Quantum Phase Transitions and Exotic Phases in Metallic Helimagnets I.Ferromagnets and Helimagnets...

Quantum Phase Transitions and Exotic Quantum Phase Transitions and Exotic Phases in Metallic HelimagnetsPhases in Metallic Helimagnets

I. Ferromagnets and Helimagnets

II. Phenomenology of MnSi

III. Theory 1. Phase diagram 2. Disordered phase 3. Ordered phase

Dietrich Belitz, University of Oregon

with Ted Kirkpatrick, Achim Rosch,

Sumanta Tewari, Thomas Vojta

APS March Meeting Denver 2March 2007

I. Ferromagnets versus Helimagnets

Ferromagnets:

0 < J ~ exchange interaction (strong) (Heisenberg 1930s)

Ferromagnets:

Helimagnets:

c ~ spin-orbit interaction (weak)q ~ c pitch wave number of helix

(Dzyaloshinski 1958,

Moriya 1960)

Ferromagnets:

Helimagnets:

Moriya 1960)

Crystal-field effects ultimately pin helix (very weak)

Ferromagnets:

Helimagnets:

Moriya 1960)

Crystal-field effects ultimately pin helix (very weak)

Examples: MnSi, FeGe

1. Phase diagram

• magnetic transition at Tc ≈ 30 K (at ambient pressure)

(Pfleiderer et al 1997)

1. Phase diagram

• transition tunable by means of hydrostatic pressure p

1. Phase diagram

• Transition is 2nd order at high T, 1st order at low T t tricritical point at T ≈ 10 K (no QCP in T-p plane!

1. Phase diagram

• In an external field B there are “tricritical wings”

(Pfleiderer, Julian, Lonzarich 2001)

1. Phase diagram

• In an external field B there are “tricritical wings”

• Quantum critical point at B ≠ 0

(Pfleiderer, Julian, Lonzarich 2001)

2. Neutron Scattering

• Magnetic state is a helimagnet with q ≈ 180 Ǻ, pinning in (111) direction

• Short-ranged helical order persists in the paramagnetic phase below a temperature T0 (p). Pitch little changed, but axis orientation much more isotropic than in the ordered phase (helical axis essentially de-pinned)

• No detectable helical order for T > T0 (p)

3. Transport Properties

• Non-Fermi-liquid behavior of the resistivity:

3. Transport Properties

• Non-Fermi-liquid behavior of the resistivity:

• Over a huge range in parameter space, the resistivity behaves as ρ ~ T 1.5 o

T1.5(K1.5)

III. Theory

1. Nature of the Phase Diagram

Basic features can be understood by approximating the system as a FM

III. Theory1. Nature of the Phase Diagram

Tricritical point due to fluctuation effects (coupling of fermionic soft modes to magnetization)

DB, T.R. Kirkpatrick, T. Vojta, PRL 82, 4707 (1999)

III. Theory1. Nature of the Phase Diagram

Tricritical point due to fluctuation effects (coupling of fermionic soft modes to magnetization)

DB, T.R. Kirkpatrick, T. Vojta, PRL 82, 4707 (1999)

Wings follow from existence of tricritical point

DB, T.R. Kirkpatrick, J. Rollbühler, PRL 94, 247205

(2005)

Critical behavior at QCP determined exactly!

2. Disordered Phase: Interpretation of T0(p)

Basic idea: Liquid-gas-type phase transition with chiral order parameter

(cf. Lubensky & Stark 1996)

Borrow an idea from liquid-crystal physics:

Important points: • Chirality parameter c acts as external field conjugate to chiral OP

• Perturbation theory Attractive interaction between OP fluctuations!

Condensation of chiral fluctuations is possible

• Perturbation theory Attractive interaction between OP fluctuations!

Condensation of chiral fluctuations is possible

• Prediction: Feature characteristic of 1st order transition (e.g., discontinuity in

the spin susceptibility) should be observable across T0

Proposed phase diagram :

Analogy: Blue Phase III in chiral liquid crystals

Proposed phase diagram :

(J. Sethna) (Lubensky & Stark 1996)

Other proposals:

Superposition of spin spirals with different wave vectors (Binz et al 2006)

Spontaneous skyrmion ground state (Roessler et al 2006)

Stabilization of analogs to crystalline blue phases (Fischer & Rosch 2006, Fischer et al 2007)

(NB: All of these proposals are also related to blue-phase physics)

3. Ordered Phase: Nature of the Goldstone mode

Helical ground state:

breaks translational symmetry

soft (Goldstone) mode

3. Ordered Phase: Nature of the Goldstone mode

Helical ground state:

breaks translational symmetry

soft (Goldstone) mode

Rotational symmetry anisotropic dispersion relation

“ helimagnon”

(cf. chiral liquid crystals)

4. Ordered Phase: Specific heat

Internal energy density:

Specific heat: helimagnon contribution

total low-T specific heat

5. Ordered Phase: Relaxation times and resistivity

Quasi-particle relaxation time: 1/(T) ~ T 3/2 stronger than FL T 2 contribution!

(hard to measure)

Resistivity: (T) ~ T 5/2 weaker than QP relaxation time,

cf. phonon case (T3 vs T5)

(hard to measure)

(T) = 2 T 2 + 5/2 T 5/2 total low-T resistivity

(hard to measure)

(T) = 2 T 2 + 5/2 T 5/2 total low-T resistivity

Experiment: (T→ 0) ~ T 2 (more analysis needed)

6. Ordered Phase: Breakdown of hydrodynamics

• Use TDGL theory to study magnetization dynamics:

Bloch term damping Langevin force

• Bare magnetic response function:

helimagnon frequency

damping coefficient

• One-loop correction to

• The elastic coefficients and , and the transport coefficients and all acquire singular corrections at one-loop order due to mode-mode coupling effects:

Strictly speaking, helimagnetic order is not stable at T > 0

In practice, cz is predicted to change linearly with T, by ~10% from T=0 to T=10K

• Analogous to situation in smectic liquid crystals (Mazenko, Ramaswamy, Toner 1983)

• At T = 0 , all renormalizations are finite!

(Special answer to a more general question: As T -> 0, classical mode-mode coupling

effects die (how?), while new quantum mode-mode coupling effects may appear)

IV. Summary

Basic T-p-h phase diagram is understood

IV. Summary

Possible additional 1st order transition in disordered phase

IV. Summary

Helimagnons predicted in ordered phase; lead to T2 term in specific heat

IV. Summary

NFL quasi-particle relaxation time predicted in ordered phase

IV. Summary

Resistivity in ordered phase is FL-like with T5/2 correction

IV. Summary

Hydrodynamic description of ordered phase breaks down

IV. Summary

Hydrodynamic description of ordered phase breaks down

Main open question: Origin of T3/2 resistivity in disordered phase?

Acknowledgments

• Ted Kirkpatrick• Rajesh Narayanan• Jörg Rollbühler• Achim Rosch• Sumanta Tewari• John Toner• Thomas Vojta

• Peter Böni• Christian Pfleiderer

• Aspen Center for Physics

• KITP at UCSB

• Lorentz Center Leiden

National Science Foundation

Quantum Phase Transitions and Exotic Phases in Metallic Helimagnets I.Ferromagnets and Helimagnets...

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