Quantum Phase Transitions and Exotic Phases in the Metallic Helimagnet MnSi

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Quantum Phase Transitions and Exotic Phases in the Metallic Helimagnet MnSi. Dietrich Belitz, University of Oregon with Ted Kirkpatrick, Achim Rosch, Thomas Vojta, et al. Ferromagnets and Helimagnets II.Phenomenology of MnSi Theory 1. Phase diagram 2. Disordered phase - PowerPoint PPT Presentation

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<ul><li><p>Quantum Phase Transitions and Exotic Phases in the Metallic Helimagnet MnSi</p><p>Ferromagnets and Helimagnets</p><p>II.Phenomenology of MnSi</p><p>Theory 1. Phase diagram 2. Disordered phase 3. Ordered phaseDietrich Belitz, University of Oregonwith Ted Kirkpatrick, Achim Rosch, Thomas Vojta, et al.</p><p>UO Colloquium</p></li><li><p>I. Ferromagnets versus HelimagnetsFerromagnets: 0 &lt; J ~ exchange interaction (strong) (Heisenberg 1930s)</p><p>UO Colloquium</p></li><li><p>I. Ferromagnets versus HelimagnetsFerromagnets: Helimagnets:0 &lt; J ~ exchange interaction (strong) (Heisenberg 1930s)c ~ spin-orbit interaction (weak)q ~ c pitch wave number of helix (Dzyaloshinski 1958, Moriya 1960)</p><p>UO Colloquium</p></li><li><p>I. Ferromagnets versus HelimagnetsFerromagnets: Helimagnets:0 &lt; J ~ exchange interaction (strong) (Heisenberg 1930s)c ~ spin-orbit interaction (weak)q ~ c pitch wave number of helix (Dzyaloshinski 1958, Moriya 1960) HHM invariant under rotations, but not under x - x Crystal-field effects ultimately pin helix (very weak)</p><p>UO Colloquium</p></li><li><p>II. Phenomenology of MnSi1. Phase diagram magnetic transition at Tc 30 K (at ambient pressure) (Pfleiderer et al 1997)</p><p>UO Colloquium</p></li><li><p>II. Phenomenology of MnSi1. Phase diagram magnetic transition at Tc 30 K (at ambient pressure) transition tunable by means of hydrostatic pressure p(Pfleiderer et al 1997)</p><p>UO Colloquium</p></li><li><p>II. Phenomenology of MnSi1. Phase diagram magnetic transition at Tc 30 K (at ambient pressure) transition tunable by means of hydrostatic pressure p 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!)(Pfleiderer et al 1997)TCP</p><p>UO Colloquium</p></li><li><p>II. Phenomenology of MnSi1. Phase diagram magnetic transition at Tc 30 K (at ambient pressure) transition tunable by means of hydrostatic pressure p 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!) In an external field B there are tricritical wings(Pfleiderer et al 1997)(Pfleiderer, Julian, Lonzarich 2001)TCP</p><p>UO Colloquium</p></li><li><p>II. Phenomenology of MnSi1. Phase diagram magnetic transition at Tc 30 K (at ambient pressure) transition tunable by means of hydrostatic pressure p 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!) In an external field B there are tricritical wings Quantum critical point at B 0(Pfleiderer et al 1997)(Pfleiderer, Julian, Lonzarich 2001)TCP</p><p>UO Colloquium</p></li><li><p>II. Phenomenology of MnSi1. Phase diagram magnetic transition at Tc 30 K (at ambient pressure) transition tunable by means of hydrostatic pressure p 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!) In an external field B there are tricritical wings Quantum critical point at B 0 Magnetic state is a helimagnet with q 180 , pinning in (111) d d direction(Pfleiderer et al 1997)(Pfleiderer, Julian, Lonzarich 2001)(Pfleiderer et al 2004)TCP</p><p>UO Colloquium</p></li><li><p>II. Phenomenology of MnSi1. Phase diagram magnetic transition at Tc 30 K (at ambient pressure) transition tunable by means of hydrostatic pressure p 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!) In an external field B there are tricritical wings Quantum critical point at B 0 Magnetic state is a helimagnet with q 180 , pinning in (111) d d direction Cubic unit cell lacks inversion symmetry (in agreement with DM)(Pfleiderer et al 1997)(Pfleiderer, Julian, Lonzarich 2001)(Pfleiderer et al 2004)(Carbone et al 2005)TCP</p><p>UO