Abstract
The pressure dependence of the order parameter in superfluid \(^3\hbox {He}\) is amazingly simple. In the Ginzburg–Landau regime, i.e., close to \(T_\mathrm{c}\), the square of the order parameter can be accurately measured by its proportionality to NMR frequency shifts and is strictly linear in pressure. This behavior is replicated for superfluid \(^3\hbox {He}\) imbibed in isotropic and anisotropic silica aerogels. The proportionality factor is constrained by the symmetry of the superfluid state and is an important signature of the corresponding superfluid phase. For the purpose of identifying various new superfluid states in the p-wave manifold, the order parameter amplitude of superfluid \(^3\hbox {He}\)-A is a useful reference, and this simple pressure dependence greatly facilitates identification.
Similar content being viewed by others
References
D. Vollhardt, P. Wölfle, The Superfluid Phases of Helium 3 (Taylor and Francis, Routledge, 1990)
A.J. Leggett, Rev. Mod. Phys. 47, 331 (1975)
W.P. Halperin, H. Choi, J.P. Davis, J. Pollanen, J. Phys. Soc. Jpn. 77, 111002 (2008)
M.R. Rand, Nonlinear spin dynamics and magnetic field distortion of the superfluid \(^3\)He-B order parameter. Ph.D. thesis, Northwestern University (1996)
P.E. Schiffer, Studies of the superfluid phases of helium three and the magnetization of thin solid films of helium three. Ph.D. thesis, Stanford University (1993)
P. Schiffer, M.T. O’Keefe, H. Fukuyama, D.D. Osheroff, Phys. Rev. Lett. 69, 3096 (1992)
J. Pollanen, J.I.A. Li, C.A. Collett, W.J. Gannon, W.P. Halperin, Phys. Rev. Lett. 107, 195301 (2011)
J. Pollanen, J.I.A. Li, C.A. Collett, W.J. Gannon, W.P. Halperin, J.A. Sauls, Nat. Phys. 8, 317 (2012)
D.D. Osheroff, Phys. Rev. Lett. 33, 1009 (1974). https://doi.org/10.1103/PhysRevLett.33.1009
M.R. Rand et al., Physica B 194, 805 (1994)
C.M. Gould, Physica B 178, 266 (1992)
V.V. Dmitriev, A.A. Senin, A.A. Soldatov, A.N. Yudin, Phys. Rev. Lett. 115, 165304 (2015)
E.V. Thuneberg, Phys. Rev. B 36, 3583 (1987)
H. Choi, J.P. Davis, J. Pollanen, T.M. Haard, W.P. Halperin, Phys. Rev. B 75, 174503 (2007)
H. Choi, J.P. Davis, J. Pollanen, T.M. Haard, W.P. Halperin, Phys. Rev. B 87, 019904(E) (2013)
D. Rainer, J.W. Serene, Phys. Rev. B 13, 4745 (1976)
E.V. Thuneberg, S.K. Yip, M. Fogelström, J.A. Sauls, Phys. Rev. Lett. 80, 2861 (1998)
N.D. Mermin, C. Stare, Phys. Rev. Lett. 30, 1135 (1973)
A.D. Gongadze, G.E. Gurgenishvili, G.A. Khardze, Sov. Phys. JETP 51, 310 (1980)
Y.M. Bunkov, G.E. Volovik, Europhys. Lett. 21, 837 (1993)
W.F. Brinkman, H. Smith, Phys. Lett. 51, 449 (1975)
L.R. Corruccini, D.D. Osheroff, Phys. Rev. B 17, 126 (1978)
V.V. Dmitriev et al., Phys. Rev. B 59, 165 (1999)
J.J. Wiman, J.A. Sauls, Phys. Rev. B 92, 144515 (2015). https://doi.org/10.1103/PhysRevB.92.144515
H. Choi, K. Yawata, T.M. Haard, J.P. Davis, G. Gervais, N. Mulders, P. Sharma, J.A. Sauls, Phys. Rev. Lett. 93, 145301 (2004)
J.J. Wiman, J.A. Sauls, Phys. Rev. Lett. 121, 045301 (2018). https://doi.org/10.1103/PhysRevLett.121.045301
Acknowledgements
The authors acknowledge contributions from Jim Sauls, Johannes Pollanen, Jia Li, and Josh Wiman. Research was supported by the National Science Foundation, Division of Materials Research: DMR-1602542.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zimmerman, A.M., Nguyen, M.D. & Halperin, W.P. NMR Frequency Shifts and Phase Identification in Superfluid \(^3\hbox {He}\). J Low Temp Phys 195, 358–364 (2019). https://doi.org/10.1007/s10909-018-2087-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10909-018-2087-9