Magnetic Excitations of Stripes E. W. Carlson D. X. Yao D. K. - PowerPoint PPT Presentation

Magnetic Excitations of Stripes E. W. Carlson D. X. Yao D. K. Campbell

Stripes: Why? HTSC Dilemmas Superconductivity from a non-Fermi liquid High pairing scale despite strong repulsion Metallic Charge Stripes: Spin-Charge Separation Non-Fermi liquid normal state (Luttinger liquid) Pair the spin degrees of freedom, and avoid the Coulomb repulsion. EC, V. Emery, S. Kivelson, D. Orgad in “Physics of Unconventional Superconductors” ed. Bennemann and Ketterson, (2004)

Inherent Competition T Pairing Josephson coupling think local stripe order think “ “stripe phonon stripe phonon” ” think local stripe order think superconductivity stripe fluctuations Static Stripes Fluctuating Stripes Good pairing Bad pairing Bad phase coherence Good phase coherence EC, V. Emery, S. Kivelson, D. Orgad in “Physics of Unconventional Superconductors” ed. Bennemann and Ketterson, (2004)

Stripes Unidirectional modulation in charge and spin Charge: quasi-one-dimensional (rivers of charge) Spin: 2D Magnetic texture

Stripes Have 2D Magnetic Texture � � Real Space Reciprocal Lattice Vectors 2D spin waves disperse out of the reciprocal lattice vector positions

Neutron Scattering in Cuprates and Nickelates Disappearance of ( � , � ) peak with doping Appearance of satellite � � peaks AFM signal averages to zero � � antiphase domain walls bond-centered bond-centered site-centered site-centered OR OR

Neutron Scattering in Cuprates and Nickelates Charge Peaks related by X2 � � bond-centered bond-centered site-centered site-centered OR OR

Checkerboards and Plaids? Antiphase Domain Walls in Antiferromagnetism Hoffman et al., Science (2002) Vershinin et al., Science (2004) Spin Peaks in Wrong Direction! Charge Peaks

Odd Spacing Site-centered � Magnetic Reciprocal � Lattice Vectors Bond-centered � �

Odd Spacing Site-centered � Intensities � Bond-centered � �

Odd Spacing Site-centered � Observing weight here � rules out site-centered Bond-centered stripes � �

Even Spacing Site-centered � Magnetic Reciprocal � Lattice Vectors Bond-centered � �

Even Spacing Site-centered � Intensities � Bond-centered � �

Inelastic Response: Spin Waves

Site or Bond-Centered Site-centered p=3 Bond-centered p=3 J a J b J b J a J a > 0 (AFM) J b > 0 (AFM) J a > 0 (AFM) J b < 0 (FM) Semiclassical Spin Waves

Low Energy Velocities 1 1 bond-centered site-centered 1 2 3 1 2 3 Spin wave cones may remain rather isotropic for bond-centered stripes, despite microscopic anisotropy.

Spin Wave Dispersions • Bond-centered has one more band Site-centered, p=3 6 • Bond-centered has weight at (0, π ) J b = 0.4 J a • Bands repel, do not cross Resonance unlikely from crossings Batista et al., PRB (2001) Bond-centered, p=3 5 π J b = - 1.0 J a � π � EC, Yao, et al., PRB (2004)

Data YBCO6.6, S. Hayden et al., Nature 429, 531 (2004) Stripe-ordered LBCO, S. Hayden et al., Nature 429, 534 (2004)

Symmetrize E=1.5J a E=1.5J E=2.5J a E=3.5J a E=2.5J E=3.5J E=0.5J E=0.5J a a a a a

VB4 J b = -.1 J a Vertical, Bond-centered, Spacing = 4 E=1.0J a E=2.0J a E=3.0J a E=1.0J E=2.0J E=3.0J E=4.0J a E=4.0J a a a a E=1.5J a E=1.5J E=2.5J a E=3.5J a E=2.5J E=3.5J E=0.5J E=0.5J a a a a a

VB4 J b = -.56 J a Vertical, Bond-centered, Spacing = 4 E=1.0J a E=2.0J a E=3.0J a E=1.0J E=2.0J E=3.0J E=4.0J E=4.0J a a a a a E=1.5J a E=1.5J E=2.5J a E=3.5J a E=2.5J E=3.5J E=0.5J a E=0.5J a a a a

VS4 Jb = Ja Vertical, Site-centered, Spacing = 4 E=1.0J a E=2.0J a E=3.0J a E=1.0J E=2.0J E=3.0J E=4.0J a E=4.0J a a a a E=1.5J a E=1.5J E=2.5J a E=3.5J a E=2.5J E=3.5J E=0.5J E=0.5J a a a a a

Other Stripe Patterns Diagonal “DB4”

DB2 J b = -.1 J a Diagonal, Bond-centered, Spacing = 2 E=0.5J a E=1 J a E=1.5 J a E=0.5J E=1 J E=1.5 J E=2 J a E=2 J a a a a E=0.75J a E=0.75J E=1.25 J a E=1.75J a E=1.25 J E=1.75J E=0.25J E=0.25J a a a a a

Other Stripe Patterns Staircase Globally diagonal Locally vertical Antiphase domain walls M. Granath, PRB (2004) Smooth transition from diagonal to vertical peaks Fermi Surface Arcs

SB2 J b = -.1 J a Staircase, Bond-centered, Spacing = 2 E=0.7J a E=1.6 J a E=2.6J a E=0.7J E=1.6 J E=2.6J E=4.0 J a E=4.0 J a a a a E=1J a E=1J E=2.0 J a E=3.6J a E=2.0 J E=3.6J E=0.4J E=0.4J a a a a a

Conclusions 2D magnetic texture - Stripes produce 2D spin waves. - Finite energy weight at ( π , π ) is natural from stripes, but not from a pure antiferromagnet. Resonance peak - Unlikely from crossing (bands repel) Bond-centered stripes: - Ferromagnetic coupling across domain wall - One more band than site-centered - Odd spacing has new elastic peaks , forbidden for site-centered stripes - Isotropic spin wave cones - “Legs” of scattering Comparison to Recent Cuprate Data - Low energy could be semiclassical spin waves - High energy is not