Modulated phases, magnetic phase diagrams, and the Lifshitz point in MnP from the mean field theory

Zięba, Andrzej; Slota, Monika; Kucharczyk, Mariusz

doi:10.1103/physrevb.61.3435

Cited by 16 publications

(24 citation statements)

References 38 publications

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“…Knowing that the ordinary fixed point P * ord is located at c = ∞, one can study the effect of the Hamiltonian's boundary term (c/2) B φ 2 for large but finitec to leading order in 1/c. Expanding the free propagator (7) in powers of 1/c p giveŝ…”

Section: Boundary Operator Expansionmentioning

confidence: 99%

“…(1,1) ∞ In this appendix, we briefly describe the calculation of the Laurent expansion of the one and two-loop graphs of the function G (1,1) ∞ (x, x ′ ) to the required orders in ǫ −1 . The Dirichlet propagator (66) to which the free propagator (7) reduces forc = ∞ can be written aŝ…”

Section: Appendix A: Laurent Expansion Of the Feynman Integrals Ofĝmentioning

confidence: 99%

“…Let us indicate that we have setc = 0 by a subscript zero. The free propagator (7) in this case reduces tô…”

Section: Appendix A: Laurent Expansion Of the Feynman Integrals Ofĝmentioning

confidence: 99%

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Boundary critical behavior atm-axial Lifshitz points for a boundary plane parallel to the modulation axes

2003

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The critical behavior of semi-infinite d-dimensional systems with n-component order parameter φ and short-range interactions is investigated at an m-axial bulk Lifshitz point whose wave-vector instability is isotropic in an m-dimensional subspace of R d . The associated m modulation axes are presumed to be parallel to the surface, where 0 ≤ m ≤ d − 1. An appropriate semi-infinite |φ| 4 model representing the corresponding universality classes of surface critical behavior is introduced. It is shown that the usual O(n) symmetric boundary term ∝ φ 2 of the Hamiltonian must be supplemented by one of the formλ m α=1 (∂φ/∂xα) 2 involving a dimensionless (renormalized) coupling constant λ. The implied boundary conditions are given, and the general form of the field-theoretic renormalization of the model below the upper critical dimension d * (m) = 4 + m/2 is clarified. Fixed points describing the ordinary, special, and extraordinary transitions are identified and shown to be located at a nontrivial value λ * if ǫ ≡ d * (m) − d > 0. The surface critical exponents of the ordinary transition are determined to second order in ǫ. Extrapolations of these ǫ expansions yield values of these exponents for d = 3 in good agreement with recent Monte Carlo results for the case of a uniaxial (m = 1) Lifshitz point. The scaling dimension of the surface energy density is shown to be given exactly by d + m (θ − 1), where θ = ν l4 /ν l2 is the anisotropy exponent.

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Section: Boundary Operator Expansionmentioning

confidence: 99%

Section: Appendix A: Laurent Expansion Of the Feynman Integrals Ofĝmentioning

confidence: 99%

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Boundary critical behavior atm-axial Lifshitz points for a boundary plane parallel to the modulation axes

2003

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“…[3, p. 59]). Their discovery triggered considerable theoretical [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24] and experimental interest [25,26], which has continued over the years, and after a phase of somewhat reduced intensity, has regained a lot of momentum recently [27,28,29,30,31,32,33]-in particular, on the theory side [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51].…”

Section: Introductionmentioning

confidence: 99%

Bulk and boundary critical behavior at Lifshitz points

Diehl

2005

Pramana - J Phys

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Lifshitz points are multicritical points at which a disordered phase, a homogeneous ordered phase, and a modulated ordered phase meet. Their bulk universality classes are described by natural generalizations of the standard φ 4 model. Analyzing these models systematically via modern fieldtheoretic renormalization group methods has been a long-standing challenge ever since their introduction in the middle of the 1970s. We survey the recent progress made in this direction, discussing results obtained via dimensionality expansions, how they compare with Monte Carlo results, and open problems. These advances opened the way towards systematic studies of boundary critical behavior at m-axial Lifshitz points. The possible boundary critical behavior depends on whether the surface plane is perpendicular to one of the m modulation axes or parallel to all of them. We show that the semi-infinite field theories representing the corresponding surface universality classes in these two cases of perpendicular and parallel surface orientation differ crucially in their Hamiltonian's boundary terms and the implied boundary conditions, and explain recent results along with our current understanding of this matter.

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“…The appropriate terms of the free energy have been introduced in the spirit of the Landau phenomenological theory, assuming that both order parameters m x and q are small near LP. This leads to the additional coefficients A q and B q (15). According to the Landau idea we have assumed that A q is a linear function of the distance from, in this case, the Lifshitz point, and A ′ (20) and B q are temperature and field independent near the LP.…”

Section: The Ferromagnetic Layers Are Coupled By Interlayer Interactionsmentioning

confidence: 99%

Isothermal magnetocaloric effect in the vicinity of the Lifshitz point in Mn_0.9Co_0.1P

Plackowski

Matusiak

Sznajd

2011

Physica Status Solidi (b)

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The magnetic field -temperature (B − T ) phase diagram of the Mn 0.9 Co 0.1 P single crystal is studied in the vicinity of the Lifshitz point by means of isothermal magnetocaloric coefficient (M T ) and AC susceptibility measurements. Results confirm previously reported shape of the B − T phase diagram and locations of characteristic temperatures and fields. At the Curie temperature (T C ) the critical exponent ω, which describes a singularity of M T as a function of magnetic field (M T ∝ B −ω ), is estimated for B parallel to the easy axis to be equal to ω ≈ 0.35. Below T C an evidence of a new enigmatic phase, reported previously for pure MnP, is found in susceptibility data also for Mn 0.9 Co 0.1 P. However, the range of existence of this phase is significantly larger here, than in MnP. At the Lifshitz point we observe a sharp peak in the imaginary part of the magnetic susceptibility. A phenomenological theory is introduced to describe the field dependence of the critical lines from the disordered phase (paramagnetic) to ordered phases (ferromagnetic and modulated). The temperature and field dependences of the magnetocaloric coefficient and susceptibility are also calculated within the same framework.

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Modulated phases, magnetic phase diagrams, and the Lifshitz point in MnP from the mean field theory

Cited by 16 publications

References 38 publications

Boundary critical behavior atm-axial Lifshitz points for a boundary plane parallel to the modulation axes

Boundary critical behavior atm-axial Lifshitz points for a boundary plane parallel to the modulation axes

Bulk and boundary critical behavior at Lifshitz points

Isothermal magnetocaloric effect in the vicinity of the Lifshitz point in Mn_0.9Co_0.1P

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Modulated phases, magnetic phase diagrams, and the Lifshitz point in MnP from the mean field theory

Cited by 16 publications

References 38 publications

Boundary critical behavior atm-axial Lifshitz points for a boundary plane parallel to the modulation axes

Boundary critical behavior atm-axial Lifshitz points for a boundary plane parallel to the modulation axes

Bulk and boundary critical behavior at Lifshitz points

Isothermal magnetocaloric effect in the vicinity of the Lifshitz point in Mn0.9Co0.1P

Contact Info

Product

Resources

About

Isothermal magnetocaloric effect in the vicinity of the Lifshitz point in Mn_0.9Co_0.1P