X-ray- and neutron-scattering measurements of two length scales in the magnetic critical fluctuations of holmium

Thurston, T. R.; Helgesen, Geir; Hill, J. P.; Gibbs, Doon; Gaulin, B. D.; Simpson, P. J.

doi:10.1103/physrevb.49.15730

Cited by 61 publications

(53 citation statements)

References 46 publications

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“…with small discontinuities. The results are summarized in Tables I and II [108] 0.37(10) [109] 0.39(3) [110] 0.39(2) [111] 0.39(4) [112] 0.39(4) [112] 0.41(4) [113] 1.14(10) 0.57(4) [114] 0.38(1) Dy [115] 0.335(10) [116] 0 We highlight four striking characteristics [118] of these data. Their consequences for the physics of frustrated magnets will be discussed in more details in the following.…”

Section: The Experimental Situationmentioning

confidence: 98%

Nonperturbative renormalization-group approach to frustrated magnets

2004

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This article is devoted to the study of the critical properties of classical XY and Heisenberg frustrated magnets in three dimensions. We first analyze the experimental and numerical situations. We show that the unusual behaviors encountered in these systems, typically nonuniversal scaling, are hardly compatible with the hypothesis of a second order phase transition. Moreover, the fact that the scaling laws are significantly violated and that the anomalous dimension is negative in many cases provides strong indications that the transitions in frustrated magnets are most probably of very weak first order. We then review the various perturbative and early nonperturbative approaches used to investigate these systems. We argue that none of them provides a completely satisfactory description of the three-dimensional critical behavior. We then recall the principles of the nonperturbative approach -the effective average action method -that we have used to investigate the physics of frustrated magnets. First, we recall the treatment of the unfrustrated -O(N ) -case with this method. This allows to introduce its technical aspects. Then, we show how this method unables to clarify most of the problems encountered in the previous theoretical descriptions of frustrated magnets. Firstly, we get an explanation of the long-standing mismatch between different perturbative approaches which consists in a nonperturbative mechanism of annihilation of fixed points between two and three dimensions. Secondly, we get a coherent picture of the physics of frustrated magnets in qualitative and (semi-) quantitative agreement with the numerical and experimental results. The central feature that emerges from our approach is the existence of scaling behaviors without fixed or pseudo-fixed point and that relies on a slowing-down of the renormalization group flow in a whole region in the coupling constants space. This phenomenon allows to explain the occurence of generic weak first order behaviors and to understand the absence of universality in the critical behavior of frustrated magnets.

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Section: The Experimental Situationmentioning

confidence: 98%

Nonperturbative renormalization-group approach to frustrated magnets

2004

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“…In fact, experimental situation concerning the critical properties of these rare-earth helimagnets has remained confused for years now, in the sense that different authors reported significantly different exponent values, or even different order of the transition, for the same exponent of the same material. For example, the reported values of the exponent β are scattered from 0.21 (Tb; X-ray) [13], 0.23 (Tb; neutron) [14], 0.25(Tb; neutron) [9], 0.3(Ho; neutron) [15], 0.335(Dy; Mösbauer) [8], 0.37(Ho; X-ray) [16], 0.38(Dy; neutron) [17], 0.39(Ho; neutron) [18] to 0.39(Dy; neutron) [18].…”

Section: (B) Chiralitymentioning

confidence: 99%

Untitled

Kawamura¹

1998

J. Phys.: Condens. Matter

341

470

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Recent theoretical and experimental studies on the critical properties of frustrated antiferromagnets with the noncollinear spin order, including stacked-triangular antiferromagnets and helimagnets, are reviewed. Particular emphasis is put on the novel critical and multicritical behaviors exhibited by these magnets, together with an important role played by the 'chirality'. §1. Introduction Phase transitions and critical phenomena have been a central issue of statistical physics for many years. In particular, phase transitions of magnets or of 'spin systems' have attracted special interest. Thanks to extensive theoretical and experimental studies, we now have rather good understanding of the nature of phase transitions of standard ferromagnets and antiferromagnets. By the term 'standard', I mean here regular and unfrustrated magnets without quenched disorder and frustration. They include ferromagnets and unfrustrated antiferromagnets with the collinear spin order.One key notion which emerged through these studies is the notion of universality. According to the universality hypothesis, a variety of continuous (or secondorder) phase transitions can be classified into a small number of universality classes determined by a few basic properties characterizing the system under study, such as the space dimensionality d, the symmetry of the order parameter and the range of interaction. If one is interested only in the so-called universal quantities, such as critical exponents, amplitude ratios and scaled equation of state, various phase transitions should exhibit exactly the same behavior. In the case of standard bulk magnets in three spatial dimensions (d = 3), universality class is basically determined by the number of the spin components, n. Physically, the index n is related to the type of magnetic anisotropy: Namely, n = 1 (Ising), n = 2 (XY ) and n = 3 (Heisenberg) correspond to magnets with easy-axis-type anisotropy, easy-plane-type anisotropy and no anisotropy (isotropic magnets), respectively. The critical properties associated with these n-component O(n) universality classes have been extensively studied and are now rather well understood. From the renormalization-group (RG) viewpoint, these critical properties are governed by the so-called Wilson-Fisher O(n) fixed point.

