On the search for a Lifshitz point in UPd2Si2

On the search for a Lifshitz
point in UPd2Si2
T. Plackowski, D. Kaczorowski and J. Sznajd
Institute for Low Temperature and Structure Research, Polish
Academy of Sciences,Wrocław, Poland
środa, 16 marca 2011
PARA
T
C
Para
IC
IC
g
środa, 16 marca 2011
Multicritical
Lifshitz Point
Lifshitz point
Hornreich, Luban, and Shtrikman 1975
środa, 16 marca 2011
•
At the LP the lines of para (P),
incommensurate (IC) and ordered (C) phases
join with common tangents.
•
The phase transition to the ordered phase is of
second order (continuous).
•
The modulation vector of the IC phase goes to
the C phase value (e.g. to zero for ferro, and
2/3 for ferri ++-) continuously at the LP.
PRB 43, 13232 (1991)
Crystal structure
of UNi2Si2 (UPd2Si2)
środa, 16 marca 2011
AF
H
T < 85
środa, 16 marca 2011
Ferri
UPd
2Si2
85<T<96.5
Incommensurate
Longitudinal Spin
Density Wave
LSDW
PRB 43, 13232 (1991)
UNi2Si2: 103 < T < 124
UPd2Si2: 96.5 < T < 138.4
środa, 16 marca 2011
Temperature dependence of the specific heat
środa, 16 marca 2011
Temperature dependence of the specific heat
środa, 16 marca 2011
Temperature variations of the specific heat measured
with increasing and decreasin the temperature in an
external magnetic field of different strenght
środa, 16 marca 2011
Temperature dependence of the magnetization in
several mgnetic fields
środa, 16 marca 2011
Magnetic phase diagram
M
środa, 16 marca 2011
Six layer model
H=-
n
n+1
j1∑Si Si
-
n
n+2
j2∑Si Si
- k∑SinSjn Sin+1 Sjn+1 - h∑Sin
mn = <Sin>
6
m = 1/6 ∑ mn ,
n+1
φ2 = m1 + m2 + m3 - m4 - m5 - m6
φ3 = m1 - m3, φ4 = m2 - m6, φ5 = m1 - m4, φ6 = m3 - m6
AF - order: φa = φ5 = φ6
Ferri - order: φf = φ3 = φ4
środa, 16 marca 2011
Landau free energy for ferrimagnetic phase transition
r
ANNNI model k = 0
fL = f0 + J(t A2-J2-4Jt)/6t φf2 + J3A(1- A2) φf3
A = tanh[(h+2Jm)/t], J = j1 + j2
Critical point
r = 0 ANNNI: h = 0 or t = 0
Ext. ANNNI model k ≠ 0
r = -A 3 J 3 -18 A 2 J k m t + 18kmt(J+8t)+A (J 3 -12kt 2 )
środa, 16 marca 2011
Landau isolated critical point
r = 0,
-J2 - 4 J t + J2A2 = 0,
6m(J + 6km 2)-3(J + 3km 2)A = 0
tc ,hc
0.8
0.6
0.4
0.2
0.0
0.0
środa, 16 marca 2011
0.1
0.2
0.3
0.4
0.5
0.6
0.7
k
Conclusion
środa, 16 marca 2011
•
Lines separating the phases IC, Ferri and P meet at
the multicritical (M) point with common tangents.
•
The experimantal data suggest that the P-Ferri
transition above the critical point can be continuous
one (at least M = LICP).
•
The field tends to bring IC wave vector closer to
the commensurate phase value 2/3 as the
temperature nears that of the ferrimagnetic phase,
as expected at LP.
•
Conjecture: M point of UPd2Si2 can be a LP.