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Magnetic transitions under high magnetic fields

V. Simonet Institut Néel, CNRS/UJF, Grenoble, France

X-ray Spectroscopy in High , SOLEIL 2010 17/11/10 2 Outline of the lecture

Introduction: effect of external magnetic field

Magnetization processes and frustration

Metamagnetism in metals

Competing degrees of freedom

Level crossing

Quantum

Conclusion

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 3 Outline of the lecture

Introduction: effect of external magnetic field

Magnetization processes and frustration

Metamagnetism in metals

Competing degrees of freedom

Level crossing

Quantum magnetism

Conclusion

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 4 Introduction: effect of external magnetic field

Zeeman term: competition with other terms in energy

Metamagnetism: transition (1st or 2nd order) towards new magnetic state (≠ moments orientation and/or magnitude) Most often AFM towards FM

1st order 2nd order

Magnetization plateaus: constant magnetization M at M=0 or at finite M before saturation

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 5 Introduction: effect of external magnetic field

Zeeman term: competition with:

Exchange interactions molecular field up to 1000 T and magnetocrystalline anisotropy 100s of T : high fields needed

quantitative information on interactions, energy levels, etc…  + new model systems

Tools : NMR, neutron scattering, magnetic susceptibility, magnetization, Torque, specific heat, IR/optical spectroscopy, ESR, ultra-sound… and of course X-rays

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 6 Introduction: effect of external magnetic field

Historical (1967) example in FeCl2 H // easy-axis

Note: 10 kOe = 1 T

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 7 Introduction: effect of external magnetic field

Metamagnetic transitions in simple collinear antiferromagnets

Exchange anisotropy Zeeman terms

Weak anisotropy: spin-flop Strong anisotropy: spin-flip

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 8 Introduction: effect of external magnetic field

More complicated situations with:

≠ anisotropies (easy-axis, easy-plane, multi-axis)

≠ kinds of magnetic interaction: direct superexchange anisotropic dipolar antisymmetric Dzyaloshinsky-Moryia

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 9 Introduction: effect of external magnetic field

More complicated situations with: ≠ kinds of magnetic interaction: double exchange (in doped systems with mixed valency)

RKKY

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 10 Introduction: effect of external magnetic field

More complicated situations with:

Other degrees of freedom: Quadrupolar interactions, charge, orbit, lattice Itinerant versus localized electrons

Condition for magnetism stability: spontaneous band splitting

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 11 Introduction: effect of external magnetic field

More complicated situations with:

Other degrees of freedom: Quadrupolar interactions, charge, orbit, lattice Itinerant versus localized electrons (RKKY, Kondo screening)

Zeeman thermal/quantum fluctuations splitting E1, S1 Level crossings gap E0, S0 Frustration H c H

Magnetic ground states and routes towards its breaking under fields

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 12 Outline of the lecture

Introduction: effect of external magnetic field

Magnetization processes and frustration

Metamagnetism in metals

Competing degrees of freedom

Level crossing

Quantum magnetism

Conclusion

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 13 Magnetization processes and frustration All pair interactions can not be simultaneously satisfied Disorder Competition of interactions:

J1/J2 chain helix for with

J J2 Topological frustration : ex. triangular based lattice 1 Ising ?

Heisenberg triangular kagomé pyrochlore

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 14 Magnetization processes and frustration

 Complex (non-collinear, non-coplanar) magnetic structures or disordered GS with massive degeneracy, spin , spin ices

≠ configurations of spins are very close in energy  may be selected by field Magnetization plateaus

Plateaus can be stabilized by thermal or quantum fluctuations (order by disorder)

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 15 Magnetization processes and frustration

Classical spins: Plateaus usually correspond to collinear spin arrangement

Quantum spins: Ex. 1/3 plateau Oshikawa criterion: Mplateau/Msat is an rational fraction. ex. M/Msat=1/3 in kagome and triangular HAF, M/Msat=½ in J1/J2 square lattice

up up up dn Honecker, Can. J. Phys. (2001)

max frustration for J2/J1=0.5

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 16 Magnetization processes and frustration

Examples:

