c. geibel- magnetic frustration in intermetallic compounds
TRANSCRIPT
Magnetic frustration in intermetallic compounds
Introductory remarks
Frustrated systems with localized moment
Itinerant magnetic systems with frustration
! Intermetallic compounds, not metallic oxides
! No spin glass
C. Geibel
Max-PIanck Institute for Chemical Physics of solids
Dresden, Germany
Frustration in intermetallic compounds
Rare earth
localized moments
large total angular moment at high T
! but at low T reduced by
crystal field effects
Ce, Yb effective doublet at low T
very strong spin orbit coupling
often large anisotropy
not a problem
Exchange mechanism: RKKY
! long range (1/r3)
Unlikely that only NN (and NNN)
exchange is relevant
Probably a severe problem
Two types of magnetic moments
3d metals: Itinerant magnetism
no stable local moment
Effective interaction defined by
Fermi surface
description in terms of NN-
interactions not appropriate?
completely different approaches
needed?
Maximum of generalized
susceptibility (Q)
Sharp peaks on Fermi surface
or broad hills?
Appropriate structures?
Many structures with topological frustrated sublattices
Example: CaCu5 structure type, here CeCo3B2
- Co site: kagome lattice
- Ce site: triangular
huge number of compounds with magnetic atoms
on different sites
But evidence for frustration rather exceptional
Problem:
no directional bonding in metals
Very difficult to get well defined
2- or 1-dimensional systems
Ce
Co
B
RTX compounds with ZrNiAl structure
ZrNiAl structure : Hexagonal
R: Rare earth element Magnetism
T: transition metal non-magnetic
X: p-metal: Al, In, Sn, Bi
R -atoms distorted Kagome lattice
equivalent bonds but triangle tilted
Very complex antiferromagnetic structures
evidence for frustration
B. Fåk et al.
G. Ehlers et al. (1997) YbNiAlH. Maletta et al. (1994) TbNiAl
C(T) and ( )T:
Pronounced transition at TN = 3.6 K
paramagnetic to antiferromagnetic
Further transition at TN2= 1.4 K
Specific heat (Trovarelli et al., 2000)YbPtIn
Mössbauer spectroscopy (Bonville et al., 2007):
TN2 < T < TN:
only tiny ordered moment along hard c axis
no ordered moment along easy basal plane
T < TN2:
large ordered moment on 2/3 of Yb-sites
no ordered moment on 1/3 of Yb sites
! absence of ord. moment persist until 60 mK
Mössbauer spectra
Umeo et al. (2004), Morosan et al.(2004)
Transition at TM1 = 0.8 K
strong fluctuations above TN
Efluc 10K >> TN
Kondo or frustration?
1rd order transition at TM2= 0.6 K
YbAgGe: Frustration and Kondo?
B-T phase diagram
(T), ( )T and C(T)
Elastic neutron scattering:
Fåk et al. (2005), Fåk et al. (2005)
TM2 < T < TM1:
incommensurate along c
sum of basal plane components = 0
T < TM2: commensurate along c
AF-order in basal plane
YbAgGe: magnetic structure
neutron peak intensity
Mössbauer (Bonville et al., 2007)
inhomogeneous line broadening
modulated structure down to 60 mK?
Lines are still broaden above TM1
evidence for fluctuating Yb moments
fl 1 B 3·109 s-1
modulation of Yb moment
YbAgGe: dynamic magnetic susceptibility
Inelastic neutron scattering (Fåk et al., 2005)
dynamic suscept. dominated by quasi elastic spin fluctuations, no spin waves
no Q dependence within basal plane strong Q dependence along c*
in plane frustration?
quasielastic scatt. along c*q dependence of and
in plane
along c*
RB4: tetragonal structure
early investigation in 1960-1980
Etourneau et al., (1979):
steps in magnetization curves
Z. Fisk et al. (1981):
multiple magnetic phase transitions
recently reanalyzed in terms
of Shastry Sutherland lattice
RB4 compounds: frustrated Shastry Sutherland lattice?
a
bc
R
B
R12 close to R13
in M(B) plateaus at M =1/2 MSat
(T) and M(B) of ErB4
(Michimura et al. 2006)
Similar steps in M(B) in most RB4 compounds
Step at M(B) = 1/2 Msat in most RB4
independently of R element independently of field direction
not related to crystal field scheme related to intersite interactions
M(B) of TmB4 (Iga et al. 2007)B-T phase diagram of TmB4
DyB4 : dipolar and quadrupolar frustration?
