Quantum Phase Transitions in Itinerant Ferromagnets *



I. Introduction

  1. Experimental Overview
  2. Conventional Theory

II. Generalized Mean-Field Theory

  1. Breakdown of Landau Theory
  2. Generalized Mean-Field Theory

III. Soft-Mode Field Theory

  1. Effective Action
  2. Analysis

IV. Summary and Conclusion


Dietrich Belitz +

University of Oregon


* With T.R. Kirkpatrick, M.T. Mercaldo, J. Rollbühler,
S. Sessions, T. Vojta
+ belitz@physics.uoregon.edu







I. INTRODUCTION


1. Experimental Overview


Itinerant ferromagnets whose Tc can be tuned to zero include,


Clean materials all show tricritical point , with 2nd order transition at high T, and 1st order transition at low T:

MnSi

UGe2

ZrZn2

( Pfleiderer et al 1997 )

( Pfleiderer & Huxley 2002 )

( Uhlarz et al 2004 )


T=0 1st order transition persists at nonzero magnetic field, ends at quantum critical point




Schematic
phase
diagram:


This behavior of clean systems appears to be universal


URuReSi shows 2nd order transition with non-mean-field exponents (e.g., = 3/2) ( Bauer et al 2002 )




2. Conventional Theory


Consider Landau theory with order parameter m = average magnetization


(Free) energy density:


Equation of state:


Landau theory predicts


Sandeman et al 2003 , Shick et al 2004 Band structure in UGe2 leads to u < 0
Origin of 1st order transition at T = 0


Hertz 1976 Mean-field theory correctly describes T = 0 transition for all d > 1 in clean systems,
and for all d > 0 in disordered ones.



II. GENERALIZED MEAN-FIELD THEORY


1. Breakdown of Landau Theory


Hertz's conclusion is now known to be incorrect: Soft modes in addition to OP fluctuations

Breakdown of Landau theory for d 3 (clean), and d 4 (dirty), respectively
( TRK & DB 1996 ; TRK, DB, et al 1997 ff )


Phase transition physics is determined by the soft modes in the problem.

These are,

Note:

particle-hole excitations soft for all values of t

They are the Goldstone modes of a spontaneously broken symmetry ( Wegner 1979 )

Generic Scale Invariance

It is impossible to construct a local field theory in terms of the OP only.
This is one way in which the LGW paradigm can break down

This is not revolutionary. Analogous effects occur at other phase transitions,

    • Nematic-to-smectic-A in liquid crystals ( Chen, Lubensky, Nelson 1978 )

    • BCS superconductors (academic case) ( Halperin, Lubensky, Ma 1974 )

    • Critical dynamics in classical fluids ( Kawasaki 1976 , Halperin & Hohenberg 1977 )

    and in particle physics,

    • Fermi theory of weak interactions



2. Generalized Mean-Field Theory ( DB, TRK, TV 1999 )


Conclusion: Landau theory misses mode-mode coupling contribution to the equation of state:

Generalized mean-field equation of state (d=3):


Effects of nonzero temperature (T) and disorder (G) :


Effect of nonzero magnetic field (h):



III. SOFT-MODE FIELD THEORY (DB et al 2001a , 2001b , TRK & DB 2002 )


Keep all soft modes explicitly!

two fields:

OP fluctuations

p-h fluctuations

two time scales:

Critical time scale

z = 3 (clean), or z = 4 (disordered)

fermionic time scale

z = 1 (clean), or z = 2 (disordered)


Construct coupled field theory for both fields


The resulting effective action has been analyzed at various levels:



IV. SUMMARY AND CONCLUSION


Low-Tc itinerant ferromagnets are remarkably complex and interesting.


The T = 0 transition is 1st order for generic reasons: A fluctuation-induced 1st order transition
preempts the continuous Landau transition.


Crucial for this mechanism: Fermionic modes and the resulting two time scales in the problem.


Theory explains


Sufficiently strong non-magnetic disorder drives transition 2nd order.

New universality class, which is solved exactly. Agrees with experimental results on URuReSi.