Determination of critical observablesusers.physik.fu-berlin.de/~ag-baberschke/teaching... · 2008. 9. 2. · Freie Universität Berlin Swedish-GermanSummer School, Sweden14.-19. Sept

Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 20081

Klaus BaberschkeKlaus Baberschke

Institut fInstitut füür Experimentalphysikr ExperimentalphysikFreie UniversitFreie Universitäät Berlint Berlin

Arnimallee 14 DArnimallee 14 D--14195 Berlin14195 Berlin--Dahlem GermanyDahlem Germany

PHASE TRANSITIONS IN FERROMAGNETIC MONOLAYERSPHASE TRANSITIONS IN FERROMAGNETIC MONOLAYERS??

e-mail: [email protected]://www.physik.fu-berlin.de/~bab

4. Curie - Weiss susceptibility, χ ac measured by means of mutual inductance, MOKE, and XMCD.

5. How do we determine TC and the critical exponents?

6. Non linear χ ac , the interpretation of higher harmonics in χ ac .

Lecture 2

Determination of critical observables

Determination of critical observablesas BH wanted


U. Bovensiepen et al., ECOSS 17, Surf. Sci. 402-404, 396 (1998)

4. Curie - Weiss susceptibility χac measured by means of mutual inductance, MOKE, and XMCD.

µ = 1 + ?



K. B. # 171

In many papers χ is given in arb. units, why ? Use SI-units!

N gives nice information. Nin-plane may be 10-3 – 10-5, but > 0


2 peaks in the ac-susceptibility

see lecture 1


ac MOKE and ac XMCD

JMMM, 146, 256 (1995)

JMMM, 135, L1 (1994)


Oscillatory Curie Temperature in Ultrathin Ferromagnets: Experimental Evidence


Up

Uaux

Ui

1

Ui

2

∆ µ χU ~ -1 i =

p = 4×10-11 mbar17 mOe < Hac < 1.6 Oeω0 = 213 Hzcompensation < 10 mOe

50 K < T < 650 K∆T = 3-5 mK/s∆T/TC ˜ 10-4

0|ˆ =∂∂

= Hdef HM

χ

200300

0

4

8

12

Cu2Cu3Cu4Cu4.5Cu 5

Cu5.5Cu6

T (K)300 300 300 300 300 300

Cun /Co2.5/Cu(100)

3χ'

(10

SI U

nits)

50200

0

2

4

6

Cu1

Cu2

Cu2.5Cu 3

Cu3.5Cu

4

Cu4.5Cu5Cu5.5Cu 6

T (K)200 200 200

Cun/Co

2.2/Cu(100)

200 200 200 200 200 200

3χ'

(10

SI U

nits)

ac Susceptibility of Cun/Co/Cu(100)


2.7(2) ML

1 2 3 4 5 6

-4

-3

-2

-1

0

1

2

3

4

∆TC

(K)

d Cu (ML)

C. Rüdt, A. Scherz and K. B., J. Magn. Magn. Mater. 285, 95 (2004)

2.2 ML Co

2.5 ML Co

theory

Φ

Λ∆ +d

dA

=(d)TCπ2

sin

2/4 1.22 2.7

2 11

π−≈−ΦΛ

)(=)(=

)(=A

Oscillatory TC: Experimental Evidence


0 1 2 3 4 5 6 7

300

350

450460

0 1 2 3 4 5 6 7

150

175

200

225

350400

T C(K

)

dCu (ML) d

(a) (b)

Cu (ML)

T C(K

)

2.2 ML Co 2.5 ML CoI. Change in the magnetic moment of the top layer in

Co/Cu(100)→Large drop of TCµCo 32 % enhanced at the vacuum interfaceµCo 17 % reduced at the Cu interface(A. Ney et al., Europhys. Lett. 54, 820 (2001), UHV-SQUID)TC ∝ µ2 yields:Co2/Cu(100): TC=370 KCu1/Co2/Cu(100): TC=220 K

II. Modification of electronic band structure at the Cu/Co interface→Monotonic decrease of TCCu2-8/Co20/Cu(100): change of effective mass due to Quantum-Well states(P. Johnson et al., Phys. Rev. B 50, 8954 (1994), ARUPS)

III. Quantum-Well effects→Oscillations of TCas theoretically predicted by P. Bruno, MPI Halle(M. Pajda et al., Phys. Rev. Lett. 85, 5425 (2000))

Origin of TC Change: Three Different Mechanisms


Plausibility of oscillatory amplitude of TC

KTatomµeVJ

atomµeV=JKTcap

Ccap

erC

4/2

/50100 int

≈∆⇔≈

⇔≈∆

Dramatic change in TC due to three different mechanisms

• Change of the magnetic moment at the Cu/Co interface• Modifications of the electronic bandstructure at the Cu capping layer• Oscillation of TC due to the formation of QW-states

(XMCD) (FMR)

(FMR) (ac susceptibility)

