Hall effect indicates destruction of large Fermi surface at a heavy-fermion quantum critical point

Quantum critical points (QCPs) -– phase transitions at absolute zero in temperature -- are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet [1]. An important unsolved question concerns whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin density wave type [2], or suddenly as expected if the heavy electrons are abruptly localized by magnetism [3]. Here we report measurements of the low-temperature Hall coefficient ($R_H$) -- a measure of the Fermi surface volume -- in the heavy-fermion metal YbRh$_2$Si$_2$ upon field-tuning it from an antiferromagnetic to a paramagnetic state. $R_H$ undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP [4].\\[0.2cm] [1] R.~M.~Martin, {\em {Phys.\ Rev.\ Lett.}}{ \bf 48}, {362-- 365} (1982); P. ~Fulde, {in \em {Narrow-Band Phenomena -- Influence of Electrons with both Band and Localized Character}} (ed.\ Fuggle, J.~C.) 27--29 (Plenum Press, New York, 1988); M.~Oshikawa, {\em {Phys.\ Rev.\ Lett.}}{ \bf 84}, 3370--3373 (2000).\\[0.2cm] [2] J.~A.~Hertz, {\em {Phys.\ Rev.\ B}}{ \bf 14}, 1165--1184 (1976); A.~J.~Millis, {\em {Phys.\ Rev.\ B}}{ \bf 48}, 7183-- 7196 (1993).\\[0.2cm] [3] A.~Schr\"{o}der \emph{et~al.}, {\em {Nature}}{ \bf 407}, 351- -355 (2000); P.~Coleman \emph{et~al.}, {\em {J.\ Phys.: Condens.\ Matter}}{ \bf 13}, R723--R738 (2001); Q.~Si \emph{et~al.}, {\em Nature}{ \bf 413}, 804--808 (2001).\\[0.2cm] [4] S.~Paschen \emph{et~al.}, to appear in {\em Nature}.\\[0.2cm] In collaboration with: T.~L{\"u}hmann, S.~Wirth, P.~Gegenwart, O.~Trovarelli, C.~Geibel, F.~Steglich, P.~Coleman, and Q.~Si.