechanism in melt-spun Nd 6 Fe 3 Al 1 and Nd 6 Fe 2 Co 1 Al 1 alloys, Phys. Rev. B 66, pp , 22.

20 Merci Beaucoup!

21 -R. Sato Turtelli, D. Triyono, H. Sassik, R. Grössinger, J. Fidler, G. Badurek, W. Steiner, The microstructure of Nd-(Fe,Co)-Al alloys, RQR Conference -R. Sato Turtelli, D. Triyono, R. Grössinger, H. Michor, J.H. Espina, J.P. Sinnecker, H. Sassik, J. Eckert, G. Kumar, Z.G. Sun, G.J. Fan, Coercivity Mechanism in melt-spun Nd 6 Fe 3 Al 1 and Nd 6 Fe 2 Co 1 Al 1 alloys, Phys. Rev. B 66, pp , 22. -D. Triyono, R. Sato Turtelli, R. Grössinger, H. Michor, K.R. Pirota, M. Knobel, H. Sassik, T. Mathias, S. Höfinger, J. Fidler, Temperature dependence of hysteresis loops and acsusceptibility of as-cast and Nd 6 Fe 3 Al 1 hard magnetic alloys,j. Magn. Magn. Mater , pp. 1321, 21. -R. Sato Turtelli, D. Triyono, R. Grössinger, K.R. Pirota, M. Knobel, P. Kerschl, J. Eckert, S. Kato, Temperature dependence of the magnetic relaxation of Nd 6 Fe 3 Al 1 and Nd 6 Fe 2 Co 1 Al 1 alloys, Proc. of 17 th Int. Workshop on RE-Magnets and Their Applications, pp.161, 22. -R. Sato Turtelli, J.P. Sinnecker, W. Steiner, G. Wiesinger, R. Grössinger, D. Triyono, Non-equilibriun magnetic properties of melt-spun Nd 6 Fe 3 Al 1 alloys, to be published.

22 On applying a field H, the wall will bow and when H increases sufficiently the wall will break away from the center pin. However, the wall can also break free in a field lower than H (critical field in absence of thermal activation), if thermal energy is available to supply the activation energy which is necessary to take the bowed wall from its minimum energy position to its maximum energy position where it can break away. For strong pinning the activation energy, neglecting internal demagnetizing effects, is given by [17] 3 / 2 1/ 2 4bf H E = 1 3 (1) H where f is the maximum restoring pinning force from a single pin and 4b is the wall width. The condition which must be satisfied for strong domain-wall pinning is 3 f β = > 1, (2) 8πbγ where γ is the domain-wall energy. Thus the pinning is strong for small b (narrow domain thickness) or for large f/γ. For a 18 domain wall, the thickness and the energy are given by δ = 4b = π A/ K and (3) γ = 4 A.K (4) respectively, where A and K are exchange and anisotropy constants. The coercive field H c, in the region where the intrinsic magnetic properties can be considered constant, is given by H c = H H τ ln k τ 4bf B 2 / 3 T 2 / 3, (5) where k B is the Boltzmann constant, τ is the time duration of measurement and τ is a time constant of order s.

23 Under the influence of thermal fluctuations these narrow domain walls give arise to a magnetic aftereffect by the formation of domain wall kinks. The small domain walls move in an intrinsic lattice potential known as Peierls potential of the domain wall with a periodic distance D. The critical radius r c of domain wall kink and the activation energy are respectively given by [11]: r c 2 σ πσ = and E = (3) 2M H D 2M H D s c s c whereσ = 4 A.K, is the kink energy by unit length, A is the exchange energy and K is the anisotropy energy; M s is the saturation magnetization. Combining (3) and (2) and introducing now a constant N α 1/D that can be related to the density of thermal fluctuation of defects, one obtains: t ln τ 8πAK 1 = N (4) ktm s H c Equation (4) shows that the relaxation time is proportional to the inverse of the coercivity.

24 .2 S v (MA/m).16 x = 2. x = S v (MA/m) x = 2. x = 2.5 model Temperature (K) Coercive field (MA/m) S v = ah c b ( ) H 1. 5 c