Transient 1/3 plateau in kagome 1/3 plateau in HAF triangular lattice: CsCuBr4 [Cu (titmb) (OCOCH ) ].H O 3 2 3 6 2 Tanaka et al., Prog. Theor. Phys. Narumi et al., Europhys. Lett. 2004 Suppl.2002; Ono et al. PRB 2004

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 17 Outline of the lecture

Introduction: effect of external magnetic field

Magnetization processes and frustration

Metamagnetism in metals

Competing degrees of freedom

Level crossing

Quantum magnetism

Conclusion

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 18 Metamagnetism in metals

3d itinerant magnetism in intermetallic R-M compounds

Collective electrons metamagnetism: YCo2, LuCo2, ThCo5 Close to conditions required for magnetism onset 1st order transition from non-magnetic state to

Goto et al., JMMM 1990 Givord et al., J. Appl. Phys. 1979

ThCo5

YCo2

50 100 150 Applied field (kOe) X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 19 Metamagnetism in metals

4f magnetism (lanthanide metals and R-M intermetallics) RKKY (long-range, frustrating) + CEF anisotropy complex H–T phase diagrams

Diversity of structures: ex. collinear Gd Tb, Dy helix Ho conical Er sine wave modulated Tm

For weakeasy-planeeasy-axis anisotropy

Rare earth metals, hexagonal space group

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 20 Metamagnetism in metals

4f magnetism (lanthanides metals and R-M intermetallics) weak anisotropy Gd-based metamagnetic systems Spin-flop transitions, mostly driven by isotropic and anisotropic exchange

ex. GdGa2

Ball, Gignoux, Schmitt

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 21 Metamagnetism in metals

4f magnetism (lanthanides metals and R-M intermetallics)

easy-axis, easy-plane anisotropy ex. Tm, Er, Ho sine wave modulated, conical, helix Er, helix competition commensurate/incommensurate Rhyne et al. several transitions at H=0 J. Appl. Phys. 1968 Resurgence of ≠ phases under H At H≠0 Mutlistep metamagnetism with change of propagation vector, spin-flip (progressive reversal of spinsplateaus) Spin-slip (successive lock-in transitions), Helixhelifanfan, etc

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 22 Metamagnetism in metals

4f magnetism (lanthanides metals and R-M intermetallics)

Multiaxis-anisotropy (ex cubic symmetry) Multistep metamagnetism with non-collinear H induced phases Role of strong quadrupolar coupling ex. DyAg (antiferroquadrupolar coupling)

B//[100] B//[110] B//[111] B (T) (T) B

Morin et al., JMMM 1989 Yoshii et al. Physica B 2004 T (K) T (K) T (K) X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 23 Metamagnetism in metals

4f magnetism (R-M intermetallics) Ferromagnetic metamagnetic systems when H applied along hard direction, ex. ErNi5

Zhang et al., JMMM 1994

3d-4f magnetism : permanent R2M17 and R2M14B coupling of M and R: /kg) Ho2Co17 T=4.2 K H competing with 3d-4f exchange 2 Quantitative determination of the exchange and anisotropy parameters

Franse et al., PRB 1985 Magnetization (Am Tomiyama, J. Appl. Phys. 1991 10 20 30 Magnetic field (T) X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 24 Outline of the lecture

Introduction: effect of external magnetic field

Magnetization processes and frustration

Metamagnetism in metals

Competing degrees of freedom

Level crossing

Quantum magnetism

Conclusion

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 Competing degrees of freedom

Competing interactions RKKY and Kondo: Heavy fermions superconductors f-electrons metamagnetism Hybridization effects: f-electrons from localized to itinerant with T

Heavy fermions state suppressed above field μBH≈kBTKondo

U moment UPd2Al3

URu2Si2

UPd2Al3 UPt3

Sugiyama et al. Physica B 2000

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 Competing degrees of freedom

