Response to “Comment on ‘Analysis of asymmetric giant magnetoimpedance in field-annealed Co-based amorphous ribbon’ ” [Appl. Phys. Lett. 77, 1727 (2000)]

Abstract

In a Comment [D. X. Chen, L. Pascual, and A. Hernando, Appl. Phys. Lett. 77, 1727 (2000)] on our recent letter [C. G. Kim, K. J. Jang, D. Y. Kim, and S. S. Yoon, Appl. Phys. Lett. 75, 2114 (1999); 76, 1345 (2000)] Chen et al. claimed that the unidirectional anisotropy due to bias field is unphysical one for the description of asymmetric giant magnetoimpedance (GMI) profiles. The symmetric two peaks of GMI profiles measured in the normal sample with an uniaxial anisotropy, allow one to take the minimum energy condition which assumes a jump of magnetization under the field from a metastable state to a stable one. However, the divergence in a calculated GMI profile should appear even in case of a uniaxial anisotropy of normal sample where there is no jump. Divergence indicates the asymmetry and hysteresis in GMI profile. The analysis of this calculation in Chen et al.’s Comment is simply a matter of hysteresis in GMI profile for the increasing and decreasing field, even in a normal sample with uniaxial anisotropy. Even though the hysteresis is ignored by taking the minimum energy condition, the asymmetric profiles with the negligible hysteresis are well ascribed by the model with two kinds of anisotropy fields, as proposed in our previous letter [C. G. Kim, K. J. Jang, D. Y. Kim, and S. S. Yoon, Appl. Phys. Lett. 75, 2114 (1999); 76, 1345 (2000)]. In this model the bias field is quite physical, and is based on the observed experimental results in a specially prepared sample.

Yang-Mills instantons sitting on a Ricci-flat worldspace of double D4-branes

“…As was noted in [13,14,16] cates that the YM field now does not disturb the geometry while the geometry still does have effects on the YM field. Consequently the geometry, which is left intact by the YM field, effectively serves as a "background" spacetime which can be chosen somewhat at our will (as long as it satisfies the vacuum Einstein equation R µν = 0) and here in this work, we take it to be the gravitational instanton.…”

“…Next, noticing that both the r =constant sections of the frame manifold and the SU(2) YM group manifold possess the geometry of round S 3 , one may naturally choose the left-invariant 1-forms {σ a } as the "common" basis for both manifolds. Thus this YM gauge connection ansatz, A a = f (r)σ a can be thought of as a hedgehog-type ansatz where the group-frame index mixing is realized in a simple manner [14,16]. Then coming back to our present interest, namely the GI given in eq.…”

“…Here in this section, eventually in order to construct the SU(2) YM instanton solutions particularly in the background of TN and EH gravitational instantons, we begin by presenting a "simply physical" and hence perhaps the most direct algorithm for generating the YM instanton solutions practically in all species of known GI [16]. As we shall see in a moment, the essence of this method lies in writing the (anti) self-dual YM equation by employing truly relevant ansatz for the YM gauge connection and then directly solving it.…”

“…Thus this failure for the geometry to be that of exactly round S 3 keeps us from writing down the associated ansatz for the YM gauge potential right away. Apparently, if the geometry were that of round S 3 , one would write down the YM gauge field ansatz as A a = f (r)σ a [14,16] with {σ a } being the left-invariant 1-forms introduced earlier. The rationale for this choice can be stated briefly as follows.…”

“…Even the works involving more general background spacetimes including gravitational instantons (GI) were mainly confined to the case of asymptotically-locally-Euclidean (ALE) spaces which is one particular such GI and employed rather indirect and mathmatically-oriented solution generating methods such as the ADHM construction [15]. Recently, we [16] have proposed a "simply physical" and perhaps the most direct algorithm for generating the YM instanton solutions in all species of known GI. Thus in the present work, we would like to employ this recently developed method to construct SU(2) YM instanton solutions in the background of Ricci-flat D4-brane worldspace described by 4-dimensional gravitational instantons such as Taub-NUT (TN) or Eguchi-Hanson (EH) metric.…”