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