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“…Furthermore, it has been shown at least in Ho [10] and SrTiO 3 [11,12] that the NC is sample dependent, and that its critical behavior is different from that of the BC, with larger critical exponents. The NC component was found to depend on surface preparation [12,13], and to arise from a near surface skin region (typically 10 to 100 µm-thick).…”

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confidence: 99%

“…Longrange strains are believed to be due to dislocation dipoles, at least in Ho (Ref. [10]) and Tb (Ref. [25]).…”

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confidence: 99%

SrTiO3Displacive Transition Revisited via Coherent X-Ray Diffraction

et al. 2007

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We present a Coherent X-ray Diffraction study of the antiferrodistortive displacive transition of SrTiO3, a prototypical example of a phase transition for which the critical fluctuations exhibit two length scales and two time scales. From the microbeam x-ray coherent diffraction patterns, we show that the broad (short-length scale) and the narrow (long-length scale) components can be spatially disentangled, due to 100 µm-scale spatial variations of the latter. Moreover, both components exhibit a speckle pattern, which is static on a ∼10 mn time-scale. This gives evidence that the narrow component corresponds to static ordered domains. We interpret the speckles in the broad component as due to a very slow dynamical process, corresponding to the well-known central peak seen in inelastic neutron scattering.PACS numbers: 68.35.Rh;77.84.Dy Although most issues concerning the application of scaling theory to structural phase transitions have been settled long ago (see e.g. [1]), two frequently observed scattering features remain unaccounted for within standard scaling theory: the "neutron" central peak (CP) and the "x-ray" narrow component (NC). Remarkably, both features were first evidenced in studies of the critical behavior associated with the T c =100-105 K antiferrodistortive transition in the perovskite SrTiO 3 .The first issue concerns the time scale of the critical fluctuations. While far above T c , the fluctuations time scale is governed by the inverse soft-phonon frequency, a few degrees above T c a narrow central (i.e. zerofrequency) line appears in the inelastic neutron scattering data [2,3], whose weight grows critically on approaching T c . Its frequency width ∆ν is too small to be resolved by neutron techniques [4], but EPR measurements [5] have set an upper bound of ∆ν <0.6 MHz. There is substantial evidence [6,7] that the CP phenomenon is connected with slowly-relaxing or frozen bulk defects, such as vacancies or interstitials, but direct measurements of the relaxation time associated with these defects is still missing.Beside this second time-scale, another unresolved issue concerns the occurrence of a second length-scale in the critical fluctuations. As previously mentioned, the structural phase transition in SrTiO 3 has been the first example [8] where a narrow Lorentzian-squared (L 2 ) component in the critical x-ray scattering profiles has been observed close to T c , in addition to the usual and broader Lorentzian (L) component (BC). It is now well established by high resolution x-ray diffraction techniques that critical fluctuations close to structural and magnetic phase transitions involve two distinct pretransitional scattering components [9], each one corresponding to a diverging length scale, as T approaches T c .Furthermore, it has been shown at least in Ho [10] and SrTiO 3 [11,12] that the NC is sample dependent, and that its critical behavior is different from that of the BC, with larger critical exponents. The NC component was found to depend on surface preparation [12,13], and to a...

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X-ray- and neutron-scattering measurements of two length scales in the magnetic critical fluctuations of holmium

Cited by 61 publications

References 46 publications

Nonperturbative renormalization-group approach to frustrated magnets

Nonperturbative renormalization-group approach to frustrated magnets

Untitled

SrTiO3Displacive Transition Revisited via Coherent X-Ray Diffraction

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