Ferromagnetic Trilayers

Capped ferromagnetic monolayer Cu/Co/Cu(100)


5. How do we determine TC and the critical exponents?


L.J. de Jongh and H.E. Stanley, Phys. Rev. Lett. 36, 817 (1976)

L.J. de Jongh, Physica 82B, 247 (1976)

L.J. de Jongh and A.R. Miedema, Adv. Phys. 23, 1 (1974)

Dimensional crossover




(Fe2 / V5)50 (001): critical behavior at TC

1

||int

exp1

−

+= N

χχ

γχχ −+ ⋅= tt 0int )(N≈ thickness / diameter ≈10-3


Forced manipulation of TC and γ

50 K < T < 650 K∆T = 3-5 mK/s∆T/TC ˜ 10-4

PRB 65, 220404 (2002)

Summary: Usually TC and ? or ß are fitted together in a log-log plot. This is very dangerous, small changes of ~ 0.4 K can change the exponent dramatically. Exponents need to be fitted to χ int (after correction for N) NOT to χ exp.


C. Rüdt et al., Phys. Rev. B 69, 014419 (2003) and ICM 2003

= +χ χ′ χ′′n n n(T) (T) (T)i

M (T) = 1/ dt M(T,H) (i n t)n 0 0τ ωexp0

τ0

∫Sketch of the field-, temperature-, and time-dependent magnetization M(H,T,t) subjectto an oscillating magnetic field H(t). (a) and (b) represent the paramagnetic case forT>TC, whereas (c) and (d) show theferromagnetic response for T<TC. Thephase-shift ∆t between the oscillatingmagnetic field H(t) and the responsefunction M(T,t) due to hysteretic effects isindicated (d). τ0 is the oscillation period.

T<TC

H0

⇒

⇒

H

M

H

M

t

M

t

T>TC

t

M

H

(a)

(d)(c)

(b)

∆t

τ0

6. Non linear ?ac , the interpretation of higher harmonics in ?ac.


Measurement of higher harmonics

χdef =

χexp =

∂M

∆M∂H

∆H

H=0• • •

χ ω(T,H, )quasistatic 213 Hz10 mOe < H < 1.6 Oe0

Up

Uaux

Ui1

Ui2

∆ µ χUi ~ -1 =

-200

0

200x 1 x 3

-200

0

200x 5 x 7

0.98 1.00

-200

0

200x 9

0.98 1.00

x 11

TC TC

χ (S

I uni

ts)

n

T/TC


Hysteresis close to TC

0 1 2 3 4

-2

0

2 0.975 0.98 0.99 1.0 1.01

M(a

rb.u

nits)

t (ms)

T/ TC

M(a

rbun

its)

-0.8 0 0.8

-2

0

2

H (Oe).

Time-dependent magnetizations M(t) calculated via a Fourier analysis of themeasured susceptibility coefficientsχn(T), for reduced temperatures0.975<T/TC<1.01. Fourier coefficientsup to order n=11 have been used.

Hysteresis loops M(H) for different reducedtemperatures T/TC.

M(T,t)= H (T, ) exp(-in t)0 n 0 0Σχ ω ω∞

-∞


(a) (b)

χ1,pm'

χ1,fm'

0.98 1.00

100

200

0.98 1.00

'χ

1(S

I un

its)

T / TC0.96 0.98 1.00 1.02

0

0.5

1

0.96 0.98 1.00 1.02

0

1

Theory, K4

Theory, K2

Experiment

H

HC

MS

0 = 0.8 Oe

MS

T / TC

HC (O

e)

Theoretically and experimentally MS(T), normalized to unity (left axis), and HC(T) (right axis) as a function of T/TC.HC(T) has been calculated for both a uniaxial (K2) and a quartic (K4) in-plane anisotropy.

MS and HC close to TC

Separation of χ′1(T)=χ′1,fm(T)+χ′1,pm(T) into a ferromagnetic (blue) and a paramagnetic part (red).(a) theory and (b) experiment. In (b) thepara- and ferromagnetic contributions areonly drawn schematically (hatched areas).

Tmax < TC




Summary•This summer school is dealing with phase transitions in nanomagnetism,

that is to say, the physics close to TC .At elevated T the „T = 0 language“ may be inappropriate.

Do not interpret your measurements in a simple MFA.

•Static exchange- and anisotropy-fields, and T=0 DOS are insufficient,spin wave excitations, spin fluctuations are important for a proper description.

•The ac-susceptibility contains very reach information,but “a conclusive analysis …is complex” (BH et al.) .

Many mistakes (incompleteness) have been published in the literature.

•Nanomagnetism is clearly important for technological applications, but it opens also a huge field to study fundamentals,

which may be inaccessible in 3D bulk.

Documents

Determination of critical observablesusers.physik.fu-berlin.de/~ag-baberschke/teaching... · 2008. 9. 2. · Freie Universität Berlin Swedish-GermanSummer School, Sweden14.-19. Sept