Magnetic phase diagram of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>YbRh</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Si</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> : The

We report the determination of the magnetic phase diagram of the heavy fermion metal <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>YbRh</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi>Si</a:mi> <a:mn>2</a:mn> </a:msub> </a:mrow> </a:math> in magnetic fields up to 70 mT applied perpendicular to the crystallographic <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>c</b:mi> </b:math> axis. By a combination of heat capacity, magnetocaloric, and magnetoresistance measurements, we map two antiferromagnetic phases: the electronic AFM1 below 70 mK and electronuclear AFM2 below 1.5 mK. The measurements extend into the microkelvin regime to explore the quantum phase transitions in this system. We demonstrate how the hyperfine interaction significantly modifies the phase diagram and the putative field-tuned quantum critical point. The determination of the rich magnetic properties of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>YbRh</c:mi> <c:mn>2</c:mn> </c:msub> <c:msub> <c:mi>Si</c:mi> <c:mn>2</c:mn> </c:msub> </c:mrow> </c:math> is essential to understanding the interplay of the two magnetic orders and superconductivity in this compound.