Specific heat and magnetization
Watanuki et al., 2006
For B = 0 two transitions at
TN1 = 20 K and TN2 = 13 K
Step M(B) = 1/2 Msat at B 5T
B-T phase diagram of DyB4
Evidence for quadrupolar ordering
Entropy at TN1: S(TN1) = R·ln4
ordering phenomena occur
within a quasi quartet
both dipolar and quadrupolar
moment
Ultrasound measurements
strong softening of C44 down to TN2
anomaly at TN2
strong evidence for
quadrupolar ordering
High resolution XR diffraction
(Okuyama et al. 2005)
splitting of (006) reflection
very small monoclinic distortion
angle ac or bc = 89.84º
T dependence of elastic constants
Watanuki et al., 2005
Resonant XR scattering
Intensity at forbidden (100) reflectionOkuyama et al., 2005:
RXS near LIII edge of Dy
at forbidden (001) reflection
T depend. of Intensity and HWHM
Magnetic and quadrupolar structures
Magnetic moments from neutrons
Ji et al., 2007
Magnetic structure T < TN2
Phase II: TN2 < T < TN1
AF moment collinear along c
Phase III: T <TN2
additional non-collinear moment
in ab plane
quadrupolar short range correlations
- ferro projection on ac plane
- antiferro projection on bc plane
Okuyama et al., 2005
Yb2Pt2Pb: new example for Shastry-Sutherland lattice?
buckling of Pt layer
doubling of c parameter
two crystallographic
sligthly different Yb sites
Kim et al., cond. mat. 0801.4875
Mo2FeB2structure
quite common
Yb2Pt2Pb:
first system where
frustration relate to
Shastry-Sutherland
lattice was invoked
tetragonal U2Pt2Sn structure
superstructure of Mo2FeB2 structure
d1 d3 > d2 d4
Shastry-Sutherland
lattice well defined
Experimental evidence for frustration effects
Susceptibility
Specific heat and entropy
Sharp peak in C(T) at TN = 2.1 K
strong contribution of fluctuations
in C(T) above TN up to 10 K
but Kondo effect in (T) only
very weak
evidence for frustration effect
Maximum in (T) along easy plane
just above TN
! cannot be explained by CEF effects
! cannot be explained by Kondo effect
evidence for frustration effect
RInCu4: spin and orbital frustration?
Cubic C15b (AuBe5) structure
R atoms form fcc lattice
Specific heat (Fritsch et al., 2005)
Evidences for frustration
large ratio CW/TN 11
only small part of the entropy
recovered at TN
Prototype of itinerant frustrated system: YMn2
Cubic laves phase (C15 structure)
Mn atoms: corner shared tetrahedra
AF-state below TN = 100 K (Balou et al., 1987)
Sum of spins on each tetrahedron cancels
Additional long wave distorted helical component
Magnetic order suppressed
by slight substitution of
Y by Sc or Mn by Al or
weak hydrostatic pressure
Strong enhancement of the
electronic specific heat
Sommerfeld Coefficient
= 150 mJ/(mol· K2)
(Wada et al., 1987)
Magnetic excitations
Inelastic neutron scattering
(Ballou et al., 1996)
Spin fluctuation spectra
broad in Energy,
no apparent gap
Intensity Q-dependent
- Maximum near
Q = G +/- (2/2, 2/3, 0)
- Maximum extended along
zone boundary
Evidence for frustration
No magnetic scattering in first and some other Brillouin Zones
Evidence for short-lived 4-sites collective spin-singlets
C. Lacroix , B. Canals: can be explained suprinsigly well by a localized
spin model
Intensity map (Ballou et al., 1996)
-Mn: further itinerant frustrated magnet?
-Mn: high temperature phase of Mn
can easily be quenched to low T
Simple cubic structure - 20 atoms in elem. Cell
- 2 different Mn sites
Large Sommerfeld coefficient = 70 mJ/(mol· K2)
No magnetic
transition
but doping
with Al induces
spin Glass
behavior
but both eff
and CW
decrease with
Al content !
susceptibility (Nakamura et al.,
1997)
eff and CW = f(Al-content)
x0 0.5
NbFe2: a frustrated itinerant ferromagnet?
hexagonal AB2
Laves phase
two B (Fe) sites
B atoms in 6h
kagome lattice
Metallographic phase diagram
large homogeneity range Nb1-yFe2+y
Advantage; system can easily be tuned
Disadvantage: homogeneity problems
Very hard to get homogeneous single crystals
NbFe2: just at a critical point!
Susceptibility, magnetization
Shiga et al. 1987, Yamada et al. 1988
Nb or Fe rich Nb1-yFe2+y
is ferromagnetic
ferromagnetic state becomes
unstable in stochiometric NbFe2
transition towards a AF state
Phase diagram
Yamada et al., 1988
Phase diagram (Crook et al., 1995)
NbFe2: suceptibility and specific heat
Specific heat (Brando et al., 2008)
susceptibility (Brando et al., 2008)Susceptibility
Ferro- and AF- state can clearly
be discerned
effective moment decreases
continuously across critical point
Specific heat
only tiny anomalies at TNy
At critical point (y = -0.012)
C(T)/T increases towards low
temperatures fluctuations
Summary
Evidence for magnetic frustrated intermetallic compounds
Experimental and theoretical level of understanding lower than for
isolating spin systems
Interaction between frustrated magnetic system and conduction electrons
can lead to additional interesting properties