View
3
Download
0
Category
Preview:
Citation preview
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: bab@physik.fu-berlin.dehttp://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
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 20082
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 + ?
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 20083
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 20084
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
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 20085
2 peaks in the ac-susceptibility
see lecture 1
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 20086
ac MOKE and ac XMCD
JMMM, 146, 256 (1995)
JMMM, 135, L1 (1994)
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200872
Oscillatory Curie Temperature in Ultrathin Ferromagnets: Experimental Evidence
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 20088
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)
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 20089
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
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200810
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
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200811
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)
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200812
5. How do we determine TC and the critical exponents?
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200813
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
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200814
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200815
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200816
(Fe2 / V5)50 (001): critical behavior at TC
1
||int
exp1
−
+= N
χχ
γχχ −+ ⋅= tt 0int )(N≈ thickness / diameter ≈10-3
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200817
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.
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200818
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.
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200819
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
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200820
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∞
-∞
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200821
(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
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200822
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200823
Freie Universität Berlin Swedish-German Summer School, Sweden 14.-19. Sept. 200824
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.
Recommended