Colloquium</p></li><li><p>2. Neutron Scattering(Pfleiderer et al 2004) Ordered phase shows helical order, see above</p><p>UO Colloquium</p></li><li><p>2. Neutron Scattering(Pfleiderer et al 2004) Ordered phase shows helical order, see above</p><p> Short-ranged helical order persists in the paramagnetic phase below a temperature T0 (p)</p><p>UO Colloquium</p></li><li><p>2. Neutron Scattering(Pfleiderer et al 2004) Ordered phase shows helical order, see above </p><p> Short-ranged helical order persists in the paramagnetic phase below a temperature T0 (p)</p><p> Pitch little changed, but axis orientation much more isotropic than in the ordered phase (helical axis essentially de-pinned)</p><p>UO Colloquium</p></li><li><p>2. Neutron Scattering(Pfleiderer et al 2004) Ordered phase shows helical order, see above</p><p> Short-ranged helical order persists in the paramagnetic phase below a temperature T0 (p)</p><p> Pitch little changed, but axis orientation much more isotropic than in the ordered phase (helical axis essentially de-pinned)</p><p> No detectable helical order for T &gt; T0 (p)</p><p>UO Colloquium</p></li><li><p>2. Neutron Scattering(Pfleiderer et al 2004) Ordered phase shows helical order, see above </p><p>Short-ranged helical order persists in the paramagnetic phase below a temperature T0 (p)</p><p> Pitch little changed, but axis orientation much more isotropic than in the ordered phase (helical axis essentially de-pinned)</p><p> No detectable helical order for T &gt; T0 (p)</p><p> T0 (p) originates close to TCP</p><p>UO Colloquium</p></li><li><p>2. Neutron Scattering(Pfleiderer et al 2004) Ordered phase shows helical order, see above</p><p> Short-ranged helical order persists in the paramagnetic phase below a temperature T0 (p)</p><p> Pitch little changed, but axis orientation much more isotropic than in the ordered phase (helical axis essentially de-pinned)</p><p> No detectable helical order for T &gt; T0 (p)</p><p> T0 (p) originates close to TCP</p><p> So far only three data points for T0 (p)</p><p>UO Colloquium</p></li><li><p>3. Transport Properties Non-Fermi-liquid behavior of the resistivity: Resistivity ~ T 1.5 o over a huge range in parameter spaceT(K)T1.5(K1.5)T1.5(K1.5)(cm)p = 14.8kbar &gt; pc(cm)(cm)</p><p>UO Colloquium</p></li><li><p>III. Theory1. Nature of the Phase Diagram Basic features can be understood by approximating the system as a FM </p><p>UO Colloquium</p></li><li><p>III. Theory1. Nature of the Phase Diagram Basic features can be understood by approximating the system as a FM Tricritical point due to many-body effects (coupling of fermionic soft modes to magnetization) Quenched disorder suppresses the TCP, restores a quantum critical point! DB, T.R. Kirkpatrick, T. Vojta, PRL 82, 4707 (1999) </p><p>UO Colloquium</p></li><li><p>III. Theory1. Nature of the Phase Diagram Basic features can be understood by approximating the system as a FM Tricritical point due to many-body effects (coupling of fermionic soft modes to magnetization) Quenched disorder suppresses the TCP, restores a quantum critical point! DB, T.R. Kirkpatrick, T. Vojta, PRL 82, 4707 (1999) NB: TCP can also follow from material-specific band-structure effects (Schofield et al), but the many-body mechanism is generic </p><p>UO Colloquium</p></li><li><p>III. Theory1. Nature of the Phase Diagram Basic features can be understood by approximating the system as a FM Tricritical point due to many-body effects (coupling of fermionic soft modes to magnetization) Quenched disorder suppresses the TCP, restores a quantum critical point! DB, T.R. Kirkpatrick, T. Vojta, PRL 82, 4707 (1999) NB: TCP can also follow from material-specific band-structure effects (Schofield et al), but the many-body mechanism is generic Wings follow from existence of tricritical point DB, T.R. Kirkpatrick, J. Rollbhler, PRL 94, 247205 (2005) Critical behavior at QCP determined exactly! (Hertz theory is valid due to B &gt; 0)</p><p>UO Colloquium</p></li><li><p> Example