Competing interactions RKKY and Kondo: Heavy fermions superconductors

Coexistence magnetic long-range order and Incommensurate CeCoIn5

neutron work NMR work Kenzelmann et al. PRL 2010 Koutroulakis et al. PRL 2010 X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 Competing degrees of freedom Spin, charge and orbital degrees of freedom: in doped magnetic oxides: ex. Colossal MR manganites 3+ 4+ perovskite R1-xAxMnO3, mixed valence state Mn /Mn field-induced metamagnetic transition Sm Ca MnO From AFM charge/orbital order 1/2 1/2 3 Nd1/2Ca1/2MnO3 To FM metal state Pr1/2Ca1/2MnO3 with resistivity change

Nd1/2Sr1/2MnO3

Pr1/2Sr1/2MnO3

Kuwahara et al., Science 1995 Kuwahara et al., PRL 1999 Temperature (K) Tomioka et al., PRL 1995 Magnetic field (T) Tokunaga et al., PRB 1998 X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 Competing degrees of freedom Muliferroics: coupled magnetic and dielectric properties, often complex non-collinear  frustration

Ex. MnWO4 Taniguchi et al. PRL 2006

P flop caused by H-induced magnetic Tokunaga et al. JPSJ 2010

Also: pulsed fields up to 50 T in BiFeO3: P and M transition at ≈18 T X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 29 Competing degrees of freedom

Examples: spin ices in pyrochlores (Ho,Dy)2Ti2O7 Dipolar FM+multiaxial anisotropy+frustration

H2O ice rule Sakakibara et al.,PRL 2003

rule

From spin ice to Kagome ice state with H//(111) within the plateau, the ice rule is not broken: spin liquid in the Kagome planes; triangular planes fully aligned along H

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010

17/11/10 30 Competing degrees of freedom

Examples: Cr spinel, pyrochlore lattice, frustration+lattice 3+ (Hg, Cd, Zn)Cr2O4 Cr S=3/2 At H=0, structural distorsion +AF transition

CdCr2O4

up up up dn

½ plateau at 10, 28, 120 T (Hg, Cd, Zn) stabilized by distortion (Spin-Peierls like). High field IN22 (ILL)

Ueda et al. PRL 2005; Matsuda et al. Nature Phys. 2007; Matsuda et al. PRL 2010 X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 Competing degrees of freedom

Examples: spinel pyrochlores, frustration+lattice Hc1=5.25 T, Hc2= 9.7 T GeNi2O4 and GeCo2O4 S=1 S=3/2 31 2 magnetic magnetic transition transitions + struct. transition

Diaz et al. PRB 2006 Hc1=30 T Matsuda et al. EPL 2008 Hc2= 37 T Complex metamagnetism magnetic domains and structure associated to structural distortion?

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 32 Outline of the lecture

Introduction: effect of external magnetic field

Magnetization processes and frustration

Metamagnetism in metals

Competing degrees of freedom

Level crossing

Quantum magnetism

Conclusion

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 33 Level crossings Low spin – high spin transitions

4f magnetism: CEF metamagnetic system

Example Pr metal, hexagonal PrNi5 singlet ground state no LRO 6 CEF from J=4 multiplet /formula) B M ( μ CEF levels transforms under application of H ≠ crystallographic direction Energy (K) (K) Energy ≠ level (anti-)crossing crossing anticrossing Bal et al., JMMM 1992 Applied Field (Tesla) X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 34 Level crossings Low spin – high spin transitions

Example with Fe(II) spin cross over compound

At H=0, high-low spin transition + thermochromic effect

Increase of optical reflectivity with increasing H (up to 140 T) Field-induced low-high spin transition Richter et al., JMMM 2007

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 35 Level crossings Clusters = finite spins system  discrete energy levels  possible field-induced (anti)-crossings High magnetic field processes in Magnetization dodecanuclear Fe(III) ring cluster (Fe12)

Inagaki et al., JPSJ 2003

dM/dH at 0.1 K

Plateaus of 2, 4, 6, 8, 10 μB Crossing of levels |ST=0,1,…,30 > gap=13.6 K  intraring interaction=40.7 K

