Three-dimensional magnetization process in HoFe11Ti

Yuri Janssen, J.C.P. Klaasse, E. Brück, F.R. de Boer, K.H.J. Buschow,J. Kamarád1, N.V. Kudrevatykh2

1: Institute of Physics, Praha2: Institute of Physics and Applied Mathematics, Ekaterinburg

B

MI

II

Outline

- Introduction- Experiment- Results- Conclusion

Research of rare-earth (R) – transition-metal (T) compounds

Modern permanent magnets: - SmCo5 (1960s) - Nd2Fe14B (1984) - RFe11Ti (1990s)

Requirements: - large magnetization- high ordering temperature- high coercivity

large magnetocrystalline anistropy

Magnetic R-T coupling essential for coupling between:

- large magnetization (T) - high anisotropy (R)

Hund’s rules ==>

Light-R (Nd, Sm) – T : parallel coupling => ferromagnets

Heavy-R (Gd, ..Ho, Tm) – T : antiparallel coupling => ferrimagnetsMTMR

M

M

MTMR

HoFe11Ti

Tetragonal crystal structure: ThMn12-type (s.g. I4/mmm)Ti stabilizes crystal structure

[001]

[100] [010]

HoFe11Ti: R-T coupling strong!

Ho and Fe sublattice moments remain antiparallel

B

[001][001]

MFe = 20 B/f.u.

MHo = 10 B/f.u.

M = 10 B/f.u.

Strong coupling HoFe11Ti excellent system for research on magnetocrystalline anisotropy

Eanisotropy = K1sin2 + K2 sin4 + K3 sin6 + K4 sin4cos4 + K5sin6cos4

Tetragonal structure

[100]

[010]

[001]

Ho has large orbital momentum==> at low temperature, higherorder K play a role

HoFe11Ti: easy-axis system ( M // [001] )

Magnetic free energy determines equilibrium magnetization

F = Eanisotropy + EZeeman = Eanisotropy - B.M

Only K1 Higher order K

MS

0

B // [100]

B // [001]

M

B

MS

0

B // [100]

B // [001]

M

B

Outline

- Introduction- Experiment- Results- Conclusion

Magnetization B // main directions

Different in-plane results! K4, K5 important

Magnetic-phase transition when field in plane

0 1 2 3 4 50

2

4

6

8

10

B // [100]

B // [110]

B // [001]

T = 5 K

HoFe11Ti

MZ ( B

/f.u

.)

B (T)

Bdem ~ 0.3 TMS

HoFe11Ti : possible 3D-process

3D magnetometry (SQUID, high-field magnet)

Requirements:

- Pickup coils in three directions

- Sample single domain (homogeneous magnetization)

Bdem.=NM[001]

M

[001]

[001]

Bsingle=Bdem./cos

Choose [001] = 75° single domain when B ~ 1.1 T

Sample single domain: projection of B on [001]

Magnetizationfor B in(110) plane

Above 1.1 T, sample single domainTransition occurs above 1.1 T

0 1 2 3 4 50

2

4

6

8

10

12

B in (110)[001] = 75°

HoFe11

Ti

T = 5 K

MZ ( B

/f.u.

)

B (T)

MS sin 75

0 1 2 3 4 50

2

4

6

8

10

12

B in (100)

[001] = 73°

HoFe11

Ti

T = 5 K

MZ ( B

/f.u.

)

B (T)

Above 1.1 T, sample single domainTransition occurs above 1.1 T

Magnetizationfor B in(100) plane

MS sin 73

Measurement configuration

Mz // B

Mx near [001]

My Mx Mz

After measurement:

project Mx, My, Mz

on [100], [010], [001]

Mtot

Mz

Mx

[001]

[001]

B

Outline

- Introduction- Experiment- Results- Conclusion

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

Mz

My

Mx

Mtot

HoFe11TiB in (110)[001] = 75°

T = 4.2 K

M ( B

/f.u

.)

B (T)

My nearly zero

Conclusion: 2D process

Magnetizationfor B in(110) plane

Magnetization for [100] and [010] equal, as expected

0 2 4 6 8 10 12 140

2

4

6

8

10

12Mtot.

M[001] M[010]

M[100]

HoFe11

TiB in (110)

[001] = 75° T = 4.2 K

M ( B

/f.u.

)

B (T)

Magnetizationfor B in(110) plane

Projectiononcrystalaxes

My becomes non-zero! 3D process

Magnetizationfor B in(100) plane

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

Mtot.

Mx

My

Mz

T = 4.2 K

HoFe11Ti B in (100)[001]= 73°

M ( B

/f.u

.)

B (T)

B in (100) plane: 3D process

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

M[010]

Mtot.

M[001]

M[100]

T = 4.2 K

HoFe11

Ti B in (100)

[001]= 73°

M ( B

/f.u

.)

B (T)

Magnetizationfor B in(100) plane

Projectiononcrystalaxes

Transition: first-order (follows from coexistence) Outlook: mechanism for coexistence ? microscopy

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12B in (110)

[001] = 75°

Coexistence High-field phase

Low- field phase

M ( B

/f.u.

)

B (T)

2 4 6 8 100.0

0.5

1.0

B (T)

f

Abadìa et al., J. Phys.:Condens. Matter 10 (1998), 349 Calculations: M.-H. Yu

B = 3 T

B = 4 T

Calculations based on anisotropy parameters*

B in (110) plane

2D process

First order

B in (100) plane

3D process

First order

B = 5 T

B = 6 T

Conclusions:

-At the magnetic phase transition, a 3D magnetization process occurs- This phase transition is first order

* Asti and Bolzoni, J. Magn. Magn. Mater. 20 (1980), 29

M // [001] M [001]

0 30 60 90

B = 0.45

B = 0.417

B = 0.35

K1 = 1 a.u.

K2/K

1 = -1.5

K3/K

1 = 1

B = 0

Mag

net

ic e

ner

gy (

a.u

.)

(deg)

Some combinations of K1, K2, K3 (..K4, K5) ==> local minima inmagnetic energy as a function of angle with [001] ==> First order magnetization

process (FOMP)*