of a more general principle: Hertz theory is valid if the field conjugate to the order parameter does not change the soft-mode structure (DB, T.R. Kirkpatrick, T. Vojta, Phys. Rev. B 65, 165112 (2002)) Here, B field already breaks a symmetry no additional symmetry breaking by the conjugate field mean-field critical behavior with corrections due to DIVs in particular, d m (pc,Hc,T) ~ -T 4/9</p><p>UO Colloquium</p></li><li><p>2. Disordered Phase: Interpretation of T0(p)Basic idea: Liquid-gas-type phase transition with chiral order parameter (cf. Lubensky &amp; Stark 1996)</p><p>Borrow an idea from liquid-crystal physics:</p><p>UO Colloquium</p></li><li><p>2. Disordered Phase: Interpretation of T0(p)Basic idea: Liquid-gas-type phase transition with chiral order parameter (cf. Lubensky &amp; Stark 1996)</p><p>Important points: Chirality parameter c acts as external field conjugate to chiral OP</p><p>Borrow an idea from liquid-crystal physics:</p><p>UO Colloquium</p></li><li><p>2. Disordered Phase: Interpretation of T0(p)Basic idea: Liquid-gas-type phase transition with chiral order parameter (cf. Lubensky &amp; Stark 1996)</p><p>Important points: Chirality parameter c acts as external field conjugate to chiral OP</p><p> Perturbation theory Attractive interaction between OP fluctuations! Condensation of chiral fluctuations is possible</p><p>Borrow an idea from liquid-crystal physics:</p><p>UO Colloquium</p></li><li><p>2. Disordered Phase: Interpretation of T0(p)Basic idea: Liquid-gas-type phase transition with chiral order parameter (cf. Lubensky &amp; Stark 1996)</p><p>Important points: Chirality parameter c acts as external field conjugate to chiral OP</p><p> Perturbation theory Attractive interaction between OP fluctuations! Condensation of chiral fluctuations is possible</p><p> Prediction: Feature characteristic of 1st order transition (e.g., discontinuity in the spin susceptibility) should be observable across T0Borrow an idea from liquid-crystal physics:</p><p>UO Colloquium</p></li><li><p>Proposed phase diagram :</p><p>UO Colloquium</p></li><li><p>Proposed phase diagram :</p><p>UO Colloquium</p></li><li><p>Analogy: Blue Phase III in chiral liquid crystalsProposed phase diagram :(J. Sethna)</p><p>UO Colloquium</p></li><li><p>Analogy: Blue Phase III in chiral liquid crystalsProposed phase diagram :(J. Sethna) (Lubensky &amp; Stark 1996)</p><p>UO Colloquium</p></li><li><p>Analogy: Blue Phase III in chiral liquid crystalsProposed phase diagram :(J. Sethna)(Lubensky &amp; Stark 1996) (Anisimov et al 1998) </p><p>UO Colloquium</p></li><li><p>Other proposals: Superposition of spin spirals with different wave vectors (Binz et al 2006), see following talk.</p><p> Spontaneous skyrmion ground state (Roessler et al 2006)</p><p> Stabilization of analogs to crystalline blue phases (Fischer &amp; Rosch 2006, see poster)(NB: All of these proposals are also related to blue-phase physics)</p><p>UO Colloquium</p></li><li><p>3. Ordered Phase: Nature of the Goldstone modeHelical ground state:</p><p> breaks translational symmetry soft (Goldstone) mode</p><p>UO Colloquium</p></li><li><p>3. Ordered Phase: Nature of the Goldstone modeHelical ground state:</p><p> breaks translational symmetry soft (Goldstone) mode</p><p>Phase fluctuations:</p><p>Energy: ??</p><p>UO Colloquium</p></li><li><p>3. Ordered Phase: Nature of the Goldstone modeHelical ground state:</p><p> breaks translational symmetry soft (Goldstone) mode</p><p>Phase fluctuations:</p><p>Energy: ??</p><p> NO! rotation (0,0,q) (a1,a2,q) cannot cost energy, yet corresponds to f(x) = a1x + a2y H fluct &gt; 0 </p><p> cannot depend on</p><p>UO Colloquium</p></li><li><p>3. Ordered Phase: Nature of the Goldstone modeHelical ground state:</p><p> breaks translational symmetry soft (Goldstone) mode</p><p>Phase fluctuations:</p><p>Energy: ??</p><p> NO! rotation (0,0,q) (a1,a2,q) cannot cost energy, yet corresponds to f(x) = a1x + a2y H fluct &gt; 0 </p><p>...</p></li></ul>