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 36 Outline of the lecture

Introduction: effect of external magnetic field

Magnetization processes and frustration

Metamagnetism in metals

Competing degrees of freedom

Level crossing

Quantum magnetism

Conclusion

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 37 Quantum spin systems Quantum systems with an energy gap between the singlet ground state and the triplet excitations Closure of the gap with H: Nature of Field induced magnetic phase? 1D systems: incommensurate spin correlations 2D, 3D systems: Magnetization plateaus, Bose Einstein condensation of triplons

E

Zeeman splitting

S = 1 ? Ferro Gap accessible HC1 : EG system with J≈EG small enough ex. EG = 20 K  HC1 ≈ 15 T S = 0 H Hc1 Hc2 = Hsat

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 Spin-Peierls Spin=1/2 Liquid) withoutgap(Luttinger chain Haldane spin=1 anisotropy, J frustrated 1D systems Ex. → destabilized by: Incommensurate Spinfluctuations withoutgapunderfield Ni(C 5 D opens a opens 14 N X-ray Spectroscopy inHighMagnetic Field,SOLEIL 2 ) 2 N 3 Quantum spinsystems (PF with gap 6 gap ) :NDMAP 1 /J 2 chain, spin ladder, alternate chain, chain, alternate ladder, spin chain,

Energy (meV) Zheludev et al., PRB 2003 & 2004 2004 & 2003 PRB al., et 2010 H (T) H c1

17/11/10 38

39 Quantum spin systems 1D systems

Ex. spin-Peierls CuGeO3 spin-lattice coupling alternate chain

Structural & magnetic incommensurate modulation Solitonic lattice

Hase et al. PRL 1993 Regnault et al. PRL 1996 Kiryukhin et al. PRL 1996 …

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 40 Quantum spin systems 2D, 3D dimer systems

Triplets described as hard core bosons on a lattice (triplons) Sz=-1 H acts as chemical potential Sz=0

S =1 New states in applied magnetic field z

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 41 Quantum spin systems 2D, 3D dimer systems If kinetics energy dominates, triplons can acquire a common phase: Bose Einstein Condensation Transverse long range canted magnetic order

Ex. Ba2Cu2Si2O6 (Han purple pigment)

NMR @ 40 -600mK

Giamarhi and Tsvelik, PRB 2000,

Jaime et al., PRL 2004 (Ba2Cu2Si2O6) X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 42 Quantum spin systems 2D, 3D dimer systems when repulsive interactions dominates (frustration): triplons may form a commensurate superlattice  magnetization plateaus

Ex. SrCu2(BO3)2 Shastry-Sutherland lattice

Onizuka et al.,JSPS 2000 Kodama et al. Science 2002

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 43 Conclusion

Metamagnetism is one of the most common feature in systems with rare-earth or transition metal beyond simple spin-flip, spin-flop in collinear AFM, Field induced magnetism (metamagnetism, magnetization plateaus) due to frustration due to level crossing due to different degrees of freedom (spin, charge, lattice, orbit) due to quantum and thermal fluctuations

Often associated to magnetoelastic effects, magnetostriction, structural distortion…

In many ≠ systems: dimer systems, multiferroics, frustrated compounds, heavy fermions, manganites, molecular magnetism… Pbm of low temperatures?

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10 44 What I did not speak about: Domain reorientation, quasi-1D conductors Nano-structured, films, multi-layered magnetic compounds + all I forgot… Acknowledgements:

C. Berthier (LNCMI) J.E. Lorenzo, D. Givord, S. de Brion, R.-M. Galéra, M. Amara A. Ralko, E. Lhotel, R. Ballou , B. Canals (IN) B. Grenier (CEA-Grenoble, UJF), E. Ressouche (CEA-Grenoble)

Bibliography: ”Théorie duy magnétisme” A. Herpin, Presses universitaires de France (1968). ”Handbook on the physics and chemistry of rare-earths” vol. 20, D. Gignoux, D. Schmitt, eds. K. A. Gschneider, Jr. and L. Eyring, Elsevier Science (1995). “Magnetic properties of intermetallic compounds” “High magnetic fields: Applications in and spectroscopy”, eds C. Berthier, L. P. Lévy, and G. Martinez (Springer-Verlag) Berlin (2002).

X-ray Spectroscopy in High Magnetic Field, SOLEIL 2010 17/11/10