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Asymptotic Behavior of the Generalized Schottky Anomaly and Characteristics of the Anomalies for Ferromagnet and Antiferromagnet

New Phys.: Sae Mulli 2019; 69: 939~943
Published online September 30, 2019;
© 2019 New Physics: Sae Mulli.

Seung-Yeon KIM*

School of Liberal Arts and Sciences, Korea National University of Transportation, Chungju 27469, Korea

Correspondence to:
Received July 22, 2019; Revised August 7, 2019; Accepted August 8, 2019.
cc This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The Schottky anomaly is an abnormal finite peak appearing universally at low temperature for the specific heats of most kinds of materials. %and it is the most important method %in investigating the unknown energy spectrum of new materials in a low temperature. Current studies on the Schottky anomaly are mainly based on either a paramagnetic spin system in an external magnetic field $B$ or the one-dimensional Ising model with the coupling constant $J$ in the absence of an external magnetic field. Here, we study the generalized Schottky anomaly, corresponding to an abnormal finite peak at low temperature, for the specific heat of a ferromagnetic or antiferromagnetic spin system in an external magnetic field. %The maximum location of the Schottky anomaly or the generalized Schottky anomaly is simply called the Schottky temperature $T_s$. In particular, we find, for the first time, the asymptotic formula $T_s(B)=0.8336(B+2|J|)/k_B$ for the Schottky temperature of the Ising ferromagnet in an external magnetic field. In addition, we compare the characteristics of the generalized Schottky anomalies of the Ising ferromagnet and the Ising antiferromagnet in an external magnetic field. We find that the maximum of the generalized Schottky anomaly lies above $0.4392k_B$ for the Ising ferromagnet in an external magnetic field for $0.
PACS numbers: 05.50.+q, 05.10.$-$a, 05.70.$-$a, 75.50.Ee
Keywords: Generalized Schottky anomaly, Asymptotic behavior

September 2019, 69 (9)
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