1 Magnetic transitions under high magnetic fields V. Simonet Institut Néel, CNRS/UJF, Grenoble, France X-ray Spectroscopy in High Magnetic Field, 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 magnetism 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: phase 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 liquid, 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 ferromagnetism 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 weakeasy-planeeasy-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 spinsplateaus) Spin-slip (successive lock-in transitions), Helixhelifanfan, 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 magnet R2M17 and R2M14B coupling of M and R: ferrimagnetism /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 superconductivity Incommensurate spin density wave 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.,